Development Economics: Inframarginal Versus Marginal Analysis

Citation preview

DEVELOPMENT ECONOMICS INFRAMARGINAL VERSUS MARGINAL ANALYSES

Jeffrey Sachs and Xiaokai Yang

The final version: July, 2000

will be published by Blackwell in 2000

To Our Parents

ii

Preface The core of classical mainstream economics represented by William Petty and Adam Smith was development economics. The classical development economics differed from neoclassical development economics in two aspects. It focused on development implications of division of labor and it emphasized the role of the market (the invisible hand) in exploiting productivity gains from the division of labor. As shown in this textbook, inframarginal analysis of individuals' networking decisions is essential for formalizing the classical development economics. Here inframarginal analysis is the total cost-benefit analysis across corner solutions in addition to the marginal analysis of each corner solution. If the optimum value of a decision variable takes on its upper or lower bound, the optimal decision is a corner solution. Formally, it relates to nonlinear programming, mixed integer programming, dynamic programming, the control theory, and other nonclassical mathematical programming. The first decision that you have to make when you get in the university is to choose a major. If you choose economics as your major, then you do not go to classes of chemistry and physics, but you take classes of microeconomics, macroeconomics, and econometrics. We call such a decision an inframarginal decision, since values of decision variables discontinuously jump between zero and interior values as you shift between majors. After you have chosen a major, you allocate your limited time between the fields in this major. This decision of resource allocation for a given major (or occupation) is called marginal decision since standard marginal analysis is applicable to this type of decision. The aggregate outcome of all students' choices of their majors in a university generates division of students among majors and fields, which is analogous to a structure of division of labor in society. But when Alfred Marshall formalized classical economics within a mathematical framework in the end of the 19th century, he did not know inframarginal analysis. He made an assumption of dichotomy between pure consumers' decisions and firms' decisions to avoid inframarginal analysis of corner solutions. Within the neoclassical framework, each pure consumer must buy all goods from the market and cannot choose her level of self-sufficiency or its reciprocal: level of specialization. Hence, the focus of economics shifted from inframarginal analysis of problems of economic development concerning how the degree of scarcity can be reduced by division of labor in society to marginal analysis of problems of resource allocation for given degree of scarcity. Neoclassical development economics departures, by following the neoclassical framework, from classical development economics. Hence, neoclassical development economics loses the central position that classical development economics occupied in the mainstream economics. Some neoclassical development economists departure from classical development economics also by their advocacy for state-planned industrialization and development. Since the 1950s, economists have applied inframarginal analysis to various decision problems. However, many economists still follow Marshall’s assumption of dichotomy between pure consumers and firms, under which the corner solution is exceptional and the interior solution is the rule. Hence, implications of formal inframarginal analysis for investigating effects of network size of division of labor on economic development could

iii

not be fully explored until the late 1970s. This text shall show that if a Smithian framework is adopted, the interior solution is never optimal and corner solution is a rule rather than an exception. Hence, marginal analysis is not enough and inframarginal analysis is essential for exploring implications of the division of labor for economic development. Recent renaissance of classical development economics not only revives the spirit of the classical development economics, but also provides new frameworks for inframarginal analysis of network of division of labor. Hence it creates an opportunity for bring development economics back to the core of modern mainstream economics. The new thinking of development economics is associated with the literature of the economics of property rights, transaction costs, and institutions, the literature of new economic history school, the formal models of endogenous transaction costs, the formal models of high development economics (general equilibrium models with economies of scale), the endogenous growth models, and the literature of endogenous specialization. The formal general equilibrium models of division of labor and transaction costs also echo recent rethinking of development policies, represented by Bhagwati, Krueger, Srinivasan, and the World Bank. The current text organizes the literatures under an overarching framework with emphasis of inframarginal analysis of network of division of labor and related transaction costs. As one of the referees points out, “this book does bring recent literature on development to bear in a cohesive way. It manages to simplify complex ideas and tie them together.” Not only structuralist views of Lewis (1955) and Chenery (1986) and many neoclassical views of economic development, but also many nonmainstream views, such as ones of Alizadeh (1984), Bacha (1978), Emmanuel (1972), Frank (1995), Myrdal 1957, Nelson 1956, Palma 1978, Prebisch (1988), and Smith and Toye (1979) are reassessed using the inframarginal analysis and formal models in this text. Despite innovative structure of the text, standard topics on population (chapters 2, 5, 7, 11, 13), income distribution (chapters 3, 5, 6), human capital (chapters 14, 16), entrepreneurship (chapter 8), dual structure, structural changes (chapters 3, 5, 6, 12), industrialization (chapter 12), and urbanization (chapter 13) in development economics are covered by comparing new and old models. In addition, empirical evidences for or against the new and old models are reviewed (for instance in chapters 1, 2, 5, 7, 11, 12, 13, 14, 16). Since, as suggested by two of the referees of the text, the main purpose of the text is to teach theories of development economics in a systematical and coherent way and to bring considerable analytic machinery to bear on important problems of economic development, it reviews empirical research rather than covering details of regressions. The coverage of empirical research is thus selective. For instance, a large part of recent empirical research of some microeconomic development problems (for instance, Case and Deaton, 1998, 1999a, b, and Deaton and Paxson, 1998a, b) is not covered in the text. This text can be used at two different levels. Since each chapter includes a part of descriptive intuition behind the formal models and mechanism at work, with aids of graphical illustrations in each chapter, the text can be used for third or fourth year courses of development economics. The focus for the undergraduate courses is on training of economic thinking. If the text is used for the purpose, questions for assignments and examinations can be chosen from the questions in the end of each chapter and difficult algebra in the text and exercises in the end of each chapter can then be skipped. The

iv

questions not only expose students to different ideas and controversies, they also include important readings from the documentation of economic history, classic pieces, empirical findings, and interesting debates. Teachers will find that the graphs used in the text to describe topological properties (the number of trade connections between individuals and the number of goods involved in the division of labor) of evolution of division of labor in the Smithian models are much more intuitive than conventional demand and supply curves. Hence, if a teacher can use demand and supply curves to teach neoclassical development economics without mathematics, she will certainly feel much comfortable to teach materials in this text, using the graphs of evolution of division of labor without mathematics. The text can be used for a course of development economics at graduate level. The focus for the graduate course is on formal basic training as well as on innovative, creative, and critical economic thinking. For the part of basic training, students are asked to pay more attention to duplication of major models in the text and to work out main exercises in the end of each chapter. One hour spent on duplicating the models is as effective as 8 hours spent on listening and reading. The formal training is characterized by strong accumulation effects. If each model covered in the lectures is duplicated and well understood, the studies will become increasingly easier. But if one of the major models cannot be duplicated or a lecture is missed out, the studies may become increasingly more difficult later on. For the part of creative and critical thinking, students are asked to pay more attention to the trial-error process in designing models and in choosing one from many possible frameworks. Not only all original ideas must stand the test of rigorous deduction, of logical consistence, and of empirical evidences, but also insights that might be too sophisticated to be formalized by any available mathematical instruments are encouraged. Questions and exercises in the end of each chapter include many good thesis topics for master and Ph.D. programs. Free assistance can be obtained for such programs from the authors upon request. You may contact the authors via [email protected], [email protected] or [email protected]. The website www.inframarginal.com provides updated information on research, teaching, dissertations, contact information of economists in the field, and conferences related to this text. We are developing a teaching and research franchise of this text. If you are interested in developing an independent unit of the franchise, such as an undergraduate version of this text without advanced mathematics or a version of this text focusing on country specific economic development rather than general theories of development economics, please contact us. We will provide basic training, assistance for applying technical substance covered in this text, answers to questions in the text, and other materials that are essential for the independent franchise units. This text is a response to increasing demand for a text and a survey from which technical substance of inframarginal analysis of economic development can be systematically learnt. It covers many new research results of the inframarginal analysis and compares it with conventional marginal analysis of economic development. Some of the new research results are published for the first time. We hope that the reader will experience exciting intellectual adventure and find inframarginal analysis of development of the network of division of labor as a bridge between the mainstream economics and this era of networking and globalization.

v

Many individuals and institutions contribute to this project. We are first greatly grateful to Ken Arrow, Fischer Black, James Buchanan, John Gallup, Edwin Mills, YewKwang Ng, Hugo Sonneschein, and Lloyd Renolds for their supports for research projects that relate to this book. We are also greatly indebted to our coauthors of various research papers which are covered in this text: Jeff Borland, Been-Lon Chen, Wen-Li Cheng, John Gallup, Ben Heijdra, Geoff Hogbin, Chien-fu Lin, Monchi Lio, Mong-Chun Liu, Pak-Wai Liu, Siang Ng, Yew-Kwang Ng, Katharina Pistor, Steven Radelet, Bob Rice, He-Ling Shi, Guangzhen Sun, Jianguo Wang, Ian Wills, Kar-yiu Wong, Wing Thye Woo, Shuntian Yao, Dingsheng Zhang, Yiming Zhao, and Lin Zhou. We have benefited immensely from comments and criticisms on research papers and books that relate to this text from Olivier Blanchard, Gary Becker, Avner Ben-Ner, Steven Cheung, Cyrus Chu, Eric van Damme, Herbert Dawid, Jurgen Eichberger, Karl Farmer, Robyn Frandson, John Gallup, Robert Gilles, Gene Grossman, Oliver Hart, Michael Kremer, Heinz Kurz, Lachie McGregor, Douglas North, Eric Maskin, Yingyi Qian, Lloyd Reynolds, Peter Ruys, Andre Shleifer, Hugo Sonnenschein, Sherwin Rosen, Donald Smythe, Willy Spanjers, Guoqiang Tian, Yingjiang Wang, Andrew Warner, Chenggang Xu, Gang Yi, Weiying Zhang, and participants of numerous seminars and conference sessions. Many students at Harvard University, Monash University, Peking University, Chinese University of Hong Kong, University of Hong Kong, National University of Taiwan, and University of Louisville provide useful feedback to the teaching of the materials covered in this text. Special thanks go to Jeff Borland, Monchi Lio, Yingyi Qian, Sherwin Rosen, Mei Wen, and Julan Du for drawing several references cited in the text to our attention. Lijun Chen, Mei Wen, and Yiming Zhao have done an excellent job for research assistance related to this text. Our gratitude also goes to Andrew Warner, eleven anonymous reviewers of the draft of this text for their helpful comments, and Blackwell editors who commission the unusually large scale review process. The financial support for this project and related research from the Center for International Development at Harvard University, Australian Research Council, National Taiwan University, Institute of Economics of Academia Sinica, the National Sciences Council of the Republic of China, Guanghua School of Management of Peking University, and Centre for Economic Research at Tilburg University is gratefully acknowledged. Last, but not least, without love, patience, and strong support of our families, it is hard to image the completion of this book. We hereby express our deepest love and thanks to Sonia Ehrlich, Xiaojuan Wu, Adam, Lisa, Hannah, Xiaoxi, James, and Edward. Of course, any remaining errors are solely our own responsibility.

Jeffrey Sachs and Xiaokai Yang November, 1999, at Cambridge, MA.

vi

DEVELOPMENT ECONOMICS Inframarginal Versus Marginal Analyses Table of content Preface ............................................................................................................................................ v Chapter 1: Introduction ................................................................................................................. 1 1.1. Classical Development Economics and Capitalist Economic Development.................................. 1 1.2. Breakdown of the First Global Capitalist System and Neoclassical Development Economics ..... 7 1.3. A Return to Classical Development Economics .......................................................................... 13 1.4. The Scientific Approach to Development Economics ................................................................. 19 Key Terms and Review....................................................................................................................... 23 Further Reading .................................................................................................................................. 24 Questions ............................................................................................................................................ 24

Part I: Geography and Microeconomic Mechanisms for Economic Development .. 35 Chapter 2: Geography and Economic Development................................................................... 35 2.1. Uneven Economic Development in Different Parts of the World............................................... 35 2.2. Geography and Division of Labor............................................................................................... 40 2.3. Empirical Linkages of Geography and Economic Development ................................................ 44 2.3.1. Geographical Correlates of Economic Development........................................................... 44 2.3.2. Geography and Levels of per capita Income........................................................................ 47 2.3.3. Geography and Growth of per capita Income...................................................................... 49 2.3.4. Geographical Effects on Economic Policy Choices ............................................................. 53 Key Terms and Review....................................................................................................................... 55 Further Readings................................................................................................................................. 55 Questions………………………...……………………………………………………………………55

Chapter 3: Driving Force I - Exogenous Comparative Advantage and Trading Efficiency..... 57 3.1. Use the Concept of General Equilibrium to Figure Out Mechanisms for Economic Development ............................................................................................................................................................ 57 3.2. A Ricardian Model with Exogenous Comparative Technological Advantage and Transaction Costs ................................................................................................................................................... 61 3.3. Analysis of Decisions vs. Equilibrium Analysis of Development ............................................... 69 3.4. Per capita Real Income, GDP, GNP, and PPP ............................................................................. 77 3.5. Economic Development and Trade Policy................................................................................... 79 3.6.Comparative Endowment Advantage and Transaction Efficiency ............................................... 87 Key Terms and Review....................................................................................................................... 95 Further Reading .................................................................................................................................. 95 Questions ............................................................................................................................................ 96 Exercises ............................................................................................................................................. 99

Chapter 4: Driving Force II - Endogenous Comparative Advantage and Trading Efficiency 102 4.1. Endogenous vs. Exogenous Comparative Advantages .............................................................. 102

vii

4.2. Configurations and Corner Solutions in a Smithian Model ....................................................... 104 4.3. How the Markent Coordinates Division of Labor to Utilize Network Effects and Promote Economics Development .................................................................................................................. 114 4.4. More Examples .......................................................................................................................... 123 4.5. Pattern of Trade.......................................................................................................................... 129 Key Terms and Review..................................................................................................................... 131 Further Reading ................................................................................................................................ 132 Questions .......................................................................................................................................... 132 Exerxcises ......................................................................................................................................... 136

Chapter 5: Driving Force III - Economies of Scale and Trading Efficiency .......................... 140 5.1. Economies of Scale and Economic Development...................................................................... 140 5.2. General Equilibrium Models of Economic Development with Trade offs Between Economies of Scale, Consumption Variety, and Transaction Costs ........................................................................ 141 5.3. The Ethier Model with Transaction Costs.................................................................................. 148 5.4. The Murphy-Shleifer-Vishny (MSV) Model of Big Push Industrialization .............................. 154 5.5. The Sachs and Yang Model with Economies of Scale, Endogenous Degree of Industrialization, and Transaction Costs ....................................................................................................................... 158 Key Terms and Review..................................................................................................................... 163 Further Reading ................................................................................................................................ 163 Questions .......................................................................................................................................... 163 Exercises ........................................................................................................................................... 165

Chapter 6: Coexistence of Endogenous and Exogenous Comparative Advantages and Patterns of Development and Trade ......................................................................................................... 168 6.1. Underdevelopment and Dual Structure with Underemployment ............................................... 168 6.2. A Smithian Model with Dual Structure in the Transitional Stage of Economic Development.. 170 6.3. General Equilibrium and Its Inframarginal Comparative Statics ............................................... 173 6.4. Trade Pattern in the Presence of Both Endogenous and Exogenous Comparative Advantages and the Relationship Between Income Distribution and Development ................................................... 179 6.5. Development Strategies and Trade Patterns............................................................................... 181 6.5.1. A Consumer's Decision ...................................................................................................... 182 6.5.2. Possible Trade Structures .................................................................................................. 182 6.5.3. Production of Agricultural Good z..................................................................................... 184 6.5.4. Production of Final Manufactured Good y ........................................................................ 184 6.5.5. Production of Intermediate Goods ..................................................................................... 184 6.5.6. Local Equilibrium in Structure A ....................................................................................... 185 6.5.7. Local Equilibrium in Structure C....................................................................................... 185 6.5.8. Local Equilibrium in Structure D....................................................................................... 187 6.5.9. Local Equilibrium in Structure E ....................................................................................... 188 6.5.10. Local Equilibrium in Structure F ..................................................................................... 189 6.6. General Equilibrium and Inframarginal Comparative Statics .................................................... 189 6.7. Comparison with Conventional Wisdom Based on the Models with CRS ................................ 192 Key Terms and Review..................................................................................................................... 197 Further Reading ................................................................................................................................ 197 Questions .......................................................................................................................................... 198 Exercises ........................................................................................................................................... 201

Chapter 7: Structural Changes, Trade, and Economic Development ...................................... 205 7.1. Endogenous Trade Theory and Endogenous Number of Consumer Goods............................... 205 7.2. A Model of Economic Development with Fixed Learning Costs .............................................. 207 7.3. How Are Demand and Supply Functions Determined by Individuals’ Levels of Specialization?

viii

.......................................................................................................................................................... 210 7.4. Inframarginal Comparative Statics of the Optimum Decisions ................................................. 214 7.5. How is the Level of Division of Labor in Society Determined in the Market?.......................... 215 7.6. Inframarginal Comparative Statics of General Equilibrium and Many Concurrent Development Phenomena........................................................................................................................................ 215 7.7. Emergence of International Trade from Domestic Trade........................................................... 224 7.8. Comovement of Division of Labor and Consumption Variety .................................................. 225 7.9. Emergence of Professional Middlemen and Trade Pattern ........................................................ 230 7.10. Trade off Between Economies of Specialization and Coordination Costs............................... 232 Key Terms and Review..................................................................................................................... 233 Further Reading ................................................................................................................................ 234 Questions .......................................................................................................................................... 234 Exercises ........................................................................................................................................... 238

Part II: The Institution of the Firm, Endogenous Transaction Costs, and Economic Development .................................................................................................................. 242 Chapter 8: Economic Development, the Institution of the Firm, and Entrepreneurship........ 242 8.1. What is the Institution of the Firm? ........................................................................................... 242 8.2. Why are Claims to Residual Rights of the Firm Essential for Nurturing Entrepreneurship? -The Story behind the Model..................................................................................................................... 244 8.3 The Emergence of the Firm from the Evolution of Division of Labor........................................ 247 8.3.1. Economies of Roundabout Production............................................................................... 247 8.3.2. The Corner Equilibria in Four Structures.......................................................................... 248 8.3.3. General Equilibrium Structure of Transactions and Residual Rights ................................ 254 8.4. The Distinction Between ex ante and ex post Production Functions and the Role of the Institution of the Firm in Economic Development............................................................................................. 257 8.5. Coase Theorem and Other Theories of the Firm........................................................................ 259 Key Terms and Review..................................................................................................................... 263 Further Reading ................................................................................................................................ 264 Questions .......................................................................................................................................... 264 Exercuses .......................................................................................................................................... 268

Chapter 9: Endogenous Transaction Costs, Contract, and Economic Development .............. 271 9.1 Endogenous Transaction Costs and Economic Development ..................................................... 271 9.2. Endogenous Transaction Costs Caused by Moral Hazard ......................................................... 275 9.3. Game Models and Endogenous Transaction Costs .................................................................... 288 9.3.1. Game Models ..................................................................................................................... 288 9.3.2. Nash Equilibrium ............................................................................................................... 289 9.3.3. Subgame Perfect Equilibrium ............................................................................................ 291 9.3.4. Bayes Equilibrium .............................................................................................................. 293 9.3.5. Sequential Equilibrium ...................................................................................................... 294 9.4. The Role of Nash Bargaining Game in Reducing Endogenous Transaction Costs caused by Trade Conflict ............................................................................................................................................. 299 9.5. Endogenous Transaction Costs caused by Information Asymmetry and Holding Up ............... 302 9.5.1. Economic Development and Endogenous Transaction Cost caused by Adverse Selection 303 9.5.2. Alternating Bargaining Game in a Model of Endogenous Specialization.......................... 305 9.5.3. Economic Development and Endogenous Transaction Costs Caused by Holding Up....... 307 9.5.4. How Can Endogenous Transaction Costs be Eliminated by Consideration of Reputation? ...................................................................................................................................................... 309 9.6. The Grossman-Hart-Moore Model of Incomplete Contract....................................................... 310 9.7. Non-Credible Commitment and Soft Budget Constraint ........................................................... 313

ix

Key Terms and Review..................................................................................................................... 315 Further Reading ................................................................................................................................ 316 Questions .......................................................................................................................................... 317 Exercises ........................................................................................................................................... 320

Chapter 10: Transaction Risk, Property Rights, Insurance, and Economic Development .... 323 10.1. Uncertainties in Transactions and the Economics of Property Rights ..................................... 323 10.2. Economic Development and the Trade off between Economies of Division of Labor and Coordination Reliability.................................................................................................................... 328 10.3. Endogenization of Coordination Reliability in Each Transaction and Substitution between Competition and Better Enforced Property Rights .......................................................................... 332 10.4. Why Can Insurance Promote Economic Development? .......................................................... 343 10.5. Economic Development and Endogenous Transaction Costs caused by Moral Hazard .......... 348 Key Terms and Review..................................................................................................................... 355 Further Reading ................................................................................................................................ 356 Questions .......................................................................................................................................... 356 Exercises ........................................................................................................................................... 356

Part III: Urbanization and Industrialization ............................................................. 363 Chapter 11: Urbanization, Dual Structure between Urban and Rural Areas, and Economic Development ............................................................................................................................... 363 11.1. Why and How Cities Emerge from the Division of Labor....................................................... 363 11.2. The Fujita-Krugman Model of Urbanization based on the Trade off Between Economies of Scale and Transaction Costs ............................................................................................................. 366 11.3. Emergence of the Dual Structure between Urban and Rural Areas from the Division of Labor .......................................................................................................................................................... 368 11.4. Why Can the Geographical Concentration of Transactions Improve Transaction Efficiency? 372 11.5. Simultaneous Endogenization of Level of Division of Labor, Location Pattern of Residences, Geographical Pattern of Transactions, and Land Prices.................................................................... 380 Key Terms and Review..................................................................................................................... 391 Further Reading ................................................................................................................................ 392 Questions .......................................................................................................................................... 392 Exercises ........................................................................................................................................... 393

Chapter 12: Industrialization, Structural Changes, Economic Development, and Division of Labor in Roundabout Production.............................................................................................. 395 12.1. The Features of Industrialization ............................................................................................. 395 12.2. Industrialization and Evolution of Division of Labor in Roundabout Production ................... 402 12.3. Corner Equilibria and the Emergence of New Industry ........................................................... 403 12.4. General Equilibrium, Industrialization, and Structural Changes.............................................. 406 12.4.1. Changes in the Employment Shares of the Industrial and Agricultural Sectors .............. 409 12.4.2. The Number of Possible Structures of Transactions Increases More Than Proportionally as Division of Labor Evolves in Roundabout Production ............................................................ 411 12.5. Evolution in the Number of Producer Goods and Economic Development............................. 414 Key Terms and Review..................................................................................................................... 419 Further Reading ................................................................................................................................ 419 Questions .......................................................................................................................................... 420 Exercises ........................................................................................................................................... 424

x

Part V: Dynamic Mechanisms for Economic Development...................................... 426 Chapter 13: Neoclassical Models of Economic Growth ........................................................... 426 13.1. Exogenous vs. Endogenous Growth ........................................................................................ 426 13.2. The Ramsey Model and the AK Model ................................................................................... 429 13.3. R&D Based Endogenous Growth Models ............................................................................... 436 Key Terms and Review..................................................................................................................... 443 Further Reading ................................................................................................................................ 443 Questions .......................................................................................................................................... 444 Exercises ........................................................................................................................................... 445

Chapter 14: Economic Development Generated by Endogenous Evolution in Division of Labor ……………………………………………………………………………………………… …...448 14.1. Economies of Specialized Learning by Doing and Endogenous Evolution in Division of Labor .......................................................................................................................................................... 448 14.2.A Smith-Young Dynamic Model with Learning by Doing....................................................... 451 14.3.Optimum Speed of Learning by Doing and Evolution of Endogenous Comparative Advantage .......................................................................................................................................................... 452 14.3.1. The Function of Contracts .............................................................................................. 452 14.3.2. An Individual's Dynamic Decision Problem................................................................... 453 14.3.3. Dynamic Equilibrium...................................................................................................... 455 14.4. Endogenous Evolution of the Extent of the Market, Trade Dependence, Endogenous Comparative Advantages, and Economic Structure.......................................................................... 465 14.5. Empirical Evidences and Rethinking Endogenous Growth Theory......................................... 467 Appendix 14.1: The Relationship between the Control Theory and Calculus of Variations ........... 474 Key Terms and Review..................................................................................................................... 475 Further Reading ................................................................................................................................ 475 Questions .......................................................................................................................................... 476 Exercises ........................................................................................................................................... 477

Chapter 15: Social Experiments and Evolution of Knowledge of Economic Development .... 478 15.1. How Does Organization Knowledge Acquired by Society Determine Economic Development? .......................................................................................................................................................... 478 15.2. A Static Model with Endogenous Length of the Roundabout Production Chain and Endogenous Division of Labor.............................................................................................................................. 483 15.3. Interactions Between Dynamic Decisions and Evolution in Organization Information .......... 485 15.4. Walrasian Sequential Equilibrium and Concurrent Evolution in Organization Information and Division of Labor.............................................................................................................................. 490 Key Terms and Review..................................................................................................................... 500 Further Reading ................................................................................................................................ 500 Questions .......................................................................................................................................... 500 Exercises ........................................................................................................................................... 502

Part V: Macroeconomics of Development .................................................................. 504 Chapter 16: Investment, Saving, and Economic Development................................................. 504 16.1. Neoclassical vs. Classical Theories of Investment and Saving................................................ 504

xi

16.2. Neoclassical General Equilibrium Models of Self-Saving and Interpersonal Loans ............... 504 16.3. Smith and Young's Theory of Investment and Savings ........................................................... 512 16.3.1. The Model......................................................................................................................... 512 16.3.2. Configuration Sequence and Structure Sequence ............................................................ 513 16.3.3. Dynamic Corner Equilibria in 16 Structure Sequences ................................................... 516 16.4. Investment, Capital, and Division of Labor in Roundabout Production .................................. 518 16.4.1. Dynamic General Equilibrium ......................................................................................... 519 16.4.2. Non-topological Properties of Economic Growth and Sudden Decline of Interest Rates 523 16.4.3. Endogenous Decision Horizon and Effect of Liberalization Reforms on Opportunities for Lucrative Investment .................................................................................................................... 525 Key Terms and Review..................................................................................................................... 527 Further Reading ................................................................................................................................ 527 Questions .......................................................................................................................................... 527 Exercises ........................................................................................................................................... 527

Chapter 17: Money, Division of Labor, and Economic Development...................................... 530 17.1. Neoclassical vs. Classical Theories of Money ......................................................................... 530 17.2. A Smithian Model of Endogenous Monetary Regime and Economic Development ............... 534 17.3. Possible Structures and Monetary Regimes ............................................................................. 535 Key Terms and Review..................................................................................................................... 542 Further Reading ................................................................................................................................ 543 Questions .......................................................................................................................................... 543 Exercises ........................................................................................................................................... 543

Chapter 18: Endogenous Business Cycles, Cyclical Unemployment, and Endogenous, Longrun Growth.................................................................................................................................. 545 18.1. Rethinking Macroeconomic Phenomena in Economic Development...................................... 545 18.2. Long-run Regular Efficient Business Cycles, Cyclical Unemployment, Long-run Economic Growth, and Division of Labor in Producing Durable Goods........................................................... 552 18.3. A Smithian Dynamic Equilibrium Model of Business Cycles, Unemployment, and Economic Development..................................................................................................................................... 556 18.4. Cyclical vs. non-cyclical Corner Equilibria ............................................................................. 558 18.4.1. Regime Specification, Configurations and Market Structures ......................................... 558 18.4.2. The Dynamic Corner Equilibrium in Autarky .................................................................. 559 18.4.3. Market Structure C........................................................................................................... 560 18.4.4. Market Structure P ........................................................................................................... 563 18.4.5. Welfare and Policy Implications of the Model ................................................................. 565 18.5.General Price Level, Business Cycles, and Unemployment Rate ............................................. 566 18.6.Emergence of Firms and Fiat Money from the Division of Labor............................................ 569 Key Terms and Review..................................................................................................................... 571 Further Reading ................................................................................................................................ 572 Questions .......................................................................................................................................... 572 Exercises ........................................................................................................................................... 574

Chapter 19: Economic Transition ............................................................................................. 579 19.1. Understanding Economic Transition........................................................................................ 579 19.2. The Socialist System and Evolution in Division of Labor ....................................................... 582 19.3. Driving Mechanisms for Transition ......................................................................................... 593 19.4. Market-oriented Reforms Associated with the Transition of Constitutional Rules ................. 597 19.5. Market-oriented Reforms in the Absence of Constitutional Order .......................................... 600 19.6. Trade offs between Reliability and the Positive Network Effects of Division of Labor and between Incentive Provision and Stability ........................................................................................ 617

xii

Key Terms and Review..................................................................................................................... 623 Further Reading ................................................................................................................................ 623 Questions .......................................................................................................................................... 624 Exercises ........................................................................................................................................... 626

References................................................................................................................................... 627 Index ........................................................................................................................................... 644

xiii

Chapter 1: Introduction

1.1. Classical Development Economics and Capitalist Economic Development The focus of classical mainstream economics, represented by William Petty, A.R.J. Turgot, Adam Smith, and others, is on the development implications of division of labor. 1 In a sense, the core of classical mainstream economics is development economics. This core includes the Smith theorem: Division of labor is the mainspring of economic progress (1776, chapter 1 of book I), division of labor is dependent on the extent of the market (chapter 3 of book I), and the extent of the market is determined by the transportation condition (pp. 25-32). Also, Smith's conjecture on the intrinsic relationship between specialization and the use of money (p. 37), his theory of capital that investment is a vehicle for increasing division of labor in roundabout production (p. 371), and his conjecture on the role of the invisible hand in coordinating the network of division of labor are part of this core. In addition, this core comprises Petty's theory of urbanization that cities can promote the division of labor by reducing transaction costs (Petty, 1683, pp. 471-2), and Turgot's conjecture on the relationship between the division of labor, the introduction of money, the extension of commerce, and the accumulation of capital (Turgot, 1766). 2 We refer to this core of classical mainstream economics as classical development economics. The policy prescription of classical development economics is represented by Smith's following statement, which is consistent with Britain's liberal policy regime in the 17th -19th centuries, as well as with liberalization policy reforms in 19th century Western Europe: 3 "Little else is requisite to carry a state to the highest degree of opulence from the lowest

1

According to Lewis (1988),"The theory of economic development established itself in Britain in the century and a half running from about 1650 to Adam Smith's The Wealth of Nations (1776)." Hagen (1980, p. 72) also claimed "Adam Smith was a growth theorist." Sen (1988, p. 10) indicates that "Petty is regarded, with justice, as one of the founders of modern economics and specifically a pioneer of quantitative economics. He was certainly also a founder of development economics. Indeed, in the early contributions to economics, development economics can hardly be separated out from the rest of economics, since so much of economics was, in fact, concerned with problems of economic development. This applies not only to Petty's writings, but also to those of the other pioneers of modern economics, including Gregory King, Francois Quesnay, Antoine Lavoisier, Joseph Louis Lagrange, and even Adam Smith. An Inquiry into the Nature and Causes of the Wealth of Nations was, in fact, also an inquiry into the basic issues of development economics."

2

Petty (1671, I, pp. 260-61) noted that specialization contributes to skillful clothmaking and pointed out that Dutch could convey goods cheaply because they specialized each ship for a specific function. In another place, Petty gave a more striking example of the division of labor in the manufacture of a watch. Turgot (1751, pp. 242-3) had linked the development of division of labor with the concurrent increases in inequality of income distribution and in living standard for even the humblest member of society.

3

According to North (1981, pp. 158-68) and Groenewegen (1977), Britain's domestic liberal policy regime and France's liberal reforms under Turgot preceded Smith's advocacy for the role of the invisible hand which was followed by Britain's liberal international trade regime.

1

barbarism, but peace, easy taxes, and tolerable administration of justice; all the rest being brought about by the natural course of things" (cited from Jones, 1981, p.235). We call the development experience that is associated with classical development economics capitalist economic development. Max Weber (1927), Rosenberg and Birdzell (1986), Braudel (1984), and North (1981) have stressed that capitalist economic development is a result of capitalist institutions. The capitalist institutions affect the level of division of labor and the related extent of the market via their effects on trading efficiency, while the level of division of labor and the extent of the market affect development performance, which in turn drives institutional changes. Also, the geographical and physical environment in Western Europe and the North Atlantic were favorable for the evolution of institutions and division of labor. Many historians consider the driving force of the development of capitalist institutions as the absence of a single overarching political power in Europe and the rivalry between hostile sovereignties, which created the opportunity for social experiments with a great variety of institutions within a relatively short period of time. This rivalry also created great pressure for rulers to creatively mimic those institutions that enhance economic performance, and thereby, their power. Baechler (1976, p. 79) states: "Fundamental springs of capitalist expansion are, on the one hand, the coexistence of several political units within the same cultural whole and on the other, political pluralism which frees the economy." McNeil (1974, p.125) also indicates that "The political pluralism of early modern Europe was, I think, fundamental and distinctive. When all the rest of the civilized world reacted to the enhanced power cannon gave to a central authority by consolidating vast, imperial states, the effect in western and central Europe was to reinforce dozens of local sovereignties, each consciously competing with its neighbors both in peace and, most especially, in war. Such a political structure acted like a forced draft in a forge, fanning the flames of rival ideologies and nurturing any spark of technical innovation that promised some advantage in the competition among states." Hall (1987), Mokyr (1990), Jones (1981, pp. 226-35), Braudel (1984, pp. 128-29), Weber (quoted from MacFarlane, 1988, pp. 186-87), and Laslett (1988, p. 235) also support this view. Baechler (1976, p. 77-113) indicates that the probability for such a pluralist geopolitical structure to be sustained for a long period of time in the absence of any political hegemonism is very low, since all power tends toward the absolute. Several explanations for the occurrence of this improbable phenomenon are proposed. One is to attribute it to particular geographical conditions of Western Europe and the Mediterranean that are favorable for long-distance trade between city states and unfavorable for a unification war (Baechler, 1976, and Mokyr, 1990, 1993). Around the Mediterranean and the English Channel, a great portion of highly populous areas was either coastal or island. The favorable conditions for trade were crucial for the emergence and evolution of capitalist institutions (Jones, 1981, p.233). This pluralism in international arena ensured that several cultures and sovereignties could challenge each other on a nearly equal footing. In contrast, East Asian geopolitical structure ensured the hegemonism of Chinese culture prior to the invasion by Occidental cultures. No other culture could challenge it. Japanese, Mongolian, and Manchurian were conquered culturally by the Chinese, regardless of whether they subordinated to, or were rulers of, China. China is a mainland country, so it is easy to win a unification war and very expensive for inland trade. Hence, the variety of

2

institutional experiments in East Asia was much smaller than that in Western Europe until Japan's Meiji Restoration. In particular, Britain's geographic conditions ensured that they could avoid war with other countries at low defense expenses, and keep the continuous evolution of its unique Anglo-Saxon culture and common law tradition, along with a transportation advantage for trade. The pursuit of riches was legitimated under the prevailing ideology, so that talents were diverted from military, religious, and bureaucratic careers to business activities prior to and during the Industrial Revolution (Baechler, 1976, pp. 93-95). Competition among crown courts, local courts, and Church courts in Britain and amongst the state, the Church, and the decentralized feudal system were also considered as conducive to the checks and balances on the top of the political arena in the Western Europe (Baechler, 1976, pp. 78-80). Another unique feature of Western Europe was the development of free cities prior to the formation of nation-states. The free cities and related international trade became the cradle of capitalist institutions and economic development. In contrast, cities were princely fortresses in ancient Asia. The particular conditions nurtured the political and legal institutions in Britain in the th 18 century, then the institutions spread to the rest of Western Europe via creative imitations and revisions in the 19th century. These fundamental institutions provided conditions for the emergence of many important economic institutions, which significantly reduced transaction costs and therefore promoted the evolution of division of labor. Structural changes caused by this evolution are called industrialization, which includes increases in the income share of industrial output and in investment rate and saving rate (Lewis, 1955, Chenery, 1979, Kuznets, 1966, Kaldor, 1957). According to classical development economics, the increase in income share of industrial output is a transition from a self-sufficient society, where no division between agriculture and industry exists and each individual produces all industrial and agricultural goods for herself, to a high level of division of labor between professional farmers and manufacturers (Lewis, 1954 and Ranis, 1988, p. 88). Increases in income share of the sector producing producer goods and in related investment imply the development of division of labor in roundabout production, which endogenously generates technical progress. This industrialization process increases aggregate productivity and individuals' utilities (real income). The development performance then, in turn, affects the evolution of ideology and related institutions in a competitive arena between rival sovereignties. Hence, capitalist economic development can be analyzed at five levels. At first, we consider geopolitical structure, such as the absence of an overarching political power in Europe. This structure determines the evolution of ideology, norms, moral codes, and political and legal institutions at the second level, which determines the evolution of commercial institutions, industrial organization, and business practices at the third level, which determines the evolution of division of labor and related economic structure at the fourth level, which determines aggregate productivity and welfare at the fifth level, which in turn affects the evolution of ideology, norms, and institutions (North, 1994). The second and third levels of analysis (institutions) have received substantial attention from

3

the literatures of property rights and the new economic history school. According to the literatures, the evolution of capitalist institutions has the following features. 4 (1) The government's credible commitment to constitutional order with due process emerged from the significant variety of institutional experiments in Western Europe. The legal basis for private property rights and state enforcement of private contracts based on rational procedure emerged from this constitutional order. Also, predictable laws and a professional bureaucratic administration were conducive to the reduction of transaction costs. Under this credible commitment mechanism, the rational state not only provided many services, such as standard measures of weight and distance, currency, and infrastructure (the highway system, the census, etc.), but also the state itself was governed by law (constitutional and public law). Automatic registration of private firms replaced the approval system and government monopoly for enterprise. The licensing system has no longer been subject to state opportunism since free association became a legitimate ideology and practice in Western Europe in the 19th century. State taxation power became subject to approval of representatives, and the King's coffer was separated from the Bank of England (Huang, 1991 and Pipe, 1999). These new institutions effectively restricted state opportunism. Also, Equity Law created a mechanism under which new cases could override outdated cases in the presence of justice, which made Common Laws very adaptive to a changing world (Huang, 1991). This very adaptive legal system spontaneously created many rules to protect private property rights, in particular rights to residual returns and control of firms, business names, and brands. According to Mokyr (1990, 1993), the legal protection of the residual rights were more important than patent laws for technical and managerial inventions and innovations. This institutional evolution in Britain and Western Europe in the 17th-19th centuries created an opportunity for solving the paradox of state power: how to tame the Leviathan. Legitimate and powerful state violence could then be used to protect individuals' rights via checks and balances at the top level of the political arena (MacFarlane, 1988, pp. 18991). 5 (2) A special government policy regime of laissez faire and many government institution innovations emerged in Britain after the Glorious Revolution and were later mimicked by other Western European countries. Under this regime, Mercantilist industrial policies, intervention trade policy, and medieval regulations were abolished. This is represented by 1846 unilateral free trade in the UK, and 1860 Cobden Chevalier Treaty (Sachs and Warner, 1995). Many innovative government institutions, such as the central bank system (for instance, the Bank of England as the first central bank, 1694), bankruptcy laws, the postal system, the government library system, the public school system, the publicly funded highway system, and national galleries and museums emerged from the rivalry between national governments. The tradition of free migration in Western Europe also created great pressure for enhancing government’s capacity for managing public affairs. 4

Economists agree to their disagreement about the theory of economic history. Hence, the hypothes on development history reviewed in this chapter are only small part of many competing ones. 5 According to La Porta., Lopez-de-Silanes, Shleifer, and Vishny (forthcoming), common laws which spontaneously emerges from litigation rather than made by the government, is more conducive than civil (continental) laws, made by the government, to economic development. However, since major west European countries imitated constitutional judiciary (judicial review) from the US, the constitutional rules under the common law and continental system have been converging.

4

(3) In this institutional environment, a set of market institutions emerged and developed. Private contracting for labor, land, capital, and other properties gradually substituted for non-market institutions. For instance, the labor market substituted for serfdom, slavery, and corvee. Private ownership of land and related markets substituted for, hereditary, non-alienable, and patrimonial land relationships, common fields, and estates with servile obligations. The capital market substituted for government’s predatory, monopolistic, and interventionist role in money lending (for instance, the repeal of usury laws in Britain). Also, the market for technology and intellectual properties substituted for the government monopoly of technology and its infringement upon intellectual property rights (for instance, Statute of Monopolies, 1624, in Britain). Many commercial institution innovations emerged from this liberal institutional environment. They include modern double-entry accounting and bookkeeping, commercial instruments such as loans, stock shares, mortgages, bills of exchange, deeds of trust, insurance, power of attorney, franchising, and joint stock companies with limited liability. The capitalist institutions spread on a global scale in the 19th century. The first episode of global capitalism, of course, came about as much through the instruments of violent conquest and colonial rule as through economic reform and development of international institutions. Starting around 1840, Western European powers wielded their superior industrial, and hence military, power to challenge traditional societies around the world. France began to colonize North Africa in the 1830s and 1840s; Britain forced its way into China in the Opium Wars, 1839-42; Britain and France defeated Russia in the Crimean War, 1854-56; and Britain completed the conquest of India in 1857. Among the populous societies of Asia and the Near East, only Japan was able to mobilize social and political institutions to support market reforms, implementing history's first "shock therapy" reforms following the 1868 Meiji Restoration. 6 By the 1870s, a global market had begun to take shape along the following economic lines. Western Europe and the United States constituted the main industrial powers. A major push toward industrialization, especially in east-central Europe, followed the unification of Germany. Russia began a period of rapid industrialization, partly through the building of foreign-financed railways across Russian Eurasia. Japan had begun its dramatic opening to the world economy through the adoption of capitalist institutions and free trade. Note that early Japanese industrialization took place entirely under free trade, since the dominant Western powers imposed low Japanese tariff levels through "unequal treaties" that lasted until the end of the century. Latin America, after a half century of post-independence upheaval, finally settled into market-based, export-led growth in the 1870s, based on raw materials exports and capital imports (primarily for railroad construction). Africa, which lagged farthest behind, was gobbled up by the Western European powers in an orgy of imperialist competition that reached its height between 1880 and 1910. Trade barriers remained low among these economies for several decades, from the 1860s to 1914. 7 6

See Beasley (1995) for a detailed analysis of the economic, political, and social reforms of the Meiji period. 7 The era of 19th century free trade is usually dated from 1846, when Britain unilaterally liberalized by repealing the Corn Laws. In fact, liberalization had begun earlier, with the abolition of export duties in 1842 and the reduction of import duties in 1842 and 1845. The next decisive step was the CobdenChevalier Treaty of 1860, which liberalized British-French trade. The new German Reich was established

5

As in the late twentieth century, the emergence of the first global capitalist system was based on the interaction of technology and economic institutions. Long-distance transport and communications achieved breakthroughs similar to those in the present (Headrick, 1981). The Suez Canal, completed in 1869, and the Panama Canal, completed in 1914, dramatically cut international shipping times, as did the progressive development of faster and larger steamships from the 1840s. New railways in India, Russia, the United States, and Latin America, often built with foreign finance, opened vast, fertile territories for settlement and economic development. The spread of telegraph lines and transoceanic cables from the 1850s linked the world at electronic speed. Military innovations, particularly the breach-loading rifle introduced in the 1840s, combined with mass-production made possible by industrialization, decisively shifted the military advantage to Europe. Medical advances, particularly the use of quinine as a preventative against malaria, played a pivotal role in the spread of European settlements, domination, and investment, especially in Africa. Without a doubt, these technological breakthroughs were as revolutionary in underpinning the emerging global system as those of our own age. On the economic level, key institutions similarly spread on a global scale. International gold and silver standards became nearly universal after the 1870s, eventually embracing North and South America, Europe, Russia, Japan, and China, as well as other European colonies and independent countries. By 1908, roughly 89 percent of the world's population lived in countries with convertible currencies under the gold or silver standard. 8 Basic legal institutions, such as business and commercial codes, were widely adopted. These were based on European models, mainly the Napoleonic Code, which absorbed some important features of Common Laws. New multilateral institutions were established, such as the Universal Postal Union in 1878. The system was highly integrative, as in the present. A network of bilateral trade treaties kept protectionism in check in most countries (the United States and Russia, where tariff rates were relatively high, being the exceptions). Nations as diverse as Argentina and Russia struggled to adjust their economic policies, and especially their financial policies, to attract foreign investment, particularly for railway building. The adoption of a stable currency tied to gold was seen as a key step in the strategy of international integration. In Russia, Count Witte recalled how he outmaneuvered the by Bismarck on free trade principles and low tariff in the early 1879s. It is often suggested that this free trade era ended in 1879 with a renewed wave of protectionism, starting with Bismarck's acceptance of the famous tariff of bread and iron, which raised imports duties on agriculture and steel. Higher tariffs soon followed in France and Italy. In fact, even with these tariff increases, average tariff rates remained low until World War I, and nontariff barriers (for example, quotas and exchange controls) were virtually nonexistent. According to data assembled by Capie (1983, table 1.3, p. 8), average tariff revenues as a percentage of total imports stayed below 10 percent in France, Germany, and the United Kingdom; between 10 and 20 percent in Italy; between 20 and 30 percent in the United States; and between 20 and 40 percent in Russia. 8 See Eichengreen and Flandreau (1994, p. 9). The countries on the gold or silver standards in 1908 include, in Europe: United Kingdom, France, Belgium, Switzerland, Italy, Germany, Netherlands, Portugal, and Romania; in North America: United States and Canada; in Central America: Mexico, Nicaragua, Guatemala, Honduras, Salvador, and Costa Rica; in South America: Peru, Chile, Brazil, Venezuela, and Argentina; in Asia and Middle East: the Ottoman Empire, Egypt, and Persia. The national currencies were convertible into gold in all cases except the following: Italy, Austria, Spain, Portugal, Nicaragua, Guatemala, Peru, Chile, Brazil, and Venezuela. The Italian and Australian currencies were stable though not convertible.

6

conservative tsarist court to introduce the gold standard at the end of the 19th century (Owen, 1994, pp. 15-16). In Latin America, liberal market regimes stabilized under both democratic (Argentina and Chile) and authoritarian (Brazil and Mexico) political regimes. In all four cases, overall growth of GDP and exports was very rapid, indeed historically unprecedented. India similarly enjoyed rapid export growth between 1870 and 1914 under British rule. In a series of important papers, Jeffrey Williamson and his collaborators have shown that the open international system at the end of the 19th century produced an era of economic convergence (Jeffrey Williamson, 1992, 1993, and O'Rourke and Williamson, 1994). Peripheral countries in Europe, such as Ireland and the Scandinavian countries, experienced rapid growth that narrowed the gap in real wages with the more advanced countries, the United Kingdom, France, and Germany. Former European colonies in Latin America and the South Pacific (Australia and New Zealand) similarly achieved convergent growth rates based on export-led growth. In a massive study of long-term growth in forty-one developing countries, Lloyd Reynolds similarly finds that the open international economy of 1850-1914 was crucial in promoting the onset of rapid economic growth in much of the developing world outside of Europe and North America (Reynolds, 1985). Reynolds notes that "politics apart, the main factor determining the timing of turning points has been a country's ability to participate effectively in the trade opportunities opened by expansion of the world economy" (Reynolds, 1985). He then points out the wide range of countries that were indeed able to avail themselves of the burgeoning trade opportunities, including almost all of Latin America (with the exception of Venezuela); much of Asia, including but not limited to Ceylon, Burma, Malaya, Thailand, Japan, Taiwan, and the Philippine; and parts of Africa, including Algeria, Nigeria, Ghana, the Ivory Coast, Kenya, Uganda, Tanganyika, and Southern Rhodesia (Reynolds, 1985, pp. 34-35). Capitalist economic development has spread mainly as capitalist institutions have spread around the world from their home base in Western Europe. This diffusion process is driven by challenges and competition between different societies, which might be associated with war, conquest, and colonization. Hence, the spread of capitalist institutions could be either a creative imitation process or a painful imposition process.

1.2. Breakdown of the First Global Capitalist System and Neoclassical Development Economics Keynes (1971) rightly intuited in 1919 that the Humpty Dumpty of world markets and shared institutions would not soon be put back together in the harsh peace that followed World War I. Indeed, the war and its aftermath laid waste to the emergent global capitalist system for more than half a century. The financial underpinnings of the late 19th century liberal order were not reestablished. British dominance in the international financial system was ended by the Great War, and neither US leadership nor international cooperation took its place (Kindleberger, 1973, Eichengreen, 1994). Financial instability and the failure of the gold standard rocked the 1920s and contributed to the Great Depression of the 1930s. The export-led growth of the primary producers in Latin America and elsewhere was undermined by low and unstable commodities prices in the

7

1920s, and then was devastated by the Great Depression, which brought about the utter collapse of the terms of trade, intense protectionism in Europe and the United States, and the end of capital inflows. Political upheaval accompanied economic and military upheaval. Most important was the Bolshevik Revolution in Russia in 1917, and the emergence of fascist states in Italy and Germany in the 1920s and 1930s, respectively. In Latin America, the traditional political power of the landholders and mine owners was undermined by the collapse in the terms of trade. The free trade regimes of the late 19th century were replaced by a revolutionary regime in Mexico and authoritarian regimes in Argentina, Brazil, and Chile that were heavily influenced by the state planning of the communist and fascist regimes in the Soviet Union and Europe. 9 Throughout the world, state planning, authoritarianism, and militarism competed with limited government and market-based economies. Whether or not economic theory offered insights and predictions about these alternative strategies, political leaders felt compelled to push for new and radical experimentation. Two events prior to the WWII strengthened the tendency of economics to move away from classical development economics. One is the Great Depression in 1930; the other is the relatively successful industrialization of the Soviet Union in the 1930s. Krueger (1995) indicates that the two events and Keynes' advocacy for state intervention and investment fundamentalism were crucial for the formation of the spirit of neoclassical development economics. According to inframarginal analysis of the trade off between the positive network effect of division of labor on aggregate productivity and the reliability of a larger network of transactions in chapter 10, as transaction conditions are improved and the risk of coordination failure for each transaction declines, the benefit of a larger network of division of labor outweighs the increased aggregate transaction risk. Hence, the equilibrium network size of division of labor and the equilibrium aggregate risk of coordination failure of the whole network increase side by side. This implies, on the one hand, a greater degree of industrialization and higher aggregate productivity, and on the other hand, greater likelihood for a coordination failure of the larger network of division of labor. Hence, to a certain degree, the Great Depression is a "crisis of success" and a sort of cost of successful industrialization and globalization that we have to pay. This is just as if we choose a higher risk of being killed when we choose to drive on freeway. This decision is rational and efficient as long as the expected benefit from doing so outweighs the higher risk of being injured or killed in a traffic accident. If people really understood this mechanism for economic development, they would not turn to communism and to the distrust of the market mechanism when such an event takes place. 10 Also, as the cobweb model in chapter 19 shows, as globalization and liberalization develops, the sensitivity of the feedback mechanism in response to the coordination failure will increase. The efficient balance of the trade off between stability and sensitivity of the market feedback mechanism implies that the stability of the larger network of division of labor will decrease and the risk of devastating crisis will increase. 9

See Thorp (1984) for very insightful essays on the country-by-country experience. As Baechler (1976) considered the rivalry between sovereignties as the driving force of the evolution of capitalist institutions in the 17th-19th centuries, Krueger (1995) considers the rivalry between governments in international arena as the driving force for the return to liberalization reforms in the 20th century. 10

8

When Keynes did not understand the trade off, he suggested we go back to the autarchic state to avoid this risk of a great crisis. 11 We would conjecture that if development economics could better explain the development mechanism behind the Great Depression, the thinking in the 1950s on state-planned development would not have been as influential. 12 In chapter 10, we cover general equilibrium models that explain the development mechanism with concurrent increases in aggregate productivity and in aggregate risk for coordination failure. The complicated trade offs among moral hazard, transaction costs, and the positive effect of insurance on the reliability of the network of division of labor are investigated in connection to the recent Asia financial crisis. These models formalize Sachs' (1998) seemingly paradoxical notion of “crisis of success.” They show that as transaction conditions are improved, the equilibrium network of division of labor expands and the efficient aggregate risk for coordination failure increases because of the trade offs among economies of division of labor, reliability of the network of transactions, and transaction costs. Insurance can be used to enlarge the scope for trading off one against the others of the conflicting forces, at the cost of increasing moral hazard. Hence, there is a trade off between the positive effect of insurance on the reliability of the network of division of labor and the distortions caused by moral hazard. The complicated trade offs imply that simply reducing moral hazard or following a simple slogan of liberalization will not necessarily ensure the efficient balance of these trade offs. Repeating the overreaction to the Great Depression by resorting to communism, central planning, protectionism, or interventionism is also not the right way out. An inframarginal analysis of the general equilibrium mechanism of the crisis and development in chapter 10 will provide a balanced comprehension of new development phenomena generated by globalization. The second event that reversed the tide came from the industrialization experience of the Soviet Union in the 1930s and that of China in the 1950s. This is a special pattern of state-planned, big push industrialization. The major features of this pattern are as follows.13 Mimicking all successful patterns of industrialization in developed capitalist economies, such as a high saving rate, an increasing income share of heavy industry producing capital 11

The changing zeitgeist is captured by Keynes, in his remarkable lecture "National Self-Sufficiency" delivered in Ireland in 1933, when the world was in the depths of the Great Depression (Keynes, 1933). In the lecture, Keynes rejects the commitment to free trade and the international harmonization of institutions, declaring the late-19th-century experience a massive, and apparently inevitable, failure. In Keynes' view, the international system led to war, by stoking the competition among the leading powers: "The protection of a country's existing foreign interests, the capture of new markets, the progress of economic imperialism these are a scarcely avoidable part of a scheme of things which aims at the maximum geographical diffusion of capital wherever its seat of ownership" (Keynes, 1933, p. 236). For this reason, countries are best linked by ideas and culture, not economic and financial entanglements. Keynes writes: "I sympathise, therefore, with those who would minimise, rather than with those who would maximise, economic entanglements between nations. Ideas, knowledge, art, hospitality, travel - these are the things which should of their nature be international. But let goods be homespun whenever it is reasonably and conveniently possible; and, above all, let finance be primarily national" (Keynes, 1933, p. 236). 12 In addition to Communism and Fascism, Welfare State was a much more successful response to the Great Depression. 13 Zaleski (1980) have documented the role of mimicry by Soviet planners of Western production patterns. Lenin's works, for instance (1939), indicate that he was very familiar with the features of industrialization in a developed capitalist economy.

9

goods, the Taylor scientific management approach, mass production, standardization, comprehensive investment programs, and internal organizational patterns of large capitalist corporations. However, the mimicry was not via the market and private property rights, as happened in Taiwan and South Korea in the 1960s and 1970s. Instead, the imitation was conducted by the central planning system through infringements upon private property rights which created the industrialization patterns in capitalist economies. The precondition for the success of state-planned big push industrialization is to mimic whatever succeeds in a capitalist economy. Many economists predicted that such a system could not succeed, since it destroyed the incentive mechanism that created the successful industrialization pattern (see, for instance, von Mises, 1922). But they were surprised by the relatively successful industrialization in the Soviet Union in the 1930s. The short-run success impressed the leaders of many newly independent countries, who were busy with the task of state building. In particular, they believed that in a reverse engineering of capitalist institutions, they could repeat industrialization by mimicking capitalist industrial patterns and by ignoring fundamental capitalist institutions, including the legal system, constitutional order, behavior norms, and moral codes. Then the mainstream thinking on economic development converted from liberalism to the conviction of stateplanned economic development and industrialization. Since classical development economics did not establish a sound theoretical foundation, economists could not really comprehend the mechanism of modern economic development and the real reason for the Soviet Union's short-run success. They were easily converted to neoclassical development economics. Despite the short-run success of the Soviet-style big push industrialization, the fall of the Soviet Union pronounced the long-run failure of state-planned economic development, compared to Hong Kong's pattern of market-led industrialization, which is a modern version of Britain's development pattern. As Britain's original capitalist development experience spread to Europe in the 19th century, Hong Kong's capitalist development experience was followed by Taiwan, South Korea, Thailand, and China. As Sachs (1996) suggests, the fatal long-run negative effects of the Soviet-style state-planned big push industrialization via mimicking the successful industrial pattern of the developed country and infringing upon private property rights will outweigh its short-run positive effect on economic development once the potential for mimicking has been exhausted. The disintegration of the Soviet Union, along with reforms in China and other developing countries, symbolize a shift in development policy regime, which is associated with a shift of development economics back to its classical origin. The final support for a move away from classical development economics came from the idea that a great variety of institutional experiments might be helpful for discovering the institutions that are most conducive for economic development, represented by Keynes (1933). He stressed that countries simply demanded the right to experiment with new economic models, since the old ones no longer commanded respect and assent. He joined the chorus for experimentation, vividly exemplifying the end of intellectual faith in global capitalism by the 1930s. His point was that there is no prospect for the next generation of a uniformity of economic systems throughout the world, such as existed, broadly speaking, during the 19th century; that we all need to be as free as possible of interference from economic changes elsewhere in order to make out own favorite experiments towards the ideal social republic of the future; and that a deliberate movement towards greater national self-sufficiency and economic isolation would make

10

our task easier, insofar as it can be accomplished without excessive economic cost (Keynes, 1933, p. 241). This line of thinking is supported by historians' documentation of the fact that experiments with a more active role of the government and different institutions in the US and the European continent generated growth performance superior to Britain’s in the second half of the 19th century (see Craft, 1997). 14 In response to these events, the term "development economics" was coined after World War II, becoming a field of applied economics that is relevant only to less developed or underdeveloped countries. 15 We call this development economics that was established after the WWII neoclassical development economics, which pays more attention to the fourth and fifth levels of analysis of development (structural changes, such as an increase in income share of industrial output, and productivity progress). Neoclassical development economics rejects the universal applicability of classical development economics and the capitalist development experience. It does not pay much attention to the intimate relationships between the evolution of division of labor and the institutional evolution that affects transaction costs, and between the evolution of division of labor and structural changes. It is characterized by the following features: the belief in protection trade policy (import substitution) as a necessary policy to provide protection for infant industries and industrialization; the distrust of private entrepreneurship, the market, and related international trade; specific and comprehensive government industrial policies and investment programs; the belief that government, as a paternalistic benevolent planner, and state-owned firms should take the leading role in development (state-planned industrialization); pessimism that exports from developing countries could grow (the theories justifying worries about a shortage of foreign investment and a shortage of foreign exchange); investment fundamentalism (i.e., high saving rate is the engine of growth); specific and sometime comprehensive planned targets for development; 16 urban biased price controls and other interventionist policies; marginal analysis; and partial equilibrium or disequilibrium analysis (see Krueger, 1995, 1997 and Behrmand and Srinivasan, 1995 for a critical assessment of the development strategies). We call the economic development guided by neoclassical development economics stateplanned economic development. The shift from capitalist economic development to state-planned development was associated with the shift of development economics from the core of mainstream economics to its periphery. The latter shift started with Alfred Marshall (1890). Chapters 8-12 of book IV in Marshall's principles text are full of insights into the development implications of division of labor. He described the network of division of labor as an economic organism. Unfortunately, Marshall could not formalize his insights into 14

Sachs and Warner (1995) document the surge of protectionism in the end of the 19th century. Chapter 3 in this text uses the Ricardian model to explain this phenomenon. The inframarginal analysis has simultaneously endogenized trade regime and the equilibrium level of market integration.

15

For instance, Arndt (1989), Bliss (1989), Bhagwati (1984), Hischman (1981), Lewis (1984), Livingstone (1983), Meier and Seers (1984), Sen (1983), and Stern (1989) consider development economics as a field of applying economics to less developed countries. 16

In the 1950s the governments in Soviet Union, China, and India set up many specific development targets, such as increases in per capita income, life expectance, literacy, medical aid, public utility, output levels of steel, machine tools and grain, per capita consumption of cloth, education, housing, investment, and nutrition level, see, for instance, Beharman and Srinivasan (1995).

11

development economics in a mathematical framework. This formalization must specify an individual's decision in choosing her occupation and her level of specialization. Choosing a professional occupation is a yes-or-no decision. If you choose economics as your major during your college education, you do not go to classes of chemistry and physics, but you do go to classes of micro- and macro- economics and econometrics. To say “yes” to a major and say “no” to other majors is an inframarginal decision, in the sense that decision variables discontinuously jump between zero and a positive value as one shifts between majors. For a given major that you have chosen, you compare the relative marginal cost and relative marginal benefit between two fields to choose the optimum allocation of your limited time between different fields in the major that you have chosen. This is called marginal decision. In terms of mathematics, marginal analysis is classical mathematical programming, and inframarginal analysis is associated with linear and nonlinear programming and other nonclassical mathematical programming. Inframarginal analysis is a total benefit-cost analysis across corner and interior solutions, in addition to marginal analysis of each corner and interior solutions. 17 When you compare your life with the lives of your high school classmates who currently specialize in other occupations, you can see that inframarginal decision is often more important than marginal decision. Inframarginal analysis is essential for formalizing classical development economics. But Marshall did not know how to handle inframarginal analysis when he tried to formalize classical mainstream economics within a mathematical framework. Hence, it is not surprising that Marshall could not formalize his insights into classical development economics within a mathematical framework. In order to get around the corner solution, he made the very unrealistic assumption that society is divided between pure consumers, who do not make production decisions, and firms, which are exogenously given. This dichotomy, together with the assumptions of a quasi-concave utility function and a convex production set, ensures that interior solutions may occur in equilibrium. 18 Then, marginal analysis of interior solution can work. Within this neoclassical framework of marginal analysis, pure consumers have to buy all goods from the exogenously given market and firms, and cannot choose their level of self-sufficiency or its reciprocal, the level of specialization. Hence, the focus has shifted from the development implications of division of labor to marginal analysis of demand and supply. Marginal analysis cannot be used to investigate individuals' decisions in choosing their occupation patterns and levels of specialization. It cannot explain the emergence and evolution of markets as a result of the evolution of division of labor. The fatal flaw of this framework is that the equilibrium and Pareto optimum allocation of resources are always associated with an exogenously given production possibility frontier (PPF). Hence, we cannot use this framework to address the classical question of economic development: Why aggregate productivity can be increased by an increase in the level of division of labor in the absence of changes in production functions and endowments, and how the invisible hand coordinates division of labor to promote 17

The optimum solution of a decision problem is a corner solution if some decision variables take on their upper or lower bound values. The optimum solution is an interior solution if all decision variables do not take on the bound values. 18 Marshall assumed concavity (diminishing marginal utility) which implies but is not implied by quasiconcavity of utility function.

12

economic development. Since it cannot predict the emergence and evolution of markets, it is not applicable to studies of economic development and a decrease of the degree of scarcity. Marshall was aware of the fatal flaw of neoclassical marginal analysis of demand and supply. He suggested the use of the concept of external economies of scale to describe the effects of social division of labor on economic development. However, Allyn Young (1928, p. 533) argued that the use of the notion of large scale production misses the phenomenon of economies of division of labor. He (p. 539) emphasized Smith's classical general equilibrium view of network of division of labor: "The mechanism of increasing returns is not to be discerned adequately by observing the effects of variations in the size of an individual firm or of a particular industry, for the progressive division of labor and specialization of industries is an essential part of the process by which increasing returns are realized. What is required is that industrial operations be seen as an interrelated whole." However, Marshall's formalization of marginal analysis of demand and supply established the neoclassical mainstream of economics in the following sense. Marshall's mathematical structure of marginalism gives the teaching of economics a well organized structure. Within this structure, not only can different generations of economists and students share a common dictionary, but teachers can also set up good questions and exercises in classrooms and in examinations for which unique, correct answers are expected. What teachers demonstrate on the blackboard can be exactly duplicated by many students. This common mainstream facilitates division of labor between different generations of economists and between different fields of economics. Unfortunately, the neoclassical mainstream does not carry the core of classical mainstream thinking on the development implications of division of labor. As an unexpected consequence of Marshall's success in formalizing marginal analysis of demand and supply, the core of classical economics concerning economic development has been forgotten. As indicated by Young (1928, pp. 538-40), the "possibility of economic progress" can not be fully understood without this core. The failure of the Soviet-style social experiment with the socialist system shows that it is impossible to have successful social experiments if the rights for experimentation are monopolized by a totalitarian government and if individuals have no rights to experiment with various institutions via voluntary trade of property rights in the free market and under a fair constitutional order. The conviction that less developed countries can catch up by mimicking the legal and economic systems of the capitalist developed countries in the absence of the constitutional order was challenged by the defeat of Nazi and Japan in the WWII. It has been challenged again by the transition of Taiwan, South Korea, and other Asian countries from an authoritarian regime to democracy.

1.3. A Return to Classical Development Economics There were scattered efforts to keep classical development economics alive when development economics shifted from liberalism to advocacy for state-planned development. Rosen (1983, p. 44) indicated that Young (1928) was "the zenith of the analysis of the connection between specialization and economic development." Young criticized technology fundamentalism, which claimed exogenous technological progress to be the

13

engine of economic development, and investment fundamentalism, which claimed an ifand-only-if positive relationship between current saving and future productivity. He considered increases in per capita capital as increases in division of labor in roundabout production. This view of capital is consistent with Smith's classical view of investment, that investment is a vehicle for increasing division of labor in roundabout production (Smith, 1776, p. 371). According to Young and Smith, society's capacity to create and absorb new knowledge and to invent new technology is determined by the extent of the market, which is in turn determined by the level of division of labor. Marshall (1890, p. 256) also attributed the invention of the steam engine by Boulton and Watt to a deep division of labor in inventing activities. Young proposed the Young theorem: "The securing of increasing returns depends on the progressive division of labor"; "Not only the division of labor depends upon the extent of the market, but the extent of the market also depends upon the division of labor"; "Demand and supply are two sides of the division of labor" (or reciprocal law of demand). The Young theorem implies that not only can new technology not be invented, but also, even if it were invented, it would be a commercially nonviable luxury in the absence of a sufficiently high level of division of labor and a related, sufficiently great extent of the market. Houthakker (1956) formalizes Smith's concept of endogenous absolute advantage using a graph. He shows that this concept might be more general than Ricardo's concept of exogenous comparative advantage, and that the trade off between economies of specialization and transaction costs may be used to explain the endogenous progress of aggregate productivity. But as Stigler (1976, pp. 1209-1210) noted, “The last of Smith’s regrettable failures is one for which he is overwhelmingly famous – the division of labor. How can it be that the famous opening chapters of his book, and the pin factory he gave immortality, can be considered a failure? Are they not cited as often as any passages in all economics? Indeed, over the generations they are. The failure is different: almost no one used or now uses the theory of division of labor, for the excellent reason that there is scarcely such a theory. … there is no standard, operable theory to describe what Smith argued to be the mainspring of economic progress. Smith gave the division of labor an immensely convincing presentation – it seems to me as persuasive a case for the power of specialization today as it appeared to Smith. Yet there is no evidence, so far as I know, of any serious advance in the theory of the subject since his time, and specialization is not an integral part of the modern theory of production." The scattered efforts to keep classical development economics alive gradually became an increasingly more influential flow of thoughts. Several separate literatures contributed to this development. First, the literature on the economics of property rights, transaction costs, and institutions, represented by Coase, pioneered the renaissance of classical development economics. The literature of new economic history, represented by North, and the literature of constitutional economics and new political economics, represented by Buchanan, pushed this line of thinking further. The literature of formal models of transaction costs and contracts then consolidated the position of this research line in mainstream economics. Second, criticisms of neoclassical development economics since the 1980s by World Bank and prominent development economists, such as Krueger

14

and Srinivasan, put this line of thinking in policy practice. 19 Finally, a recent surge in the literature of general equilibrium models of high development economics, represented by Fujita, Krugman, Venables, Murphy, Shleifer, and Vishny, the literature of endogenous growth, represented by Aghion and Howitt, Lucas, Grossman and Helpman, and Romer, and the literature of endogenous specialization, represented by Becker, Murphy, Rosen, and Yang provide sophisticated technical vehicles for formalizing classical development economics. The main purpose of this text is to systematically cover all of the new literatures that resurrect classical development economics in a modern body of formalism. We call the synthesis of the new literatures new development economics. In what follows, we briefly outline the new literatures one by one. A group of economists who study the economics of property rights, transaction costs, and institutions consider their theories as the inheritor of classical development economics. They are very critical of neoclassical development economics. Among them, Coase (1946, 1960) and Buchanan and Stubblebine (1962) have proposed the notion of inframarginal analysis. 20 Cheung (1970, 1983), Coase (1937, 1960), and Barzel (1982, 1985) apply this inframarginal analysis to criticism of Pigou's marginal analysis of externality and public goods. Their theory of the endogenous degree of externality suggests that this degree is determined by the efficient trade off between transaction costs in specifying and enforcing property rights, and the distortions caused by inaccurate specification and enforcement. The theory is later formalized by several models of Holmstrom and Milgrom (1994), Milgrom and Roberts (1992), and Yang and Wills (1990) in the literature of endogenous externality. In particular, Yang and Ng (1993) and Lio (1996) explore the intimate relationship between the distortions, transaction costs, aggregate productivity, and the level of division of labor. Many models of the principalagent relationship, general equilibrium models with transaction costs and endogenous specialization, and game models with strategic interactions have formalized the ideas about property rights, transaction costs, contracts, and institutions. Milgrom and Roberts (1992), Hart (1995), Bolton and Scharfstein (1998), Gibbonst (1998), Holmstrom and Roberts (1998), Maskin and Xu (1999), and Yang and S. Ng (1998) have provided reviews of the literatures.

19

Though neoclassical marginal analysis is used by many economists to criticize state planned development strategy proposed by early neoclassical development economics, our text will show that inframarginal analysis can provide a much more powerful vehicle for criticizing this development strategy. 20 Coase (1946, p.173) noted “a consumer does not only have to decide whether to consume additional units of a product; he has also to decide whether it is worth his while to consume the product at all rather than spend his money in some other direction”. He applies this inframarginal analysis to criticize marginal cost pricing rule (1946) and Pigou's marginal analysis of externality (1940). Buchanan and Stubblebine (1962) coined term inframarginal analysis. Koopman (1957) and Arrow, Enthoven, Hurwicz, and Uzawa (1958) are among those economists who initiated formal inframarginal analysis in economics. Becker (1982) and Rosen (1977) are among those economists who initiated formal inframarginal analysis of specialization and division of labor. The application of inframarginal analysis to a decision problem can be found from Kendrick (1978), Little and Mirrless (1980), Becker (1981), and Rosen (1983). Its application to the theory of incomplete contract can be found from Grossman and Hart (1986) and Hart (1995). The application of inframarginal analysis to general equilibrium models can be found from Yang and Wills (1990), Yang and Borland (1991), Dixit (1987, 1989), Yang and Shi (1992), Yang and Ng (1993), and from chapters in this text. Yang and S. Ng (1998) provide a recent survey of inframarginal analysis of division of labor.

15

Also, the new economic history school represented by North (1981, 1990), Mokyr (1990, 1993), and others has echoed the new development of the economics of property rights, transaction costs, and institutions. It shows that the development experience of 18th and 19th century Britain and Western Europe, and the classical thinking of economic development, are very relevant to currently developing countries. According to them, impediments to economic development are various transaction costs that are caused by state opportunism and deficient institutions. In particular, North spells out the intimate relationship between the evolution of division of labor, transaction costs, institutions, and economic development. Recently, many general equilibrium models of endogenous specialization and transaction costs have formalized many ideas proposed by the new economic history school. We shall cover this line of rethinking of development economics, comprising the literature of endogenous transaction costs caused by opportunism and the models formalizing the ideas of the new economic history school, in Part III. 21 Even if the new literatures can be dismissed as the voices of those who are out of the field of development economics, the criticisms of neoclassical development economics by policy makers, represented by the World Bank (1996, 1997) and by prominent development economists Krueger (1995, 1997) and Behrman and Srinivasan (1995), can hardly be ignored. According to these criticisms, governments' predatory and expropriate policies, the non-credible commitment to constitutional order, and their distrust of the market (domestic as well as international), state opportunism that takes economic development as a hostage of the vested interests of the privileged class, rather than market failure, are real obstacles for economic development. More precisely, a great deal of market failure in developing countries is indeed caused by state opportunism and the absence of constitutional order (Sachs and Pistor, 1997 and Sachs and Woo, 1999). Again, new policy prescriptions are quite similar to what was suggested by the successful development experience of 18th century Britain and 19th century Western Europe and advocated by Smith and other classical development economists. The distinctive feature of our era is that capitalist institutions have spread to virtually all of the world for the first time in history. In addition, new political economics, represented by Buchanan (1991), develops the research on the effects of constitutional rules on rent seeking and state opportunism, which affect economic development in the developed countries. This literature shows that the political-economic mechanism dictating the evolution of constitutional rules is much more important than the political-economic mechanism that determines policy making under given constitutional rules. Some ideas in the rethinking of development policies and in the literature of new political economics have been formalized by models of the commitment game (surveyed in Maskin and Xu, 1999) and other game models, which will be covered in this text. Development economics has come full circle. This circle suggests that if we did not really understand the development mechanism underlying the early successful development experience of Britain and Western Europe along with new development 21

Recent development economics texts, for instance Ray (1998) and Meier (1995), cover part of the literature of endogenous transaction costs, such as Stiglitz's models of moral hazard and tenancy. But they do not cover the literature of endogenous externality, the models of commitment game, the economics of property rights and transaction costs, and new economic history school.

16

phenomena, such as the Great Depression, previous mistakes will be repeated again and again and useful lessons cannot be exploited. Although many economists since the 1950s have become familiar with the technical substance of inframarginal analysis (non-linear programming), which is essential for formalizing classical development economics, economists did not apply the new tools to formalizing classical development economics until the end of the 1970s. Since then, three literatures have stimulated the rethinking of development economics. They provide the technical substance for formalizing classical development economics. All three research lines feature general equilibrium analysis of the network of division of labor. This text will cover all three of the lines of rethinking and synthesize them with the above three literatures (economics of property rights and transaction costs, the new economic history school, and studies of liberal reforms and political economy). In chapter 3, inframarginal analysis is applied to the Ricardian model and the Heckscher-Ohlin model. It is shown that equilibrium aggregate productivity can endogenously increase as a result of the evolution of the network of division of labor. This inframarginal analysis of the Ricardian model and the Heckscher-Ohlin model identifies a general equilibrium mechanism of economic development. The equilibrium and efficient aggregate productivity is not on the PPF if the transaction cost coefficient for a unit of goods traded is very large. As transaction conditions are improved, the equilibrium network of division of labor expands and aggregate productivity becomes closer to the PPF. The interesting feature of this model is that the equilibrium aggregate productivity increases as the equilibrium network of division of labor and the related extent of the market expands, even if economies of scale are absent. This type of increasing returns to a larger network of division of labor in the absence of economies of scale is called by Young (1928) "social increasing returns," by Buchanan (1994) "generalized increasing returns," and by Rosen (1978) "superadditivity." Also, this general equilibrium mechanism for economic development implies that aggregate productivity increases as an outcome of the interactions between self-interested decisions. In the two types of models, as the equilibrium network of division of labor expands in response to improvements in transaction conditions, the following development phenomena concur. The equilibrium level of specialization for each individual or each country increases, the extent (or thickness) of the market increases, and the degree of market integration, degree of production concentration, and variety of occupation configurations increase. The degree of commercialization and trade dependence, degree of interpersonal dependence, and aggregate productivity increase. The inframarginal analysis can also explore a general equilibrium mechanism that simultaneously determines the interdependent policy regime and the level of division of labor. In chapters 4 and 7, we formalize Smith's notion of endogenous comparative advantage, which means that differences in productivities between various specialists are consequences rather than causes of division of labor (Smith, 1776, p. 28). The notion of endogenous absolute advantage may be more general than Ricardo's notion of exogenous comparative advantage, since the former may exist between ex ante identical individuals, while the latter does not exist if all individuals are identical in all aspects. The SmithYoung models of endogenous comparative advantage are used to investigate the equilibrium mechanism of economic development. This equilibrium analysis of economic development suggests that aggregate productivity and the degree of endogenous

17

comparative advantage will increase in response to improvements in transaction conditions even if tastes (demand side) and production conditions (supply side) do not change. In part III, the Smith-Young models of endogenous comparative advantage are used to explore the implications of entrepreneurship and the institution of the firm for economic development. It also investigates how endogenous transaction costs caused by opportunism prevent the realization of economic development and evolution in division of labor. In chapter 11, several Smith-Young models with endogenous urbanization formalize Petty's idea on the intimate relationship between urbanization and division of labor. In chapter 12, Young's idea about the relationship between industrialization and division of labor in roundabout production is formalized. Chapter 14 uses a Smith-Young dynamic general equilibrium to formalize Young's idea on the spontaneous coevolution in the network of division of labor and in the extent of the market. In chapter 15, a Walrasian sequential equilibrium model formalizes Austrian theory of entrepreneurial discovery and bounded rationality. It predicts spontaneous coevolution in organization information acquired by the society via social experiments and in division of labor. In chapters 16, 17, and 18, Smith, Turgot, and other classical economists' ideas on the relationship among investment, money, business cycles, economic development, and division of labor are formalized. In particular, technology and saving fundamentalisms are criticized using these dynamic general equilibrium models. All of the Smith-Young models show that as soon as the right tool of the trade for formalizing classical development economics is at the command of economists, the spirit of classical mainstream economics can be resurrected in a modern body of inframarginal analysis, and development economics can then be brought back to the core of modern mainstream economics. In chapters 5, 6, 11, and 13, general equilibrium models with economies of scale and economies of variety of goods (Dixit-Stiglitz, 1977, Ethier, 1982, Krugman, 1979, 1980, Krugman-Venables, 1995, 1996, Murphy-Shleifer-Vishny, 1989, Fujita-Krugman, 1995, Romer, 1987, 1990) are used to formalize the high development economics of Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), Myrdal (1957), and Hirschman (1958). These models show that as economists have commanded the technical substance of general equilibrium models with economies of scale, many development problems, such as the network effects of industrial linkage, circular causation, and interdependent decisions in different sectors, industrialization, dual structure, and urbanization can be much better investigated using the general equilibrium analysis. These models show that not only the degree of industrialization is dependent on the degree of urbanization, but the latter is also determined by the former. Also, the number of goods, the network size of industrial linkage, productivity, and the extent of the market are interdependent. Some of the models show that each player's decision in choosing her trade network is dependent on the size of the network of trade and industrial linkage, while the network size is determined by all players' participation decisions. The Romer models (1987, 1990) and other dynamic equilibrium models of economic development in chapter 13 formalize Young's conjecture about the spontaneous evolution of the number of producer goods, which was called by Young (1928) the "qualitative aspect of division of labor," and the interdependence between the emergence of new

18

goods and the evolution of the extent of the market. All of the models of high development economics show that the very function of the market is to network selfinterested decision-makers in order to utilize the gains from economic development, though the function might be imperfect. All of the formal general equilibrium models focus on the classical question of economic development, namely, why one county is wealthier than others or how scarcity can be reduced by the division of labor, rather than on the neoclassical question of what the resource allocation is in the market for a given degree of scarcity. In many of the new development models, symmetry is assumed, so that resource allocation is too trivial to be interesting at all: the quantities of all goods consumed and produced are the same in a model with ex ante identical individuals and symmetric tastes and production and transaction conditions. But very interesting stories of economic development, such as the evolution of division of labor and related extent of the market, structural changes, and industrialization can be told by the models. Asymmetries are introduced in chapters 6, 8, 11, 17, 18 to tell stories about urbanization, the emergence of dual structure, cities, money, business cycles, and the institution of the firm from the evolution of division of labor. 1.4. The Scientific Approach to Development Economics All of the new models of economic development and transaction costs share a common feature: they are based on a scientific approach to development economics. This scientific approach divides economic analysis between four levels in a hierarchical structure. At the bottom level of the hierarchy, the mathematical concepts of functions and sets are used to describe the environment of economic development. For instance, utility functions are used to describe individuals’ preferences, and production functions and production sets are used to describe production conditions. The notions of budget constraint and related ownership structure and pricing rules, or more general game rules in game models, are used to describe the institutional environment. At the second level of the hierarchy, mathematical programming is used to describe individuals’ self-interested decisions. The results of the analysis at this level are referred to as the comparative statics of the decision in a static model, or the dynamics and comparative dynamics of the decision in a dynamic model. Such results explain individuals’ self-interested decisions by prices and the development environment, which encompasses preferences, production conditions, and institutional arrangements. At the third level of the hierarchy, more sophisticated mathematical tools are used to describe the outcome of interactions between self-interested decisions. The results of the analysis at this level are called the comparative statics of general equilibrium in a static model and the dynamics and comparative dynamics of general equilibrium in a dynamic model. Such results explain how the outcomes of interactions between self-interested decisions and related development performance change in response to changes in the economic environment. Development economists pay particular attention to those comparative statics or dynamics that predict changes in equilibrium aggregate productivity. In this text, the equilibrium models that formalize classical development economics are used to predict evolution in division of labor and related structural changes.

19

All analysis at the three levels just described is referred to as positive analysis of economic development. When development economists conduct positive analysis, they do not ask what is good or bad, or what should be done to change matters, for they are not then concerned with value judgments. What they are trying to do is to use thought experiments to figure out what is going to happen under certain conditions and what is the mechanism for economic development. The following process is typical of such thought experiments. Beginning with some assumptions about intangible preferences and behaviors, economists use rigorous mathematics to establish connections between the intangible and tangible phenomena. One example of such a tangible phenomenon is the structural change whereby the income share of the industrial sector increases with per capita income. They can thus infer intangible relationships from the tangible. If the observed phenomena are consistent with their predictions based on the established connection, then their assumptions about the intangible are accepted as working hypotheses, which can be used to explain development phenomena. If the thought experiment generates predictions concerning tangible phenomena that are incompatible with observations, the hypothesis underlying the thought experiment is then rejected. Some conjectures can never be falsified. For example, consider the statement: “An increase in inequality of income distribution will decrease the welfare of a country.” Here, the inequality can be measured by the Gini coefficient or the variance of income distribution. Most economists accept the Pareto rankable measurement of welfare (see the definition of Pareto optimum in chapter 3). But if economic development generates changes that are not Pareto rankable, for instance, increases of some individuals' utilities are at the cost of others' utilities, then it is nearly impossible to find a measure of a country's welfare that is accepted by all economists. This is not only because utility is intangible and cannot be directly measured and compared between individuals, but also economists cannot find a universally accepted functional form or set of weights to specify a country's welfare as a function of all individuals' utilities. Without a well defined measurement of the country's welfare, there is no way to test or falsify the above statement. On the other hand, the following statement can be falsified. “Deterioration of a country's terms of trade is associated with a decrease in per capita income in this country.” Data on a country's terms of trade and per capita income can be collected. If the average price of all goods exported in terms of the average price of all goods imported decreases, while per capita real income increases, then the statement is falsified. P. Sen (1998) uses data to falsify this statement. He has also found that deterioration of the terms of trade and dramatic increases in trade volume and in total factor productivity may concur. In chapters 3 and 6, we shall use inframarginal analysis of general equilibrium models to show that the concurrent phenomena may take place if positive productivity gains from an enlarged network of division of labor caused by improvements in transaction conditions outweigh the negative effects of deteriorated terms of trade. This general equilibrium view about the relationship between economic development and the terms of trade can be intuitively illuminated by the following fact. The terms of trade of the computer sector have deteriorated dramatically in the past two decades, while productivity progress in this sector far outweighs the deterioration of terms of trade. Hence, an increase in the income share and productivity of this sector and the deterioration of its terms of trade concur.

20

Falsification of a hypothesis does not invalidate the chain of mathematical logic linking the assumption and the prediction in the hypothesis, provided of course that the process of deduction is mathematically correct. Hence, rejection of the hypothesis may be attributable to the unrealistic assumptions, or it may be attributable to a problem with the analytical framework itself. Thus, by safeguarding against incorrect logic in the thought experiment that generates a hypothesis, mathematics can help us to narrow down the list of possible explanations for the empirical rejection of that hypothesis. This enables us to focus our attention on the assumptions and the analytical framework. This text will review emerging empirical research that tests new development economics against observations. For instance, North (1958) provides empirical evidence for a positive correlation between the employment share of the transaction sector and economic development. Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997), Gallup and Sachs (1998), and Sachs and Warner (1995, 1997) provide empirical evidence for the positive effects of transaction conditions on economic development. Yang, Wang, and Wills (1992) provide empirical evidence for a positive correlation between the evolution of division of labor, improvements in transaction conditions, and economic development. As Albert Einstein suggested, however, "It is quite wrong to try founding a theory on observable magnitudes alone. … It is the theory which decides what we can observe" (quoted in Heisenberg, 1971, p. 31). New development economics covered in this text might challenge many conventional interpretations of empirical observations and may develop new concepts that lead to unconventional observations. At the fourth level of the hierarchical structure of development economics, economists raise questions that involve value judgments, such as, “Is the outcome of interactions between self-interested decisions (equilibrium) in a competitive market based on the private ownership system good for society as a whole?” The analysis at this level is referred to as welfare or normative analysis of economic development. The following examples explain why the scientific approach to analyzing economic development is useful. First, we consider a striking feature of neoclassical development economics which is inconsistent with the scientific approach. In the 1950s, normative analysis of economic development received a great deal of attention from development economists when a sound theoretical foundation for the positive analysis of general equilibrium mechanism of economic development was yet to be established. Many indices were suggested to measure the effects of development on welfare (see Sen, 1988), and many policy prescriptions were made to pursue what was believed to be the best for society in the absence of sound positive analysis. This was partly because development economists were not familiar with the technical substance of inframarginal analysis and general equilibrium models. Also, it was based on the assumption that economists, or the governments for which some economists work, are benevolent central planners who can make value judgements on behalf of individual citizens. Even if the assumption is valid, this approach is naïve, since it ignores complicated trade offs between many variables associated with the indices in raising utility and complicated interactions between conflicting self-interested decisions that somehow trade off utility of one person against another's utility. Hence, in this text, we do not follow this approach of neoclassical development economics. Instead, we follow a scientific approach. That is, we first make assumptions

21

about the environment for economic development, then use mathematics to figure out the general equilibrium development mechanism and establish a connection between intangible behaviors and tangible development phenomena. Then we test the hypothesis generated by thought experiments against observations. We can thus recommend to decision makers those equilibrium mechanisms that are compatible with empirical observations as working hypotheses. In chapters 3 and 4, we will show that with localized increasing returns and network effects of division of labor the equilibrium network size of division of labor that emerges in the decentralized market is Pareto optimal. The very function of the market is to coordinate self-interested decisions to fully utilize the network effects of division of labor net of transaction costs. In chapters 5, 6, 11, and 13 we will investigate the coordination difficulty of the efficient network of industrial linkage which may occur when global economies of scale exist in a neoclassical framework with a dichotomy between pure consumers and firms, though the market can utilize most of the network effects of industrialization and urbanization. Part III will focus on the endogenous transaction costs caused by interest conflicts and opportunism and their effects on economic development. We will establish the connection between intangible endogenous transaction costs and utility on the one hand, and tangible per capita income and trade volume on the other. Hence, we can use a sophisticated way to infer intangible endogenous transaction costs and distortions and their effects on economic development from tangible development phenomena. Since economic transition and reforms are considered as a subfield of development economics (Roland, 2000), we will apply the theories covered in this text to economic transition in chapter 19. The scientific approach to development economics is based on the extensive application of mathematics. This application can facilitate the division of labor between different generations of economists and students or between specialized fields of economics by raising communication efficiency in debating, teaching, and research. From the point of view of classical development economics, Marshall's insights into the development implications of division of labor are far superior to his marginal analysis of demand and supply. But the former is not in modern mainstream economics, while the latter is part of the core of modern mainstream economics, because the former is not but the latter is formalized within a mathematical framework. This illustrates the implications of mathematical formalism for the formation of mainstream economics. In addition, as Debreu (1991) indicates, mathematics not only provides better tools of the trade for economics, but also may affect economists' framework for thinking in a profound way. The history of the theory of labor surplus and the literature of high development economics illustrates his point. According to Lewis (1988) and Ranis (1988), Lewis' original motivation for developing the theory of labor surplus was to explore the development mechanism that generates evolution in division of labor. According to this idea, dual structure is between self-sufficient production of goods and commercialized and specialized production of goods, rather than between the agricultural and industrial sectors. But Lewis could not find the right tool to formalize his original idea. We know today that this right tool is the inframarginal analysis of decision making in choosing the level of specialization. As Krugman (1995) points out, the proponent of the labor surplus model could not even play with a tractable general equilibrium model with increasing returns. In the 1950s and

22

1960s, most development economists can only barely manage general equilibrium models with constant returns to scale. They were not familiar with inframarginal analysis of this kind of models either. Hence, Lewis, Fei, and Renis used marginal analysis of the model with constant returns to scale to formalize their ideas. As a result, their final models are far away from classical development economics and from their own original thinking. The ad hoc assumption of disequilibrium in the labor market and exogenous technical progress or capital accumulation in the industrial sector becomes the driving force of economic development in their models. We shall show in chapters 3, 4, and 6 that their original ideas can be appropriately formalized using inframarginal analysis of the Ricardian and Smithian models with endogenous specialization. Krugman (1995) indicates that high development economics about circular causation, coordination problems of the network of industrial linkages, and economies of scale was more interesting than the model of labor surplus. But economists could not manage general equilibrium models with economies of scale to formalize high development economics in the 1950s. Krugman attributes the success of the labor surplus model compared to high development economics to this low level of analytical formalism of high development economics. In this text, we will show that many ideas of high development economics can be formalized using general equilibrium models with increasing returns. The stories based on the models are much more interesting than those based on labor surplus models. This history of development economics demonstrates that some insightful ideas may not be included in mainstream development economics if they are not appropriately formalized within a mathematical framework. A limited capacity in managing mathematical formalism was very often a bottleneck in development economics. Since the application of mathematics in the research of economic development is a gradual evolutionary process, usually the most simple and thereby very unrealistic mathematical models are developed before more sophisticated and realistic ones. Hence, it is common that some very insightful ideas are too complicated to be formalized by any mathematical models that can be commanded by economists, while those tractable models are too simple and naïve. Hence, the following two extremes are inappropriate. One is to worship mathematical formalism and ignore nonmathematical insights into economic development. The other is to totally ignore the implications of mathematical formalism. As development economics becomes part of the core of modern mainstream economics, it becomes universally applicable. This implies, on the one hand, that it is applicable not only to less developed countries, but also to developed countries. On the other hand, economic mechanisms that drove economic development in Britain, Western Europe, and the US in the 18th and 19th centuries are, to a great extent, the same as those driving the economic development of East Asia and other currently developing countries. Poverty in the 16th and 17th century Britain, in the 18th century France, and in the 19th century Japan is, to a great extent, the same as that in currently less developed countries. Chapters 3-6 and 19 will use inframarginal analysis of evolution of division of labor to investigate advantages and disadvantages of the latecomer of industrialization and their evolution over different development stages. The relationship between income distribution, endogenous transaction costs, and economic development will be examined in chapters 3-6 and 9. The general equilibrium analysis yields some predictions that are

23

substantially different from economics of underdevelopment which was quite popular in the 1950s and 1960s. Many new development phenomena caused by globalization and information revolution are the very features of economic development in the developed world. The questions in the end of this chapter give several examples of the new features that can be analyzed by new development economics. With the power of new development economics, we can not only figure out the mechanism that enables the poor to catch up to the wealthy, but also predict some megatrends of future economic development. An example of the megatrends given in the questions is the increasing income share of the resource cost in handling noise in information transmission and a higher risk for coordination failure of an increasingly more integrated and larger network of division of labor and exchanges. This trend causes increases in frustration and mental pressure, which might enlarge the market for counseling and psycho-services in the new century. Since this text resurrects the spirit of classical development economics in a modern body of analytical formalism, its spirit is older and its body is younger than neoclassical development economics. Hence, the new development economics is particularly powerful in analyzing the new development phenomena of networking and globalization.

Key Terms and Review Classical development economics vs. neoclassical development economics Scientific approach to development economics Positive, normative, and empirical analysis of economic development Why is general equilibrium analysis essential for understanding the mechanisms for economic development? Marginal analysis vs. inframarginal analysis of economic development Why is inframarginal analysis essential for formalizing classical development economics?

Further Reading Classical development economics: Turgot (1766), Groenewegen (1977), Lewis (1988), Sen (1988), Petty (1671, 1683), Marshall (1890), Smith (1776), Meier and Seers (1984), Robbins (1968), North and Thomas (1970); Neoclassical development economics: Sen (1983, 1985), Arndt (1989), Bliss (1989), Bhagwati (1984), Lewis (1955, 1984), Livingstone (1983), Meier and Seers (1984), Adelman (1961), Meier (1994), Stern (1989), Rosenstein-Rodan, (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), Fei and Renis (1964), Myrdal (1957), Hirschman (1958, 1981), Chenery (1979), Kuznets (1966), Kaldor (1957); Criticisms of neoclassical development economics: Stiglitz (1989), Bhagwati (1984), Stigler (1976), Kornai (1991, 1992), Young (1928), Krueger (1995, 1997), Behrman and Srinivasan (1995), World Bank (1991, 1996, 1997), Cheung (1970), Coase (1960); Economics of property rights and transaction costs: Coase (1937, 1946, 1960), Cheung (1970, 1983), Barzel (1982, 1985, 1997), Buchanan (1975), Milgrom and Roberts (1992), Hart (1995), Bolton and Scharfstein (1998), Gibbonst (1998), Holmstrom and Roberts (1998), Yang and Wills (1990), Maskin and Xu (1999); New economic history school: North (1981, 1990, 1994), McNeill (1974), Mokyr (1990, 1993), Landes (1998), Rosenberg and Birdzell (1986), MacFarlane (1988), Braudel (1984), Fairbank (1992), Weber (1927, 1961, 1968), Baechler (1976), Chandler (1990), Pipe (1999); General equilibrium models with economies of scale: Murphy, Shleifer, and Vishny (1989), Krugman (1991, 1995), Fujita and Krugman (1995),

24

Krugman and Venables (1995); Literature of endogenous growth: Judd (1985), Lucas (1993), Romer (1987, 1990, 1993), Grossman and Helpman (1995), Grossman (1993), Barro and Sala-iMartin (1995), Aghion and Howitt (1998); Literature of endogenous specialization: Young (1928), Stigler (1951, 1976), Houthakker (1956), Rosen (1978, 1983), Becker (1981), Yang and S. Ng (1998); Constitutional economics: Buchanan (1989, 1991).

Questions Classical development economics 1. Following Marshall, Young (1928) described the technical progress associated with division of labor as a development in which a production process becomes fragmented and disintegrates into specialized tasks while new machinery is introduced to perform these tasks. In his comment on Knight (1921), he stated clearly that: “You (- Knight) miss the point, I fear, of Marshall’s ‘external economies.’ They are the economies (in general) of greater specialization and div. of labor” (quoted from Blitch, 1983, p. 362). See also Blitch (1995) for a detailed account of Young’s perspectives on external economies. Compare this defense of Marshall to Young's criticism of Marshall's notion of external economies of scale, and discuss the connection and differences between economies of division of labor and economies of scale. 2. Use the following examples to criticize technology fundamentalism and saving and investment fundamentalism. China's telecommunications market is monopolized by the state telecommunications company. Hence, despite very advanced technology and equipment, which are superior even to that in many developed countries, the prices of telecommunications services are 2 to 600 times of those in the US. Due to weak protection and enforcement of intellectual properties, many companies of Chinese software are unable to survive, despite a large population size that might be associated with a very large market for Chinese software. 3. Automobile manufacturing technology is now available to the Chinese as it was to Ford in 1903 (when Ford Motor Company was established). Currently, per capita income in China is not lower than it was in the US in 1908 (when the Ford Model T came to the market). But why cannot the Chinese counterpart of the Ford Motor Company appear in the 20th century? You may assume that Mr. Ford is now in China, at the age of 16. The following conditions indicate that he cannot set up his company, and cannot make a fortune from his Model T. Use this example to illustrate whether the policy prescription of classical or neoclassical development economics is more relevant to the currently developing country. (1) Mr. Ford was a country boy when he moved to Detroit, Michigan in 1879. If the young Ford were now in rural China and wanted to move to a city, he would not be able to get permanent residential registration in a Chinese city. Without this registration, he would have to pay much higher rent for housing, and would even be unable to get housing at all in some large Chinese cities. Also, an automobile manufacturing company would be fined severely by the government if it hired him. Hence, his chances to learn automobile manufacturing skills would be very slim. Suppose that Mr. Ford already set up his Ford Motor Company in a Chinese city. He would have to bribe the government officers for urban residential registration of his employees. The rationing of houses and a statemonopolized land distribution system means that he would have a very difficult time providing housing for his employees. (2) Mr. Ford could successfully sell his Model T in the 1910s because of his dealer franchise network, which created a high level of division of labor between production and

25

distribution and between franchisees at different localities. But in China, any private wholesale and retail network cannot operate without a license issued by a government committee, which is usually headed by the government officer who monopolizes the local wholesale and retail network. The interest conflict between any private wholesale and retail network and the state monopoly in that wholesale and retail network implies that Mr. Ford would have a very slim chance of approval for his dealer franchise network from the government committee. In the US in the beginning of the 20th century, more than one hundred start-ups of motor vehicle manufacturing companies created a competitive environment that nurtured Mr. Ford's success. There is no such free entry into automobile manufacturing in China. China has an approval system for setting up firms. In other words, the automatic registration system which had been institutionalized in the Western world since the 19th century is not available in China. In addition, in China there is a list of sectors in which domestic private firms are not allowed to operate. This list includes banking, automobile manufacturing, telecommunications, railroad, and freeway construction. Hence, Mr. Ford would be unable to set up his company at all if he were an entrepreneur in China in the 1990s. (3) State opportunism and a predatory government policy in China engender a government monopoly in the capital market, imposing arbitrary fees and expropriate taxes on private firms. This implies that even if Mr. Ford got the chance to set up his Ford Motor Company, he might be unable to get adequate capital and to make a profit. The state-monopolized banking system implies that personal checks, mortgages for purchases of automobiles, and many other mediates of exchanges are not available to many ordinary Chinese. This substantially limits the market for Ford's cars. (4) Ford's lobbying campaign to promote a better infrastructure under a democratic system utilizes "externality" associated with infrastructure. But the state monopoly in constructing infrastructure in China and restriction on free association generates a lot of rent seeking activities and opportunistic behavior. Mr. Ford would not have much of a chance to promote a motor-related infrastructure in China. (5) In China, local government monopoly in many sectors fragments China's market. Local governments' monopolistic distribution system carries out a protection policy that restricts the sale of goods produced by those firms that are not under local government control. Mr. Ford would have a hard time penetrating the fragmented local markets. 4. Some economists take the study of specialization and division of labor as a subfield of economics. Comment on this view in connection to Houthakker’s assertion (1956, p. 182) that “there is hardly any part of economics that would not be advanced by a further analysis of specialization.” Use some examples to discuss his points. 5. Smith and Turgot used the general equilibrium view of division of labor and economic development to criticize the mercantilists' partial equilibrium view on the relationship between trade and development. According to this mercantilists' view, a great trade surplus will contribute to a country's wealth. Hence, the government should manipulate the terms of trade by using tariff and other trade policies. According to Smith's general equilibrium view, as domestic division of labor within a country or international division of labor between countries increases, wealth will be increased. Since demand and supply are two sides of division of labor, worries on trade deficit and shortages of foreign exchanges are groundless, provided the gains from the division of labor and trade are not outweighed by transaction costs. The policy based on this view of development is intended to reduce the barriers of trade and transaction costs and let the invisible hand play its role in coordinating division of labor. Use this example to discuss why the notion of division of labor is a general equilibrium concept, and why Young (1928) considered marginal analysis of demand and supply that is separated from the analysis of decisions in choosing levels of specialization as a partial view. The new economic history school

26

6. Compare the British successful development experience in the 17th-19th centuries with the following facts. In some less developed countries, government behavior is predatory and expropriate. Government officers use their coercive power of the government apparatus and their taxing power to steal citizens’ property. A typical example is the Duvalier government’s behavior in Haiti during the 1950s and 1960s. According to the World Bank (1997, p. 149), the economic pillars of Haiti’s predatory state were expropriation, extortion, the inflation tax, and corruption. Significant resources were devoted to protecting Duvalier himself, 30 percent of total government expenditures during the first half of the 1960s. Agriculture, particularly coffee, was heavily taxed. Some sources estimate that Duvalier transferred more than $7 million a year out of Haiti for personal purposes. Large-scale bribes also took place, through deals with foreign investors on projects that often never materialized. Extortion under the veil of “voluntary” donations was institutionalized under some political movement. According to Summers (1992), in some Sub-Saharan African country, the government pursued a patronage recruitment policy of government employment and favoritism in issuing trade licenses. Then it purposely distorted exchange rates and prices in favor of the relatives’ trade businesses. In China during the 1960s and 1970s, the government used its monopoly in the banking sector, in the distribution network, in the urban real estate sector, and in other important sectors to pursue tangible and intangible rents. The approval system for setting up private firms, the strict licensing system for setting up firms of foreign trade, and the monopolized job assignment system were used by the government to discriminate against the private businesses. A procurement system that compelled peasants to sell underpriced agricultural goods to government agents, and the residential registration system, which restricted rural residents’ mobility, were used to pursue the interests of urban residents, including the government elite, at the expense of rural residents (see Yang, Wang, and Wills, 1992). In this process, industrialization and economic development became hostages to state opportunism. 7. North (1968, 1981, p. 166) states that “productivity increase as a result of declining transaction costs had been going on since at least 1600, when the Dutch flute (a specialized merchant cargo ship) was used in the Baltic trade and subsequently adopted on other routes. The declining transaction costs – a result of reduced piracy, increases in size of ships, growing trade, and reduced turnaround time – led to substantial productivity growth beginning 150 years (at least) before the Industrial Revolution; and they, more than technological change were responsible for productivity increases.” Compare this view of technical progress to technology and investment fundamentalism, which claims that investment in research and development is the main engine of economic development. 8. Comment on Landes' (1998, p. 31) following discussion on the institutional condition for economic development. "It has been suggested that this end to danger from without launched Europe on the path of growth and development. Others would argue that freedom from aggression is a necessary but not sufficient condition. Growth and development call for enterprise, and enterprise is not to be taken for granted. Besides, medieval Europe did not lack for impediments to such initiatives. … Linked to the opposition between Greek democracy and oriental despotism was that between private property and ruler-owns-all. Indeed, that was the salient characteristic of despotism, that the ruler who was viewed as a god or as partaking of the divine, thus different from and far above his subjects, could do as he pleased with their lives and things, which they held at his pleasure. And what was true for the ruler was true for his henchmen. The martial aristocracy typically had a monopoly of weapons, and ordinary folk were careful not to offend them, arouse their cupidity, or even attract their attention; to look them in the eye was an act of impudence that invited severest punishment." 9. Use the following documentation of the differences between China and Europe to explain the differences in their development performances in the 17th-19th centuries. Landes (1998, pp. 34-36): "The concept of property rights went back to biblical times and was transmitted and

27

transformed by Christian teaching. The Hebrew hostility to autocracy, even their own, was formed in Egypt and the desert." "Despotisms abounded in Europe, too, but they were mitigated by law, by territorial partition, and within states, by the division of power between the center (crown) and local seigneurial authority. Fragmentation gave rise to competition, and competition favored good care of good subjects. Treat them badly, and they might go elsewhere. Ecumenical empires did not fear flight, especially when, like China, they defined themselves as the center of the universe. There was no other place to go." Fairbank (1992): "Oriental societies, organized under centralized monolithic governments in which the bureaucracy was dominant in almost all aspects of large-scale activity – administrative, military, religious, and economic – so that no sanction for private enterprise ever became established …” Imperial governments carried out the industrial policy of limiting commerce and promoting agriculture. Fairbank (1992, p. 179). The merchant was kept in check by the official as an ally whose activities could be used and milked in the interest of either the officials personally or of the state. As Etienne Balazs pointed out, commercial transactions were always subject to the superintendence and taxation of the officials. Government monopolies of staple articles, like salt and iron in ancient times, or like tea, silk, tobacco, salt, and matches more recently, expressed the overriding economic prerogatives of the state. No merchant class had been allowed to rise independently and encroach upon these prerogatives. This was ensured in practice by the official disregard for private property. This meant that official patronage and support were necessary to protect any big commercial undertaking. The result was a close community of interest between the merchant and the official. … In short, capitalism failed to prosper in China because the merchant was never able to become established outside the control of the landlord gentry and their representatives in the bureaucracy. In feudal Europe the merchant class developed in the towns. Since the landed ruling class were settled in their manors upon the land, the European towns could grow up outside the feudal system instead of being integrated in it." 10. Analyze the driving force of the evolution of capitalist institutions in connection to the following historical facts. Weber (1968, pp. 1212-64): Trade and cities are the progenitors of modern capitalism. Towns precede princes. Occidental cities had the following unique features. Cities emerged before the nation states. They had fortifications, markets, their own courts of law, and in part, autonomous law, association structure, partial autonomy (privileges, corporate rights). In Asia, cities were princely fortresses. In the Occident, "urban landed property was always alienable without restriction, inheritable, unencumbered with feudal obligations or obligated only to fixed rental payments … In Asia and in the ancient world, this distinctive treatment of urban land settlement cannot be observed with similar regularity" (Weber). Magical caste was absent in Occidental cities. The city as an institutionalized association and a "territorial corporation" protected properties from the sovereign. It provided, under merchant governance, freedom for serfs, religious minorities, and new ideas. According to McNeill (1974), the lack of an overarching sovereign under feudalism led to horizontal contractual relations. Strong monarchies in England and France consolidated after the rise of towns (also, certainly, in German lands). The rise of the limited state implies that monarchs were too weak to snuff out dissent, opposition, and countervailing pressures. The increasing consolidation of states (England, France, Prussia, Hapsburg Spain) was generally not enough to undermine internal pluralism, corporate intermediaries, etc. Hence, state consolidation generally expanded internal market. "As a general rule, a measure of expansion in foreign trade preceded the laborious unification of the internal market." The expanding internal market supported the commercialization of agriculture (specialization within agriculture). Hoffman and Norberg (1994), "In sum, all of the monarchs of early modern Europe had to confront powerful obstacles to their will; none raised revenue without negotiation, consultation, and sometimes bribery" (p. 305). "Absolutist regimes despite their pretentions were not able to borrow or tax at will. Only governments with strong representative

28

11.

12.

13.

14.

institutions could extract huge revenues and borrow large sums. Taxation and despotism were in the end incompatible." "In the end, liberty was a necessary precondition for the emergence of a strong state, a state of wealth and power" (p. 310). Discuss the institutional conditions for economic development using the following documentation of the differences between Britain and France. Letters from England by Voltaire (in exile in England, 1726-1729) already revealed the differences between England and France. Letter 9: "On the Government." A man is by no means exempt from paying certain taxes here simply because is a noble or because is a priest. All taxes are fixed by the House of Commons which, though only second in rank [to the House of Lords], is first in prestige. The Lords and the Bishops may well reject the Bill from the Commons for taxation, but they may not change anything in it; they must either pass or reject it out of hand. When the Bill is confirmed by the Lords and approved by the King, then everybody pays. Everyone gives, not according to his rank (which is absurd) but according to his income. There is no arbitrary tax or capitation, but a real tax on landed property. Letter 10: "On Commerce." In France, [the Marquis] loftily despises a business man, and the business man so often hears people speak disparagingly of his profession that he is foolish enough to blush. According to Mokyr (1990, pp. 234-50), the differences between Britain’s patent laws and French government prize system for invention and between people made Common Laws and government made civil laws explain the differences in development performance between Britain and France in the 18th century. Landes (1998) also notes more limited private rights to land in France than in Britain in the 17th century. North and Weingast's forthcoming manuscript on the comparison between North American and Latin American growth over the last three centuries suggests that state opportunism (predatory and expropriate taxation and an authoritarian regime) in Latin America explains the great difference in the development performance between North America and Latin America. Comment on their view. Use Landes' (1998, p. 222) following discussion to assess technology and saving fundamentalism of economic development in connection to Young's view on the relationship between technology progress, the extent of the market, and division of labor. "The contribution of high consumption to technological progress struck contemporaries, and more of them as the British advance grew. Without taking a course in Keynesian economics, French merchants understood that mechanization made for high wages, that high wages made for increased demand for manufactures, and that effective demand made for increased prosperity. 'Thus, by the working of a system that seems paradoxical, the English have grown rich by consuming' (Defoe, Daniel, 1728/1928). Paradoxical indeed: such dispendious habits ran against the old wisdom that counseled thrift and abstemiousness, habits congenial to French peasants compelled to avarice. One result was a manufacture that aimed at a large national and international market and focused on standardized goods of moderate price – just the kind that lent themselves to machine production. 'The English,' wrote Charles marquis de Biencourt, 'have the wit to make things for the people, rather than for the rich,' which gave them a large and steady custom." According to North and Weingast (1989), the Constitutional Monarch and parliamentary democracy that emerged from the British Glorious Revolution in 1688 provided the credible commitment of the government to the constitutional order. This significantly reduced the government's predatory behavior and state opportunism. Hence, endogenous transaction costs caused by rent seeking and opportunism were reduced and long-term political stability could be secured. North argues (1981, pp. 158-68) that “Toynbee wrote ‘The essence of the industrial revolution is the substitution of competition for the medieval regulations which had previously controlled the production and distribution of wealth.’ It is true that the decline in mercantilist restrictions including repeal or reform of the Statute of Artificers, poor laws, acts of settlement, usury laws, navigation acts, (corn laws), and so forth is part of the story.

29

Particularly significant to the development of more efficient markets, however, is the better specification and enforcement of property rights over goods and services; and in many cases much more was involved than simply removing restrictions on the mobility of capital and labor – important as those changes were. Private and parliamentary enclosures in agriculture, the Statue of Monopolies establishing a patent law, and the immense development of a body of common law to better specify and enforce contracts also are part of the story.” According to Mokyr (1993, p. 47), “Many of the obsolete laws and regulations that encumbered progress (for example by mandating precise technological practices in detail) were revoked. In 1809 Parliament revoked a sixteenth century law prohibiting the use of gig mills in the woolfinishing trade, and five years later it did away with one of the pillars of regulation, the Statutes of Artificers and Apprentices.” As he describes (Mokyr, 1990, p. 268, 1993), secured rights to residual returns of firms reduced transaction costs in setting up firms and encouraged specialized entrepreneurial activities, and secured rights to intellectual properties directly improved transaction conditions for technology progress and encouraged specialized inventions of new technology. When patent laws were not enough to protect entrepreneurial ideas and rights to inventions, the institution of the firm was used to protect intellectual rights via residual rights of the firm and trade secrets. A stable and non-predatory tax system and the government’s laissez-faire policy encouraged business activities and the evolution of division of labor. The liberation of civil society with respect to the State and the separation of Crown’s coffer from the Bank of England enriched the creativity of society and restrained rent seeking. Free association (i.e., setting up private firms needs no approval or license from the government) improved transaction conditions for the evolution of the institution of the firm. Hence, endogenous and exogenous transaction costs were significantly reduced, the level of division of labor in inventing and other activities increased, and new producer goods and related new technology emerged. Is the development experience of Britain in the 17th and 18th centuries relevant to currently developing countries? Why did neoclassical development economists not pay enough attention in the 1950s to this successful development experience? Neoclassical development economics 15. Some development economists argue that mainstream economics on the function of the market is not applicable to developing countries because of the nonexistence of many markets in less developed countries. Lio (1998, see chapter 10) shows that if inframarginal analysis is used to formalize classical development economics, the equilibrium number of active markets and degree of marketization can be endogenously determined by the equilibrium level of division of labor and trading efficiency. Use this example to discuss the relationship between classical development economics and neoclassical development economics. 16. Some development economists suggest using many direct measures of welfare to assess the development performance of a country. Use the scientific approach to assess this method in connection to the following discussion. India's per capital GNP is higher but life expectancy is lower than in China. Which country's people have higher utility? This is a question that has no well-defined unique answer. According to one index of the living standard which is a weighted average of per capita GNP, house affordability, pollution, traffic congestion, crime rate, and other variables that affect welfare, Japan has the highest welfare and the US is ranked number seven, behind Australia. But many Americans who have experience in Japan would not agree with this ranking. In other words, there are a lot of possible substitutions (trade offs) between each pair of development indices. Only the individual knows her utility maximization problem that efficiently trades off one against the others among these indices. Such a utility maximization problem is intangible to the government decision maker. The trade off between an individual's utility and that of others' is even more complicated. Not only is the government planner unable to figure it out, but even if she can, it is impossible to be balanced in a benevolent way. Olsen (1996) and Dowrick and Hguyen (1989) use net flow of migrants between the two countries to identify per capita utility difference between them.

30

17.

18.

19.

20.

21.

Analyze under what conditions this approach to assessing development performance is more reliable than neoclassical approach discussed above? The infant industry argument in neoclassical development economics claims that protection tariff is essential for industrialization of a less developed country because of economies of scale, learning by doing, and the network effect of industrial linkage. Other economists argue that the infant industry argument boils down to the argument of imperfect capital market. In the absence of a developed capital market, protection tariff is essential for industrialization. Comment on these views in connection to Hume's (1748, "Of Money", pp. 34-35) following the classical view on investment. "There seems to be a happy concurrence of causes in human affairs, which checks the growth of trade and riches, and hinders them from being confined entirely to one people; as might naturally at first be dreaded from the advantages of an established commerce. Where one nation has gotten the start of another in trade, it is very difficult for the latter to regain the ground it has lost; because of the superior industry and skill of the former, and the greater stocks of which its merchants are possessed, and which enable them to trade on so much smaller profits. But these advantages are compensated in some measure, by the low price of labor in every nation which has not an extensive commerce, and does not much abound in gold and silver. Manufactures therefore gradually shift their places, leaving those countries and provinces which they have already enriched, and flying to others, whither they are allured and are again banished by the same cause." Dodzin and Vamvakidis (1999) have found empirical evidence for the positive correlation between the degree of openness and the income share of the industrial sector in developing agricultural economies. Use this evidence to assess the theory of the infant industry, which claims that protection tariff is essential for industrialization of an agricultural society. Recent equilibrium models of saving and credit (see chapter 16) show that the rationale for saving, investment, and interpersonal loans is based on the gains from the intertemporal trade of goods. Saving and investment cannot take place if transaction costs (moral hazard, adverse selection, and other types of transaction costs) outweigh the gains from intertemporal trade. Use this general equilibrium view to analyze worries about the shortage of investments in developing countries and capital flight from less developed countries. An ingredient of failed development policies prevailing in the 1950s was reliance on stateowned enterprises for industrialization. This policy failure was generated by ignorance of the function of private residual rights to firms, which has been explored by the new theory of the firm and transaction costs in chapters 8 and 9. A comprehensive investment program based on Harrod-Domar's investment fundamentalism and input-output analysis is an evidence for the ignorance of the function of the market in coordinating division of labor, which is investigated in chapters 4, 7, 8. A discriminatory development policy that promotes industrialization at the cost of rural residents' welfare was due to state opportunism that took economic development hostage in pursuing the interests of the elite at the cost of the powerless. Analyze the mechanism of political economy for this policy prescription of neoclassical development economics in connection to Krueger's related analysis of rent seeking (1995, 1997). Krueger (1995, p. 2511) indicates that the pessimism of many neoclassical development economists over the contribution of trade to economic development is based on the argument of elasticity, which implies that the income share of demand for primary goods from less developed countries declines due to an income elasticity of less than one. Krueger argues that protection tariff based on this pessimism is a self-fulfilling prophecy. The model in chapter 4 shows that regardless of the income elasticity of demand for any good, as the transaction cost coefficient for traded good increases, the general equilibrium jumps from a structure with trade and high aggregate productivity to autarky with low aggregate productivity. Use this result to analyze why the argument of elasticity is not a general equilibrium view of development, and why it might be misleading.

31

22. Why did neoclassical development economics pay no attention to the difference between the successful development experience of Britain and the relatively unsuccessful development experience of France in the 18th century (see Mokyr, 1990, pp. 234-50 and 1993 for the comparison of the two)? Many policy prescriptions suggested by neoclassical development economics are similar to Mercantilism, which was rejected by the successful development experience of Britain in the 18th century and by classical development economics represented by Smith. Why is Mercantilist's mistake repeated in the 20th century 23. In the 1950s, many development economists worried about the capability of developing countries in obtaining foreign exchanges and investment. If the developing country concerned was a large one (such as India or China), they worried that the world market could not absorb goods exported from this country. Why are the worries groundless from a general equilibrium view? 24. In the 1950s, the governments in Soviet Union, China, and India set up many specific development targets, such as increases in per capita income, life expectancy, literacy, medical aid, public utility, output levels of steel, machine tools and grain, per capita consumption of cloth, education, housing, investment, nutrition levels, and decreases in infant mortality (see, for instance, Behrman and Srinivasan, 1995). Early development economics generally followed this central planning idea of economic development. Some indices to measure economic development, such as the indices of inequality of income distribution, of illiteracy, of infant mortality, and of life expectancy, were developed under this idea. Is this thinking about economic development consistent with scientific analysis of economic development? 25. Some neoclassical development economists claim that many markets are absent in the less developed country, so that the distortion in the less developed country is greater than in the developed country. But according to the economics of property rights and endogenous externality in chapter 10, the trade off between economies of division of labor and transaction costs implies that a better transaction condition in the developed country may generate more transactions and more aggregate distortion in society as a whole. Use this example to discuss why we need inframarginal analysis of the general equilibrium network of division of labor to investigate the development mechanism. 26. Some development economists argue that the experience of capitalist economic development in the 18th and 19th century Western Europe is not sufficient for successful economic development. They point to Egypt, India, Indonesia, and Latin America as examples of unsuccessful capitalist economic development. Use the differences in institutions between these countries and Britain to assess this argument. For instance, the long-time political monopoly of the ruling party in Egypt generates state opportunism, India's state-planned industrialization encourages rentseeking and other opportunism. Applicability of development economics to developed countries 27. According to Buchanan (1991), state opportunism is not only an obstacle for economic development in developing countries, but also a burden of economic development in the developed countries. He argues that the game between constitutionalists, who are concerned with constitutional rules based on a collective decision that pursues long-term social welfare, and rent-seekers who pursue the short-term interests of a particular group at the cost of longterm social welfare under given democratic rules, dictates the evolution of constitutional rules, which determine policy making. An individual may play dual roles as a constitutionalist and a rent-seeker. Use debates of trade policies, education systems, and health care systems in a democratic developed country (the US or Britain) to analyze the effect of the "super game" in forming constitutional rules and in policy making on economic development in this country. 28. Naisbitt (1990) predicts several following megatrends. Franchising will be a major business form in the US in the next century, the income share of counseling and psycho-services will increase, and individuals will be increasingly less specialized. Discuss the possibility for using

32

29.

30.

31.

32.

new development economics to predict such megatrends and modernization phenomena in developed countries. One of Bill Gates' 12 rules for the digital revolution is to read all of one’s email (Time magazine, March 22, 1999, p. 72). This is certainly not an optimum economic decision because of the trade off between information gains and resource cost in acquiring information. Several Smithian models in this text predict that the income share of information cost increases as information technology improves and negative network effect increases more rapidly than the positive network effect of division of labor and information exchange as the network expands. This implies that increasingly more resources are used for screening and deleting useless information or jargon messages. More importantly, society's capacity to handle and absorb information increases as what its each member knows, as a proportion of the total information that the society knows, decreases. Hence, the simple slogan "information era" may mislead people to think that the more information that she knows, the better. Hence, a new development feature in the US in the next century might be that it becomes increasingly more difficult to make decisions for the efficient trade off between the positive and negative network effects of information exchange. Comment on this view in connection with the dramatic and rapid negative network effects of the computer virus on modern economic life. A striking development phenomenon in developed countries that is documented in Lio (1996) is the concurrent increases in leisure time and working time for the market and the decrease in self-sufficient working time. This phenomenon implies that as individuals are more specialized in their professional jobs, they increase their purchase of services that used to be self-provided. This tendency is associated with increasing leisure time and income from the market. According to the Franchise Annual 1999, this will make the sector that offers timesaving services to the two-income family the fastest growing sector in the next thirty years. Outline the intuition behind the Lio model that predicts the concurrent development phenomena as a consequence of the expansion of the network of division of labor. An interesting development phenomenon in developed countries is documented by a survey in Economist (1998, September 5-11 issue, pp. 4-7). This survey has found that the probability that a motorist gets in a traffic jam is higher in a US city with faster upgrading their transportation infrastructure. North (1958, 1986) also finds empirical evidence for this phenomenon, that income share of transaction costs increases as transaction conditions are improved. This implies that as communication technology is improved and productivity of the computer sector increases, the income share of expenditure on computers and communications increases rather than decreases. This implies that increasingly more time and resources will be consumed in handling jargon messages and in searching and screening. Use the classical idea on network effects of division of labor to analyze this modern development phenomenon. A development phenomenon noted by Naisbitt (1990) is the rapid development of franchise networks in the U.S. and other developed economies. He claims, "Franchising is the single most successful marketing concept ever." According to the International Franchise Association (1997), "More than 550,000 franchise businesses dot the American landscape, generating more than $800 billion in sales, with a new franchise business opening somewhere in the U.S. every 8 minutes each business day." Among three types of franchise a products franchise, a brand name franchise, and a business format franchise, the last one grows much faster than the other two. In 1999, 4,177 business format franchises in the U.S. are listed in The Franchise Annual. Most of them were franchised after 1960. One of them has 20-2,000 units. It seems that classical development economics can explain this phenomenon very well. Most business format franchises (fast food franchise networks McDonald’s and Kentucky Fried Chicken are two of them) involve the division of labor between thinking and doing. The franchiser specializes in providing know-how (intangible intellectual property, which is very

33

commonly associated with an operation manual and training programs). The franchisee specializes in providing tangible goods or services, buying intangible know-how from the franchiser. Sometimes, a franchise network involves deep division of labor between the sector providing roundabout production equipment and the sector providing final services. For instance, the know-how (McDonald’s “bible”) provided by the McDonald’s franchiser includes the purchase of very specialized cooking equipment that can utilize a high level of division of labor between the roundabout sector and the final sector to improve productivity. Also, the know-how provided by the Precision Turn franchiser includes the purchase of very specialized equipment for testing and fixing car engines. If Smith applied his theory to analyze the franchise, he might say something as follows. The high level of division of labor within a particular franchise network generates high productivity on the one hand, and high transaction costs of tangible and intangible properties on the other. The common opportunism in the network is that the franchisee no longer wants to pay a franchise fee once she has acquired the necessary know-how. The franchise contract uses a hostage mechanism to restrict such opportunism. The typical franchise contract has a special clause allowing the franchiser to unilaterally terminate contract if the franchisee does not pay the franchise fee, which might be 9% of the sales revenue of the franchise. Within a certain period of time after the termination, the franchisee is not allowed to compete with the franchiser in specified territory and activities. This hostage mechanism significantly reduces the transaction costs caused by infringement upon the intellectual property rights of the franchiser, so that productivity gains from a larger network of division of labor become more likely to outweigh transaction costs. From this point of view, the boom of franchise networks in the developed countries is the evolution of division of labor between the production of intellectual properties and the production of tangible services. This new development phenomenon has the same economic mechanism as that for Smith's pin factory story. This boom of franchise networks is associated with the recently popular business practices of downsizing, disintegration, outsourcing, contracting out, and focusing on core competencies, which are considered puzzling, since their concurrence to performance progress is incompatible with the neoclassical concept of economies of scale. In chapter 8 of this text, we will use a Smithian model to explain concurrent increases in productivity and division of labor and the decrease in the average size of firms. 33. Up to 1999, more than thousand new business practices in the Internet commerce have been granted patents. One of them pays reviewers for their clicking Internet messages. This generous pricing policy makes money from a rapid expansion of network connections which repays the company in a roundabout way. The variety of pricing structures of a business network increases more than proportionally as the network of transactions expands, since the number of pricing structures is nm where m is the number of traded goods and n is the number of goods directly priced in this network. Marginal cost pricing does not work for choosing the efficient one from many pricing structures since decision variables and prices discontinuously jump between different pricing and network configurations. Use this example to illustrate why inframarginal analysis is essential for us to understand many of the new development phenomena in the networking and globalization era.

34

Part I: Geography and Microeconomic Mechanisms for Economic Development Chapter 2: Geography and Economic Development

2.1. Uneven Economic Development in Different Parts of the World Two centuries after the start of modern economic growth, a large portion of the world remains mired in poverty. Some benefits of modern development, especially gains in life expectancy and reduced infant mortality, have spread to nearly all parts of the world, though huge and tragic discrepancies remain in even these areas. In material well being, however, as measured by gross domestic product (GDP) per capita adjusted for purchasing power parity (PPP), the yawning gaps are stunning and show few signs of amelioration. According to the valuable data assembled by Angus Maddison for the Organization of Economic Cooperation and Development (1995), Western Europe outpaced Africa in average per capita GDP by a factor of around 2.9 in 1820, and by a factor of 13.2 by 1992. More stunningly, Madison puts the African per capita income in 1992 at $1,284 dollars (measured in 1990 PPP adjusted dollars), which is essentially identical to Maddison’s estimate of the average GDP per capita in Western Europe in 1820, $1,292. One area of the developing world, Asia, showed significant progress during the past thirty years, with average incomes rising from around $1,212 in 1965 to $3,239 in 1992 on the Maddison data. 1 In Africa, however, the levels of income in the 1990s were about the same as in 1970. (Maddison puts Africa’s average income at $1,289 in 1971 and $1,284 in 1992). In Latin America and the Caribbean, average income levels in 1992 ($4,820) were only 6.6 percent higher than in 1974 ($4,521). Figure 2.1 (from Gallup and Sachs 1998) shows the global map of GDP per capita as of 1995 (using PPP-adjusted estimates from World Bank 1997). Two geographical correlates of economic development are unmistakable. First, the countries in the geographical tropics are nearly all poor. 2 Almost all high-income countries are in the mid- and high latitudes. Second, coastal economies are generally higher income than the landlocked economies. Indeed, outside of Europe, there is not a single high-income landlocked country, though there are 29 non-European landlocked countries. In the next chapter, we 1

These figures refer to the unweighted average of GDP per capita of nine countries: China, Korea, Taiwan, Hong Kong, Singapore, the Philippines, Malaysia, Indonesia, and Thailand. 2 The geographical tropics refers to the area between the Tropic of Cancer (23.45 N latitude) and the Tropic of Capricorn (23.45 S latitude), the band in which the sun is directly overhead at some point during the year.

35

Figure 21 .

GDP per capita 1995

Tropic of Cancer

Tropic of Capricorn

GDP per capita 1995 $450 - 999 $1,000 - 2,699 $2,700 - 3,199 $3,200 - 4,399 $4,400 - 4,499 $4,500 - 6,499 $6,500 - 18,099 $18,100 - 21,999 $22,000 - 31,100 No Data

36

will analyze the relationship between individuals' utilities (per capita real income), per capita GDP, the extent of the market, aggregate productivity, and the equilibrium level of division of labor. We shall show that GDP relates closely to the notion of extent of the market which coevolves with the level of division of labor. Per capita GDP overstates per capita real income (utility) not only because it ignores effects of general price level, but also it includes transaction costs that reduce utility. On the other hand per capita GDP also understates per capita real income because it excludes most of self-sufficient or noncommercial income. This underestimation negatively relates to the level of division of labor. Gallup and Sachs (1998) have also made three observations about population density from data compelled in their research. First, there is no simple relationship between population density and income level. They find densely populated regions that are rich (Western Europe) and poor (India, Indonesia, and China), and sparsely populated regions that are both rich (Australia and New Zealand) and poor (the Sahel of Africa). Second, the coastlines and areas connected to the coast by navigable rivers are more densely populated than the hinterlands (we will use this term to refer to regions more than 100 km from the coast or from an ocean-navigable waterway). If we multiply GDP per capita and population density, we can calculate GDP density, measured as GDP per km2. As shown by Gallup and Sachs, the coastal, temperate, Northern-hemisphere economies have the highest economic densities in the world. Four of these areas — Western Europe, Northeast Asia (coastal China, Japan, and Korea), and the Eastern and Western seaboards of the US and Canada — are the core economic zones of the modern world. These regions are the overwhelming providers of capital goods in global trade, the world’s financial centers, and the generators of a large proportion of global production. If we take the regions within the US, Western Europe, and temperatezone East Asia that lie within 100 km of the coastline, these areas account for a mere 3 percent of the world’s inhabited land area, 13 percent of the world’s population, and at least 32 percent of the world’s GDP measured at purchasing power parity. According to recent data of the World Trade Organization (1995), just 11 countries in North America, Western Europe, and East Asia, with 14 percent of the world’s population, account for remarkable 88 percent of global exports of capital goods (machinery and transport equipment). For purposes of discussion, we define a tropical country as one in which half or more of the land area is within the geographical tropics. There are 72 tropical countries, with 41 percent of the world population, and 78 non-tropical countries, with 59 percent of the world population. Among the tropical countries, the simple average of 1995 GDP per capita (not weighted by country population) is $3,326. Among the non-tropical countries, the average is $9,027, or nearly three times greater. It is convenient to divide the nontropical countries into two sub-groups, the temperate-zone economies and the subtropical economies. For our purposes, we define sub-tropical as countries in which half or more of the land area is tropical or sub-tropical ecological zones, but in which the country’s land area is more than half outside of the geographical tropics. There are 15 sub-tropical economies, and 63 temperate-zone economies. While the tropical countries have mean income of $3,326, the sub-tropical countries have mean income of $7,874, and the temperate-zone economies have a mean income of $9,302. Among the economies that were not socialist in the postwar period, the geographical divide is even 37

sharper: non-socialist tropics, $3,685; non-socialist sub-tropics, $9,248; and non-socialist temperate, $14,828. Of the top thirty countries ranked by 1995 PPP-adjusted GDP per capita, only two are tropical, and these two are tiny: Hong Kong and Singapore. Four are subtropical, and 23 are temperate-zone. The two tropical countries account for a mere 1.0 percent of the combined population of the top 30 countries. Using geographic information system data, we can also examine the proportion of the population living in the geographical tropics in the top 30 countries, taking into account that four of the top thirty countries that we have not counted as tropical (Australia, Chile, Taiwan, and the United Arab Emirates) have a part of their populations in the tropical region. Making this adjustment, the tropical share of the top-30 population is 2.3 percent. Nearly all landlocked countries in the world are poor, except for a handful in Western and Central Europe which are deeply integrated into the regional European market, and connected by low-cost trade. 3 (Even mountainous Switzerland has the vast bulk of its population in the low-elevation cantons north of the Alps, and these population centers are easily accessible to the North Atlantic by land and river-based traffic). There are 35 landlocked countries in the world with population greater than 1 million, of which 29 are outside of Western and Central Europe. Of these 29 countries, the richest is 38th (!), Botswana, which owes it pride of place to well-managed diamond mines. The second richest is 68th, Belarus. The difference in means is striking: the landlocked countries outside of Western and Central Europe have an average income of $1,771, compared with the non-European coastal countries, which have an average income of $5,567. Of course, geography is not everything. Even geographically favored countries, such as temperate-zone, coastal North Korea, or well-located Czechoslovakia, failed to thrive under a socialist economic and political system. Nonetheless, development surely seems to be favored among the temperate-zone economies, especially the subset that: (1) is in the Northern Hemisphere; (2) has avoided socialism; and (3) has avoided being ravaged by war. In total, there are 78 non-tropical economies, of which 7 are in the Southern Hemisphere: Argentina, Australia, Chile, Lesotho, New Zealand, South Africa, and Uruguay (all in the temperate zone). Gallup and Sachs (1998) classify 46 countries as socialist during the post-war period, of which 31 are in the North temperate zone, and four are in the North sub-tropical zone. They also classify 12 non-tropical countries as war-torn. There are 12 non-tropical landlocked countries outside of Europe, of which 10 were socialist and 2 were not. With these definitions, Gallup and Sachs find the following. There are 23 countries with the most favored combination of geography and politics — Northern Hemisphere, temperate zone, coastal, non-socialist, and non-war torn — with an average income of $18,000. In fact, 22 of these countries have an average GDP per capita above $10,000, with Turkey and Morocco being the only exceptions. 4 Using a multiple regression estimate for the 78 non-tropical countries, average incomes per capita are reduced by an estimated $4,785 for being in the subtropics; $3,590 for being in the Southern hemisphere; $10,053 for being socialist; and 3

The landlocked countries in Western and Central Europe are Austria, the Czech Republic, Hungary, the Former Yugoslav Republic of Macedonia, Slovakia, and Switzerland. 4 Morocco is just on the borderline of classification as a sub-tropical country, with 48 percent of the population in the tropical and sub-tropical ecozones.

38

$5,190 for being landlocked. A summary of geographical characteristics by major region is shown in Table 2.1. For each region, they show the average GDP per capita, total population and land area, and several key variables that we will find to be closely related to economic development: the extent of land in the geographical tropics, the proportion of the region’s population within 100 km of the coastline or within 100 kilometers of the coastline or oceannavigable river, 5 the percentage of the population that lives in landlocked countries, the average distance by air (weighted by country populations) of the countries within the region to the closest “core” economic areas, 6 the density of human settlement (population per km2) in the coastal region (within 100 km of the coastline) and the interior (beyond 100 km from the coastline). Some important characteristics are the following. First, Sub-Saharan Africa, the poorest region, has several characteristics closely associated with low income in general: a very high concentration of land in the tropics, a population heavily concentrated in the interior (only 19 percent within 100km of the coast); with more than a quarter of the population in landlocked countries (the highest of any region); very far from the closest “core” markets in Europe; and with low population densities in the coastal and interior regions. By contrast, Europe, the richest region shown, is non-tropical; heavily concentrated near coastal areas; with almost no population in landlocked regions; and with moderate population density. South Asia and the transition economies (of Eastern Europe and the former Soviet Union) are, like Sub-Saharan Africa, also heavily concentrated in the interior rather than the coast. India’s great mass of population, for example, lives in the Gangetic valley, often hundreds of kilometers from the coast. South Asia is, of course, partly tropical and densely populated (indeed the most densely populated in the world), while the transition economies are non-tropical and also the least densely populated region. Latin America is the other highly tropical region, with low population densities, and with a moderately coastal population. The United States has two enormous advantages for development: a relatively high proportion of population near the coast (38 percent within 100 km of the coast, and a remarkable 67 percent if ocean-navigable river systems are included), and a temperate-zone landmass. These patterns prompt the following questions. How much has geography mattered for economic growth, once we control for economic policies and institutions? What is the general equilibrium mechanism for economic development that involves the interplay between geography, urbanization, institutions, and evolution of division of labor? If geography mattered in the past, what difference does it still make via 5

Using geographical information system (GIS) data, the coastal population is calculated in two ways. First, all land area within 100 kilometers of the open sea, except for coastline in the arctic and sub-arctic region above the winter extent of sea ice (National Geography Society (NGS), 1995) are taken, and the population within that area is measured. Additionally, river systems that accommodate ocean-going vessels on a regular basis (e.g. the Saint Lawrence Seaway and the Mississippi River) are identified, and land areas within 100 kilometers of such navigable rivers are added. Since data of direct costs of transport for these river systems are not available, there are inevitably difficulties in classification, as some ostensibly oceannavigable rivers impose very high costs for such transport. Due to the classification difficulties and the greater empirical relevance of coastal access alone, the population and land area near navigable rivers are not used in the rest of the chapter. 6 Galuup and Sachs (1999) experimented with a number of distance measures, all of which produced similar outcomes. They therefore choose the simplest: the smallest distance of the country’s capital city to one of the following three cities: New York, Rotterdam, or Tokyo.

39

the equilibrium mechanism today? Table 2.1: Geographical Characteristics of Selected Regions

Continent GDP/PC Total Population Total Land Area (million km2) Land in Tropics (%) Population w/100km of Coast (%) Population w/100km of Coast or River (%) Landlocked Population (%) Distance to Core Market (km) Coastal Density (pers/ km2) Interior Density (pers/ km2)

SubSaharan Africa 1,865 580 24

Western Europe

East Asia

South Asia 1,471 1,219 4

Transition Economie s 3,902 400 24

19,230 383 3

10,655 1,819 14

91 19

0 53

21 28 6,237 40 22

Latin America 5,163 472 20

30 43

40 23

0 9

73 42

89

60

41

55

45

4 922 109 125

0 3,396 381 91

2 5,744 387 287

21 2,439 32 16

3 4,651 52 18

Based on the evidence provided by Gallup and Sachs (1998), we believe that geography continues to matter importantly for economic development, alongside the importance of economic and political institutions. From an analytical point of view, we believe that geographical considerations should be re-introduced into development economics, which so far has almost completely neglected geographical themes. The chapter is organized as follows. Section 2.2 discusses a range of theoretical approaches linking geography and economic development. Section 2.3 provides crosscountry empirical evidence for the linkages.

Questions to Ask Yourself when Reading the Chapter What is the relationship between geographic conditions, transaction costs, level of division of labor, and per capita real income of a country? What is the relationship between geographic conditions, quality of public institutions, government policy regime, and development performance of a country?

2.2. Geography and Division of Labor While geography has been much neglected in the past decade of formal econometric studies of cross-country performance, economists have long noted the crucial role of geographical factors. Indeed, though Adam Smith (1776) is most remembered for his stress on economic institutions, Smith also gave deep attention to the geographic correlates of growth. (Smith should also be remembered for his recognition that Europe’s first-mover military advantage gave it an ability to impose huge costs on other parts of 40

the world. 7 ) Smith saw geography as the crucial accompaniment of economic institutions in determining the division of labor. Smith’s logic, of course, started with the notion that productivity depends on specialization, and that specialization depends on the extent of the market. The extent of the market in turn depends both on the freedom of markets as well as the costs of transport. And geography is crucial in transport costs: As by means of water-carriage a more extensive market is opened to every sort of industry than what land-carriage alone can afford it, so it is upon sea-coast, and along the banks of navigable rivers, that industry of every kind naturally begins to subdivide and improve itself, and it is frequently not till a long time after that those improvements extend themselves to the inland part of the country. (p. 25)

In view of the crucial role of transport costs, Smith notes that: All the inland parts of Africa, and that part of Asia which lies any considerable way north of the Euxine [Black] and Caspian seas, the antient Sycthia, the modern Tartary and Siberia, seem in all ages of the world to have been in the same barbarous and uncivilized state in which we find them at present. The sea of Tartary is the frozen ocean which admits of no navigation, and though some of the greatest rivers in the world run through that country, they are at too great a distance from one another to carry commerce and communication through the greater part of it. There are in Africa none of those great inlets, such as the Baltic and Adriatic seas in Europe, the Mediterranean and Euxine seas in both Europe and Asia, and the gulphs of Arabia, Persia, India, Bengal, and Siam, in Asia, to carry maritime commerce into the interior parts of that great continent . . . (p. 25)

Great thinkers such as Braudel (1972, 1981-84) and McNeill (1963, 1974), and important recent historians such as E. L. Jones (1981) and Crosby (1986), have placed the geography and climate of Europe at the center of their explanations for Europe’s preeminent success in economic development. Braudel pointed to the key role of the Mediterranean-based and North-Atlantic coastal economies as the creative centers of global capitalism after the fifteenth century. McNeill similarly stressed Europe’s great advantages in coastal trade, navigable rivers, temperate climate, and suitable disease patterns as fundamental conditions for European takeoff and eventual domination of the Americas and Australasia. Crosby details the advantages of the temperate zones in climate, disease ecology, and agricultural productivity. Two important essays, one by the Council on Foreign Relations (Lee, 1957), and one a generation later by Kamarck (1976) for the World Bank, synthesized these arguments in excellent surveys on Tropical Development, which have been largely ignored by the formal modelers of economic development. One of the most interesting recent attempts to ground very long-term development in geographical and ecological considerations comes from ecologist Diamond (1997), who asks why Eurasians (and peoples of Eurasian origin in the Americas and Australasia) “dominate the modern world in wealth and development” (p. 15). He disposes of 7

He noted that “all the commercial benefits” to the East and West Indies that might have resulted from increased trade “have been sunk and lost in the dreadful misfortunes” occasioned by European military advantage, which enabled the Europeans “to commit with impunity every sort of injustice in those remote countries.”

41

racialist explanations not just on moral grounds but on rigorous findings of the shared genetic inheritance of all human societies. His explanation rests instead on the long-term advantages of Eurasia in agglomeration economies and the diffusion of technologies. Human populations in the Americas and Australasia were cut off by oceans from the vast majority of human populations in Eurasia and Africa. They therefore could not share, through trade and diffusion, in technological advances in agriculture, communications, transport, and the like. Additionally, Diamond argues that technological diffusion naturally works most effectively within ecological zones, and therefore in an East-West direction along a common latitude, rather than in a North-South direction, which almost invariably crosses ecological zones. This is because plant species and domesticated animals appropriate to one ecological zone may be completely inappropriate elsewhere. Eurasia, claims Diamond, therefore enjoyed the benefit of its vast East-West axis heavily situated in temperate ecological zones, while Africa was disadvantaged by its NorthSouth axis which cut across the Mediterranean climate in the far North, the Saharan Desert, the equatorial tropics, and the Southernmost sub-tropical regions. Diamond argues that these advantages, in addition to more contingent (i.e. accidental) advantages in indigenous plant and animal species, gave Eurasia a fundamental long-term advantage over the rest of the world. Historians have also stressed the changing nature of geographical advantage over time, as technology changes. In early civilizations, when transport and communications were too costly to support much inter-regional and inter-national trade (and virtually any oceanic trade), geographical advantage came overwhelmingly from agricultural productivity rather than from access to markets. Therefore, early civilizations almost invariably emerged in highly fertile river valleys such as the Nile, Indus, Tigris, Euphrates, Yellow and Yangtze rivers. These civilizations produced high-density populations that in later eras were actually disadvantaged by their remoteness from international trade. Northern Europe could not be densely settled before the discoveries of appropriate technologies (e.g. the moldboard plow in the Middle Ages) and tools to fell the great Northern forests (Landes, 1998). Similarly, as the advantages of over-land trade and coastal-based trade between Europe and Asia gave way to oceanic commerce in the 16th century, economic advantage shifted from the Middle East and Eastern Mediterranean, to the North Atlantic. In the 19th century, the high costs of transport of coal for steam power meant that early industrialization almost invariably depended on proximity to coal fields. This advantage of course disappeared with the discoveries of petroleum refining, oil and hydro-based electricity production, and reduced cost of bulk transport. Railroads, automobiles, and air transport, as well as all forms of telecommunications, surely reduced the advantages of the coastline relative to the hinterland, but according to the evidence below, the advantages of sea-based trade remain. To summarize, we can say that leading historians and economists have long recognized geography as a crucial scaffolding for economic development, even though geography has been neglected in most recent empirical studies of comparative development. Leading thinkers have pointed to four major areas in which geography will play a fundamental direct role in economic development: transport costs, human health, agricultural productivity (including animal husbandry); and proximity and ownership of natural resources (including water, minerals, hydrocarbon deposits, etc.). The factors may also have indirect effects, if first-mover advantages or population densities affect 42

subsequent growth dynamics through agglomeration economies or other feedback mechanisms. 8 The models in this text have formalized Smith's ideas that geography affects transportation cost, which determines the extent of the market, which determines the level of division of labor, which determines in turn productivity and development performance. We develop Smithian static and dynamic equilibrium models to explore the intimate relationships between geography, trading efficiency, the equilibrium network size of division of labor, the extent of the market, urbanization, and productivity. In the models, the equilibrium network size of division of labor is determined by all individuals' networking decisions. The networking decisions determine each player's numbers of traded goods and trade partners. The trade off between transaction costs and positive network effects of division of labor on aggregate productivity determines the equilibrium level of division of labor and equilibrium aggregate productivity. Coastal areas, the areas that are close to navigable river have a greater scope for trading off economies of specialization against transaction costs than landlocked areas, so that the extent of the market and the equilibrium level of division of labor are greater in the former than in the latter. In chapter 11 we shall develop several Smithian models of urbanization. These models show that the geographical conditions that are favorable for transportation will generate great economies of agglomeration. This implies a fast coevolution of urbanization and division of labor. In chapter 12, several Smithian models with endogenous number of producer goods and endogenous degree of production roundaboutness show that the geographical conditions that are favorable for transportation will generate a larger equilibrium number of producer goods, a greater degree of production roundaboutness, and more outsourcing trade. In chapter 14, a Smithian dynamic general equilibrium model shows such favorable geographical conditions can speed up spontaneous coevolution of division of labor and extent of the market. It predicts that those countries in islands or coastal areas will enter takeoff stage of economic development earlier than hinterland or landlocked areas do. The prediction of the models is consistent with the empirical observation documented in Radelet and Sachs (1998b) that only those developing countries with good transport access to world markets have been able to establish assembly-type industries and to adopt labor intensive export-oriented industrialization pattern. So far we have stressed that geography may influence economic development directly through transportation efficiency and level of division of labor. Geography can have another potent effect by affecting the choice of economic policies and institutions. Countries with favorable geographical conditions for transportation, for example, may choose more open trade policies than countries with unfavorable geographical conditions for transportation. The Ricardian model with transaction costs and endogenous trade policy regime in chapter 3 provides a formal general equilibrium mechanism that predicts the relationship between geography and government policies. In that model, there is a trade off between positive network effect of division of labor on aggregate productivity, transportation costs, and distortions caused by tariffs. As transportation efficiency is 8

See chapter 11 for the definitions of various types of agglomeration economies and their relationship with the equilibrium level of division of labor.

43

improved, the general equilibrium discontinuously jumps from autarky first to the partial division of labor where one country produces two goods and the other country completely specializes in producing one good, then to the complete division of labor where each country produces only its comparative advantage good. For the partial division of labor, the terms of international trade is determined by the domestic terms of trade in the less developed country which is not completely specialized. In the absence of tariff, all gains from trade will go to the developed country that completely specializes. Hence, the less developed country can use import tariff to obtain most gains from trade by altering terms of international trade. But the developed country will hurt itself by imposing any positive tariff. Hence, in this transitional stage of economic development, unilateral free trade in the developed country coexists with unilateral protection tariff in the less developed country. As transportation efficiency is improved, the equilibrium is associated with the complete division of labor in which two countries have incentive to engage in a Nash tariff bargaining, in order to avoid tariff war which will exhaust gains from trade. Such Nash tariff negotiation will generate bilateral free trade. This general equilibrium mechanism which simultaneously determines trade policy regime and level of division of labor can tell the following story about the relationship between geography and policy regime. The transportation efficiency is higher in an island or coastal economy than in a hinterland or landlocked economy. Hence, the equilibrium level of division of labor is higher in the former than in the latter. The higher level of division of labor is associated with free trade policy regime, while the low level of division of labor is associated with unilateral protection tariffs. If two countries, such as Britain and France, are coastal, their favorable geographical conditions for transportation generate a high level of division of labor between them. As a result, each country can increase the share of gains from trade that it receives by increasing import tariff to manipulate terms of trade. Such tariff war will generate deadweights that exhaust all gains from trade. Therefore, both countries will have incentive to adopt multilateral free trade regime via the Nash tariff negotiations. In chapter 3, we will extend the Ricardian model with two countries to the case with three countries. It will be shown that favorable geographical conditions for transportation will increase the number of countries that might be involved in international trade. This increase in the number of potentially trading countries creates the pressure to exclude the country with higher tariff from trade even if this country has comparative advantage in producing a good. This implies a favorable geographical condition will increase the number of potentially trading countries and thereby press all countries to adopt free trade policy.

2.3. Empirical Linkages of Geography and Economic Development 2.3.1. Geographical Correlates of Economic Development The basic theories in this volume point to two broad categories of geographical factors of deep significance: transport costs, and production condition parameters that affect the degree of comparative advantage. Consider first the transport costs. Remarkably, despite the likely importance of transport costs for economic development, there are no 44

adequate measures of transport costs for a large sample of developed and developing countries. The best that we could obtain for a large number of countries is the IMF estimates of the CIF/FOB margins in international trade. These margins measure the ratio of import costs inclusive of insurance and freight (CIF) relative to import costs exclusive of insurance and freight (FOB). There are several problems with these measures, the most important being that: (1) they are only crudely estimated by the IMF staff; and (2) they depend on the composition of imports, and thus are not standardized across countries. Nonetheless, the CIF/FOB margins are informative, and predictive of economic development. The CIF/FOB margin for 1995 is 3.6 percent for the US, 4.9 percent for Western Europe, 9.8 percent for East Asia, 10.6 percent for Latin America, and a whopping 19.5 percent for Sub-Saharan Africa. 9 Gallup and Sachs estimate an equation relating the CIF/FOB band to the distance of the country to the “core” areas of the world economy (Distance, measured in thousands of kilometers), and to the accessibility of the country to sea-based trade, by including a dummy variable for non-European landlocked countries (Landlocked): CIF/FOB = 1. 06 + 0.010 Distance (1,000 km) + 0.11 Landlocked (84.9) (3.0) (2.4) N = 83, R2 = 0.32 10 As expected, there is a penalty both for distance from the core economies and for being landlocked. Each 1,000 km raises the CIF/FOB margin by 1.0 percentage points; being landlocked raises the CIF/FOB margin by 11.1 percentage points. We will show later that the CIF/FOB margin is indeed predictive of income levels and economic development. Regressing CIF/FOB on the proportion of the population within 100 km of the coast (Pop100km), Gallup and Sachs also find a negative effect, but when they include both Pop100km and Landlocked, Landlocked has more explanatory power. The coefficient on Pop100km remains negative, as expected, but drops in magnitude and is statistically insignificant. We have seen in Table 2.1 that the various regions in the world differ markedly in locations of their populations relative to the seacoast and navigable rivers. African populations especially are far from the coastline, while Europe is overwhelmingly coastal. Indeed, Africa has the highest proportion of landlocked population of any continent in the world, and especially in East Africa, the populations are heavily in the interior (beyond 100 km of the coast) even in countries with coastlines such as Kenya (coastal population equals 6 percent of the total), Mozambique (40 percent), Sudan (2 percent), and Tanzania (16 percent). The situation is made worse by the fact that Africa’s interior regions are not accessible by ocean-navigable vessels, since the river systems in Africa almost all face impassable barriers (e.g. cataracts, shallows, etc.) that prevent the entry of oceangoing vessels into the interior of the continent. 9

The data refer to unweighted country averages for the respective regions for the countries for which IMF data are available. 10 Absolute value of t statistics are in parentheses below the coefficients, and N is the number of observations.

45

The notion that the coastal access has a large effect on trade and development is plausible given what we know about the growth patterns of the most successful developing countries in the period after 1965. Almost without exception, fast-growing developing countries have based their rapid growth on labor-intensive manufacturing exports. And almost without exception, such activities have expanded in port cities or export zones close to ports. As shown in Radelet and Sachs (1998b), almost all countries with macroeconomic success in labor-intensive manufacturing exports have populations almost totally within 100 km of the coast. Geographical conditions affect the equilibrium degree of urbanization and the equilibrium level of division of labor via their effects on transportation conditions (see chapter 11). Most large cities other than garrison towns or administrative capitals typically grow up on coastlines or ocean-navigable rivers. Therefore, countries with neither coastlines nor navigable rivers tend to have less urbanization, and less growth. A simple regression estimate for 149 developed and developing countries in 1995 shows that more ocean-accessible regions in the world are indeed also more urbanized, as are economies closer to the economic core regions. In a simple regression Gallup and Sachs find: %Urban = 132.3 + 17.1 Pop100km - 10.8 LDistance (10.8) (3.6) (7.1)

R2 = 0.29 N = 149

A second major dimension of productivity linked to geography is the prevalence of infectious disease. As shown in Gallup and Sachs (1998), malaria, with an estimated incidence of between 200 and 500 million cases per year (WHO,1997a), is almost entirely concentrated in the tropics. This pattern is neither accidental, nor mainly the result of reverse causation in which poor countries are unable to eradicate a disease under control in rich countries. There is no effective prophylaxis or vector control for malaria in the areas of high endemicity, especially Sub-Saharan Africa. Earlier methods of vector control are losing their effectiveness because of increased resistance of the mosquitoes to insecticides. Standard treatments are also losing effectiveness because of the spread of resistance to chloroquine and other antimalarial drugs. The geographical extent of malaria is determined mostly by the ecology of the parasites (different species of malaria Plasmodia) and the vectors (different species of Anopheles mosquitoes). Malaria was brought under control since 1945 mainly in temperate-zone and sub-tropical environments, where the foothold of the disease (both in terms of the mosquito population and the parasite endemicity) was more fragile. Gallup and Sachs (1998) also show the extent of endemic malaria in 1946, 1966 and 1994, with its gradually retreat to the core tropics. Using data from the World Health Organization, they construct a measure of malaria intensity. A simple regression of malarial intensity on ecological zones shows that it is most intense in the tropics and somewhat less in the subtropics (relative to all other ecozones). There is also a strong “Sub-Saharan Africa” effect.

46

Malarial Intensity (scale 0-1) = -0.01+ 0.3 Wet Tropics + 0.5 Dry Tropics + 0.4 Wet Subtropics + 0.2 Dry Subtropics (0.7) (2.0) (4.9) (3.9) (1.5) + 0.5 Sub-Saharan Africa, (6.7)

N = 148

R2 = 0.74

The pattern for malaria is common for a range of infectious diseases, whose vectors of transmission depend on the tropical climate. Many diseases that are carried by mosquitoes (dengue, yellow fever, and lymphatic filariasis in addition to malaria), mollusks (e.g. schistosomiasis), and other arthropods (onchocerciasis, leishmaniasis, trypanosomiasis, Chagas’ disease, and visceral filariasis), are endemic in the tropical ecological zones and nearly absent elsewhere. While data on disease burdens by country are generally not available, the recent massive study by Murray and associates on the burden of disease (Murray and Lopez, 1996), confirms the heavy tropical concentration of infectious disease as a cause of death. A third major correlate of geography and productivity is the link of climate and agricultural output. Gallup's (1998) estimates of agricultural productivity suggest a strong adverse effect of tropical ecozones on the market value of agricultural output, after controlling for inputs such as labor, tractors, fertilizer, irrigation and other inputs. Gallup (1998) suggests that tropical agriculture suffers a productivity decrement of between 30 and 50 percent compared with temperate-zone agriculture, after controlling as well as possible for factor inputs. 2.3.2. Geography and Levels of per capita Income Gallup and Sachs (1999) have examined the linkage of output to geography both in levels and rates of change of GDP. They start with the simplest specification, writing the log level of per capita income as a function of three underlying geographical variables: (1) Tropicar, the percentage of land in the geographical tropics; (2) Pop100km, the proportion of the population within 100km of the coastline; and (3) LDistance, the minimum log-distance of the country to one of the three core regions, measured specifically as the minimum log-distance to New York, Rotterdam, or Tokyo. This relationship are estimated three times: for Maddison’s GDP estimates for 1950 and 1990, and for the World Bank’s PPP GDP estimates for 1995 on the subset of countries for which Maddison’s data are available. In all three regression estimates, reported in Table 2.2 output is a positive function of Pop100km, and a negative function of Tropicar and LDistance. The magnitude of the effects tends to increase over time, as expected. In 1950, the “penalty” for Tropicar was -0.69, signifying that tropical areas were only 50 percent (= exp(-0.69)) of per capita income of the non-tropical areas controlling for the other factors. By 1995, the effect has risen to -0.99 (or 37 percent of the non-tropical areas). Similarly, the benefit of a coastal population rose from 0.73 in 1950 to 1.17 in 1995. The suggestion is that being tropical, landlocked and distant was bad already in 1950, and adverse for growth between 1950 and 1995. 47

We now turn in more detail to the 1995 data, for which we have a wider range of possible explanatory variables. This simple level equation for GDP per capita on a PPPbasis in 1995 is first estimated, for the 150 countries with population greater than 1 million. Then growth equations for the period 1965 - 90 are considered. The explanatory variables are grouped into three broad categories: (1) variables related to transport costs and proximity to markets; (2) variables related to ecological zone; and (3) variables related to economic and political institutions. In regression (4) of Table 2.2, the explanatory variables are limited to a parsimonious set of four variables closely linked to geography: the prevalence of malaria; transport costs as measured by the CIF/FOB margin; the proportion of the country’s population near the coastline; and the endowment of hydrocarbons per capita. These four variables alone account for 69 percent of the cross-country variation in per capita income, and are all with the expected sign and statistically significant (hydrocarbons only at the 10% level). High levels of GDP per capita are associated with the absence of malaria; low transport costs; a coastal population; and a large endowment of hydrocarbons per capita. Of course, these associations are hardly a proof of causality. Not only might the explanatory variables be proxies for left out variables (e.g. malaria may be proxying for a range of tropical diseases or other liabilities), but there could also be reverse causation, in which high incomes lead to the control of malaria, or to a reduction of transport costs. In regression (6), variables related to political and economic institutions are included: Socialism, which is a dummy variable for socialist economic institutions; New State, which measures the proportion of time under colonial rule; Public, which measures the quality of governmental institutions; and Open, which measures the proportion of time between 1965 and 1990 that the country is open to international trade. These variables relate to endogenous transaction costs. The relationships between endogenous transaction costs, institutions, evolution in division of labor, and economic development will be investigated in chapters 8, 9, and 10 in part II. It is found, in line with many recent studies, that openness and quality of public institutions are highly correlated with the level of income. The socialist variable is not significant, probably because of the strong collinearity with Open and because of the smaller data set once Gallup and Sachs include the Public variable (since that variable is not available for most of the socialist economies). Newly independent countries also do not have significantly lower income levels. If the malaria index is not included, the new state variable is highly significant, which suggests the possibility that the heavy burden of disease in tropical Africa and Asia made these regions more susceptible to colonization. Gallup and Sachs find, importantly, that both policy and geography variables are strongly correlated with the level of 1995 per capita GDP. Remember that geography may be even more important than suggested by this equation, since there are reasons to believe that favorable geography plays a role in inducing growth-promoting institutions such as open trade and an efficient public bureaucracy. We examine this linkage, briefly, below. Table 2.2: Level of GDP (1) lgdp50

(2) lgdp90

(3) lgdp95

48

(4) lgdp95

(5) lgdp95 (non-Africa)

(6) lgdp95

Tropical Area (%)

-0.69 (4.13)

-0.99 (5.78)

-0.99 (5.10)

Pop 100 km (%)

0.71 (4.02)

1.00 (5.43)

1.09 (5.27)

LDistance

-0.22 (2.56)

-0.39 (4.39)

-0.34 (3.41)

Shipping (CIF/FOB)

0.85 (3.63)

1.21 (4.17)

0.36 (2.53) 0.03 (0.55)

Cost

-2.28 (2.32)

-13.50 (4.66)

Malaria index 1994 (01)

-1.55 (6.60)

-1.26 (2.69)

-1.15 (7.65)

Log hydrocarbons per person

0.01 (1.84)

0.01 (1.75)

0.01 (1.85)

Socialism

-0.05 (0.31)

New State (0-3)

-0.06 (0.98)

Trade Openness (0-1)

0.23 (7.38)

Public Institutions (010)

0.55 (3.17)

Constant

9.07 (13.58)

11.19 (16.26)

10.98 (14.10)

Observations 129 129 129 0.38 0.58 0.50 R2 Note: Absolute value of t-statistics in parentheses

10.84 (9.82)

22.64 (7.42)

6.71 (11.06)

83 0.69

52 0.56

97 0.88

2.3.3. Geography and Growth of per capita Income We now examine the forces of convergence and divergence by estimating a cross-country growth equation that allows for the possibility of catching up effects. Gallup and Sachs (1999) have run a Barro regression. They estimate a model of average annual growth during 1965-90 conditional on per capita income levels in 1965. The dates are determined by data availability. For the purposes of the growth equations, they use the Penn World Tables for measures of PPP-adjusted GDP per capita). They test whether growth is affected by the initial income level (negatively in the case of convergence, positively in the case of divergence), as well as by geographical variables holding constant the initial income and other policy and institutional variables. Table 2.3: GDP Growth (1) gr6590

(2) gr6590

49

(3) gr6590

(4) gr6590

(5) gr6590 (TSLS)

(6) gr6590

(7) gr6590

GDP p.c. 1965

-2.3

-2.4

-2.5

-2.6

-2.7

-2.3

-2.4

(7.70)

(8.02)

(8.06)

(7.87)

(7.60)

(7.41)

(7.09)

Years of secondary 0.3 (1.75) schooling Log life expectancy 1965 6.6

0.2

0.2

0.2

0.2

0.1

0.1

(1.77)

(1.32)

(1.34)

(1.15)

(0.81)

(0.89)

5.5

4.3

3.3

2.4

4.1

3.4

(7.23)

(6.21)

(4.45)

(3.60)

(1.79)

(4.53)

(3.89)

Trade Openness 1965-90 1.9 (5.49) (0-1) Public Institutions (0-10) 0.3

1.9

1.7

1.7

1.7

1.8

1.8

(4.79)

(4.79)

(4.70)

(4.39)

(4.79)

(4.66)

0.3

0.3

0.4

0.5

0.3

0.4

(2.63)

(3.32)

(3.92)

(3.66)

(3.20)

(3.47)

(3.08)

LDistance

0.0 (0.24)

Pop100km (%) Tropical area (%)

1.0

0.9

0.8

0.6

(3.07)

(3.01)

(2.64)

(1.91)

-0.9

-0.6

-0.5

-0.4

-0.7

-0.5

(2.28)

(1.35)

(1.09)

(0.82)

(1.89)

(1.44)

-1.2

-2.0

-2.6

-0.9

-1.6

(2.15)

(3.60)

(3.87)

(1.86)

(2.89)

Malaria index 1966 dMal6694

-2.5

-4.5

-1.9

(3.93)

(2.12)

(2.94)

Log coastal density Log inland density Constant Observations R2

0.3

0.2

(4.91)

(4.34)

-0.1

-0.1

(2.26)

(1.60)

-8.9

-4.1

1.3

5.9

9.8

0.7

4.1

(2.90)

(1.17)

(0.34)

(1.57)

(1.76)

(0.19)

(1.08)

75 0.71

75 0.75

75 0.77

75 0.80

75 0.78

75 0.80

75 0.82

Note: Absolute value of robust t-statistics in parentheses.

They start with a baseline equation similar to those in Barro and Sala-i-Martin (1995), in which average annual growth between 1965 and 1990 is a function of initial income in 1965; the initial level of education in 1965 (measured by average years of secondary school in the population); the log of life expectancy at birth in 1965; the openness of the economy to international trade; and the quality of public administration (regression (1) of table 2.3). Evidence for conditional convergence, and standard results for the other variables are found: average growth rate is an increasing function of education, life expectancy, openness, and the quality of public administration. In regression (2) of table 2.3, Tropicar and Pop100km are highly significant and of the expected sign. All other things equal, annual growth is 0.9 percentage points lower in tropical countries than in nontropical countries. Landlocked countries (Pop100km = 0) experienced 1.0 percentage points slower growth than coastal economies. Interestingly, the LDistance variable is not significant. This suggests that distance to the core may be 50

endogenously determined by openness and quality of public institutions during the period. If those two variables are dropped, then LDistance has the expected negative sign with statistical significance (not shown). In regression (3) of Table 2.4, Ldistance is dropped and a measure of malaria at the beginning of the period is added. Initial malaria incidence has a dramatic correlation with poor economic performance. Countries that had severe malaria in 1966 grew 1.2 percentage points per year slower than countries without falciparum malaria, even after controlling for life expectancy. The estimated effect of being in the tropics becomes smaller than it was without the malaria variable, and insignificant. Clearly, the malaria variable is picking up the explanatory power of the tropics variable. The effect of initial life expectancy is also reduced, though still large and significant. Table 2.4. Level and Changes in Malarial Prevalence between 1966 and 1994 by Ecozone Predominant Ecozone

Malaria Index 1966 Average (0-100) 1966-1994

Temperate (N=57)

0.2

-0.2

Desert (N=23)

27.8

-8.8

Subtropical (N=42)

61.7

-5.0

Tropical (N=21)

64.9

0.5

Change

Note: Countries are classified by their predominant ecozone from the following groupings: Temperate (temperate, boreal and polar ecozones), Desert (tropical and subtropical deserts), Subtropical (non-desert subtropical), and Tropical (non-desert tropical). The index and average reduction are unweighted averages over countries.

In fact, none of the countries in the sample with 100 percent of their land area subject to falciparum malaria were able to eradicate it completely over this period. The reductions in malaria were largest in the countries with the least malaria in 1966. The temperate ecozones were effectively free of falciparum malaria in 1966. The reductions in malaria occurred in the desert (non-temperate) regions, and the subtropics. There was a small increase in the malaria index for countries in tropical ecozones. The change in malaria incidence could be partly due to economic growth if growth provided countries with the economic resources and institutional wherewithal to carry out effective control programs. To account for the possible impact of economic growth on malaria reduction, Gallup and Sachs instrument the malaria change with four subtropical ecozone variables and two desert tropical ecozone variables. Regression (5) shows that the estimated impact of malaria on growth increases when change in malaria is 51

instrumented. There is no indication that faster growth is the cause of malaria reduction. Some of the countries that have had the largest increases in malaria, like India and Sri Lanka, have had steady, if unspectacular, economic growth over this period. Likewise some countries with dramatic decreases in malaria, like Namibia, had almost no economic growth. It is only after controlling for other relevant variables that the effect of malaria reduction on growth becomes apparent. The index of malaria, and malaria change, may be more than just a measure of malaria. It may be picking up the incidence of other tropical diseases not well indicated by the average life expectancy and tropical area. Among tropical diseases, malaria is widely recognized to be the most important, but the malaria index may also be a proxy for scourges like onchocerciasis, filariasis, and trypanosomiasis. Malaria occurs throughout the tropics, but severe malaria is heavily concentrated in sub-Saharan Africa. Africa currently has 90% of the estimated cases of malaria each year (WHO 1997a), and it is the only region of the world where falciparum malaria predominates. In regression (6) agglomeration effects are tested. The basic idea is to see how economic growth depends on the extent of the market which is associated with the level of division of labor according to Young (1928). A plausible measure of extent of the market is GDP per km2 within the economy in the initial year, 1965. Gallup and Sachs (1999) separate GDP per km2 on the coast and GDP per km2 in the interior, for reasons discussed earlier: high population density on the coast is likely to be associated with an increased division of labor due to a favorable transport condition, while high population density in the interior is likely to be associated with disintegrated economy and low level of division of labor due to an unfavorable transport condition. Note that ln(GDP density) = ln(GDP per km2) = ln(GDP per capita) + ln(Population per km2), and since ln(GDP per capita) is already a regressor, population density or GDP density can enter interchangeably into the regression. For countries in which the entire population is within 100km of the coast, the interior population density is put at zero. For countries in which the entire population is farther than 100km from the coast, the coastal population density is put at zero. Pop100km is also dropped as a separate regressor, since Pop100km is highly collinear with the two population density variables. The 1994 measures of Pop100km and the 1965 population levels for the country are used as a whole to calculate the population densities in the coastal and interior regions. The regression estimate is revealing. It shows that higher coastal population density is associated with faster growth, while higher interior population density is associated with lower growth. Thus, there appear to be economies of agglomeration, which are generated by network effects of division of labor, at play in the coastal regions. Large populations appear to be a net disadvantage for inland economies since adverse transportation conditions generate a low level of division of labor and a low level of market integration. Hence, a large population is divided among isolated local economies with inferior development performance. The Smithian-Young models in chapters 7, 11, and 12 provide theoretical prediction of this phenomenon. With separate inland and coastal agglomeration effects in regression (6), the estimated effect of malaria becomes less precise, slipping to a 7% significance level. On the other hand, if initial malaria and malaria change are included as in regression (7), they are both strongly significant, but the diminishing returns of interior population 52

density loses statistical significance. The limits of the degrees of freedom in data are pushed, but the results suggest that both malaria prevalence and inland population concentrations are detrimental to growth. General conclusions from the growth equations are as follows. First, both institution and geography variables matter. There is no simple “geographic determinism” nor a world in which only good institution matters. The tropics are adverse for growth, while coastal populations are good for growth. The tropical effect seems to be strongly related to the prevalence of malaria. This could be the true direct and indirect effect of that disease, or more likely, a proxy for a range of tropical maladies geographically associated with malaria. The access to coast seems to matter in lowering transport costs and in allowing for agglomeration economies and related division of labor. A dense coastal population is actually seen to be favorable to economic growth during 1965 - 90, while a dense interior population is adverse. If we summarize the implications on a region by region basis, we conclude the following. Africa is especially hindered by its tropical location; by its high prevalence of malaria; by its low proportion of the population near the coast; and by the low population density near the coast. Europe, North America, and East Asia, the core regions, by contrast, are favored on all three counts. South Asia is burdened by a high proportion of the population in the interior, a very high interior population density, and a large proportion of the land area in the tropics. The transition economies of Eastern Europe and the former Soviet Union, many of which are landlocked, are burdened by a very low proportion of the population near the coast and very low population density near the coast, but these countries are benefited by lack of exposure to tropical disease. Finally, Latin America is moderately coastal, but with relatively low coastal population densities. Also, Latin America has a moderate exposure to the problems of tropics, including the prevalence of malaria. 2.3.4. Geographical Effects on Economic Policy Choices We have noted in the theoretical section that geography may affect economic policy choices by altering the tradeoffs facing government. Two coastal countries may prefer high levels of specialization, so that they face a tariff war between countries with high levels of specialization since they can both manipulate terms of trade using tariff policies. This generates incentives for both countries achieving bilateral free trade via Nash tariff negotiations. As a result, coastal governments may choose free trade regime. An inland country may choose a low level of specialization due to adverse transportation conditions. As a result, a revenue-maximizing inland sovereign may choose to impose harsh trade taxes, thereby getting more gains from trade by manipulating terms of trade. In this section, we briefly explore this idea with the data at hand, focusing on the choice of openness versus closure to trade in the period 1965-90 as affected by geography. The first step is to check the underlying notion: that the responsiveness of growth to openness actually depends on geography. So far, Open and the geography variables are entered in a linear manner, not allowing for interactions. To check the possibility of interactions, Gallup and Sachs estimate the basic regression equation for three sets of countries: all, coastal (Pop100km ≥ 0.5) and hinterland (Pop100km < 0.5), and check the coefficient on the Open variable. Since degrees of freedom in this exercise are lost, 53

Gallup and Sachs estimate the barebones growth equation, in which annual average growth between 1965 and 1990 is a function of initial income, Openness, malaria in 1966, the change in malaria between 1966 and 1995, and the log of life expectancy in 1965. The results for the Open coefficient (β) are as follows (robust t-statistics in parentheses): All economies (N=92), β = 2.6 (6.8); coastal economies (N=46), β = 3.3 (6.5); hinterland economies (N=46), β = 1.4 (2.5). We see that the growth responsiveness to trade seems to be more than twice as high in coastal economies. The next step is to see whether more coastal economies in fact choose more open trade policies. This Gallup and Sachs do by regressing the extent of openness during 1965 - 1990 on the proportion of land within 100 km of the coast (Land100km), Tropicar, and the initial income level: Open6590 = -1.12 + 0.23 Land100km – 0.18 Tropicar + 0.19 lnGDP1965 (3.2) (2.1) (2.0) (4.5) N = 106, R2 = 0.44 There does indeed seem to be something to this line of reasoning, though the results are at best suggestive, and should be tested more carefully in later work. The early liberalizers, on the whole, were the coastal economies. This is certainly evident in East Asia, where countries such as Korea, Malaysia, Taiwan, Thailand, all opened the economy to trade early in the 1960s, much before the other developing countries. Two important geographical characteristics affect coevolution of division of labor and institutions via their impacts on transportation condition and trading efficiency. Coastal regions, and regions linked to coasts by ocean-navigable waterways, are strongly favored in development relative to the hinterlands. Landlocked economies may be particularly disadvantaged by their lack of access to the sea, even when they are no farther than the interior parts of coastal economies, for at least three reasons: (1) crossborder migration of labor is more difficult than internal migration; (2) infrastructure development across national borders is much more difficult to arrange that similar investments within a country; and (3) coastal economies may have military or economic incentives to impose costs on interior landlocked economies. All of the three factors affect trading efficiency of a landlocked country, so that as predicted in chapter 3, coevolution of division of labor and institutions is slower in such a country. High population density seems to be favorable for economic development in coastal regions with good access to internal, regional and international trade. This may be the result of the interplay between increasing returns in construction of transportation infrastructure, network effects of division of labor, and transportation efficiency. Gallup and Sachs' results show population density in the hinterland shows no such advantages, and a net disadvantage. As shown in the Chu model (see exercise 14 in chapter 7), the coexistence of a high population density and the favorable geographic condition for transportation will reduce per capita investment in transport infrastructure and increase demand for infrastructure. This will make a professional infrastructure sector emerge from enlarged scope for trading off benefit of increasing infrastructure expenditure against its cost in terms of reducing resources allocated to direct production. The professional infrastructure raises trading efficiency, thereby enlarging the scope for 54

trading off positive network effect of division of labor on aggregate productivity against transaction costs. This leads to a larger network of division of labor, higher aggregate productivity, greater degree of trade dependence, greater extent of the market, more market integration, and higher aggregate productivity. Also, several general equilibrium mechanisms developed in chapters 7 and 11 show that if geographical conditions are favorable for transportation, then a high population density is associated with an integrated market and a high level of division of labor, so that aggregate productivity is high. If geographical conditions are unfavorable for transportation, then a high population density is associated with many separated local markets and a low level of division of labor, so that aggregate productivity is low. We thus see that economies are likely to bifurcate on two pathways. The hinterland will be characterized by a negative correlation between economic development and population growth. The coastline will be characterized by a positive correlation between economic development and population growth. The two systems will interact through ever-greater pressures on migration from the hinterland to the coast. As we have discussed, tropical regions are hindered in development relative to temperate regions, probably because of higher disease burdens and limitations on agricultural productivity. Chapters 3, 4, 5, and 11 will explore general equilibrium mechanisms that predict the phenomena. In those chapters we shall draw the distinction between endogenous and exogenous comparative advantage and analyze the effect of exogenous differences in geographic conditions on economic development and urbanization. Endogenous comparative advantage may emerge between ex ante identical individuals or countries. We shall show that the interplay between endogenous and exogenous comparative advantages generates very complicated stories about effects of geography on economic development and urbanization.

Key Terms and Review Effects of the following geographic conditions on economic development: temperate zones, tropics, landlocked, coastal region, region close to ocean-navigable waterway Relationship between geographical conditions, transaction costs, quality of institutions, the level of division of labor, and development performance

Further Readings Gallup and Sachs (1999), Gallup (1998), Capie (1983), Kindleberger (1973), Reynolds (1985), Jeffrey Williamson (1990, 1992, 1993, 1994), Smith (1776), Jones (1981), Yang and Borland (1991), Sachs, Yang, and Zhang (1999), Cheng, Sachs, and Yang (1999), Braudel (1972, 19811984), Crosby (1986), Diamond (1997), E. Jones (1981), Kamarck (1976), Lee (1957), McNeill (1963, 1974), Murray and Lopez (1996), Radelet and Sachs (1998b), WHO (1997), World Bank (1997), CIA (1996, 1997), Curtin (1989).

Questions

55

1. According to Jones (1981, pp. 226-27), Europe’s very considerable geological, climatic and topographical variety endowed it with a dispersed portfolio of resources. This conduced to long-distance, multi-lateral trade in bulk loads of utilitarian goods. Taxing these goods was more rewarding than appropriating them. Bulk trade was also favored by an abnormally high ration of navigable routeways to surface area. Use the theories reviewed in this chapter to explain this historical fact. 2. Many scholars agree to the claim that "Fundamental springs of capitalist expansion are, on the one hand, the coexistence of several political units within the same cultural whole and on the other, political pluralism which frees the economy"(see chapter 1). Several explanations on the occurrence of this geo-political structure to sustain for a long period of time are proposed. One is to attribute it to particular geographical conditions of Western Europe and Mediterranean that are favorable for long-distance trade between city-states and unfavorable for unification war. Around Mediterranean and English Channel, a great portion of highly populous areas was either coastal or island. The favorable conditions for trade was crucial for the emergence and evolution of capitalist institutions (Jones, 1981, p.233). In contrast, East Asian geopolitical structure ensured hegemonism of Chinese culture prior to the invasion of Occidental cultures. Use the historical facts to analyze the relationship between political pluralism, the absence of overarching political power, institutional experiments, economic development, and geography. 3. Baechler (1976, pp. 93-95) surmises that Britain's geographic condition ensured that Britain could avoid war with other countries at low defense expenses and keep continuous evolution of its unique Anglo-Saxon culture and common law tradition, and had transportation advantage for trade. Use the hypothesis to analyze why Japan, Taiwan, and other island countries enter take off stage earlier than many inland countries. Find some counter example to the hypothesis (for instance, Cuba). Use the counter examples to analyze effects of institutions and geographical conditions. 4. Explain why Singapore has much better development performance than other tropic countries. 5. Smith did not discuss culture and economic development in any detail in the Wealth of Nations, but it seems clear that Smith, in line with much thinking of the Scottish Enlightenment, viewed human nature as universal, and did not view culture as a primary differentiating factor in economic development. After all, Smith saw the “propensity to truck, barter, and exchange one thing for another,” to be universal, not culturally specific. For example, Smith never bemoans the lack of entrepreneurial zeal in one place or another as an explanation for poor economic performance. Later thinkers such as Max Weber attributed the formation of capitalist spirit to Protestant moral codes. Landes (1998) attributes the Judaic-Christian culture to formation of the concept and institutions of private property. Recent empirical evidence for effects of culture on economic development can be found from La Porta, Lopez-de-Silanes, Shleifer, and Vishny (forthcoming). They show that Catholic tradition has negative effect and Protestant tradition has positive effects on development performance, and that common law tradition has positive and civil law tradition has negative effects on development performance. In connection to the thoughts and empirical work, discuss possible development mechanism for coevolution of culture, institutions, and per capita real income. 6. In connection to the discussion on the relationship between geopolitical structure and institutional evolution in Western Europe, analyze why landlocked Austria and Switzerland have much higher per capita income than other landlocked countries. 7. In connection to the analysis of the relationship between socialist experiment and economic development in chapter 19, analyze why landlocked Austria and Switzerland have much higher per capita income than landlocked Czech Republic, Hungary, the Former Yugoslav Republic of Macedonia, Slovakia, and Russia.

56

8. Analyze how geographical conditions affect transition performance of ex socialist economies in connection to the analysis in chapter 19. 9. Though Gallup and Sachs (1999) did not find strong evidence that distance from the core markets is endogenously determined by other variables, it is still subject to speculation that the formation of the core markets are endogenously determined by other geographical conditions and coevolution of institutions and division of labor. In connection to the models in chapters 3, 7, 11, 12, and 14 conduct thought experiment about possible development mechanisms that may explain the formation of the core markets. 10. In chapters 5, 11, and 13, several general equilibrium models of high development economics with economies of scale predict that a large size of population will generate a higher degree of urbanization, a higher degree of industrialization, a higher productivity, a larger average size of firms, a higher per capita real income, a larger number of available goods, and a higher growth rate of per capita real income. But the Smith-Young models in chapters 4, 7, 11, 12, and 14 show that if transport conditions are good, a large population size is associated with a high level of division of labor and highly integrated market, so that productivity, degrees of urbanization, industrialization and trade dependence, per capita real income and its growth rates are high, and the number of available goods is large. If transport conditions are not good, a large population size is associated with a low level of division of labor and many segregated local markets, so that productivity, degrees of urbanization, industrialization and trade dependence, per capita real income, and its growth rates are low, and the number of available goods is small. Use empirical evidence in this chapter to test the theoretical hypotheses. You may relate your discussion with the empirical evidence for rejecting various scale effects in Liu and Yang (2000),Y. Zhang (1999), the National Research Council (1986), Dasgupta (1995), C. Jones (1995a, b), reported in chapters 5, 13, and 14. 11. Design a regression of reform performance on geographical conditions of different provinces in China or of different countries in the East Europe and newly independent states. Test the claims made in this chapter.

57

Chapter 3: Driving Force I - Exogenous Comparative Advantage and Trading Efficiency 3.1 Use the Concept of General Equilibrium to Figure Out Mechanisms for Economic Development The first question that development economics must address is: why can the wealth of a nation increase for a fixed amount of available resource or why can the degree of scarcity be reduced by individuals’ decisions in choosing their pattern of organization? Many economists have answered these questions by pointing to exogenous technical progress. Exogenous technical progress is defined as technological changes that raise productivity and are independent of individuals’ decisions. In the Solow model (1956), the driving force of long-run growth in per capita income is such exogenous technical progress. A necessary condition for increases in productivity, per capita income, and output share of industrial goods in the Fei-Renis model (1964) is exogenous technical progress in the industrial sector. This method to explain economic development is not interesting because we have known since Adam Smith that individuals’ decisions in choosing their levels of specialization can endogenously determine the wealth and productivity of a nation. Smith made a vague guess about the mechanism for economic development. He proposed the well-known Smith theorem: (1) division of labor is the mainspring of economic progress (1776, chapter 1, Book I). (2) division of labor is dependent on the extent of the market (chapter 3, Book I) and (3) the extent of the market is determined by transportation condition (Book I, pp. 31-32). If we specify a state equation that entails a positive relationship between productivity and transaction conditions, then it is not an interesting economic model, since this is equivalent to specifying total factor productivity as a function of time, as in the Solow model. An economic model of development must specify some trade offs in decision making, such that the efficient balance of the trade offs endogenously determines productivity. In other words, a very high productivity, like a very low productivity, is not efficient because of the trade offs, which imply that there are costs for the extremely high productivity. Hence, in order to formalize Smith’s conjecture, our job is to formalize some trade off in individuals’ decisions of their levels of specialization. This task is not easy, since individuals’ decisions in choosing their levels of specialization involve corner solutions. Moreover, in order to understand a mechanism of economic development for society as a whole, we have to use the concept of general equilibrium that involves corner solutions to figure out the trade offs in the marketplace. The equilibrium as a consequence of interactions between individuals’ decisions is, of course, much more complicated than individuals’ decisions. There are several reasons that the concept of general equilibrium is essential for investigating mechanisms for economic development. First, economic development involves interactions between prices and quantities. Not only are all individuals’ decisions in choosing quantities produced and consumed are determined by prices, but market prices are also determined by all individuals’ decisions of quantities. In addition, there are interdependencies between markets for different goods and factors and between different individuals’ decisions. These interdependencies relate to circular causation, network effects

57

of industrial linkages, and interdependent decisions in different sectors that concern high development economists. There are infinite feedback loops between each pair of endogenous variables. For instance, as the price of a final good changes, the demand curve for labor will shift. This shift will change the price of labor, which will shift the demand curve for that final good. That shift will in turn change the price of that good, thereby shifting the demand curve for labor again. This feedback between the two markets will continue endlessly, though feedback effects attenuate after each round of feedback. Marshall’s partial equilibrium analysis considers only interactions between price and quantity in the market for a single good or factor and ignores all of the feedback loops, and therefore generating misleading predictions. Hence, partial equilibrium model is not a good vehicle for investigating mechanisms of economic development. The partial equilibrium model of Todaro (1969) is an example of this point. In the model, structural changes and migration between the rural and urban areas are explained by the wage differential between the two areas. But the wage differential is exogenously fixed. The feedback loops between wage, income, demand, and supply are all ignored. We cannot tell from this model why there is such a wage differential, nor what the mechanism is for economic development. The second reason for using general equilibrium model to investigate mechanisms for economic development relates to network effects of division of labor. Adam Smith considered division of labor as a main driving force of economic development. But as Young (1928) and Yang and Ng (1998) indicate, benefits of division of labor are network effects. An individual’s decision in choosing her level of specialization determines not only her productivity, but also the extent of the market for others’ produce, thereby setting a constraint for others’ decisions in choosing their levels of specialization. The concept of network is by nature intimately related to the concept of general equilibrium. We cannot understand network effects by looking at only part of the network. In this chapter, we will show that a network of division of labor involves individuals’ corner solutions. Hence, marginal analysis for the interior solution does not work and inframarginal analysis is essential for investigating mechanisms for economic development. Either static or dynamic general equilibrium model can be used to study the mechanism for economic development. The comparative statics of static general equilibrium model explains changes in endogenous variables by changes in parameters representing tastes and the technical, natural, and social environments. Endogenous variables may include prices, productivity, economic structure, and some institutional features of the economy. Some parameters may represent exogenous institutional conditions as well. If productivity increases and economic structure changes in response to changes in some parameters, the causation chain based on comparative statics of general equilibrium can explain mechanism of economic development as the consequence of interactions between self-interested decisions (behavior). Simple partial equilibrium models cannot count all feedback loops based on such interactions. Simple decision models cannot figure out the consequence of all direct and indirect interactions between self-interested decisions. If dynamic general equilibrium models are used to study mechanism for economic development, some dynamics of general equilibrium may generate economic development in the absence of exogenous changes in parameters. Comparative dynamics of general equilibrium can be used to investigate changes in dynamics in response to changes in parameters. Hence, dynamic general equilibrium models may have a higher degree of endogenization, which is supposed to imply more explaining power. However, dynamic

58

general equilibrium models are more difficult to manage than static general equilibrium models. In order to solve for dynamics or comparative dynamics of general equilibrium, stronger assumptions are essential for keeping the models tractable. This implies that the tractable dynamic general equilibrium models may have a lower degree of endogenization than do tractable static general equilibrium models. Therefore, we have the trade off between advantage and disadvantage of static and dynamic general equilibrium models. This text will show that many static general equilibrium models may be more powerful for investigating mechanisms for economic development that involve very interesting and sophisticated structural changes. In this chapter, we use inframarginal analysis of the Ricardian and Heckscher-Ohlin models to investigate a general equilibrium mechanism for economic development. The story behind the formal model runs as follows. There are technological comparative advantages between two types of individuals. This implies that even if a type of individual is less productive in producing all goods than an individual of other type, the productivity difference between the two types of individuals is not same across goods. Hence, the second type of individual can specialize in producing the good with smaller productivity difference, so that all individuals may gain from the division of labor and trade that generates a higher aggregate productivity than in autarky. We define comparative advantage that is based on ex ante differences of production conditions between individuals as exogenous comparative advantage. In this text, ex ante means “before individuals have made decisions” and ex post means “after individuals have made decisions, and the economy has settled down in equilibrium.” If all individuals prefer diverse consumption, then there is a tension between utilization of comparative advantages and diverse consumption. Some individuals must specialize in producing one good in order to exploit exogenous comparative advantage. But the specialization of production and diversification of consumption implies that individuals must trade. If trade involves transaction costs, then there is a trade off between transaction costs and economies of division of labor generated by comparative advantages. The trade off can be used to endogenize productivity. The production possibility frontier (PPF) is achieved when at least one type of individual completely specializes in producing one good. If a transaction cost coefficient for one unit goods traded is large, then transaction costs caused by trade outweigh productivity gains from trade. Hence, the equilibrium is autarky where production takes place below the aggregate PPF, since the marginal rates of substitution and marginal rates of transformation must be equalized for each individual. If the transaction cost coefficient is small, then productivity gains outweigh transaction costs caused by the division of labor, so that the equilibrium is the division of labor which is associated with the PPF. Since the trade off between exploitation of comparative advantage and transaction costs can be used to explain the equilibrium aggregate productivity by the trading efficiency parameter, the aggregate productivity is endogenized even if production function do not change. This general equilibrium approach to explaining productivity changes is much more interesting than technology fundamentalism which explains productivity progress by changes in production functions. It explains productivity changes as a consequence of interactions between self-interested decisions. If governments are introduced into this simple model, it can be used to predict the governments’ behavior in choosing tariff rates and in choosing amongst unilateral protection tariff, unilateral laissez faire policy, and tariff negotiation. As transaction conditions are

59

improved, the general equilibrium shifts from autarky to the partial division of labor, where one country completely specializes in producing one good and the other country produces two goods, then to the complete division of labor, where each country completely specializes in producing one good. For the partial division of labor, terms of international trade are determined by the production conditions in the country producing two goods. Hence, gains from trade all go to the country producing one good in the absence of tariff. Thus, the country producing two goods can use tariff to manipulate terms of trade in order to get a greater share of the gains. But the country producing one good will only hurt itself by imposing tariff on imported goods, since this will increase the price of goods purchased by domestic residents. This implies that when the partial division of labor occurs in equilibrium, unilateral protection tariff in the country producing two goods coexists with unilateral laissez faire policy in the country producing one good. If the complete division of labor occurs in equilibrium, each country can get a greater share of gains from trade by increasing tariff. But as the tariff rates in the two countries become sufficiently high, gains from trade can be exhausted by the deadweight caused by the tariff in the rent-seeking game. Hence, both countries may prefer a tariff negotiation in a Nash bargaining game that generates trade liberalization to the tariff war. This explains the coexistence of unilateral protection tariff and unilateral laissez faire policy regime in the early stage of economic development, and tariff negotiation that generates bilateral trade liberalization in the later stage of economic development. The driving force of this shift in trade policy is the improvements in transaction conditions that can be achieved via a better legal system, better transportation infrastructure, urbanization, or a better banking system. The shift of trade policy from protection tariff to trade liberalization is sometimes referred to as a shift from import substitution strategy to export substitution strategy (see Bruton 1998). The phenomenon of increasing income difference between the two countries as the equilibrium shifts from autarky to the partial division of labor is called by some development economists (for instance, Palma 1978, Bauer and Yamey 1957) “underdevelopment.” Protection tariff is often suggested as a policy instrument to avoid underdevelopment. But the Ricardo model with transaction costs and tariff indicates that improvements of transaction conditions can shift equilibrium from the partial division of labor to the complete division of labor, which not only generates more gains from trade but also more equal distribution of gains from trade. Many economists try to find empirical evidence for or against the claim that terms of trade are worsening for developing economies. Some of them try to measure adverse effects of worsening terms of trade on economic development (see, for instance, Morgan 1970 and Kohli and Werner 1998). Recent empirical evidence provided by Sen (1998) shows that economic development and deteriorated terms of trade may concur. We shall show that in the process of moving to a high level of division of labor, a country may receive more gains from trade even if its terms of trade deteriorate. This is because an expansion of the network size of division of labor can generate productivity gains that outweigh the adverse effect of the terms of trade deterioration. This story can be extended to the Heckscher-Ohlin model with comparative endowment advantage and transaction costs. If the ex ante difference in production conditions comes from differences in production functions between individuals, then we say there is exogenous comparative technological advantage, which will be investigated in sections 3.2 - 3.5. If it comes from differences in factor endowments between individuals, then we say there is

60

exogenous comparative endowment advantage, which will be studied in section 3.6. If two countries have different factor endowments, then they can employ the difference to increase equilibrium aggregate productivity. But if transaction efficiency is low, the efficient trade off between exploitation of comparative endowment advantage and transaction costs entails autarky and low productivity. As transaction conditions are improved, the equilibrium aggregate productivity and level of division of labor increase.

Questions to Ask Yourself when Reading the Chapter What are differences between general equilibrium mechanism and partial equilibrium mechanism for economic development? What are differences between economic development caused by exogenous technology changes and economic development caused by individuals’ decisions in choosing their patterns of specialization? What is the distinction between absolute and comparative advantages? How can we measure division of labor and economies of division of labor? How can evolution of division of labor and related structural changes take place? What are the differences between the structural changes caused by evolution of division of labor and structural changes caused by exogenous technical changes? Why may unilateral protection tariff and unilateral laissez faire regime coexist in a transitional period from autarky to a high level of international division of labor? Why may income differential between countries first increase and then decline as the economy develops from autarky to intermediate level of trade dependence, then to a high level of trade dependence? What is the distinction between comparative technology advantage and comparative endowment advantage? What is the driving force for a policy shift from protection tariff to trade liberalization?

3.2 A Ricardian Model with Exogenous Comparative Technological Advantage and Transaction Costs Before David Ricardo, economists did not pay attention to the distinction between absolute and comparative advantages. An individual has absolute advantage in producing good i if her labor productivity in good i is greater than that of the other individual. Ricardo (1817) drew economists’ attention to the distinction between this measure and the concept of comparative advantage. If person 2 is absolutely less productive than person 1 in producing both goods x and y, but the difference in productivity between the two individuals is greater for good y than for good x, then person 2 has a comparative advantage in producing good x, since her absolute disadvantage is relatively smaller in producing x than in producing y. Ricardo argued that as long as such a comparative advantage exists, a country having no absolute

61

advantage in producing any good nonetheless can gain from trade, as can the other country which enjoys absolute advantage in all lines of production. Ricardo’s theory of comparative advantage is regarded as the foundation of the modern trade theory. However, the Ricardian model has not attracted the attention it deserves. This lack of attention is attributable to the following fact. The conventional marginal analysis is not applicable to the Ricardian model because of corner solutions. There are two ways to specify the Ricardo model. One is to specify the dichotomy between pure consumers and firms. However, in the Ricardian model each country is a consumer as well as a producer. Hence, corner solution may be chosen by a country. This specification will entail multiple general equilibria based on several structures of corner and interior solutions of countries. Since in the Walrasian regime, firms’ profit is always zero in each and every structures, firms do not care about choice of structure. Pure consumers cannot choose structure of production. Therefore, local equilibrium in each structure can be a general equilibrium. This multiplicity of general equilibria rends comparative statics analysis of general equilibrium impossible (see Dixitand Norman 1980, p. 38). The second way to specify the Ricardian model is to use a Smithian framework. In this framework, each individual is specified as a consumer-producer, so that each individual can choose her level of specialization. In this framework, the general equilibrium is one of several corner equilibria, which efficiently trades off economies of division of labor generated by exogenous technical comparative advantage against transaction costs. Hence, inframarginal comparative statics of general equilibrium will generate very rich and interesting stories about economic development and trade. If the Ricardo model is specified within the neoclassical dichotomy between pure consumers and firms, domestic trade and international trade are not based on the same rationale: domestic trade is always necessary, while international trade is induced by exogenous comparative advantage. If the transaction efficiency coefficient for domestic trade and that for international trade are the same, then international trade is always Pareto superior to autarky. The framework of consumer-producers not only avoids multiple equilibria, but also allows the model to explain international trade by individuals’ choices of their patterns of specialization. Within this framework, even when the domestic and international transaction cost coefficients are the same, individuals still choose whether or not to engage in international trade, and autarky can be the unique general equilibrium structure when the transaction cost coefficient is large. There are many ways to specify transaction costs. One general specification of transaction costs is to assume a delivery function of goods such that the amount of goods that arrives at the destination is a function of the amount of goods that departs from the origin, and of other inputs essential for the delivery (see Hahn 1971, and Kurz 1974). The delivery function describes the technical conditions governing transactions. The difference between the amounts of goods at the origin and at the destination, together with any inputs employed in the delivery process, can be considered as transaction cost. This specification of transaction costs involves a notoriously unmanageable set of indices of destinations and origins. This index set, compounded with corner solutions, makes it impossible to work out the comparative statics of general equilibrium. Thus the general equilibrium implications of transaction costs in the models with this otherwise appealing specification of transaction costs cannot be explored. Hence, a specification of so-called

62

iceberg transaction cost is often used to work out general equilibrium implications of transaction costs. In a system involving iceberg transaction cost, an individual receives the fraction k when she buys one unit of a good, or pays one dollar when she buys goods with value of k dollars, where k∈[0, 1]. If sellers of goods pay transaction costs, then they receive the fraction k of each dollar paid by the buyers. These specifications imply that the fraction 1-k of goods or their value disappears in transit because of transaction costs. These transaction costs can take the form, for example, of transportation costs, costs in implementing transactions, storage costs, and costs caused by non-punctual delivery. However, the transaction cost coefficient 1-k is considered an exogenous transaction cost that can be seen before individuals have made their decisions. There are two common definitions of endogenous transaction cost. According to the more general definition, all transaction costs are considered endogenous whose levels can be seen only after individuals have made their decisions. In the consumer-producer models with ice-berg transaction costs, although the transaction cost coefficient 1-k is exogenous, the total transaction cost for each consumer-producer, and thus for society, is endogenous in terms of this general definition, since the number of transactions is endogenized in the model of consumer-producers. The second, narrower, definition of endogenous transaction cost relates to a specific type of endogenous transaction costs, namely those that are caused by a departure of general equilibrium from the Pareto optimum. Hereafter, we will adopt this second definition of endogenous transaction cost unless otherwise indicated. Endogenous transaction cost is the focus of chapters 9 and 10. Example 3.1: Ricardian model with exogenous comparative technology advantage and transaction costs. Consider a world consisting of country 1 and country 2. The set of consumer-producers is assumed to be a continuum with mass M1+M2 where Mi is the measure of individuals in country i. This assumption implies that the population size is very large, so that we would not have an integer problem when individuals are divided between different occupation configurations. Example 9.10 in chapter 9 will show that, for a finite set of consumer-producers, Walrasian equilibrium may not exist. For that case, Nash bargaining might be essential for coordinating the division of labor. The individuals within a country are assumed to be identical. Hence, two countries may be considered as two groups of ex ante different individuals. As consumer-producers, the individuals consume two goods, x and y, and decide their own configurations of production and trade activities. The utility function for each individual of group i or in country i is: (3.1)

U i = ( xi + kxi d ) β ( yi + kyi d ) 1− β

where xi, yi are quantities of goods x and y self-provided, xid, yid are quantities of the goods bought from the market, and k is the transaction efficiency coefficient. Assume that the production functions for a consumer-producer in country i are: (3.2)

xip ≡ x i + x i s = a ix lix and yip ≡ y i + y i s = a iy liy

63

where xip and yip are respective output levels of the two goods produced by a person in country i and lij is a type i-individual’s amount of labor allocated in producing good j. We call lij the level of specialization of a type i-individual in producing good j. aij is a type iindividual’s labor productivity in producing good j. The labor endowment constraint for a person in country i is l ix + l iy = 1. Let country 1 have comparative advantage in producing good x, thus a 1x a 2 x > a1y a 2 y

(3.3)

The individuals’ transformation curves for a1x = 2, a1y = 1, a2x = 3, a2y = 4 are drawn in Fig. 3.1. CD is the transformation curve of an individual in country 1 and AB is the transformation curve of an individual in country 2. Here, an individual in country 2 has absolute advantage in producing both goods.

Figure 3.1: Economies of Division of Labor Based on Exogenous Technical Comparative Advantage The consumption, production and trade decisions for an individual in country i s d s d involve choosing six variables x i , x i , x i , y i , y i , y i ≥ 0 . Since zero values are allowed, there are 26 = 64 combinations of zero and positive values of the 6 variables. Since s d buying and selling the same good incur unnecessary transaction costs, x i and x i cannot s

d

both be positive, and y i and y i cannot both be positive. Thus, the budget constraint is either p x x i s = p y y i d or p x x i d = p y y i s . Hence, we first rule out 48 combinations that satisfy any of the following conditions, which violate the budget constraint. s d s d d s d s x i = 0 and y i > 0 ; x i > 0 and y i = 0 ; x i = 0 and y i > 0 , x i > 0 and y i = 0 . Four more combinations that involve selling and buying the same good can be ruled out. Then from the remaining 12 combinations, we use the positive utility constraint d d ( U i = ( x i + kx i ) β ( y i + ky i ) 1− β > 0 ) to rule out 7 combinations that involve x i = x i = 0 or y i = y i = 0 . We will show later that 2 combinations that involve d

d

64

specialization in an individual’s comparative disadvantage good cannot occur in general equilibrium. Now we are left with 3 types of configurations, listed as follows: Configuration Ai (autarky) is shown in Figure 3.2. This configuration is defined by s d s d x i , y i > 0, x i = x i = y i = y i = 0, i = 1, 2 , which implies self-providing all goods. If all individuals choose configuration A, this social pattern of organization is called structure A. Configuration of partial specialization in the comparative advantage good, denoted by (xy/y)1 and (xy/x)2, is shown in Figure 3.2. Configuration (xy/y)1 is relevant for s d d s individuals in country 1 and is defined by x1 , y1 , x1 , y1 > 0, x1 = y1 = 0 , which implies self-providing goods x and y, selling good x, and buying good y; configuration (xy/x)2 is d s relevant to individuals in country 2 and is defined by x2, y2, y 2 , x 2 , y 2 > 0, x 2 = y 2 = 0 , which implies self-providing goods x and y, selling good y, and buying good x. s

d

country 1 Structure A

country 2 Structure Ba

country 1

country 2

country 1

Structure Bb

country 2 Structure C

Figure 3.2: Configurations and Structures

Configuration of complete specialization in the comparative advantage good, denoted by (x/y)1 and (y/x)2, is shown in Figure 3.2. Configuration (x/y)1 is defined by s d d s x1 , x1 , y1 > 0, x1 = y1 = y1 = 0 , which implies self-providing and selling good x and buying good y; configuration (y/x)2 is defined by y 2 , y 2 , x 2 > 0, y 2 = x 2 = x 2 = 0 , which implies self-providing and selling good y and buying good x. The notion of occupation configuration can be virtualized from Dictionary of Occupational Titles. In its 1939 edition, there were 17,500 occupational titles. In 1977, 2,100 occupational titles were added, and 840 more were added in 1996. In 1991, a new section including many computer-related occupations was added. As population is divided among the occupation configurations, a certain structure of division of labor for society as a whole occurs. s

65

d

d

s

For a two–country-two-goods economy, we may define division of labor as a structure where, at least, individuals in one country choose a pattern of specialization and the configurations of individuals in the two countries are not same. This definition implies that specialization is not sufficient for the division of labor. If population is divided between configurations (y/x)1 and (y/x)2 (two types of persons specialize in producing y), this is not associated with division of labor. Similarly, specialization of two types of persons in producing good x involves specialization, but no division of labor. There are two structures involving partial division of labor. Structure Ba consists of (xy/y)1 and (y/x)2 and structure Bb is composed of (x/y)1 and (xy/x)2. Structure of complete division of labor C consists of configurations (x/y)1 and (y/x)2. Suppose there is only one person in each country. The aggregate production schedules for the four structures are shown in Figure 3.1. We will show later that if autarky occurs in equilibrium, the aggregate production schedule occurs on the line EG. For structure Ba, an individual in country 1 completely specializes in producing x and an individual in country 2 produces two goods. The aggregate transformation curve for this structure is the segment EF in Figure 3.1. This segment can be obtained by moving individual 2’s transformation curve CD up to point E on the vertical axis. The aggregate transformation curve for structure Bb is FG, which can be obtained by moving individual 1’s transformation curve AB to the right to point G on the horizontal axis. The aggregate production for structure C is point F in Figure 3.1. Production schedule EHG is associated with the division of labor with comparative disadvantage. Later we will show this production schedule never takes place in equilibrium. To understand the distinction between occupation configuration and structure of division of labor, you may consider the university where you are studying. The first decision that you have to make when you get in the university is to choose a major. If you choose economics as your major, then you do not go to chemistry and physics classes, but you take classes in microeconomics, macroeconomics, and econometrics. This decision is to choose an occupation configuration. We call such a decision as inframarginal decision, since decision variables are not continuous between occupation configurations. They discontinuously jump between 0 and a positive value as you shift between majors. After you have chosen a major, you allocate your limited time between the fields in this major. This decision of resource allocation for a given occupation configuration is called marginal decision, since standard marginal analysis can be applied to this type of decision. The aggregate outcome of all students' choices of their majors in a university generates a division of students among majors and fields, which is equivalent to a structure of division of labor in our model. The general equilibrium of the world economy is defined as a resource allocation and a structure of trade network that satisfy (1) each individual maximizes utility at a given set of prices with respect to configurations and quantities of production, trade, and consumption; (2) the set of prices clears the market. The individuals make their utility maximization decisions based on the inframarginal analysis. The inframarginal analysis is that for each configuration, individuals apply marginal analysis to solve for the optimum quantities of consumption, production and trade, and then apply total cost-benefit analysis to compare their utilities across all configurations and choose the configuration that gives the highest utility. Here, marginal

66

analysis is equivalent to your decision to allocate your time between different fields after you have chosen a major and total cost-benefit analysis is equivalent to your decision to choose a major. Marginal analysis is about “how much” and total cost-benefit analysis is about “yes or no.” If you say “yes” to a major, you spend time studying it. If you say “no” to a major, you do not allocate any time to it. There is a partial or corner equilibrium for a given structure and the general equilibrium is one of the four corner equilibria. Because of complexity of inframarginal analysis, we need a two step approach to solve for equilibrium. We first apply nonlinear programming to solve the individuals’ utility maximization problems and use the market clearing condition to find the partial equilibrium for each of the four structures, we then use total benefit-cost analysis to identify the general equilibrium. For instance, given structure Ba, the decision problem for individuals choosing configuration (xy/y)1 in country 1 is: U 1 = x1 β ( y1 + ky1 d ) 1− β max x1, x1s y1 , y1d , l1 x ,l1 y

s. t.

x1 + x1 s = a1x l1x , y1 d = p x1 s ,

y1 = a1 y l1 y l1x + l1 y = 1

where all decision variables can be positive or zero and p ≡ px/py is the price of x in terms of y. Note that variables underneath the symbol Max are decision variables. Inserting all constraints into the utility function to eliminate x1, y1, y1d, l1x yields: U1 = (a1x l1x-- x1s)β [a1y (1-l1x)+ kpx1s]1-β It is not difficult to see that ∂U1/∂l1x > 0 for any positive l1x if p > a1y/ka1x and if the optimum value of x1s is given by ∂U1/∂ x1s = 0. This implies that the utility can always be increased by increasing l1x if p > a1y/ka1x, or the optimum value of l1x is at its upper-bound value. Due to the endowment constraint of working time, this implies that an individual should not produce y and should specialize in producing x if p > a1y/ka1x. That is, individuals in country 1 should choose configuration (x/y)1 instead of configuration (xy/y)1 if p > a1y/ka1x . Following a similar reasoning, it can be shown that individuals in country 1 will choose configuration A1 instead of (xy/y) if p < a1y/ka1x. Hence, individuals in country 1 will choose (xy/y)1 only if the market relative price satisfies p = a1y/ka1x . This condition is analogous to the zero profit condition in a standard general equilibrium model with constant returns to scale. With the condition, the first order condition ∂U1/∂x1s = 0 yields the optimum value of x1s as a function of l1x. Inserting it into the constraints in the original decision problem, we have: p = a1y/k a1x, y1 = a1y (1-l1x),

x1 = βa1x, x1s = a1x (l1x-β), y1d = a1y (l1x-β)/k

Let us figure out the intuition behind this nonlinear programming. If the price of x in terms of y, discounted by transaction cost in the world market, is lower than a type-1 individual’s marginal rate of transformation a1y/a1x in autarky, then the optimum decision is to choose autarky, producing both x and y. If p > a1y/ka1x, then marginal utility of l1x always increases as l1x increases. Hence, the optimum decision is to specialize in 67

producing x. But for p = a1y/ka1x, the individual is indifferent between autarky and configuration (xy/y)1. Hence, configuration (xy/y)1 will be chosen if the market clearing condition in equilibrium ensures that demand and supply of occupation configuration (xy/y)1 can be realized. In configuration (xy/y)1 there is a trade off between the quantity of x self-provided x1 and quantity sold x1s. The former directly contributes to utility and the latter indirectly increases utility by increasing more good y that is exchanged from x1s. The efficient balance of the trade off is determined by the first order condition which implies that marginal direct utility cost of x1s equals marginal indirect utility of x1s. In this solution, the optimum value of l1x is indeterminate. Its equilibrium value will be determined by the market clearing condition. This is analogous to a standard equilibrium model with constant returns to scale technology where the zero profit condition determines prices and the market clearing condition, together with demand functions, determines equilibrium quantities. The decision problem for individuals in country 2 is: U 2 = ( kx 2 d ) β y 2 1− β max d s x 2 y2 , y2

y2 + y2 s = a2 y ,

s. t.

y2 s = p x2 d

The first order conditions imply: ka 2 y a1x d s β, y 2 = (1 − β )a 2 y , y 2 = px 2d = βa 2 y x2 = a1 y where p = a1y/k a1x is the equilibrium price of good x in terms of good y. s d From the market clearing condition M 1 x1 = M 2 x 2 , we obtain l1x = (ka2yM2β/a1yM1) +β, which is less than 1 (an individual's endowment of labor) if and only if (or iff for short) a2y/a1y < M1(1-β)/M2βk. That is, structure Ba can be chosen iff a2y/a1y < M1(1β)/M2βk. Using the same approach as we used above, we can find the corner equilibria for Structure A, Bb and C. The results are summarized in Table 3.1. Table 3.1: Four Corner Equilibria in the Ricardian model

Struc- Relative tures price (px/py) A N.A.

Relevant Interval

Parameter Per Capita Real Income (Utility)

Ba

a1y/ka1x

Bb

ka2y/a2x

k < k1 ≡ M1a1y(1-β)/βM2a2y< 1 k < k2 ≡ M2a2xβ/(1-β)M1a1x U1(x/y) which holds iff p U2(y/x) which holds iff p>(a2y/a2x)k 2β-1 The two inequalities jointly imply (a2x/a2y) > (a1x/a1y) which contradicts the assumption (a2x/a2y) < (a1x/a1y). Similarly, it can be shown that other structures involving specialization in comparative disadvantage goods cannot occur in general equilibrium. Next, we apply the total benefit-cost analysis and the definition of general equilibrium again to find out under what conditions each of the structures listed in Table 3.1 occurs in general equilibrium. Consider structure Ba first. Structure Ba is the general equilibrium structure if the following three conditions hold. First, under the corner equilibrium relative price in this structure p = a1y/ka1x, individuals in country 2 prefer specialization in y (configuration (y/x)) to the alternatives, namely autarky (configuration A) and specialization in x (configuration (x/y)). In other words, the following conditions hold: (3.4a) (3.4b)

U2(y/x) ≥ U2(A) which holds iff k≥k0≡[(a2x/a2y)/(a1x/a1y)]0.5 U2(y/x) ≥ U2(x/y) which holds iff k≥k3≡[(a2x/a2y)/(a1x/a1y)]0.5/β

Second, general equilibrium requires that all individuals in country 1 prefer configuration (xy/y) to the alternatives, that is: (3.5a) (3.5b)

U1(xy/y) ≥ U1(x/y) which holds iff a1y/a1x ≥ kp = a1y/a1x U1(xy/y) ≥ U1(y/x) which holds iff 1 ≥ k

Third, no individual in country 1 is completely specialized in x, i.e.: l1x < 1, which holds iff k [(a2xa2y)/(a1xa1y)]0.5, the corner equilibrium in structure Ba is the general equilibrium if k∈(k0, k1) and M1(1-β)/M2β > [(a2xa2y)/(a1xa1y)]0.5, where k1 ≡ a1yM1(1β)/a2yM2β. Similarly, we can identify the conditions for other structures to occur in general equilibrium. These conditions are summarized in Table 3.2. Table 3.2 reads that if k < k0, the general equilibrium structure is autarky (structure A). If k > k0 and M1/M2 > (a2xa2y/a1xa1y)0.5β/(1-β), the general equilibrium occurs in structure Ba if k < k1, and in structure C if k > k1. If k > k0 and M1/M2 < (a2xa2y/a1xa1y)0.5β/(1-β), the general equilibrium occurs in structure Bb if k < k2, and in structure C if k > k2. It is important to note that the structures are compared within relevant parameter subspaces. For instance, structure Ba can be chosen only if M1/M2 < (a2y/a1y)β/(1-β). Table 3.2: General Equilibrium and Its Inframarginal Comparative Statics of the Ricardo Model 71

Parameter Intervals

Equilibrium Structure

k > k0 k < k0

A

M1/M2 > (a2xa2y/a1xa1y)0.5β/(1-β)

M1/M2 < (a2xa2y/a1xa1y)0.5β/(1-β)

k ∈ ( k0 , k1 )

k ∈ ( k1 ,1)

k ∈( k0 , k2 )

k ∈( k2 ,1)

Ba

C

Bb

C

where k0 ≡ (a2xa1y/a1xa2y)0.5, k1 ≡ (1-β)a1yM1/βa2yM2, k2 ≡ βa2xM2/(1-β)a1xM1. In this text we define level of division of labor for society by all individuals' levels of specialization and diversity of occupation configurations. If all individuals' levels of specialization in a structure are not lower than their levels of specialization in another structure and some individuals have higher levels of specialization in the former than in the latter, we say that the level of division of labor in the former structure is higher than in the latter. If all individuals' levels of specialization are not lower in a structure than in another structure, but the diversity of occupation configurations in the former is greater than in the latter, we say that the level of division of labor is higher in the former than in the latter. If some individuals' levels of specialization in a structure are higher than in another structure, but other individuals' levels of specialization in the former are lower than in the latter, then it is much more difficult to compare the levels of division of labor in the two structures. A more rigorous definition of level of division of labor that is applicable to the comparison can be found from Yang (2000). Table 3.2 implies that as the transaction efficiency coefficient increases from a small value to k0, and then to k1 or k2, the general equilibrium jumps from autarky to partial division of labor, then to complete division of labor. Whether the transitional structure is Ba or Bb depends on the relative size of the two countries compared to relative tastes and relative productivity. Such discontinuous jumps of equilibrium structure and endogenous variables across corner equilibria in response to changes of parameters are referred to as inframarginal comparative statics of general equilibrium. Since we assume (a1x/a2x)> (a1y/a2y) or country 1 has comparative advantage in producing good x, we can take r = r1r2 ≡ (a1x/a2x)/(a1y/a2y) as a measure of the degree of exogenous technical comparative advantage. A derivative of k0, k1, k2 with respect to r1 and r2 yields: ∂k0/∂ r1, ∂k0/∂ r2,

∂k1/∂ r2, ∂k2/∂ r1 < 0

This implies that for a given value of k, the greater the degree of comparative advantage, the more likely k > ki (i = 0, 1, 2) or the more likely the equilibrium level of division of labor is higher. A close examination of all conditions for structure C to be the general equilibrium indicates that they require either that 1>k1 and M1/M2 > (a2xa2y/a1xa1y)0.5β/(1-β), or that 1>k2 and M1/M2 < (a2xa2y/a1xa1y)0.5β/(1-β). The two conditions imply that the requirement for C to be equilibrium is either: (a2y/a1y)β/(1-β)> M1/M2 > (a2xa2y/a1xa1y)0.5β/(1-β) or (a2y/a1y)β/(1-β)< M1/M2 < (a2xa2y/a1xa1y)0.5β/(1-β) 72

This implies that the relative population size of the two countries is neither too large nor too small. Since individuals in one country have a higher level of specialization in structure C than in structure Ba or Bb and since the level of division of labor positively relates to individuals' levels of specialization, structure C has a higher level of division of labor than structure Ba or Bb. Our result implies that the more the relative population size is in balance with relative tastes and relative productivity, the more likely the equilibrium level of division of labor is higher. Now we consider the implications of inframarginal comparative statics for development economics. To this end, we need to work out production schedule in autarky. If autarky is the general equilibrium, then marginal rate of substitution equals marginal rate of transformation for each individual. This implies: βyi/(1-β)xi = aiy/aix or (x1/a1x)/(y1/a1y) = β/(1-β) = (x2/a2x)/(y2/a2y) where the subscript i represents country i. This, together with the production functions xi = aixliy, yi = aiyliy, and the endowment constraint lix+liy = 1 imply that l1x = l2x = β, l1y = l2y = 1-β. Using all of the conditions to eliminate taste parameter β, or using the production functions, the endowment constraints, and the conditions l1x = l2x and l1y = l2y we can then show that the equilibrium production schedule in autarky must satisfy: Y = y1+y2 = (a1y+a2y)[1-X/(a1y+a2x)], where X = x1+x2. This is the line EG in Fig. 3.1. The slope of this line is dY/dX = -(a1y+a2y)/(a1x+a2x), which is between -a1y/a1x and -a2y/a2x. In other words, this line is flatter than line FG and steeper than line EF in Fig. 3.1. Hence, production takes place at a point on EG if autarky is the general equilibrium. The exact position of the equilibrium production schedule on EG is dependent on the value of taste parameter. From Fig. 3.1, we can see that the aggregate production possibility frontier (PPF) is EFG. Since line EG is lower than the PPF, the aggregate productivity in autarky is lower than that for the division of labor which is associated with the PPF. As transaction conditions are improved, the equilibrium aggregate productivity will discontinuously jump from line EG to the PPF. The difference between EFG and line EG can then be defined as economies of division of labor. It is interesting to see that there exist economies of division of labor even if there are no economies of scale or the aggregate production set is convex in the Ricardian economy. The aggregate production set is the area enclosed by the vertical and horizontal axes, lines EF and FG and its boundaries in Fig. 3.1. This implies productivity chosen by the decision makers in the equilibrium will endogenously increase as transaction conditions are improved. If transaction efficiency is low, then the high productivity associated with the PPF is not Pareto efficient because of the trade off between economies of division of labor and transaction costs. Rosen (1978) calls economies of division of labor superadditivity, which is a kind of economies of interpersonal complementarity. It implies that equilibrium aggregate productivity for society increases as the equilibrium network size of division of labor increases. This is called by Buchanan (1994) “generalized increasing returns” and by

73

Allyn Young (1928) “social increasing returns” which may exist in the absence of economies of scale. Individuals’ levels of specialization and the diversity of individuals’ occupation configurations are two aspects of the network. The inframarginal comparative statics of general equilibrium provides a general equilibrium mechanism for economic development. In this mechanism, exogenous comparative advantage and transaction efficiency are driving forces of economic development. Exogenous changes in production functions or endowments are not needed for the economic development if transaction conditions are improved. Also, exogenous changes in tastes are not needed for structural changes in this economic development process. Suppose that transaction efficiency is improved from a level lower than k0 to a level higher than k0, then to a value of k greater than k1 or k2. Then the general equilibrium jumps from autarky, to the partial division of labor, then to the complete division of labor. In autarky each individual produces all goods that she consumes and there is no division between different occupations such as between farmers and manufacturers. As transaction conditions are improved, different professional occupations emerge from the evolution of division of labor. This process can be considered as structural changes. Suppose x is food and y is cloth. Since the number of professional farmers in structure C is smaller than the number of individuals producing food which is the population size in autarky, this structural change caused by evolution of division of labor looks like a transfer of labor from the traditional agricultural sector to the industrial sector. But in essence the structural change is a process in which each individual’s level of specialization increases and the degree of diversity of occupation configurations increases, the degree of market integration increases, the number of markets for different goods increases, new traded goods emerge, the degree of interpersonal dependence and connection increases, the extent of the market and related network size of division of labor rises, the degree of production concentration increases, and productivity increases. As the general equilibrium jumps from Ba to C due to improvements in transaction conditions, occupation configuration (xy/y), is replaced with new occupation configuration (x/y), which has a higher level of specialization than (xy/y). This process of destructive creation (Schumpeter , 1934), such as the replacement of handicraftsmen by specialized workers in large firms described by Rosenberg and Birdzell, (1986, pp. 14584), Mokyr (1990, 1993, pp. 26-110), and Marx (1967), involves emergence of new occupations and the disappearance of old ones. It could be quite painful if the transitional costs are considered. We now consider the common wisdom that as terms of trade of a country deteriorate, the gains that this country receives from trade will fall. Many development economists consider worsening terms of trade as a cause of underdevelopment. The inframarginal comparative statics of our model show that this is not a general equilibrium view and might be misleading. Consider Tables 3.1 and 3.2. Suppose that M1/M2 > (a2xa2y/a1xa1y)0.5β/(1-β) and the initial value of k is k'∈((a2xa1y/a1xa2y)0.5, (M1/M2)(a1y/a2y)β/(1-β)). Hence, the equilibrium structure is Ba where country 1 exports x and imports y at the relative price px/py = a1y/k'a2y. Assume now that the transaction efficiency is improved, so that the value of k is k">(M1/M2)(a1y/a2y)β/(1-β), which is greater than k'. Hence, the equilibrium jumps to structure C where the relative price is (M2/M1)(a2y/a1x)β/(1-β). This implies that country 1's terms of trade deteriorate as the

74

improvement in transaction efficiency drives the equilibrium to jump from Ba to C, if k' < (M1/M2)(a1y/a2y)(1-β)/β. It is straightforward that the parameter subspace for such a structural change is not empty. Therefore, as transaction efficiency is improved within this parameter subspace, country 1's per capita real income increases from autarky level despite deteriorated terms of trade. This is because improvements in transaction conditions will expand network of division of labor and raise equilibrium aggregate productivity, so that productivity gains might outweigh the deterioration of terms of trade. The inframarginal comparative statics of the general equilibrium can be summarized in the following proposition. Proposition 3.1: The general equilibrium structure is determined by the two countries’ relative productivity, relative preference, relative population size and the level of transaction efficiency. Given other parameters, improvements in transaction efficiency can make the general equilibrium structure jump from autarky to partial division of labor and then to complete division of labor. For given transaction conditions, relative population size, and relative tastes for the two goods, the greater the degree of comparative advantage, the more likely the equilibrium level of division of labor is higher. For given transaction conditions, the more the relative population size is in balance with relative tastes and relative productivity, the more likely the equilibrium level of division of labor is higher. As the equilibrium level of division of labor increases, the equilibrium aggregate productivity for society as a whole increases. In the process of moving to a higher level of division of labor, a country may receive more gains from trade even if its terms of trade deteriorate.

It is interesting to note that the general equilibrium market price may not be determined by the conventional marginal cost pricing rule in the model with exogenous comparative advantage. When structure Ba (or Bb) is the general equilibrium, the market price of good x in terms of y equals country 1’s (or country 2’s) marginal opportunity cost including (or excluding) transaction cost. When structure C is the general equilibrium, the market price of x in terms of y is determined by the total demand and supply in both countries and does not equal either country’s marginal opportunity cost of producing x. This observation substantiates Coase’s argument (1946) that one should use total cost-benefit analysis in addition to marginal analysis in price determination. Other examples of non-marginal cost pricing can be found in chapter 4 in this text, in the literature of industrial organization (see Tirole, 1989 Chapter 3), and in the literature of labor contract (Azriadis 1975, Baily 1974, and Gordon 1974). In the Ricardian model, an increase in k (or a decrease in transaction cost coefficient 1-k) can increase total transaction costs because the increase in k can generate a jump of the general equilibrium from a low level to a high level of division of labor and increase the number of transactions. This implication of transaction costs can be used to explain why the income share of transaction costs increases as transaction efficiency is improved. North (1986) has found empirical evidence for this phenomenon. In order to formalize Smith’s conjecture that the invisible hand can efficiently coordinate individuals’ decisions in choosing their patterns of specialization, we must prove that the general equilibrium is Pareto optimal. The Pareto optimum is a resource allocation and a network structure of division of labor in which no individual can increase

75

her utility without reducing others’ utilities. A revealed preference argument can be used to prove that in the Ricardo economy with consumer-producers, the general equilibrium is Pareto optimal. The logic of the proof can be outlined as follows. We may use an argument of negation to establish the first welfare theorem. Suppose that the equilibrium is not Pareto optimal, so that there exists a feasible resource allocation that is Pareto superior to the general equilibrium resource allocation. This implies that at least one individual’s utility is greater in this alternative allocation than in equilibrium and other individuals are at least indifferent between the equilibrium and the alternative allocation. We now specify artificial budget constraints for all individuals' consumption, production, and trade flows given by the alternative allocation under the equilibrium prices. The person receiving greater utility in the alternative allocation must pay more than her income in the alternative allocation under the equilibrium prices since, by the definition of optimization, her optimum decision under the equilibrium prices cannot achieve more utility than in the equilibrium. All other individuals must have a binding budget in the alternative allocation under the equilibrium prices. Aggregating all individuals' artificial budget constraints and canceling prices, it can be shown that the aggregate endowment constraint is violated. Hence, the alternative allocation is infeasible. This establishes the first welfare theorem. The first welfare theorem implies that the most important function of the market is to coordinate all individuals’ decisions in choosing their patterns of specialization to utilize positive network effect of division of labor net of transaction costs. Zhou, Sun, and Yang (1998) have proved an existence theorem of general equilibrium for a general class of models of endogenous specialization. In their model, the set of ex ante different consumer-producers is a continuum, preferences are rational, continuous, and increasing, and both constant returns and local increasing returns are allowed in production. The Ricardian model in this chapter and the Smithian model with economies of specialization in chapter 4 are just special cases of their model. They have also established the first welfare theorem and the equivalence between the set of competitive equilibria and economic core for this general class of models of endogenous specialization. The results imply that if transaction costs outweigh exogenous comparative advantage in a structure or if the corner equilibrium in this structure is not Pareto optimal, then there is coordination difficulty in getting self-interested decision-makers to choose the constituent occupation configurations in this structure. In that case a set of relative prices to support individuals’ Walrasian decisions choosing constituent occupation configurations in this structure does not exist. The first welfare theorem implies not only resource allocation for a given structure of division of labor is efficient, but also the structure of division of labor is efficient in equilibrium. We call a corner equilibrium an efficient resource allocation for a given structure of division of labor and call the general equilibrium structure of division of labor an efficient organization or organism. The concept of organization efficiency relates to inframarginal analysis of economic development. The concept of allocation efficiency relates to marginal analysis of resource allocation. It can be shown that for the model of endogenous specialization, general equilibrium may not exist if the number of individuals is not a continuum because of an integer problem (see example 9.10 in chapter 9).

76

3.4. Per capita Real Income, GDP, GNP, and PPP

Many development economists measure development performance by per capita gross domestic product (GDP) or per capita gross national product (GNP) and their growth rates. GDP is the market value of an economy's domestically produced goods and services. GNP equals GDP plus the net factor income from abroad. Many development economists are critical of using per capita GNP as a measure of development performance. They suggest to use some social index that includes life expectance, literacy rate, infant mortality, and inequality of income distribution. There are many problems with this measurement method. First, unequal income distribution might be caused either by distortions or by evolution in division of labor. For instance, the government monopoly power in the banking sector and many other sectors generate inefficient level of division of labor and related narrow extent of the market, which is associated with extremely unequal income distribution in the 1990 China. But under constitutional order and fair competition, the evolution of division of labor may generate a new professional occupation of entrepreneurial activity. The professional entrepreneurs' job is to experiment with various patterns of economic organizations and to take risk of the experiment (see chapter 15). This implies the entrepreneurs will make fortune or go bankruptcy with a certain probability. Bankruptcy implies negative (maybe negative infinity in the case of committing a suicide) income, while successful venture may make the entrepreneur very rich, despite the fact that expected income of the entrepreneur is nearly same as in other less risk occupations. Hence, inequality of income distribution will increase as the professional entrepreneur emerges from a high level of division of labor. As long as free entry and free pricing prevail, such increase in inequality might be welfare enhancing for society as a whole. Index of life expectance, literacy rate, infant mortality is problematic for measuring welfare since there are many possible trade offs between each pair of the variables. Individuals’ welfare maximization relates to the efficient balance of the trade offs rather than maximization or minimization of the value of any single one of them. The ultimate concern of welfare analysis is with individuals' utilities. Hence, we call utility as per capita real income. We now use our simple Ricardian model to show that per capita real income differs from per capita GNP, so that measuring development performance by per capita GNP might be misleading. Suppose parameter values are within the subspace defined by k∈(k0, k1) and M1/M2 >(a2xa2y/a1xa1y)0.5β/(1-β) k1), such that structure Ba occurs in equilibrium. In this simple model per capita GNP is the same as per capita GDP because of the absence of trade in labor. Following common practice in calculating GNP, most self-provided services are not counted as part of GNP. Hence, per capita GNP in terms of good y in country 1 is I1 = px1s = (M2a2yβ/M1)-(a1yβ/k), where the equilibrium value of p is given in Table 3.1 and x1s = a1x (l1x-β) is given by the decision problem for configuration (xy/y)1 and the equilibrium value of l1x = (ka2yM2β/a1yM1) is given by the market clearing condition for structure Ba. Per capita GNP in country 2 is I2 = y2s = a2yβ, given by the decision problem for configuration (y/x)2. Similarly, we can find per capita GNP in structure C: I1 = M2a2yβ/M1 and I2 = a2yβ. From Table 3.1, it is easy to find that per capita real incomes in the two countries in structure Ba are:

77

U1(Ba) = (βa1x)β [(1-β)a1y]1-β, U2(Ba) = (βa2x)β[(1-β)a2y]1-β(k2a2ya1x/a2xa1y)β U1(C) = (βa1x)β [(1-β)a1y]1-β[βkM2a2y/M1a1y(1-β)]1-β U2(C) = (βa2x)β[(1-β)a2y]1-β [(1-β)kM1a1x÷M2a2x β]β It is not difficult to verify that when equilibrium occurs in structure Ba, U1(Ba) > U1(C), I1(Ba) < I1(C) and

U2(Ba) > U2(C), I2(Ba) = I2(C).

In other words, welfare comparison between different patterns of division of labor in terms of per capita real income (utility) is inconsistent with that in terms of per capita GNP. This shows that the analysis of development performance based on the notion of per capita GNP might be misleading. There are two reasons for misinformation of the calculation of welfare from per capita GNP. First, this notion does not count or it understates self-provided services. Hence, it may overstate welfare in a country with a high level of division of labor in comparison to a country with a low level of division of labor, which is associated with a high level of self-provided services. Second, transaction cost has a negative effect on per capita real income. But transaction costs and the income of the sector providing transaction services are counted as part of per capita GNP. Hence, per capita GNP overstates welfare of a country with a high level of division of labor that is associated with a high level of transaction cost. For instance, per capita GNP of the US was 40% higher than that of Australia in 1997. Also, we can see the level of division of labor in the US was higher than in Australia. For instance, many writers in the US depend on specialized publicity agents for publishing businesses, while no much of such specialized service is available in Australia. But the difference in per capita real income between the two countries is much smaller than the figures of per capita GNP suggest according to many individuals who had living experience in both countries in 1997. This is partly because the figure misses some noncommercialized real incomes in Australia which are commercialized in the US and partly because it ignores the fact that each individual in the US pays more transaction costs caused by a higher level of division of labor in the US than each Australian. This higher transaction cost is counted as part of per capita GNP, but has a negative effect on per capita real income (utility). The real wages in terms of good y are different between the two countries in a structure with trade. Consider structure Ba. Let the value of x produced by a person in country 1 in terms of y be equal to wage; we have p(x1+x1s) = w1l1x where w1 is the wage rate in country 1. This, together with equilibrium values of p, x1, x1s, l1x, yield the equilibrium wage rate in country 1, w1 = a1y/k. Similarly, we can find the equilibrium wage rate in terms of good y in country 2, w2 = a2y. It can be shown that w1(Ba) > w1(C) for k ∈( k0, k1) and w2(Ba) = w2(C). Recalling that U1(Ba) > U1(C), I1(Ba) < I1(C) and U2(Ba) > U2(C), I2(Ba) = I2(C) when equilibrium occurs in structure Ba, or when k ∈( k0, k1), we can see that welfare analysis in terms wage rates is closer than that in terms of per capita GNP to that in term of pre capita real income. In this general equilibrium model, we can consider nominal exchange rate between the two countries as 1 if they use the same currency. We can consider w1/w2 as a real exchange rate in terms of price difference in labor between the two countries. If the wage rate in a country is adjusted by this exchange rate, then prices of labor would be the same in the two countries. This kind of

78

adjustment is referred to as adjustment according purchase power parity (PPP). Hence, the adjustment of per capita GNP according to PPP in Maddison (1995) makes the adjusted per capita GNP closer to per capita real income. But as we have shown in this example, adjusted per capita GNP according to PPP is still different from per capita real income. Our discussion here does not consider effect of inflation on measurement of development performance. We will consider this in chapter 17 which introduces money into a Smithian general equilibrium model.

3.5. Economic Development and Trade Policy

In the early stage of economic development in the 16th century, the governments of some European countries used protection tariff as a vehicle for rent-seeking in international trade (see, for instance, Ekelund and Tollison 1981). This mercantilism was replaced by a free trade policy regime in some European countries in the 18th and 19th century. According to Smith (1776), a laissez faire regime is more conducive to economic development than protection tariff. But after World War II, many governments in developing countries still used protection tariff as a means to increase their share of gains from trade by manipulating the terms of trade. This trade policy is sometimes referred to as import substitution strategy. But the governments in Hong Kong, Taiwan, and other developing countries use tax holiday, export-process zones, and other policy instruments to reduce tariff. This trade liberalization policy is sometimes referred to as exportoriented development strategy. Many economists argue that the trade liberalization which involves tariff reduction is a powerful engine of economic development (Krueger 1997, World Bank 1996). Recently, bilateral and multilateral tariff negotiations have become a driving force of trade liberalization. The question is, why is free trade difficult to realize, and trade negotiation essential for trade liberalization, if free trade is mutually beneficial? Why do some governments choose the unilateral protection tariff and others choose unilateral laissez faire regime at the same time? How can we use general equilibrium models to explain government policy shift from protection tariffs to free trade or to tariff negotiation that leads to trade liberalization? This section will introduce government tariff into the Ricardian model to address these questions. Example 3.2: A Ricardian model with endogenous trade regime (Cheng, Sachs, and Yang, forthcoming). Based on the model in section 3.2, suppose that the government in country i (i = 1, 2) imposes an ad valorem tariff of rate ti, and transfers all tariff revenue equally to all individuals in country i. In this case, individuals’ budget constraint, for instance, for configuration (x/y), changes from pxxs = pyyd to pxxs + Ri = (1+ti)pyyd, where ti is the tariff rate in country i and Ri is the tariff revenue received by each resident in country i. Individuals take the amount of transfer as given. At equilibrium, the total transfer equals total tariff revenue. Also, we assume that the transaction efficiency coefficient for country i is ki, which may be different between countries. Using the same procedure as in section 3.3, we can solve for the corner equilibrium for each structure. The corner equilibrium solutions are presented in Table 3.3.

79

It is easy to see that if t1= t2=0 and k1= k2, Table 3.3 reduces to Table 3.1. If t1= t2=0, the Ricardian model predicts that the country that produces both goods does not get any gains from trade. This result can be clearly seen from Table 3.1 ⎯ when the general equilibrium occurs in structure Ba (or Bb), individuals in country 1 (or country 2) that produces both goods x and y get the same level of utility as they do in autarky. Table 3.3:

Corner equilibrium solutions

Structure

Price px/py

A

N.A.

Ba

a1y(1+ t1)/ k1a2x

Bb

k2a2y/(1+ t2)a2x

C

(1+βt1)βa2yM2÷ (1-β)[1+(1βt2)]a1xM1

Individual Utility

Relevant Parameter Subspace

k1 < D1(1β)a1yM1÷βa2y M2 k2 < D2βa2x M2÷(1-β)a1xM1

Country 1 (βa1x)β[(1-β)a1y]1-β ≡U1(A) [(1+L1x t1)/(1+β)t1] U1(A)

Country 2 (βa2x)β[(1-β)a2y]1-β ≡U2(A) [k1k2(a1xa2y) ÷ (a1ya2x)]βT1βU2(A)

[k1k2(a1xa2y) ÷ (a1ya2x)]1-βT21-β U1(A) [k1T3βa2yM2/(1β)a1yM1]1-βU1(A)

U2(A)[1+(1-L2x)t2]÷ [(1-β)t2] [k2T4(1-β)a1xM1÷ βa2xM2]βU2(A)

where D1 ≡ (1+t1)[1+(1-β)t2]/(1+βt1), D2 ≡ (1+βt1)(1+t2)/[1+(1-β)t2], L1x ≡ β + (1+βt1)k1βa2yM1/a1yM2[1+(1-βt2)](1+t1) >β, T1 ≡ {(1+t2)/[1+(1-β)t2]}(1-β)/β/(1+t1)[1+(1-β)t2)], L2x ≡ β - [1+(1-β)t2]k2(1-β)a2xM1/a1xM2(1+t2)(1+βt1)] 0 (or in structure Bb, ∂U2/∂t2>0), that is, given the tariff rate of the country producing one good, the country producing two goods can improve its own welfare by raising its tariff rate. This is because the latter country determines the terms of trade and can improve them by imposing a tariff, thereby obtaining a larger share of the gains from trade. The country producing two goods gains at the expense of its trading partner, and it can be shown that ∂U2/∂t1 k0, and autarky will be chosen if k < k0. Here, we ignore ex ante differences in transaction and production conditions that generate unequal real incomes between individuals. We will consider this in chapter 5. However, the utility equalization condition is more realistic than it appears. Take a businessman and his secretary as an example. Nominal incomes between them are very unequal. Everybody knows that the businessman (if successful) can make more money, so that competition to get into business school is much more intensive than that for entry to a school for secretarial training. The more intensive competition generates intangible disutility, as well as a greater financial burden since business schools rarely provide scholarships. More importantly, the businessman takes a considerable risk of bankruptcy, which may even cause suicide (implying an infinitely large negative real income). If you count all the tangible and intangible benefits and costs, the difference in real income between the businessman and his secretary is much smaller than it seems to be. If there is free entry into every occupation, utility equalization will hold. Inserting px/py = 1 into the indirect utility function ux or uy yields: k ux = u y = uD = 4 where u D is per capita real income for the division of labor, which depends on the transaction efficiency parameter k but does not depend on relative price. Hence, an individual’s demand and supply functions are given by the corner solution in configuration A if k < k 0 , and are given by the corner solutions in configuration (x/y) or (y/x) if k > k 0 . As k increases from a value smaller than k0 to a value greater than k0, demand and supply discontinuously jump from 0 to positive levels as functions of relative prices due to an increase in individuals’ levels of specialization. This is referred to as the Smithian law of demand, which is distinguished from the neoclassical law of demand. The analysis of the discontinuous shift of optimum decisions between configurations in response to changes of parameters is called inframarginal comparative statics of decision problems,

112

which are distinguished from marginal comparative statics of the decisions. The inframarginal comparative statics of demand and supply are based on total benefit-cost analysis between corner solutions. For a given configuration, marginal analysis generates marginal comparative statics of the decisions. For instance, in configuration (y/x): dxd/d(px/py) = -0.5(px/py)-2 < 0. This implies that as the price of good x increases relative to that of good y, the quantity demanded of good x by each specialist in y falls. This is referred to as the neoclassical law of demand. The analysis of how the optimum decisions continuously change within a given configuration in response to changes in parameters is called marginal comparative statics of decisions. The marginal comparative statics of the decisions are concerned with changes in the efficient resource allocation for a given configuration of specialization in response to changes in parameters within a given parameter subspace that demarcates this configuration. The inframarginal comparative statics of the decisions relate to changes in the efficient configuration of specialization as parameters shift between the subspaces that demarcate the configurations. In summary, marginal comparative statics of the decisions relate to marginal analysis, resource allocation, demand, and supply for a given configuration of specialization, and given aggregate demand. In contrast, inframarginal comparative statics of the decisions relate to inframarginal analysis of the level of specialization, which determines the extent of the market, the size of the network of division of labor, and aggregate demand (which will be defined later on). Problems of resource allocation closely relate to marginal analysis of relative quantities of goods produced and consumed and relative prices for a given network size of division of labor and related productivity. Problems of economic development relate to the question of how equilibrium productivity or its reciprocal (the degree of scarcity) is determined by individuals’ decisions in choosing their patterns of specialization and by the interactions of decisions in the marketplace. Hence, inframarginal comparative statics relate to the problems of economic development. A common practice in neoclassical economics is to separate the analysis of demand and supply from the analysis of individuals’ decisions in choosing their levels and patterns of specialization. As discussed before, this is because economists were not familiar with the mathematical tools for handling corner solutions, which are essential for the endogenization of individuals’ levels of specialization, when Marshall formalized classical economic thinking within a mathematical framework based on marginal analysis and on the dichotomy between pure consumers and firms. Unfortunately, many economists still show remarkable insistence on maintaining the neoclassical dichotomy and marginal analysis, despite the fact that many mathematical instruments for handling corner solutions are now available and the neoclassical framework is no longer essential for mathematical modeling. This chapter shows that we can abandon the neoclassical dichotomy and apply inframarginal analysis to study individuals’ decisions in choosing their levels and configurations of specialization. The spirit of classical analysis of demand and supply as two sides of division of labor can then be resurrected in the body of Smithian general equilibrium models.

113

4.3 How the Market Coordinates Division of Labor to Utilize Network Effects and Promote Economic Development

Combinations of the three configurations considered in the preceding section generate two organization structures, or structures for short. A configuration is equivalent to a major that a university student chooses and a structure is equivalent to the division of students among majors in the university. All individuals choosing configuration A (autarky) constitute a structure involving no market, no prices, no interdependence, and no interaction between individuals. The division of M individuals between configurations (x/y) and (y/x) constitutes a structure with division of labor, denoted D, where there are two markets for two goods sold by two types of specialists. Let the number of individuals choosing (x/y) be Mx and the number choosing (y/x) be My. Strictly speaking, when the set of individuals is a continuum, we should call the number of a particular type of specialists the measure of this type of specialists. There is a corner equilibrium for each structure. A corner equilibrium is defined by the relative price of the two traded goods px/py, and the numbers of the two types of specialists, Mx and My, that satisfy the market clearing condition and utility equalization condition for a given structure. In a corner equilibrium, individuals maximize their utility with respect to configurations in the given structure and with respect to quantities of goods produced, traded, and consumed for the given corner equilibrium relative price and the numbers of individuals selling the two goods. The market clearing and utility equalization conditions are established by free choice between configurations and utility maximization behavior. According to the definition of corner equilibrium, the corner solution in configuration A chosen by M individuals is the corner equilibrium in structure A, where the market clearing condition always holds, since self-demand and self-supply are two sides of selfprovided quantities in the structure. In structure D, free choices between configurations (occupations) and utility maximizing behavior will establish the utility equalization condition. From Table 4.2, it can be seen that the indirect utility function of a specialist in x is an increasing function of px/py, and the indirect utility function of a specialist in y is a decreasing function of px/py, as shown in Fig. 4.2 where p ≡ px/py. Hence, the utility equalization condition is associated with the intersection point E in Fig. 4.2. The upward-sloping straight line in Fig. 4.2 is an x specialist’s indirect utility function, which looks like a supply curve. The downward-sloping curve is a y specialist’s indirect utility function, which looks like a demand curve. The corner equilibrium relative price in structure D is determined by the intersection point between the two curves. If the relative price px/py is at point B, then the utility of a specialist in x is greater than that of a specialist in y, so that all individuals will specialize in x and nobody will specialize in y. This implies that the corner equilibrium in structure D cannot be established. Therefore, the utility equalization condition determines the corner equilibrium relative price of traded goods in structure D, that is: ux = kpx/4py = uy = kpy/4px

or px/py = 1.

114

Figure 4.2: Indirect Utility Functions and Corner Equilibrium Relative Price

We will show that if the model is not symmetric, then the corner equilibrium relative price is determined by relative tastes and relative production and transaction conditions. In structure D, the market demand for good x is: Xd ≡ My xd = My py /2 px , while the market supply of good x is: (4.8)

Xs ≡ Mx xs = Mx /2

where xd = py /2 px , and xs = 1/2 are given by Table 4.2. The market demand function for x not only exhibits the demand law (i.e., the quantity demanded of a good decreases as its price increases relative to that of the good sold by the buyer), but is also an increasing function of the number of specialists in y. The market supply function of x is an increasing function of the number of specialists of x. If the C-D utility function is replaced with the constant elasticity of substitution (CES) utility function as shown in section 4.4, then the market supply function will exhibit the supply law (i.e., the quantity supplied of a good increases with the price of this good relative to that of the good bought by the seller). In a Walrasian regime, prices are determined by a Walrasian auction mechanism. The Walrasian auctioneer calls a set of relative prices of all traded and nontraded goods. All individuals report to the auctioneer their optimum quantities of goods to be traded for the given set of prices. Then the auctioneer adjusts relative prices according to excess demands, raising or lowering the price of a good according to whether its excess demand is positive or negative. This tatonnement process continues until the excess demands for all goods tend to 0. This is referred to as a centralized pricing mechanism. The Walrasian auction mechanism will establish the market clearing condition for good x: Xd = My py / 2 px = Xs = Mx / 2, or px / py = My / Mx

115

This equation implies that competition in the market and free choice of configurations establish an inverse relationship between the relative prices of goods x and y and the relative numbers of individuals selling goods x and y. Free choice with respect to configurations (occupations), together with free choice of quantities to produce, trade, and consume, are the driving forces that establish a corner equilibrium. Summing up all individuals’ budget constraints, we can express the excess demand for x as a function of the excess demand for y even if the market is not cleared. Hence, the market clearing condition for good y is not independent of that for good x. Thus, we do not need to consider that market clearing condition. This is referred to as Walras’ law which states that for n traded goods and factors, there are only n-1 independent market clearing conditions. The market clearing condition for x, the utility equalization condition, and the population equation Mx + My = M yield the corner equilibrium in structure D: px / py = 1,

Mx = My = M/2.

Inserting the corner equilibrium relative price of traded goods back into demand and supply functions and indirect utility functions yields the corner equilibrium quantities to produce, trade, and consume and the corner equilibrium utility level, which we call per capita real income, denoted by uD. The corner equilibrium values of endogenous variables are no longer functions of prices. Due to symmetry, per capita real income depends only upon the parameter k. x = y = xs = ys = xd = yd = ½,

uD = k/4.

For an asymmetric model, all the endogenous variables will depend upon the parameters of relative transaction and production conditions and relative tastes for the two goods. We call the corner equilibrium values of endogenous variables, including the relative price of traded goods and the numbers of individuals selling different goods, a resource allocation for a given structure. A corner equilibrium sorts out resource allocation for a given structure. In the Smithian framework, there are multiple corner equilibria, and the general equilibrium is only one of these. All the information about the two corner equilibria in structures A and D is summarized in Table 4.3. Table 4.3: Two Corner Equilibria

Structure

Relative rice

A D

dy/dx = 1 px / p y = 1

Number of specialists Mx = My = M/2

116

Quantities of goods x = y = 0.5a x = y = xs = y s = x d = yd = ½,

Per Capita real income 2-2a k/4

We distinguish per capita real income, which is the corner equilibrium value of the indirect utility function in a structure, from the indirect utility function, which is the optimum value of utility for a configuration. We now further examine the nature of the pricing mechanism in the Walrasian regime in the Smithian model. Though we use a Walrasian auction mechanism to describe the pricing mechanism, this centralized pricing mechanism is not essential in the Smithian framework. The Walrasian pricing mechanism in the Smithian framework can be decentralized. In the Smithian framework, prices are determined by all individuals’ self-interested decisions in choosing their occupation configurations. In principle, individuals are allowed to choose prices. But interactions between self-interested decisions in choosing occupation configurations will nullify any attempts to manipulate prices, as long as nobody can manipulate the numbers of individuals choosing various occupation configurations. As shown in (4.8), the market relative price of the two traded goods is inversely determined by the corresponding relative number of individuals selling the two goods and the relative outputs of individual sellers. Since an individual’s output level is trivial compared to the very large number of individuals who can choose any occupation configuration, the relative price cannot be manipulated by an individual’s output level as long as the relative number of different specialist producers cannot be manipulated. This justifies the pricetaking behavior for each individual, despite the assumption that each individual is allowed to choose prices. In the Smithian model, the tatonnement process is a negative feedback mechanism. Suppose that the relative price px /py is higher than the equilibrium price. Then it must be true that ux > uy, so that individuals will shift from configuration (y/x) to configuration (x/y). This reduces My/Mx, and therefore reduces px/py through (4.8). This adjustment will continue until the equilibrium is established. A general equilibrium is defined by a set of relative prices of traded goods, a set of numbers of individuals choosing different configurations that constitute a structure, and individuals’ quantities of goods produced, traded, and consumed that satisfy the following conditions: (i) each individual’s decision with regard to quantities and configuration maximizes her utility for the given equilibrium relative prices of traded goods and the given equilibrium numbers of individuals choosing different configurations; (ii) the set of relative prices of traded goods and numbers of individuals choosing different configurations clear markets for all traded goods and equalize all individuals’ utilities. It is easy to see that a corner equilibrium satisfies these two conditions for a general equilibrium, except that individuals’ choices of configurations are confined within a given structure. Hence, the general equilibrium is the corner equilibrium, in which each constituent configuration is preferred by those choosing it over alternative configurations. From (4.6) and (4.7), we can see that individuals prefer either of the two specialization configurations to autarky if k > k0 and p = 1. Also, (4.6) and (4.7) imply that if k < k0, a relative price does not exist that ensures higher utility in both configurations of specialization than in autarky. Hence, the division of labor between two types of professional occupations is impossible to be coordinated via a relative price. This implies that the general equilibrium is autarky if k < k0. In summary, our two-step procedure to solve for a general equilibrium in the Smithian model runs as follows. A corner equilibrium is first solved for each structure.

117

Then individuals’ utilities under the corner equilibrium prices are compared between configurations to identify a parameter subspace within which each constituent configuration of this structure is at least as good as any other alternative configuration. Within this parameter subspace, this corner equilibrium is a general equilibrium. As the parameter space is partitioned, we can identify within each of the parameter subspaces which corner equilibrium is the general equilibrium. It can be seen that as the number of goods increases, the number of possible structures increases more than proportionally. As a result, the two-step approach to solving for general equilibrium becomes very cumbersome. Sun, Yao, and Yang (1999) have generalized the Smithian model to the case with very general preferences and production and transaction conditions, and have developed a much simpler two-step approach to solving for general equilibrium. Their two-step procedure needs the concept of Pareto optimum corner equilibrium, which is the corner equilibrium with the greatest per capita real income. They have shown that general equilibrium exists if the set of consumer-producers is a continuum, and that a general equilibrium is the Pareto optimum corner equilibrium. Hence, we can solve for corner equilibrium for each feasible structure, then compare per capita real incomes between corner equilibria to identify the general equilibrium. The following theorem is the theoretical foundation of this two-step approach. Yang (1988) proves this theorem for a specific Smithian model. Sun, Yang, and Yao have proved this theorem for a general class of Smithian models with ex ante identical consumer-producers. For simplicity, we call it the Yao theorem. Theorem 4.1 (Yao theorem): For an economy with a continuum of ex ante identical consumer-producers with rational, continuous, and convex preferences, and production functions displaying economies of specialization, and individual specific limited labor, a Walrasian general equilibrium exists, and it is the Pareto optimum corner equilibrium.

Proof of the Yao theorem: Since the proof of the existence of equilibrium is very cumbersome, we provide here only the proof of the second part of the Yao theorem. (i.e., the general equilibrium is the Pareto optimum corner equilibrium.) Without loss of generality, we may assume that goods {1, …, n} are traded at any corner equilibrium. Denote this corner equilibrium E. Here, n ≤ m, and m is the number of all traded and nontraded goods. Assume that the values of prices for these traded goods are (p1, …, pn) in this corner equilibrium and the general equilibrium values of the prices are (p1*, …, pn*). Now without loss of generality, we may assume that: p1*/p1 = max j {pj*/pj, j = 1, …, n} which implies for j = 1, …, n, (4.9)

p1*/pj* ≥ p1/pj.

The Wen theorem implies that an individual does not sell other goods if she sells good 1. Also, we have noted that indirect utility function is an increasing function of the price of a good sold and a decreasing function of the prices of goods purchased. This together with (4.9) imply that the utility for selling good 1 under p* is not lower than that under p.

118

Thus, under p*, an individual can do at least as well as those individuals selling good 1 at the corner equilibrium under p if she chooses the same production and trade plan as theirs. It follows that: (4.10)

u1(p*) ≥ u1(p) = u(p),

where u1(p*) is an individual's utility from a configuration in the corner equilibrium E under the general equilibrium prices, u1(p) is her utility from this configuration under the corner equilibrium prices in E, and u(p) is the per capita real income in the corner equilibrium E. The last equality in (4.10) is due to utility equalization in any corner equilibrium. But by definition of general equilibrium, any configuration chosen by any individual in general equilibrium generates at least the same utility as in any alternative configuration under the general equilibrium prices. This implies: (4.11)

u(p*) ≥ u1(p*)

where u(p*) is per capita real income in general equilibrium. (4.10) and (4.11) together imply u(p*) ≥ u(p), that is, per capita real income in general equilibrium is not lower than in any corner equilibrium. In other words, the general equilibrium is the Pareto optimum corner equilibrium. Q.E.D. We will use the Yao theorem frequently in this text. For the model in this section, the Yao theorem implies the following inframarginal comparative statics.

119

Proposition 4.1: The general equilibrium is the corner equilibrium in structure D if uD > uA, or if k > k0 ≡ 22(1-a), and is autarky if k < k0. Since economies of specialization are individual specific, or increasing returns are localized, we can apply the argument of revealed preferences used in chapter 3 to prove that a general equilibrium in this model is Pareto optimal. The rigorous proof of the first welfare theorem for a broad class of general equilibrium models allowing endogenous as well as exogenous comparative advantages can be found in Zhou, Sun, and Yang (1998). This result implies that the most important function of the market is to coordinate individuals’ decisions in choosing their patterns of specialization, in order to fully exploit positive network effect of division of labor net of transaction costs. If transaction costs outweigh economies of division of labor, coordination of the division of labor between various occupations will fail, so that the general equilibrium is autarky. If economies of division of labor outweigh transaction costs, the market can always utilize positive network effect of division of labor. Hence, in this model, coordination failure of division of labor comes from transaction costs. According to the first welfare theorem, either in the case of coordination failure or in the case of coordination success of division of labor, we have market success, due to the trade off between economies of division of labor and transaction costs.

Figure 4.3: Partition of Parameter Space Proposition 4.1 has partitioned a two-dimension space of parameters k and a into two subspaces, as shown in Fig. 4.3. Since we assume k∈[0, 1] and a ≥ 1, the feasible space of parameters is the region below horizontal line k = 1, above the line k = 0, and on the right side of the vertical line a = 1, including the boundaries of the region in Fig. 4.3. The curve k = 22(1-a) partitions the parameter space into two subspaces, one of them above the curve and the other below the curve. If values of parameters are within the first subspace, the corner equilibrium in structure D is the general equilibrium; if values of parameters are within the second subspace, the corner equilibrium in autarky is the general equilibrium.

121

( a ) Structure A, autarky

( b ) Structure D, division of labor

Figure 4.4: Autarky and Division of Labor Fig. 4.4 provides an intuitive illustration of proposition 4.1. Panel (a) denotes two representative individuals choosing autarky and panel (b) denotes two representative individuals choosing (x/y) and (y/x), respectively. The circles denote individuals; directed lines denote flows of goods. As transaction efficiency k increases from a value smaller than k0 to a value larger than k0, the general equilibrium jumps from autarky to the division of labor between two specialists. Such a jump in turn generates discontinuous jumps of all endogenous variables, emergence of markets for two goods, and of demand and supply from the division of labor, and an increase in the size of the network of the market. We call this phenomenon exogenous evolution in division of labor, since it never takes place in the absence of an exogenous change in parameters. An increase in individuals’ specialization and an increase in diversity between different occupation configurations are two facets of the evolution. As a result of this evolution, aggregate demand jumps from 0 to a positive value, the total transaction cost for society jumps from 0 to (1-k) (Mx yd + Myxd) = (1-k)M/2, and the aggregate production schedule jumps from a lower to a higher position, as indicated in Fig. 4.1, while the level of specialization of each individual increases from ½ to 1. An individual’s labor productivity of the good sold increases from 0.5a-1 ( k0, the general equilibrium is

122

the corner equilibrium in D. If k is increased, equilibrium per capita real income uD = k/4 will increase. For k < k0, the general equilibrium is the corner equilibrium in A. As a is decreased within the parameter subspace k < k0, the equilibrium values of x = y = 0.5a will change. All such changes in the equilibrium values of endogenous variables are marginal comparative statics of general equilibrium. These are changes in equilibrium resource allocation in response to parameter changes for a given structure of division of labor, since each corner equilibrium determines resource allocation for a given structure. The inframarginal comparative statics of general equilibrium deal with changes in the structure of division of labor in response to parameter changes, since the general equilibrium determines the equilibrium network structure of division of labor. If there exists a parameter subspace within which a corner equilibrium is the general equilibrium, then within this subspace the marginal comparative statics of general equilibrium are the comparative statics of the corner equilibrium. We define a profile of quantities of goods produced, traded, and consumed by all consumer-producers for a given structure as an allocation of resource for a given structure of division of labor. A corner equilibrium in the Smithian framework sorts out resource allocation for a given structure of organization. We define the task of determining a structure of division of labor as a problem of development, which relates to all individuals’ configurations of specialization, the size of the network of division of labor, variety between different occupation configurations, and productivity. The general equilibrium sorts out problems of development. The analysis of resource allocation relates to the marginal comparative statics of general equilibrium, while the analysis of economic development relates to the inframarginal comparative statics of general equilibrium. 4.4 More Examples Example 4.2: A general equilibrium model with the CES utility function. In the previous sections, supply functions in configurations with specialization are independent of prices, because of the unitary elasticity of substitution of the C-D utility function. Unitary elasticity of substitution implies that the substitution effect and the income effect cancel each other out in a consumer-producer setting. In this subsection, we use a constant elasticity of substitution (CES) utility function to illustrate the implications of the elasticity of substitution for the law of supply. The CES utility function is specified for each consumer-producer:

[

u = (x c )ρ + (y c )ρ

]

1

ρ

, x c ≡ x + kx d ,

y c ≡ y + ky d

where ρ∈(0, 1) is a parameter of elasticity of substitution. The following features distinguish the CES utility function from the C-D utility function. For the C-D function, the quantity of each consumption good must be positive for maintaining a positive utility. For the CES function, utility is positive even if the quantity of a consumption good is 0, as long as the quantity of at least one of the other consumption goods is positive. The elasticity of substitution is defined as the percentage change of relative quantity for one percentage change of relative price of two goods. The elasticity of substitution of the CES function can be calculated as follows:

123

E=

⎛ ∂u ∂y c ⎞ ⎟ d( x c y c )⎜ ⎝ ∂u ∂x c ⎠

=

d ln( x c y c )

=

1 . 1− ρ

⎛ ∂u ∂y ⎞ c c ⎛ ∂u ∂y ⎞ ⎟ ⎜ ⎟ ln d⎜ x y d ( ) ⎝ ∂u ∂x c ⎠ ⎝ ∂u ∂x c ⎠ This formula implies that relative quantities of the two goods consumed will decrease by 1 (1− ρ ) % when the relative price of the two goods increases by one percent. Since the elasticity of substitution is an increasing function of ρ, or dE/dρ > 0, the greater the value of ρ, the greater the elasticity of substitution. Since an individual’s desire for variety in consumption diminishes as the elasticity of substitution increases, the degree of desire for a variety in consumption can be defined by 1/ρ. If we let xc = yc, it is not difficult to see that consumption of two goods always generates a greater level of utility than consumption of a single good, that is, 21/ρxc > xc. We need the assumption ρ∈(0, 1) to ensure diverse consumption in equilibrium, since ρ < 0 or ρ > 1 implies specialized consumption in autarky equilibrium. Now that you are more familiar with the use of mathematical language in specifying economic models, we can quickly specify an individual’s decision problem based on the CES utility function as follows: Max: u = [( x c ) ρ + ( y c ) ρ ]1 / ρ (utility function) c d c d s.t. x ≡ x + kx y ≡ y + ky (definition of quantities to consume) c

x + xs = lx

c

y + y s = ly a (production function)

a

lx + l y = 1

(endowment constraint)

px x + p y y = px x + p y y s

s

d

d

(budget constraint)

where x, xs, xd, y, ys, yd, lx, ly are decision variables and px, py are price parameters. According to the Wen theorem, 5 configurations need to be considered. There are three autarky configurations: A1, in which one good is consumed; A2, in which two goods are consumed; and a third, which is symmetric to A1. The two configurations with specialization are (x/y) and (y/x). The optimum decisions in the various configurations are summarized in Table 4.4, where p ≡ py / px is the relative price. To familiarize yourself with inframarginal analysis, you should follow the procedure of the previous sections to solve for the optimum decisions in Table 4.4. Let us first consider the marginal comparative statics of the decisions. For a given configuration of specialization, differentiation of the corner supply functions in Table 4.4 yields: dy s dx s < 0, >0 dp dp This is referred to as the neoclassical supply law, i.e., the quantity of a good supplied increases with the price of that good. Since p ≡ py / px, the neoclassical supply law implies that the quantity of a good that is supplied not only increases with the price of that good, but also decreases with the price of the good purchased by the specialist supplier. This is consistent with the feature of classical demand and supply analysis: demand and supply

124

are two sides of specialization. It is easy to verify from Table 4.4 that neoclassical demand law holds for this model based on the CES utility function. Table 4.4: Corner Solutions Based on the CES Utility Function

Config Quantities elfuration provided A1 A2 (x/y)

(y/x)

Corner supply functions

x=1

Corner demand functions 0

0 ⎛ 1⎞ ⎝ 2⎠

Corner indirect utility functions

a

x= y=⎜ ⎟

0

ρ ⎡ ⎤ 1− ρ ⎛ ⎞ k ⎢ x = 1+ ⎜ ⎟ ⎥ ⎢ ⎝ p⎠ ⎥ ⎥⎦ ⎣⎢

ρ ⎡ ⎤ y = ⎢1 + ( kp) 1− ρ ⎥ ⎣ ⎦

dx d > 0, dp

−1

−1

2

0

ρ ⎡ ⎤ 1− ρ p ⎛ ⎞ s ⎢ x = 1+ ⎜ ⎟ ⎥ ⎢ ⎝k⎠ ⎥ ⎣ ⎦

−1

−ρ ⎡ ⎤ y s = ⎢1 + ( kp) 1− ρ ⎥ ⎣ ⎦

−1

1 1 − aρ

ρ

xs y = p

ρ ⎡ ⎤ 1− ρ ⎞ ⎛ k ⎢1 + ⎜ ⎟ ⎥ ⎢ ⎝ p⎠ ⎥ ⎥⎦ ⎣⎢

x = py

ρ ⎡ ⎤ 1− ρ 1 + kp ( ) ⎢ ⎥ ⎣ ⎦

d

d

s

1− ρ

ρ

1− ρ

ρ

dy d k 1 ≡ ⎜ 2 ⎝ ⎠ transaction efficiency increases from a value smaller than k1 to the one larger than k1, the general equilibrium will jump from autarky to the division of labor. Example 4.3: An asymmetric model. In the model we have discussed, there are too many symmetries. Hence, equilibrium values of endogenous variables are independent of relative tastes and relative production conditions. In this example, we examine the implications of relative tastes and relative production conditions for the equilibrium resource allocation and the level of division of labor. Assume that all ex ante identical consumer-producers have the following utility and production functions: u = ( x + kx d ) α ( y + ky d ) 1−α , α ∈(0, 1) x + xs = lx , y + y s = ly . a

b

125

The corner equilibrium relative price in structure D is p y p x = k 1− 2 α . Its derivative with respect to k is positive when α < ½, and is negative when α > ½. The corner equilibrium relative number of the two types of specialists is Mx / My = αk1-2α/(1-α). Its derivative with respect to k has similar features. The general equilibrium is the division of labor if: 1

⎛ ⎞ 2α ( 1− α ) (αa ) αa [b(1 − α )]b( 1−α ) ⎟ k > k2 ≡ ⎜ ⎝ [αa + (1 − α )b]αa + ( 1−α ) b α α (1 − α ) 1−α ⎠ and autarky if k < k 2 . The equation k = k2, which involves four parameters, partitions the four-dimension space of parameters a, b, α, and k into the two subspaces. You should follow the procedure in chapters 3 and 4 to solve for individuals’ decisions, the marginal and inframarginal comparative statics of the decisions, the two corner equilibria, the general equilibrium, and finally, for the marginal and inframarginal comparative statics of the general equilibrium. The comparative statics of general equilibrium describe how the consequences of interactions between self-interested decisions change in response to changes in environment. They differ from the comparative statics of decisions. From the corner solutions in Table 4.2, we can see that the decisions for a given configuration are functions of relative prices and parameters of production and transaction. For instance, the neoclassical demand law for a given configuration dyd/d(py/px) = -0.5 (px /py)2 is part of the marginal comparative statics of decisions. From the corner solution for a given configuration in example 4.2, we can see that the optimum decision, which is a corner solution in a configuration, is also a function of parameters of tastes and production. If the maximum amount of working time is a parameter rather than a specific number, then the optimum decision is a function of the endowment parameter as well. The inframarginal comparative statics are associated with discontinuous jumps of the optimum decisions between configurations as parameters of prices, tastes, endowments, and production and transaction conditions shift between the parameter subspaces that demarcate different configurations. Hence, the marginal and inframarginal comparative statics of decisions explain the optimum quantities of consumption, production, trade, and the optimum configuration of specialization by parameters of prices, tastes, endowments, and production and transaction conditions. From Table 4.2, we can see that the comparative statics of decisions may be represented by the following mapping: Parameters of tastes, transaction Quantities demanded and supplied, and production conditions, endowments, ⇒ resource allocation, utility, prices, numbers of different specialists configuration of specialization Recalling Table 4.3 and proposition 4.1, we can see that the general equilibrium relative price, numbers of different specialists, and quantities of consumption, production, and trade are determined by parameters of tastes, endowments, population size, and production and transaction conditions. The marginal and inframarginal comparative statics of general equilibrium explain relative price, numbers of different specialists, structure of division of labor, per capita real income, and resource allocation by the parameters as summarized by the following mapping:

126

Parameters of tastes, endowment, production and transaction conditions, population size

Quantities demanded and supplied, ⇒ relative prices, numbers of specialists, structure of division of labor

Hence, prices and numbers of individuals choosing different configurations are explaining parameters in the comparative statics of decisions, while in the comparative statics of general equilibrium, they are endogenous variables, themselves explained by parameters of tastes, endowments, production and transaction conditions, and population size. It should be noted that the comparative statics of decisions relate only to individuals’ occupation configurations, since an individual cannot choose a structure of division of labor for society. The comparative statics of general equilibrium relate to the structure of division of labor for society as a whole, since the general equilibrium is the outcome of interactions among all individuals’ optimizing decisions. It is not difficult to see that inframarginal comparative statics of general equilibrium are a rich source of the explaining power of economic development and related structural changes. The model in this chapter is similar to the model in the previous chapter, in that the production possibility frontier (PPF) may not be associated with the Pareto optimum. The general equilibrium structure is A, which is Pareto optimal if k < k0. But the PPF is associated with structure D, not with structure A (recall Fig. 4.1). The trade off between economies of division of labor and transaction costs implies that the Pareto optimum that is associated with the utility frontier is not the same as the PPF if transaction efficiency is low. As transaction efficiency is improved, the general equilibrium and the Pareto optimum move closer to the PPF. The endogenization of aggregate productivity implies that the degree of scarcity is endogenously explained by individuals’ decisions concerning their levels of specialization, and is ultimately determined by transaction efficiency. Hence, problems of economic development occupy a central place in the model of endogenous network of division of labor. Although the model in the current chapter is a static model, inframarginal comparative statics of general equilibrium can explain not only productivity progress, increases in per capita real income and consumption, and other “growth phenomena,” but can also explain the emergence of the market, increases in diversification of economic structure and in the extent of the market, and other “development phenomena.” From Fig. 4.1, we can see that if transaction efficiency is low, the general equilibrium is the corner equilibrium in autarky and the production takes place on curve ECG, which is lower than the PPF (EFG). As transaction efficiency is sufficiently improved, production schedule jumps from ECG to point F. This generates productivity progress and an increase in the network size of division of labor, which are two aspects of economic development. Example 4.4: Effects of a tax on allocation and organization efficiencies. Consider the Smithian model of example 4.1 with k = 1, and with taxation introduced. A benevolent and efficient government imposes a tax rate t on each dollar of goods sold, then evenly distributes the tax revenue among M consumer-producers. Hence, the income transfer that each individual receives from the government is r = t(Mxxs+ Myys)/M if the structure D is the general equilibrium. Applying inframarginal analysis and using the symmetry of the model, we can solve for the corner solutions in the three configurations A, (x/y), and

127

(y/x). Then the utility equalization and market clearing condition in structure D yields the corner equilibrium in D, as follows: px/py = 1, Mx = My = M/2, x = y = 1/(2-t), xs = ys = xd = yd = (1-t)/(2-t), uD = (1-t)/(2-t)2,

r = px(1-t)t/(2-t)

where uD is per capita real income in structure D, which is a monotonically decreasing function of the tax rate t. This implies that the tax causes a distortion resulting in a reduction of utility. The Pareto optimum tax rate is 0. But the corner equilibrium relative price in structure D is the same as in the corner equilibrium with no tax. Aggregate relative resources allocated to the production of the two goods, Mx/My = 1, and aggregate relative consumption and production of the two goods, (Mxx + Myxd)/(Mxyd + Myy) = 1, are Pareto optimal. However, each individual’s relative consumption of the two goods is not Pareto optimal. The relative consumption is x/yd = 1/(1-t) > 1 for an x specialist, and is xd/y = 1-t < 1 for an y specialist. Also, you can verify that each individual’s resource allocation is inconsistent with the first order condition for the Pareto optimum problem that maximizes the x specialist’s utility for a constant utility of the y specialist. The tax encourages individuals to allocate too much resource for self-provided consumption, and correspondingly discourages production for and consumption from the market. Hence, this allocation inefficiency may also cause organization inefficiency. Since, by definition, autarky does not involve trade, no tax revenue can be collected in autarky, so per capita real income in autarky is the same as in example 4.1. The general equilibrium will be the corner equilibrium in structure D in the absence of tax when k = 1. But a sufficiently high tax rate will make uD smaller than per capita real income in autarky, 2-2a even if k = 1. If k < 1, then we can show that the critical value of k, which ensures that division of labor will be the general equilibrium, is smaller in the absence of tax than when the tax is imposed. Hence, if k is between the two critical values, then the general equilibrium in the absence of tax is the division of labor, while the general equilibrium in the presence of tax is autarky. This example illustrates the interdependence between allocation efficiency and organization efficiency. The allocation inefficiency caused by the tax also causes an inefficient general equilibrium level of division of labor and an inefficient productivity level. The next example illustrates the conflict between allocation efficiency and organization efficiency in a Smithian model. Example 4.5: Conflict between allocation efficiency and organization efficiency. Suppose that in the model in example 4.1, the utility function is u = (x+kxd)α(y+kyd)1-α. Then we can solve for corner equilibria in autarky and in structure D as follows: uA = [αα(1-α)1-α]a uD = [αα(1-α)1-α]k2α(1-α), Mx = αk1-2αM/(1-α+αk1-2α),

px/py = k2α-1, My = (1-α)M/(1-α+αk1-2α)

The general equilibrium is the division of labor iff k > k1 ≡ [αα(1-α)1-α](a-1)/2α(1-α). It is easy to show that the critical value k1 is minimized with respect to α at α = ½, and that Mx = My = M/2 at α = ½. That is, as the difference between α and ½ increases, k1 increases. For a larger k1, k is more likely to be smaller than k1, so that autarky instead of

128

the division of labor is more likely to occur in equilibrium. In other words, as the differential in tastes for different goods tends to 0, the general equilibrium is more likely to be the division of labor. This indicates a possible conflict between organization efficiency, which relates to higher productivity and economic development, and efficiency of resource allocation, if one good is more preferred than the other. Under this circumstance, in order to accommodate taste differential, a high level of division of labor and related high productivity may have to be sacrificed. Example 4.6: Free entry and free pricing. In a Smithian model, the power to manipulate the relative numbers of different specialists has a more crucial impact on efficiencies of resource allocation and organization than does the power to manipulate relative prices. This result can be used to criticize Lange’s theory of market socialism, which emphasizes the importance of price flexibility in achieving allocation efficiency. According to the theory of market socialism, the government adjusts prices according to excess demand and directs managers of state enterprises to choose profit-maximizing quantities of outputs and inputs. Many economists have pointed out that self-interested government officials have no incentive to price commodities in accordance with excess demand because of the absence of residual claimants of profits. According to our model in this chapter, even if a system of flexible prices clears the market, self-interested government officials may still manipulate the relative numbers of different specialists, for instance, restricting free entry into the banking sector and into entrepreneurial activities, such that the market clearing prices of the services provided by the officials are high. This form of market socialism is not much better than the Soviet-style socialist system, under which government-controlled prices do not clear the market and the great excess demand becomes the source of the power of the central planning authorities. The government officials gain a great deal of tangible and intangible benefit from that power.

4.5 Pattern of Trade

In this section, we examine the trade pattern in a Smith-Young model of endogenous comparative advantage. In both the Ricardo and Heckscher-Olin models of exogenous comparative advantage in the preceding chapter, the equilibrium pattern of trade is determined by exogenous comparative technology and endowment advantages. But in the Smith-Young model of endogenous comparative advantage, all individuals are ex ante identical in all aspects, so that the equilibrium trade pattern cannot be explained by exogenous comparative advantage. In this section, we specify a Smith-Young model with three goods and show that if not all goods are involved in the division of labor, those goods which have more significant economies of specialization in production and/or higher transaction efficiencies are more likely to be involved in trade. Example 4.7: A model of endogenous comparative advantage with three goods. Consider a model with M ex ante identical consumer-producers. Each of them has the following utility function, production functions, and endowment constraint of labor: u = (x+kxxd) (y+kyyd) (z+kzzd),

129

x+xs = Max {lx - a, 0}, lx + ly + lz = e

y+ys = Max {ly - b, 0},

z+zs = Max {lz - c, 0},

where a, b, and c are fixed learning and training costs in producing goods x, y, and z, respectively. The fixed learning cost generates economies of specialization, which implies that average labor productivity increases with a person's level of specialization in producing a good. Each individual is endowed with e units of labor. The transaction efficiency coefficient for good i is ki. It is assumed that a > b > c and kx > ky > kz. Applying inframarginal analysis, we can solve for the inframarginal comparative statics of general equilibrium, which indicate that the general equilibrium jumps from autarky to the partial division of labor with two traded goods, and then to the complete division of labor with three traded goods. There are three corner equilibria for the partial division of labor. In one, denoted as structure Pxy, goods x and y are traded; in structure Pxz, goods x and z are traded; and in structure Pyz, goods y and z are traded. Denoting the complete division of labor D and autarky A, information about the corner equilibria in the five structures is summarized in Table 4.5. Table 4.5: Trade Pattern in a Model of Endogenous Comparative Advantage

Structure A Pxy Pxz Pyz D

Corner equilibrium prices px/py = (kx/ky)0.5[(e-b-c)/(e-a-c)]1.5 px/pz = (kx/kz)0.5[(e-b-c)/(e-a-b)]1.5 py/pz = (ky/kz)0.5[(e-a-c)/(e-a-b)]1.5 px/py = (kx/ky)1/3(e-b)/(e-a), pz/py = (kz/ky)1/3(e-b)/(e-c)

Corner equilibrium per capita real income [(e-a-b-c)/3]3 (kx ky)0.5[(e-b-c) [(e-a-c)]1.5/33 (kx kz)0.5[(e-b-c) [(e-a-b)]1.5/33 (kz ky)0.5[(e-b-a) [(e-a-c)]1.5/33 (kx ky kz)2/3(e-a)(e-b)(e-c)/33

Applying inframarginal analysis to each individual's decision in choosing a configuration, it can be shown that under the assumptions that a > b > c, kx > ky > kz, and kx, ky are neither too great nor too small, the general equilibrium structure is Pxy. Individuals have incentives to deviate from their configurations in structure Pxz or Pyz under the corner equilibrium prices in either of the two structures. The inframarginal comparative statics of general equilibrium can also be obtained by directly applying the Yao theorem to information in Table 4.5. If taste parameters are different across goods, it can be shown that if not all goods are traded, then those goods that are more desirable are more likely to be traded (see exercise 21). The results are summarized in the following proposition about trade pattern in a model of endogenous comparative advantage. Proposition 4.2: If transaction efficiencies are neither too high nor too low, not all goods are traded in equilibrium. Those goods which have more significant economies of specialization in production or higher transaction efficiencies, or are more desirable, are more likely to be traded.

This proposition can be used to explain why markets for some goods do not exist. The nonexistence of many markets in developing economies is often used to justify

130

development economics as a field separate from standard microeconomics. The inframarginal analysis of the Ricardian model, the HO model in chapter 3, and the SmithYoung model in this chapter suggests that the number of active markets in equilibrium can be endogenized in a standard microeconomic framework. Hence, inframarginal analysis can explain why the markets for many goods and services do not exist in a developing economy, and under what conditions the markets will emerge from economic development process.

Key Terms and Review

Configuration and corner solution. Why is the decision problem that involves a corner solution much more complicated than the interior decision? Implication of the Wen theorem for inframarginal analysis Trade off in allocating resources for a given configuration of specialization vs. trade off in choosing a configuration of specialization Marginal analysis of the problem of resource allocation vs. inframarginal analysis of the problem of economic development Relationship between the trade off in decision making and the second order condition Corner demand function, corner supply function, and corner indirect utility function vs. demand function, supply function, and indirect utility function Demand law, supply law, and the law of specialization Difference between marginal and inframarginal analyses of demand and supply Marginal comparative statics vs. inframarginal comparative statics of decisions Network effect of division of labor How does the market coordinate division of labor and utilize network effect of division of labor Structure based on configurations and corner equilibrium based on corner solutions General equilibrium vs. corner equilibrium Marginal vs. inframarginal comparative statics of general equilibrium Difference between an individual’s demand and supply functions, total market demand and supply functions, and aggregate demand and supply functions Implications of Walras’ law for solving for a corner equilibrium Implications of free pricing and free choice between occupation configurations for coordination of the network of division of labor Why may marginal cost pricing not work in a Smithian general equilibrium model? Allocation efficiency vs. organization efficiency Implications of institution for the equilibrium level of division of labor through its effect on transaction efficiency Why may the Pareto optimum not be associated with the production possibility frontier? Implications of transaction efficiency for the disparity between the Pareto optimum and the PPF and for reducing scarcity

131

Implication of the trade off between economies of division of labor and transaction costs for endogenizing productivity, network size of division of labor, and trade dependence What is the relationship between decisions in choosing an occupation configuration and the size of network of division of labor? Smithian aggregate demand law Relationship between production and transaction conditions and trade pattern in a Smith-Young model of endogenous comparative advantage

Further Reading Classical literature of specialization: Arrow (1979), Pettry (1671), Tucker (1756, 1774), Smith (1776), Turgot (1751), Babbage (1832), Rae (1834), Walker (1874), Groenewegen, P. (1987), Meek and Skinner (1973), Rashid (1986), Stigler (1951, 1974), Anonymous (1701); Inframarginal analysis: Buchanan and Stubblebine (1962), Coase (1946, 1960), Young (1928), Houthakker (1956), Wen (1998), Yang and Y-K. Ng (1993), Yang (1994), Rosen (1978, 1983), Becker (1981), Hadley (1964); Marginal analysis of endogenous specialization: Baumgardner (1988), Becker and Murphy (1992), Tamura (1991), Locay (1990), Kim (1989). Network effects: Buchanan and Stubblebine (1962), Farrell and Garth (1985), Katz and Shapiro (1985, 1986), Lievowitz and Margolis (1994); Criticism of marginal cost pricing: Coase (1946, 1960), Yang and Y-K. Ng (1993, ch. 2), Yang (1988, 1994); Neoclassical general equilibrium models with transaction costs and constant returns to scale technology: Hahn (1971), Karman (1981), Kurz (1974), Mills and Hamilton (1984), Schweizer (1986).

Questions 1. In the last decade, many shops specializing in changing engine oil have emerged in the US. They are usually organized through franchise networks, which reduce transaction costs caused by a deep division of labor between the franchiser and the franchisees. The franchiser specializes in planning, advertising, designing the operation manual, choosing specialized equipment, and management, while the franchisee specializes in changing engine oil. Since the franchiser specializes in producing intangible intellectual properties, it is very easy for the franchisee to infringe upon the franchiser’s property. (For instance, the franchisee refuses to pay the franchise fee as soon as she has acquired the know-how in the operation manual provided by the franchiser.) Thus, a special form of contract has evolved, which gives the franchiser great discretionary power to terminate the contract, and which increases the degree of specificity of the franchisee’s investment in the business (For instance, within 15 years after the termination of the contract, the franchisee is not allowed to engage in the engine oilchanging business within a certain territory.) Such clauses provide a mechanism of hostage, which significantly enhances transaction efficiency of intellectual properties of the franchiser. Use the model in this chapter to explain why this type of contract is essential for deepening the division of labor within the sector providing engine oil-change services, and between this sector and the rest of the economy. 2. Rosenbert and Birdzell (1986, pp. 163-65) provide historical evidence for endogenous comparative advantage and related endogenous productivity progress. According to data of trade and production during 1720-1900, not only British production responded to demand

132

from overseas market, but trade also stimulated productivity progress, which created more demand. Use the notion of general equilibrium and the model in this chapter to explain this historical fact. 3. According to E. Jones (1981, p. 267) and North (1981), trade based on exogenous comparative advantage prior to the Industrial Revolution generated endogenous comparative advantage and more trade. Design a model to formalize the interactions between endogenous and exogenous comparative advantages (see chapter 6). 4. Compare the Smithian model in this chapter with the neoclassical model based on the dichotomy between consumers and firms. 5. A businessman found that many managers of hotels and restaurants need popular music tapes for their customers, but they do not have time to keep track of the constantly changing tastes of customers for popular music. He then created a business to specialize in providing popular music tapes to managers. He specialized in identifying the most popular music and added a margin to the price of the tapes he had chosen and then sold them to the managers. His business became very successful. Use the model in this chapter to explain how the businessman created demand and supply for professional services by deepening division of labor. If you use neoclassical analysis of demand and supply to consider this case, how would you explain the demand and supply of music tapes? Why cannot that analysis predict created demand and supply based on an endogenous level of specialization and productivity, which is the most interesting feature of modern entrepreneurism and economic development? 6. When Lady Thatcher retired as Prime Minister of Britain, she was worried about whether her humble pension would be enough to support the very expensive life style to which she had been accustomed. She was approached by a company which specializes in cultivating public relations. The contract between her and the agent helped her to make so much money from public speaking throughout the world that she was able to earn much more than she made as Prime Minister. Explain why the division of labor between specialized agents and specialized movie stars, public figures, and singers occurs in the market place. Explain why many writers in New York use agencies to find publishers and to sign publication contracts for their commercial books on their behalf, while the division of labor between academic writers and specialized publication agents is not common. In particular, why do academics never use professional publication agents for submitting research papers to refereed journals on their behalf? 7. What are network effects of division of labor? What is the difference between network effects of division of labor and economies of scale? Why can we not understand demand and supply if we do not understand the network effects of division of labor? Chenery (1979) and Kuznets (1966) explain structural changes by increases in per capita income. Use the concept of network effect of division of labor to analyze interdependencies between structural changes and increases in per capita incomes and between the extent of the market and level of division of labor in connection to Chenery and Kuznets’ theory. 8. Before the 1830s, economists rarely used the concept of economies of scale. The notions they used were benefits and costs of specialization and division of labor, which relate, in essence, to the economies of interpersonal complementarity and the network effect of division of labor. At the end of the 19th century, the notion of economies of scale became popular. Use the model in this chapter to illustrate why coordination failure caused by economies of scale disappears if the notion of economies of scale is replaced by the notion of economies of specialization and division of labor. 9. Use the model in this chapter to explain why Allyn Young claimed that demand and supply are two sides of division of labor, and why we cannot understand what demand and supply are if we do not understand how individuals choose their levels and patterns of specialization. 10. Use the Wen theorem, which helps to keep inframarginal analysis tractable, to explain why, in the late 19th and 20th centuries, the analysis of demand and supply shifted from inframarginal

133

analysis of decision making in choosing a level of specialization which is essential for economic development to marginal analysis of resource allocation for a given level of specialization and productivity. 11. Why is the notion of general equilibrium a powerful vehicle for analyzing the development implications of the network effects of division of labor? What is the difference between the interdependence between quantities of goods chosen by individuals for given prices and the market equilibrium prices, and the interdependence between individuals’ decisions in choosing their levels of specialization? 12. In the models in this chapter, improvements in transaction conditions can generate evolution in division of labor. This evolution is associated with structural changes. For instance, the number of professional farmers (producing food x) in structure D is smaller than the number of all individuals producing x, which is the population size in autarky. If the general equilibrium jumps from autarky to D because of an improvement in transaction conditions, the resulting structural change appears to be a transfer of labor from the traditional agricultural sector to the industrial sector producing cloth y. Compare this equilibrium mechanism for economic development and structural changes with that in the theory of labor surplus of Lewis (1955) and Fei and Renis (1964). (According to the theory of labor surplus, as technology in the industrial sector exogenously changes or as capital accumulates, labor is transferred from the traditional agricultural sector to the industrial sector.) 13. Suppose a student raises a concern about coordination failure in utilizing the network effects of division of labor in the model in this chapter. She suggests that if there is no central planner, the market cannot select the Pareto optimum corner equilibrium from the multiple corner equilibria. Analyze the coordination mechanism in the marketplace and address her concern. 14. Use your daily experience to explain how the decentralized market coordinates individuals’ decisions in choosing occupation configurations and levels of specialization to utilize the network effect of division of labor. If economies of division of labor outweigh transaction costs, but nobody is willing to choose some occupation configuration, how can the market sort out the coordination problem? 15. Many individuals prefer occupation configurations of medical doctors, lawyers, and high executive positions in large companies to those of doormen, janitors, and garbage collectors. If all individuals refuse to choose occupations in the latter group, then coordination failure of division of labor occurs. How can the market sort out this coordination problem? In neoclassical marginal analysis, the function of free pricing in equilibriating demand and supply is used to explain how the market coordinates conflicting self-interested decisions. In addition to free pricing, our analysis in this text also emphasizes free choice of occupation configurations in coordinating the division of labor, and inframarginal analysis across occupation configurations in utilizing the network effects of division of labor. Discuss the implications of the difference between inframarginal analysis and marginal analysis of demand and supply. 16. Many development economists argue that due to network effects of industrial linkage, market failure will retard industrialization. Hence, a government policy to pursue big-push industrialization may overcome such coordination failure. Use the model in this chapter to analyze this view. 17. Network effect is a basic feature of division of labor. Smith and Young emphasized the function of the market in coordinating the network of division of labor, though they did not use the word “network.” Why did economists until recently pay no attention to this feature of the market and the function of the invisible hand in coordinating division of labor? Why was network effect not the focus of economics in the 19th century nor in most of the 20th century? 18. Some economists argue that inframarginal analysis of specialization is relevant only to the evolution of division of labor that occurred before the Industrial Revolution. They claim that in a modern economy, each individual is completely specialized and buys everything from the

134

market, so that the assumption of an exogenous level of specialization of individuals is acceptable. Comment on this view in connection with the following cases: (a) The emergence of CNN (the Cable News Network) is very much a modern phenomenon. According to the model in this chapter, an improvement in transaction efficiency (which might be caused by new telecommunication facilities) or a spontaneous evolution of division of labor will make commercially viable a higher level of division of labor between specialized media. The corner equilibrium that involves the finer division of labor between CNN (which specializes in reporting news through TV networks) and other media will be the general equilibrium. Whether or not the demand for and supply of CNN's professional services are "effective" depends on the general equilibrium level of division of labor, since demand and supply are two sides of the division of labor. But this in turn is determined by the efficient balance point between the economies of specialization and transaction costs. (b) The Wall Street Journal (“Manufacturers Use Supplies to Help Them Develop New Products,” December 19, 1994, p. 1; see also “Enterprise: How Entrepreneurs Are Reshaping the Economy and What Big Companies Can Learn?” Business Week, October 22, 1993, and “Management Focus,” The Economist, March 5, 1994) reported that each wave of mergers between modern corporations is associated with more specialization and division of labor. In particular, the latest wave of rationalization in the corporate sector has the characteristic that many companies have moved to separate some of their functions from their core business. Services that were once self-provided are now bought from more specialized suppliers. This phenomenon, variously called de-integration, down-sizing, outsourcing, contracting out, and focusing on core competencies in the business community, relates to evolution in division of labor. (c) The recent boom in franchise networks in the US (see question ?? in chapter 1). (d) The development of the market for the automatic toothbrush is a modern phenomenon, one that converts self-sufficient production and consumption of tooth brushing to specialized production of the automatic toothbrush and commercialized consumption. You may analyze the commercialization of the robot. If the production cost of robot has been significantly reduced so that each family can afford to use the robot for housekeeping. Then you may find that the income share of the commercialized housekeeping will be higher than the income share of food or automobiles. 19. Discuss why Young’s insights into the limitations of the concept of economies of scale were not formalized and taught in mainstream textbooks until recently. 20. Why cannot the Herfindahl index of specialization, which is the output share of the main industry of a city or a sector, reflect the level of division of labor of the city or sector? 21. According to Chandler (1990), the economic growth of the United States at the end of the 19th century and in the early 20th century was generated by economies of scale and economies of scope. Clarify this statement, using the concept of economies of division of labor that you have learned in this chapter. 22. Specialization has many adverse effects on human life. It can lead to boredom and to narrowing of the mind. It prevents full exploitation of economies of complementarity between different production activities. (For instance, teaching economics generates benefits for economic research.) Nevertheless, we observe that the level of specialization still increases, and companies increasingly use slogans like “We are professional” in their advertisements. Explain this phenomenon. 23. Some economists claim that economies of specialization represent a special case of economies of scale, since economies of specialization reflect economies of scale for an individual’s labor. Use what you have learned from this chapter to assess this statement.

135

Exercises 1.

2.

3.

4.

5.

6.

7. 8.

9.

Suppose a < 1 in the production functions (4.2). Draw the transformation curve for each individual, two individuals’ aggregate transformation curves for autarky, and for the division of labor in the x-y plane. Use the graphs to define diseconomies of division of labor. Assume that a = 1 in the production functions (4.2). In the x-y plane, draw the transformation curve for each individual, and the aggregate transformation curves for the respective cases of autarky and division of labor. Use the graphs to define constant returns to division of labor. Suppose a ≤ 1 for good x and a >1 for good y in the production functions (4.2). In the x-y plane, draw the transformation curve for each individual and the aggregate transformation curves for the respective cases of autarky and division of labor. Use the graphs to identify the condition under which economies of division of labor exist. Use exercise (3) to demonstrate the following propositions: (i) Economies of specialization in producing a good are neither necessary nor sufficient for the existence of economies of division of labor. (ii) Economies of division of labor cannot exist in the absence of economies of specialization in producing all goods. (iii) Economies of division of labor cannot exist if the diseconomies of specialization in producing x dominate the economies of specialization in producing y. (iv) Economies of division of labor must exist if economies of specialization exist in producing all goods. (v) Economies of division of labor exist if economies of specialization in producing good y dominate diseconomies of specialization in producing x. In this case, economies of specialization are external economies to the sector producing x. Show that external economies of specialization cannot exist if there are no economies of specialization in all sectors. Use your analysis to address the debate between Marshall, Young, and Young’s student Frank Knight. You will recall that Marshall argued that external economies of scale relate to the benefits of division of labor, that Young argued that the concept of economies of scale is a misrepresentation of that benefit, and that Knight argued that economies of scale that are external to all firms constitute an “empty box.” Assume that three individuals have the production system given in (4.2). Follow the method used in Fig. 4.1 to draw aggregate production schedules for autarky, for the case wherein two persons are not completely specialized, for the case in which one person is completely specialized, and for the case in which two persons are completely specialized. Consider production function x a y b = L , where a , b > 0, and L is the amount of labor used to produce goods x and y. Use the implicit function theorem to show that for a constant L, dy/dx < 0 and d 2 y / dx 2 > 0 , i.e., the transformation curve is convex to the origin. The production function has no definition at x = 0 and y = 0. Explain why this production function is not suitable for describing economies of specialization. Explain why the neoclassical Cobb-Douglas production function y = KaLb is not suitable for describing economies of specialization. Assume that the production functions in (4.2) are xp = Max{lx-a, 0} and yp = Max{ly-b, 0}. Draw an individual’s transformation curve and the two-persons’ aggregate production schedules for autarky and division of labor. Are there economies of division of labor if b = 0? Assume that the production functions in (4.2) are xp = Max{lxα-a, 0} and yp = Max{lyα-b, 0}. Draw an individual’s transformation curve and the two-persons’ aggregate production schedules for autarky and division of labor. Analyze the difference between the case with α

136

> 1 and the case with α < 1. Identify the condition for the existence of economies of division of labor. 10. (Becker 1981, Rosen 1983) An individual maximizes the difference between benefits and costs of learning. V = w1k1t+w2k2(1-t)-C(k1, k2) with respect to t, which is the time allocated to produce good 1, and ki, which is the learning and training level in activity i, where C is the total learning and training cost, 1-t is the amount of time allocated to produce good 2, and wi is a given benefit coefficient for activity i. Solve for two corner solutions with specialization and the interior solution with no specialization. Draw the distinction between technical complementarity (∂2C/∂k1∂k2 > 0) between two learning activities in producing two goods and social complementarity based on economies of specialization. Investigate the conditions under which economies of division of labor exist in the model with both technical and interpersonal complementarity. 11. Assume that the decision problem is the same as in examples 4.2 and 4.3, but that k = 1 and that the government taxes each dollar of goods sold at the rate t, then evenly distributes the tax revenue among the population. Solve for all corner solutions and identify the conditions under which each of them is the optimum decision. Use marginal and inframarginal comparative statics to analyze the effect of the tax. a b s s 12. Assume that the production functions in (4.2) are x + x = l x , y + y = l y , a ≠ b . Solve for equilibrium and its inframarginal comparative statics. 13. Assume that in exercise 12, k = 1 and the government taxes each dollar of good x that is

14.

15.

16.

17.

18.

19.

purchased, then evenly distributes the tax revenue among the buyers of good x. Use the marginal and inframarginal comparative statics to analyze the effect of the tax on demand and supply. Compare your answer to that of exercise 11. Consider the model in example 4.7. Identify the parameter subspace within which improvements in transaction conditions generate concurrence of deteriorated terms of trade of an occupation configuration and an increase in gains that an individual choosing this occupation receives from trade. (Lio 1998) Suppose that the utility and the production functions are the same as in (4.1). But there is a minimum consumption amount for good x, given by x + kxd ≥ x0, x0 ∈(0, 1-a). How many configurations must be considered? Solve for the corner solution for each of them. Suppose that in the equilibrium model in example 4.1, the production functions are xp = lx - a and yp = lx - b, and the utility function is u = (x+kxd)α(y+kyd)1-α where ip is the output level of good i. Solve for the general equilibrium and its inframarginal comparative statics. Suppose that in the equilibrium model in this chapter, the utility function is of the CES type and the time endowment constraint is lx + ly = 1 - c if an individual consumes one good, and is lx + ly = 1 - 2c if an individual consumes two goods. Solve for the general equilibrium and its inframarginal comparative statics. Assume that in example 4.1 the transaction efficiency coefficient for good i is ki and 1> kx > ky > 0. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the implications of the difference in transaction efficiency for the equilibrium relative price. Why is the effect of the difference in transaction efficiency different from the effect of the difference in tax rate on the equilibrium relative price? (Chu and Wang, 1998, Ng and Yang, 2000) Suppose that in exercise 16, α=0.5 and the production function of x is modified as xp = lx - a – s ∑yp where s is an externality parameter. This specification implies that there is a negative externality of production of y on production of x. Suppose that the government taxes sales of good y at the tax rate t, then returns the tax revenue to the buyers of y. Solve for the corner equilibrium for structure D, then solve for an individual’s utility value when she chooses specialization (or autarky) and all other individuals choose D (or A). Then solve for the corner equilibrium in a structure where the population is divided among autarky and specialization in x and y. Find general equilibrium

137

and its inframarginal comparative statics. Show that within a certain parameter space, Pareto improving Pigouvian tax does not exist. Use your answer to justify Coase's claim that Pigou's marginal analysis of effects of tax on the distortions caused by externality is misleading and inframarginal analysis is essential for the analysis of the distortions. 20. Work out the algebra for proving proposition 4.2. 21. Suppose that a = b = c in example 4.7, but the respective taste parameters for the three goods are α > β > γ, where α+β+γ=1. Solve for inframarginal comparative statics of general equilibrium.

138

Chapter 5: Driving Force III - Economies of Scale and Trading Efficiency 5.1. Economies of Scale and Economic Development When Marshall (1890) and other economists tried to formalize classical economics concerning development implications of division of labor, they could not find the analytical tools appropriate to well define division of labor. As discussed in chapter 3, the concept of level of division of labor is analogous to the concept of utility, which can be well defined only as a function of several variables. Level of division of labor is defined in chapter 3 as a function of all individuals’ levels of specialization and the diversity of occupation configurations. The notion of economies of division of labor is even more difficult to well define. Marshall used a one-dimension variable, the scale of a firm or a sector, to formalize the classical notion of division of labor. He was aware of the inappropriateness of the concept of economies of scale for representing the notion of economies of division of labor. He proposed a new concept of external economies of scale, and argued that external economies of scale are generated by division of labor in society as a whole rather than by the scale of a firm or a sector. 1 External economies of scale imply that a firm’s productivity increases as the size of the whole economy or of a sector increases. But according to Allyn Young (1928), Marshall’s concept of external economies of the scale is a misrepresentation of the classical concept of economies of division of labor. Since the end of the 1970s, there has been a revival of the thinking based on the concept of economies of scale, represented by Dixit and Stiglitz (1977), Ethier (1982), Krugman (1979), Judd (1985), Romer (1986, 1990), Grossman and Helpman (1989, 1990), and Murphy, Shleifer, and Vishny (MSV, 1989). Some of these works (such as some of Romer’s and Ethier’s models) follow Marshall’s idea about external economies of scale. But most of these works use the concepts of internal economies of scale and monopolistic competition. Internal economies of scale exist if a firm’s productivity increases as the size of the firm increases. Although the concept of economies of scale was considered misleading by Young, the research line built upon the concept of economies of scale has achieved relative success in explaining many development phenomena compared to the conventional development models with constant returns to scale. In the new development models, the trade off between economies of scale and benefits of a greater variety of goods is used to explain productivity progress in the absence of any exogenous technology changes. Due to the trade off, an increase in population size or in the size of the economy can enlarge 1

To defend Marshall’s concept of external economies, Young (1928) argued that in addition to preserving the observed compatibility between competition and increasing returns, Marshall proposed this concept because the benefits from social division of labor are not limited by the firm size. There are two reasons. First, a production process can be subdivided and performed by a number of different firms. Second, a further division of labor usually accompanies a further diversification of intermediate goods, and alters qualities as well as quantities of undertakings of the production process. The size of firm is too simple a variable to characterize changes in producers’ configurations.

140

the scope for trading off economies of scale against the variety of goods in the market, so that both the variety of goods and productivity may increase. In particular, Murphy, Shleifer, and Vishny (1989, 1991), Ciccone and Matsuyama (1996), and Matsuyama (1991) use this approach to analyze dual economy and industrialization. Their results, based on general equilibrium models with economies of scale and endogenous number of goods, are more powerful than labor surplus models and other general equilibrium models with constant returns to scale in explaining dual economy, structural changes, and industrialization. Recently, Yang (1994), Krugman and Venables (1995), Fujita and Krugman (1995), Baldwin and Venables (1995), Puga and Venables (1998), and Wong and Yang (1998) have introduced transaction costs into the general equilibrium models with economies of scale and endogenous number of goods. They show that the trade off between economies of scale, economies of complementarity, and transaction costs can be used to explain dual economy, structural changes, industrialization, urbanization, productivity progress, and other development phenomena in the absence of exogenous technical changes. Murphy, Shleifer, and Vishny (1989) have developed general equilibrium models with economies of scale to explore the implications of multiplicity of equilibria for formalizing the ideas on big push industrialization in the literature of high development economics. Kelly (1997) and Sachs and Yang (1999) have introduced transaction costs into the MurphyShleifer-Vishny (MSV) model to endogenize the number of modern versus traditional sectors. In this chapter, we study major models of these two types and compare them to conventional development models of dual structure, labor surplus, industrial linkage externality, and balanced vs. unbalanced industrialization. This family of new general equilibrium models of economic development will also be compared with models in chapter 4 in connection to empirical evidence. Section 5.2 uses a simplified version of the Dixit-Stiglitz model with transaction costs to demonstrate basic algebra and illustrate intuition. Section 5.3 uses the Ethier model with transaction costs to analyze structural changes, industrial linkage, and other development phenomena. Section 5.4 uses a version of the Murphy-Shleifer-Vishny model to analyze implications of multiple equilibria and economies of scale for big push industrialization. Section 5.5 uses the Sachs-Yang model with transaction costs to study the relationship between evolution in the degree of industrialization and economic development.

Questions to Ask Yourself When Reading This Chapter What are the differences between economies of scale and network effects of division of labor and the implications of the differences for studies of economic development? What are the differences among the model of labor surplus with constant returns to scale, the equilibrium models with economies of scale and endogenous number of goods, and the Smithian models with endogenous network size of division of labor? What are the relationships among circular causation, network effects of industrial linkage, big push industrialization, and the notion of general equilibrium? What are various scale effects and why are they rejected by empirical observations?

141

5.2. General Equilibrium Models of Economic Development with Trade offs Between Economies of Scale, Consumption Variety, and Transaction Costs The Dixit and Stiglitz (DS) model (1977) is a general equilibrium model that endogenizes the number of consumption goods on the basis of the trade off between economies of scale and consumption variety. The story behind this kind of model runs as follows. Consider an economy in which pure consumers prefer diverse consumption, while there are global economies of scale for pure producers (firms) in the production of each good. With the CES utility function, each good individually is not a necessity, so that the number of consumption goods is endogenized in equilibrium. A larger number of consumption goods, on the one hand, implies a higher level of direct utility because of the preference for diverse consumption; but on the other hand, the larger number may imply a lower level of indirect utility because of the higher prices of goods that are associated with smaller scales of production. The trade off between economies of scale and consumption variety can be used to endogenize the number of consumption goods. As the size of the economy is increased, the scope for trading off economies of scale against consumption variety is enlarged, so that the number of goods and per capita real income may increase concurrently. If the increase in the size of the economy is interpreted as the merging of two countries into an integrated market, or as the ad hoc opening of international trade between the two countries, then the comparative statics of the neoclassical general equilibrium can be used to explore the implications of international trade for productivity, welfare, and consumption variety. We now use the following graph to illustrate the story. Japan

US

Japan

(a) Two separate markets

US

(b) An integrated market

Figure 5.1: Economic Development Based on Economies of Scale In Fig. 5.1, there are two countries: Japan and the US. In each country, there are two individuals. Circles 1 and 2 represent two Japanese and circles 3 and 4 represent two Americans. In panel (a), there is no international trade between the two countries, and in

142

each country there are two firms producing goods x and y, respectively. Each of the two firms sells its produce to each and every domestic consumer and hires one worker. In panel (b), the two countries have merged to form an integrated market, where a Japanese firm sells good x to each and every consumer in both countries, an American firm sells good y to each and every consumer in both countries, and a multinational firm sells a new good z to each and every consumer in both countries. Firm x hires 4/3 Japanese, firm y hires 4/3 Americans, and firm z hires 2/3 Japanese and 2/3 Americans. Hence, the average size of the firm in panel (b) is larger than in panel (a). This implies that the productivity of each firm in panel (b) is higher than in panel (a) because of global economies of scale in production. Also, each consumer in panel (b) consumes three goods, while each consumer in panel (a) consumes only two goods. Hence, international trade may increase per capita real income through two possible channels. It may increase the number of consumption goods for each consumer, and it may improve productivity and thereby reduce prices of all goods through the utilization of economies of scale. 2 Gains from trade can arise between two ex ante identical countries in the absence of exogenous comparative advantage in technology and in endowments, and in the absence of differences in tastes between them. However, in order to realize those gains from trade, the two countries have to accept the shifting of workers between different sectors, which may cause temporary unemployment in the transitional period. For instance, a Japanese who in panel (a) produces good y before international trade is opened up will lose her job as a producer of good y, and will take a new job in producing good z or x after international trade is opened up in panel (b). Symmetrically, an American who produces good x before the opening of international trade will lose her job as a producer of good x, and will take a new job to produce good z or y after the opening of international trade. Suppose the government, or some interest group, does not want to see the emergence of the new sector or the associated reallocation of labor, because they generate temporary unemployment in the transitional period. If the Japanese government implements an interventionist policy to protect the firm producing good y from bankruptcy caused by international trade, or if an American interest group successfully lobbies Congress to implement a similar policy, then coordination failure in utilizing the gains from international trade will take place. The function of the market, and of a liberalization policy that allows the market to fully play its role, is to avoid such coordination failure. Example 5.1: The Dixit-Stiglitz model with the trade offs among economies of scale, consumption variety, and transaction costs. Consider an economy with M identical consumers. Each of them has the following neoclassical decision problem for consumption: (5.1)

Max: u = (∑ni=1xiρ)1/ρ s.t. ∑ ni=1 (1+t)pi xi =1

(utility function) (budget constraint)

2

Note that if production functions are homogeneous, then it is possible that the number of goods will not increase as the size of an economy increases. For this case, gains from trade come solely from the fall of prices of all goods. See exercise 6 at the end of this chapter.

143

where pi is the price of good i in terms of labor, xi is the amount of good i that is consumed, t is a transaction cost coefficient for goods purchased, n is the number of consumption goods, ρ∈(0, 1) is the parameter of elasticity of substitution between each pair of consumption goods, and u is utility level. To avoid an integer problem, which may render differentiation impossible, many writers assume that the set of goods is a continuum. If the set of goods is a continuum, all signs for summation should be understood as those for integration. If we take the first order condition for a continuous number of goods as a proxy for the first order condition for the integer programming in the model with goods 1, 2, …, m, the result based on our discrete specification is equivalent to that based on a continuum of goods. We may consider t as a consumption tax rate, and assume that all tax revenue is exhausted by the bureaucrats who collect the tax. It is assumed that each consumer is endowed with one unit of labor, which is the numeraire. Hence, each consumer’s income from selling one unit of labor is 1, her expenditure on good i is pi xi, and her total expenditure is ∑ ni=1 (1+t)pi xi. Each consumer is a price taker and her decision variable is xi. It is assumed that the elasticity of substitution 1/(1-ρ) > 1. It is easy to see that if the quantity of each good consumed is the same, then utility is an increasing function of the number of consumption goods, that is, u = (nxiρ)1/ρ and ∂u/∂n = (1/ρ)n(1-ρ)/ρxi > 0. We need the assumption ρ∈(0, 1), since for ρ < 0, which implies 1/(1-ρ) > 1, utility will be a decreasing function of the number of consumption, indicating that individuals do not prefer diverse consumption. If ρ > 1, it can be shown that the first order conditions for the optimum decisions and market clearing conditions will yield a negative number of goods (see (5.8)). The first order conditions for the consumer’s decision problem are: (5.2a) (5.2b)

(∂u/∂xi)/(∂u/∂xj) = pi/pj and ∑ ni=1 (1+t)pi xi =1

(5.2a) is the rule that relative marginal utility equals relative price, which implies the Gossen rule (i.e., the marginal utility of a dollar spent on different goods is the same) as well as the rule that the marginal rate of substitution equals the relative price. Concretely, (5.2a) is: pi xi = pj1/(1-ρ) xj pi -ρ/(1-ρ) Summing up the two sides of the equation with respect to i, and using the budget constraint (5.2b), yields: 1/(1+t) = ∑ i pi xi = pj1/(1-ρ) xj ∑ i pi

-ρ/(1-ρ)

From this equation, the demand function for good j can then be solved: (5.3)

xj = 1/(1+t)[pj1/(1-ρ)∑ipiρ/(ρ-1)] = 1/np(1+t)

where the second equality is obtained by using the symmetry condition pj =pi for all i, j = 1, 2, …, n. This can be expressed as: lnxj = -[lnpj/(1-ρ)]-ln∑ipiρ/(ρ-1)

144

Hence, the elasticity of demand for good j is: ∂lnxi/∂lnpj = -[1/(1-ρ)]-∂ln∑ipiρ/(ρ-1) /∂lnpj = -[1/(1-ρ)]- {[ρ/(ρ-1)]pj1/(1-ρ)/ ∑ipiρ/(ρ-1)} where ∑ipiρ/(ρ-1) includes one pj. Using the symmetry condition pj =pi for all i, j = 1, 2, … n again, we obtain the Yang-Heijdra (YH, 1992) formula for the own price elasticity of demand in the DS model: (5.4)

∂lnxi/∂lnpi = -[1/(1-ρ)]+[ρ/(1-ρ)n] = -(n-ρ)/(1-ρ)n.

Dixit-Stiglitz (1977) made an ad hoc assumption that the number of goods is infinitely large, and accordingly ignored the term ρ/(1-ρ)n, so that their expression for the elasticity is -1/(1-ρ). Their assumption is not legitimate, since the number of goods in this model is endogenous and is very large only for a certain range of parameter values. With their formula for the own price elasticity of demand, the negative effect of international trade on prices cannot be figured out. In exercise 6, you are asked to show that if the production function is homogeneous in the DS model, then the DS formula for own price elasticity of demand entails nonexistence of equilibrium. But if the YH formula is used, a well defined equilibrium exists for a particular parameter subspace. Next, we consider the pure producers’ decision problems. Because of global increasing returns to scale, only one firm can survive in the market for a good. If there are two firms producing the same good, one of them can always increase output to reduce price by utilizing further economies of scale, thereby driving the other firm out of the market. Therefore, the monopolist can manipulate the interaction between quantity and price to choose a profit-maximizing price. Freedom to produce new goods, however is assumed. This will drive to zero the profit of a marginal firm that has the lowest profit. Any positive profit of the marginal firm will invite a potential entrepreneur to set up a new firm to produce a differentiated good. For a symmetric model, this condition implies zero profit for all firms. This significantly simplifies the algebra and makes the DS model attractive. Assume that the production function of good j is: Xj = (Lj-a)/b, so that the labor cost function of good j is: (5.5)

L j = bX j + a

The first order condition for the monopolist to maximize profit with respect to output level and price implies that: MR = pj[1+1/(∂lnxi/∂lnpi)] = MC = b

145

where MR and MC stand for marginal revenue and marginal cost, respectively. Inserting the expression for the own price elasticity of demand ∂lnxi/∂lnpi, given in (5.4), into the first order condition yields: (5.6)

pj = b(n-ρ)/ρ(n-1).

The zero profit condition implies: (5.7)

p j X j = bX j + a .

The general equilibrium is given by (5.3a), (5.6), (5.7), and the market clearing condition Mx = X, which involve the unknowns p, n, x, X. Here, the subscripts of variables are skipped because of symmetry. Hence, the general equilibrium and its comparative statics are:

(5.8)

n = ρ+[M(1-ρ)/(1+t)a], dn/dM > 0, dn/dt < 0 p = bM/ρ[M-a(1+t)], dp/dM < 0, dp/dt > 0 x = ρ[M-a(1+t)]/bM[(1-ρ)M+(1+t)ρ], dx/dt < 0 X = Mx, dX/dM > 0, dX/dt < 0 u = ρ{[(1-ρ)M/(1+t)a]+ρ}(1-ρ)/ρ[M-a(1+t)]/bM(1+t), du/dM > 0, du/dt < 0.

It can be shown that the equilibrium labor productivity of each good is the reciprocal of the equilibrium price of each good. The comparative statics substantiate the story presented in the first part of this section, that is, the equilibrium number of consumption goods, productivity of each good, and per capita real income increase and the price of each good falls as the size of the economy increases or as the transaction cost coefficient falls. Now, let us compare the DS model with the neoclassical models with constant returns to scale and with the Smithian models in chapter 4. First, the DS model can generate gains from trade even if all countries are ex ante identical, or even if exogenous comparative advantage is absent. The gains from trade based on economies of scale are referred to by Helpman and Grossman (1991) as acquired comparative advantage. Hence, Krugman (1979) applies the DS model to explain the Linder pattern of trade, which suggests that trade volume between ex ante similar developed countries is much greater than that between ex ante different developed and less developed economies. The Linder pattern of trade is inconsistent with the neoclassical trade model with constant returns to scale and with exogenous comparative advantage, which predicts that trade volume is greater between ex ante different countries than between similar countries. Second, the DS model predicts that an increase in population size has positive effects on economic development because of economies of scale. This prediction is referred to as type I scale effect. Type I scale effect is consistent with the data of the early economic development of the US, Australia, and New Zealand, and with Hong Kong’s data after WWII. In contrast, Solow’s neoclassical growth model and other neoclassical models with constant returns to scale predict that an increase in population will have a negative impact on economic growth. This prediction is consistent with the data of many African countries

146

and with the pre-reform data in China and India. The National Research Council (1986) and Dasgupta (1995) reject the type I scale effect on the grounds of empirical evidence. The model can simultaneously explain the equilibrium number of goods and per capita real income by the size of an economy and transaction condition, and has more explaining power than many neoclassical models with a fixed number of goods. If we define the extent of the market as the product of per capita aggregate market demand for all goods and population size, then the DS model has endogenized the extent of the market. Since each pure consumer’s aggregate demand for all goods is determined by the number of goods, the DS model has endogenized the extent of the market by endogenizing the number of goods. Many economists use this feature of the DS model to explain aggregate demand and related macroeconomic phenomena. If we define the level of division of labor by each individual’s level of specialization, the number of traded goods in society, and the degree of production roundaboutness, then the DS model has endogenized one aspect of division of labor: the number of traded goods. However, it has not endogenized individuals’ levels of specialization and production roundaboutness. Let us examine the implications of the difference between the DS model and the Smithian model. Assume, in Fig. 5.1(a), that each of consumers 1 and 2 sells half her labor to each of the two Japanese firms. Since obviously, this implies that each individual is not specialized, we call this allocation of labor a pattern of nonspecialization. Suppose, alternatively, that each of the two consumers sells all her labor to a firm. Since now each individual is completely specialized, we call this allocation of labor a pattern of complete specialization. In the general equilibrium of the DS model, the two patterns of labor allocation generate the same values of all endogenous variables (relative prices, output levels, productivity of each good, and consumption of each good by each person), since the two patterns of division of labor generate the same scale of each firm. In other words, individuals’ levels of specialization in equilibrium are not well defined, so that individuals’ levels of specialization have no productivity implications. In this kind of models productivity is determined by the scale of firms rather than by individuals’ levels of specialization. Hence, the DS model cannot explain individuals’ levels of specialization by transaction efficiency. As a result, many interesting development phenomena that are explained by the Smithian models, such as evolution in division of labor and specialization and the emergence of the firm, money, and business cycles, cannot be predicted by the DS model. In the DS model, separate markets, as indicated in Fig. 5.1(a), can never exist in equilibrium if transaction conditions are the same between all individuals because of the positive effect of population size on per capita real income, and because of the fact that each pure consumer will buy all goods that are produced. Hence, the DS model cannot endogenize the degree of market integration. In contrast, Smithian models in examples 7.1 and 7.2 have endogenized the degree of market integration and the emergence of international trade from domestic trade. Therefore, the Smithian model is referred to by Smythe (1994) as endogenous trade theory. Moreover, the population size does not play an active and positive role in promoting productivity in a Smithian model, where productivity is determined by the level of division of labor, which is determined by transaction efficiency. Hence, high transaction efficiency, due to a good legal system, explains productivity progress in Hong Kong, the US, and Australia, where population growth passively provides more scope for evolution in division

147

of labor (i.e., the number of different occupations cannot exceed population size). The low transaction efficiency in pre-reform China and India and in some African countries explains the low per capita real income that coexists with a large population size. In a Smithian model, productivity progress and the emergence of new goods and technology in equilibrium can be achieved by the merging of many separate local communities into an increasingly more integrated network of division of labor, even if the population size is fixed. Hence, the Smithian model does not have a scale effect. Empirical evidence against the DS model is provided by Liu and Yang (2000), who show that productivity increases and the average size of firms decreases in many countries. In contrast, the DS model predicts that productivity goes up if and only if the average size of firms increases. This is referred to as type II scale effect. But the DS model may be extended to endogenize the degree of market integration by appropriately specifying a fixed transaction cost in setting up a trade connection or by specifying differences of transaction conditions between international and domestic trade, between countries, or between firms. Example 6.3 illustrates how this can be done. Ethier extends the DS model to endogenize the number of producer goods and productivity by specifying a trade off between economies of scale in producing producer goods and economies of complementarity between the producer goods in raising productivity of the final good. This kind of model can be used to explain dual economy and structural changes in economic development. The next section illustrates how this can be achieved.

5.3. The Ethier Model with Transaction Costs Before you become mired in the algebra and lose your capacity for economic thinking, let us first outline the story behind the model. There are two final consumption goods in an economy with M identical consumers. One of them is food that is produced by labor, with constant returns to scale technology. The other is a manufactured good that is produced from a composite producer good and labor, with constant returns to scale production function. The composite producer good is a CES function of quantities of many producer goods. There are economies of complementarity between the producer goods in raising productivity of the final manufactured good. Hence, total factor productivity of the final manufactured good is an increasing function of the number of producer goods employed. There are global economies of scale in producing each producer good. The markets for the two final goods are competitive, while the market for producer goods is monopolistically competitive. If transaction costs are introduced into the economy, there is a trade off between economies of scale and transaction costs, in addition to the trade off between economies of scale and economies of complementarity. As the population size increases, the scope for trading off one against others among economies of scale, economies of complementarity, and transaction costs is enlarged in the market. Hence, the number of producer goods increases, productivity of producer goods increases, and per capita real income increases. In particular, through the linkage between the final manufacturing sector and the intermediate sector, the labor price of the final manufactured goods declines, the total factor productivity of the manufactured good rises, and the relative output level of the manufacturing sector to the agricultural sector increases. Due to the trade off between economies of scale and transaction cost, improvements in

148

transaction conditions will generate a decrease in the labor price of the manufactured good and an increase in relative output of the manufacturing and agricultural sectors. The effects of an increase in population size on the general equilibrium productivity and relative output of the industrial and agricultural sectors are similar to development implications of labor surplus in the labor surplus model. However, an exogenous change in technology in the industrial sector and the ad hoc disequilibrium labor price are essential for structural changes in the labor surplus model. In contrast, in the Ethier model, structural changes can take place in the absence of any exogenous technical changes and of disequilibrium labor price. Compared to rough conjecture on the role of linkage between different sectors in economic development, the Ethier model explores the general equilibrium nature of economic linkage between the final manufacturing sector and the intermediate sector, as well as the implications of the linkage for economic development and structural changes. In many rough conjectures on the role of industrial linkages in industrialization (see, for instance, Rosenstein-Rodan 1943, Nurkse 1953), demand and supply of a sector depend on production conditions in another sector. The “external effects” of the linkage may be ignored by the market, or cannot be utilized because of coordination failure in a decentralized market. Hence, the government’s industrial policies may promote industrialization and economic development. In the general equilibrium model of this section, we shall show not only that demand and supply of each sector depend on demand and supply of each other sector, but also that prices and quantities are interdependent. In addition, there are infinite feedback loops between sectors, between prices and quantities, and between decisions of all players. The very function of the market is to transmit information about the interdependencies based on industrial linkages. The function of the market is much more powerful than we realize, and much more powerful than the government’s capacity to figure out the implications of the linkages. This prediction of the Ethier model is different from conventional wisdom related to debates on balanced vs. unbalanced industrialization. Some development economists argue that because of interdependencies of different industrial sectors, government policy should promote balanced and big push industrialization (see Lewis 1955, Nurkse 1953, Rosenstein-Rodan 1943, Scitovsky 1959, Thirwall 1994). Other development economists argue that because of the effects of linkage, a policy to promote unbalanced industrialization should be adopted (see Streeten 1959, Hirschman 1958). If we interpret the increase in productivity and in the number of industrial sectors as industrialization, then the Ethier model shows that the essential conditions for successful industrialization are a large population size in an integrated world market and favorable transaction conditions. These conditions can be provided through liberalization, internalization, and open-door policies. If transaction conditions are unfavorable and the population size in the integrated world market is small, then the equilibrium productivity is low and the number of professional industrial sectors is small, because of the trade offs between economies of scale, economies of linkage complementarity, and transaction costs. According to this model, many conventional industrial policies that manipulate industrial structure via increasing transaction costs are detrimental to economic development. Example 5.2: The Ethier model with endogenous number of producer goods and transaction costs.

149

Consider an economy with M identical consumers. A representative consumer's decision problem is: (5.9)

Max: u = (tz)1-α (ky)α s.t. pyy+pzz = 1

where u is a consumer's utility level, z is the quantity of the agricultural good consumed (such as food), z is the quantity of the manufactured consumption good (such as a car), and k and t are respective transaction efficiency coefficients of the agricultural and manufactured goods. Each consumer is endowed with one unit of labor, which is the numeraire. The size of the labor force (which is the population size as well) is M and the price of good i in terms of labor is pi. The demand functions for the two goods are: (5.10)

Yd = Myd,

yd = α/py,

Zd = Mzd,

zd = (1-α)/pz

where Zd and Yd are respective market demand and zd and yd are respective individual demand for the two goods. A representative firm of food maximizes the following profit subject to a given set of prices of goods and factors and a production function with constant returns to scale: (5.11)

Max: πy = pyYs-Lyd,

s.t. Ys = ALyd

where Ys is the output level of y, and Lyd is the amount of labor allocated to the production of food. The equilibrium conditions in the market for z are: (5.12)

(zero profit condition for good z) py* = 1/A Y* = Ys = Yd = αAM (equilibrium quantity of z) d Ly = αM (equilibrium quantity of labor employed to produce z)

where Ys is market supply, which is determined by market demand Yd, Y* is the equilibrium quantity of good y, Lyd is the equilibrium quantity of labor employed to produce y, and py* is the equilibrium labor price of good y. A representative car manufacturer maximizes the following profit, subject to a given set of prices of goods and factors and a production function displaying constant returns to scale and economies of complementarity between different producer goods employed to produce cars: (5.13)

Max: πz = pzZ - ∑i=1n pixi-Lz,

s.t. Z = [∑i=1n(kxi )ρ]β/ρLz1-β

where k is the transaction efficiency coefficient of each producer good, xi can be considered as all kinds of professional machine tools, and the elasticity of substitution 1/(1-ρ) is assumed to be larger than one, that is, ρ∈(0,1). Since the total factor productivity of z increases with the number of specialized machine tools n, this production function displays economies of complementarity between producer goods employed to produce z. The elasticity of substitution increases with ρ and the degree of economies of complementarity between different producer goods inversely relates to the elasticity of substitution. Hence, 1/ρ can be interpreted as the degree of economies of complementarity. For the decision

150

problem with constant returns to scale, only two of the zero profit condition and the two first order conditions for xi and Lz are independent. We can use the two first order conditions, ∂πz/∂Lz = ∂πz/∂xi = 0, to establish the connection between the quantity of labor demanded and the quantity of x demanded. (5.14)

Lzd = (1-β)pxnx/β

where the symmetry of the model is used. Using the zero profit condition in producing z and (5.14), we can obtain an expression of pzZ in terms of pxx. (5.15)

pzZ = pxnx/β

Using the production function of z and (5.14), we can obtain another expression of pzZ (5.16)

pzZ = pznβ(1-ρ)/ρ (kx)β[(1-β)pxnx/β]1-β

Let the two expressions be equal. We can then establish a connection between the equilibrium prices of z and x. (5.17)

pz = pxβ/ nβ(1-ρ)/ρ(1-β)1-β(kβ)β

If this condition is not satisfied, then the firm will either not produce z or demand an infinitely great amount of labor, which is incompatible with equilibrium due to limited supply of labor. Using (5.15) and the demand function for y in (5.10), we have: (5.18)

pxnx =β(1-α)M

where M is the population size. The firm selling producer good i maximizes the following profit with respect to the price and quantity of good i, subject to a given production function with global economies of scale: (5.19)

Max: πix = piXi - Lix,

s.t. Xi = (Lix-a)/b, or Lix = a+bXi

where Xi is the quantity of good i supplied by the monopolist and Lix is the amount of labor hired by the firm producing good i. All decision problems for firms selling other n-1 producer goods are symmetric to (5.19). Due to the complete symmetry of the model, we will skip subscript i when no confusion is caused. The market for producer goods is monopolistically competitive. Using Yang-Heijdra's formula in (5.4), the own price elasticity of the demand for producer good i is: E ≡ ∂logxi/∂logpi = -(n-ρ)/(1-ρ)n. The first order condition MR = MC for a producer of a producer good yields MR = px[1+(1/E)] = b = MC, or:

151

(5.20)

px = (n-ρ)b/(n-1)ρ.

This, together with the zero profit condition AC = [(a/X)+b] = px, yields: (5.21)

nX = (n-1)ρa/b(1-ρ).

Letting x in (5.18) equal X in (5.21), the two equations yield: (5.22)

px = β(1-α)(1-ρ)bM/a(n-1)ρ.

(5.20) and (5.22) imply: (5.23)

n = ρ+β(1-α)(1-ρ)M/a .

Inserting (5.23) back into (5.22) yields the equilibrium value of px. Plugging this value into (5.17) yields the equilibrium labor price of z. Differentiating this expression of the equilibrium price of z with respect k and M, respectively, we have: (5.24)

dpz/dM < 0 and dpz/dk < 0.

We are interested in the effects of changes in the population size M and transaction efficiency k on the number of producer goods n, prices of goods, relative size of the manufacturing and agricultural sector, productivity, and per capita real income. Let us use (5.10) - (5.24) to work out the equilibrium expressions of the variables: (5.25)

n = ρ+β(1-α)(1-ρ)bM/a, Rzy = Y/Z = (1-α)/αApz, TFPz = nβ/ρ, LPy= A, px = β(1-α)bM/ρ[ bMβ(1-ρ)(1-α)-a], LPx = X/(a+bX) = ρ(n-1)/b(n-ρ) = ρ[β(1-ρ)(1-α)M-a]/β(1-α)bM, u = (αtA)α[k(1-α)/pz1-α

where TFPz is the total factor productivity of good y, LPj is the labor productivity of producer good j, Rzy is relative output level of final manufactured goods and agricultural good, and u is equilibrium per capita real income (i.e., utility). The comparative statics of the equilibrium are summarized as follows: (5.26a) (5.26b) (5.26c) (5.26d) (5.26e) (5.26f) (5.26g)

dpx/dM < 0, dpz/dM < 0, dpz/dk < 0, dpy/dM = 0, dn/dM > 0, dTFPz/dM = (dTFPz/dn)(dn/dM) > 0, dLPx/dM > 0, dRzy /dM = (dRzy/dpz)(dpz/dM) > 0, dRzy /dk = (dRzy /dpz)(dpz/dM) > 0, du/dM = (du/dpz)(dpz/dM) > 0, du/dk = (∂u/∂pz)(dpz/dk) + (∂u/∂k) > 0,

152

where (5.26d) is used to derive (5.26e), and (5.26b) is from (5.24) and is used to derive (5.26f) and (5.26g). (5.26) yields the following proposition. Proposition 5.1: The equilibrium labor prices of the industrial goods (y and x) decrease, the equilibrium total factor productivity of the manufactured good and labor productivity of producer goods increase, the equilibrium relative output level of the industrial and agricultural sectors increases, and the equilibrium level of per capita real income increases as the population size increases. The labor price of the manufactured good decreases, and relative output level of the industrial and agricultural sectors and per capita real income increase as transaction efficiency of industrial goods is improved. If we interpret the increase in the number of producer goods and related productivity progress and emergence of new goods as industrialization, the model is more powerful than conventional development models in explaining economic development, industrialization, and related structural changes. It can predict the following concurrent phenomena of economic development as transaction conditions are improved or as the population size in the integrated world market increases. Productivity of the final manufactured goods and intermediate goods increases, the number of producer goods increases as new producer goods emerge, relative output of the industrial and agricultural sectors increases, relative price of the industrial and agricultural goods decreases, and per capita real income increases. According to this model, the best policy to promote industrialization and economic development is to pursue liberalization, internalization, and openness, which improve transaction conditions, reduce trade barriers, and increase the population size in the integrated world market. The topological properties of linkage network in the Ethier model cannot be appreciated from standard graphs of demand and supply curves. Hence, we use Fig. 5.2 to highlight economic development and structural changes predicted by the Ethier model. In Fig. 5.2., each circle with xi represents workers producing a producer good, a circle with z represents farmers producing the agricultural good, a circle with y represents workers producing the final manufactured good, thin lines represent goods flows, and thick lines represent the path of structural change in economic development caused by an increase in population size in the integrated world market or by improvements in transaction conditions. From the graphs and the specification of the model, it is clear that the whole economy is always integrated and each individual's level of specialization is not endogenized.

(a) n = 2

(b) n = 3

153

(c) n = 4

Figure 5.2: Structural Changes, Industrialization, and Economic Development in the Ethier Model This model cannot explain the following development phenomena. From (5.12), (5.15), and (5.18), it can be shown that income shares of the final manufacturing sector, the intermediate sector, and agricultural sector in terms of value of labor are (1-α)(1-β), (1-α)β, and α, respectively. They are independent of transaction condition, population size, and production conditions. Hence, the transfer process of labor from the agricultural sector to the industrial sector as an aspect of industrialization cannot be predicted by the model in the absence of changes of relative tastes. Note that relative physical output Rzy in (5.25) and (5.26) is different from relative value and relative employment. The former can be explained by transaction conditions and population size, but the latter does not change in the absence of exogenous changes in relative tastes in the model. More importantly, the equilibrium degree of market integration, individuals’ levels of specialization, and the degree of commercialization never change in this model. Similar to the DS model, this model generates type I scale effect that is rejected by empirical evidence. Casual observations indicate that there are increasing returns to specialization and division of labor in the agricultural sector. The level of division of labor in the agricultural sector evolves over time, although this evolution is slower than in the industrial sector. It is ad hoc to assume that agricultural production does not have increasing returns and cannot use roundabout productive machines and tractors. Hence, the model in this section does not provide a convincing description of a mechanism for economic development. It has a higher degree of endogenization than do the conventional development models, but it cannot formalize Smith’s conjecture about the intimate relationship between an increase in income share of the industrial sector and evolution of division of labor. According to Smith, this increase is not caused by relative taste change or by exogenous technical changes. Rather, it is caused by a faster evolution of division of labor in the industrial sector, which has lower transaction costs and seasonal coordination costs than does the agricultural sector. We will formalize this conjecture in chapter 12.

5.4. The Murphy-Shleifer-Vishny (MSV) Model of Big Push Industrialization Murphy, Shleifer, and Vishny (1989) are among economists who have first realized the implications of the equilibrium model with global economies of scale for exploring the coordination problem in industrialization process that concerns Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), and others. Their model of big push industrialization has two distinct features: (a) Each good can be produced using either a cottage technology with constant returns to scale or a modern technology with a fixed cost that generates global economies of scale. This implies that the price of any good is determined by the zero profit condition for the cottage firm, so that prices cannot transmit information of modern firms’ production conditions to consumers. This misinformation of price signals may generate distortions. (b) All firms choosing modern technology make a decision on entry into the production for other given modern firms' entry decisions. Two equilibria may coexist. In one of them, all modern firms are active, so that their profit creates income of owners that can sustain the market for goods produced by

154

all modern firms. In the other, all modern firms are inactive, so that income from zero profit cannot support a sufficiently large market for any good produced by a single modern firm. Hence, staying out the market is the optimum decision for each modern firm. In other words, the expectation of others' decisions is self-fulfilled. Example 5.3: The Murphy-Shleifer-Vishny model of big-push industrialization. There is a continuum of goods with mass 1. Two types of production functions are available to any firm in producing each good. Xj = Lj is a traditional technology in producing good j. Xj = (Lj-F)/b is a modern technology in producing good j, where Xj is the output level and Lj is the amount of labor employed in producing good j. F is a fixed production cost and b is a variable labor cost in producing a good. A worker in a cottage firm has the decision problem: Max: um = exp[∫01lnx(q)dq] subject to the budget constraint ∫01p(q) x(q)dq = yc = (Π/L)+wc, where each consumer is endowed with one unit of labor, yc is a cottage worker’s income, and wc is her wage rate. Assume that the cottage worker’s labor is the numeraire, so that wc = 1. Π is the total dividend, which equals the total profit of n modern firms. It is assumed that ownership of each and every firms is equally distributed among the population. Here, n∈[0, 1] and Π = nπ, where π is each active modern firm's profit. The population size is assumed to be L. The decision problem for a worker in a modern firm is: Max: uc = exp[∫01lnx(q)dq]-v, subject to the budget constraint ∫01p(q) x(q)dq = ym = (Π/L)+w, where ym is a modern worker’s income and w is her wage rate relative to a cottage worker’s wage rate, and v is a utility loss when one works in the modern sector. The two utility maximization problems generate indirect utility functions for the two types of workers. Let the indirect utility functions be equal. We can then obtain equation (6) in MSV (1989, p. 1011). Hence, we have: w = 1+v,

yc = (Π/L)+1,

ym = (Π/L)+w.

Let the amount of labor allocated to a modern firm be Lm. The amount of labor allocated to the cottage production is then Lc = L-nLm, where L is total labor supply or population size. Demand function for each good is: x = y/p = y = Lcyc+ nLmym . Because of constant returns to scale for a cottage firm and free entry for any cottage firm into the production of any good, an active cottage firm receives zero profit, and the price of any good in terms of cottage worker's wage rate is p = 1. A modern firm maximizes: π = px – wLm = y(α-1-v)-F(1+v) = (Lm – F)(α-1-v)-F(1+v),

155

where p = 1, x = α(Lm – F) is the production function, x = y is aggregate demand for the good produced by a modern firm, and w = 1+v, y is aggregate income. This is equation (6) in MSV (1989, p. 1012). To see the feedback loop between profit, income, demand, and production, note that y = Lcyc+ nLmym = Lc[(πn/L)+1]+ nLm[(πn/L)+w] = L+πn+nLmv. This implies that income depends on profit, while the above expression of profit suggests that profit depends on demand, which is in turn determined by income. The following features of the MSV model differentiate it from other equilibrium models with global economies of scale and monopolistic competition. In the MSV model, global economies of scale in a modern sector imply that each active modern firm is a monopolist. But this monopolist takes the price of its produce as given because of the existence of a competitive fringe of firms. In the MSV model, there are infinite equilibria within a certain parameter subspace. If all other modern firms choose not to produce, a modern firm's optimum decision is not to produce. Hence, no industrialization is an equilibrium. If all other modern firms choose to operate, a modern firm's optimum decision is to operate. This is another equilibrium of complete industrialization. Finally there is a zero profit equilibrium in which a measure of modern firms n ∈(0, 1) produce positive quantities of their goods. Since which firms produce and which do not in any of this kind of zero profit equilibrium is indeterminate and the number of firms is a continuum, there are infinite equilibria. We now consider the three types of equilibria one by one. Suppose that Lm= 0 and n = 0 (i.e., no industrialization), so that each consumer receives one unit of income and y = L. Hence, profit is negative if and only if: (5.27)

L < Fα(1+v)/(α-1-v).

This implies that if (5.27) holds, any individual modern firm that unilaterally industrializes receives negative profit, provided all other modern firms are not active. Hence, the equilibrium is n = 0 (no industrialization) if (5.27) holds. If all modern firms produce, then nLm= L, Lc = 0, n = 1, and the profit becomes: π = px – wLm = α(L-F)-L(1+v) which is positive, if and only if L > Fα/(α-1-v). This implies that for n = 1 (i.e., complete industrialization), any individual modern firm's profit is positive if L > Fα/(α-1-v). But there is no more room for further industrialization, because the upper bound of n is 1. Therefore, for L ∈ (Fα/(α-1-v), Fα(1+v)/(α-1-v)), there are at least two equilibria. One of them is n = 0 and π = 0, and the other is n = 1 and π > 0. Since the equilibrium prices of all goods are the same between the two equilibria, but per capita income is higher in complete industrialization than in the equilibrium with nonindustrialization, it can be shown that for L ∈ (Fα/(α-1-v), Fα(1+v)/(α-1-v)), the equilibrium with n = 1 is Pareto superior to the equilibrium with n = 0. Indeed, there are many other equilibria that generate zero profit for all firms. Letting the profit equal 0 yields: (5.28)

Lm = Fα/(α-1-v).

156

Using the labor market clearing condition Lc + nLm = L, we can find: (5.29)

Lc = [(α-1-v)L - Fnα]/(α-1-v).

Inserting Lm, given by (5.28), into the production function for a modern firm x = α(Lm-F) yields the quantity supplied by the modern firm. Inserting (5.28) and (5.29) into the demand function for a good, x = y = Lcyc + nLmym, we can get the quantity demanded, where yc = (Π/L)+1 = 1 and ym = (Π/L)+(1+v) = 1+v. Letting demand equal supply, we can find the zero profit equilibrium: n = [(1+v)/v]-[(α-1-v)L/vFα], which is between 0 and 1 if L ∈ (Fα/(α-1-v), Fα(1+v)/(α-1-v)). The zero profit equilibrium generates the same welfare as in the equilibrium of non-industrialization, since the cottage worker receives the same utility in the two equilibria and utility is equalized between the two types of workers in the zero profit equilibrium. The existence of the multiple equilibria can be used to tell the story of big push industrialization. Murphy, Shleifer, and Vishny suggest that if the government coordinates simultaneous investment in all modern sectors, the development trap (i.e., bad equilibrium) can be avoided. This model does not suggest the necessity of government intervention. It implies that the theory cannot predict which equilibrium will occur. If the good equilibrium occurs, government intervention is not needed. It cannot explain why the bad equilibrium has occurred in some African countries and the good one occurred in Britain, which reduced government regulations in the 18th century. The possibility for the Pareto inefficient equilibrium to occur is due to the misinformation of price signals in this model. The equilibrium price is determined by the zero profit condition of cottage firms, so that it cannot transmit information of production conditions of the modern firms to consumers. Hence, consumers may allocate too much of their income to buy goods produced by cottage firms. If the population size is large enough to overcome the misinformation or if L > Fα(1+v)/(α-1-v), then government intervention is not needed, since unique good equilibrium is n = 1 for that case. As population size increases from a low level to reach the threshold value Fα/(α-1-v), the equilibrium degree of industrialization may discontinuously jump from n = 0 to n = 1 (i.e., big push industrialization). Consider the parameter subspace L ∈ (Fα/(α-1-v), Fα(1+v)/(α-1-v)), within which there are multiple equilibria. This kind of multiple equilibria and associated inefficiencies is substantially different from the coordination problems in the prisoners' dilemma or in other models with interest conflicts of decision makers. (See chapters 3 and 9 for models with interest conflicts that generate endogenous transaction costs.) Here, there is no interest conflict between self-interested decisions. Nobody benefits from a bad equilibrium. Nobody suffers, and all consumers and modern firms gain, from a good equilibrium. Hence, a cheap talk between entrepreneurs in an industrial association is enough to sort out the coordination problem. Hence, the government's job is to ensure free association, so that such cheap talk can spontaneously occur. There are many other ways to avoid multiplicity of equilibria. If a modern firm can differentiate its produce from that produced by a cottage firm, the misinformation of price signals can be avoided, so that multiplicity of equilibria may also be avoided. Second, the

157

number of active modern sectors is not endogenized in the MSV model. If that number is endogenized by specifying the trade off between economies of scale and transaction costs, multiplicity of equilibrium may be avoided. Murphy, Shleifer, and Vishny (1989, p. 1003) suggest that transaction cost may be a cause of the development trap. Kelly introduces transaction costs into the MSV model and uses the zero profit condition to endogenize the number of active modern sectors and the degree of market integration. But because of the zero profit condition, consumers cannot obtain information from the feedback loop between positive dividend earnings and economies of scale. Hence, consumers' utility will not increase as the number of active modern sectors increases. In other words, benefits from industrialization are completely eaten up by transaction costs. Sachs and Yang (1999) have devised a method to specify the zero profit condition for the marginal modern firm and to keep positive profits for other active modern firms. This can endogenize the number of active modern sectors, while keeping the original flavor of the feedback loop between dividend earnings and economies of scale that can be exploited in the MSV model. 5.5. The Sachs and Yang Model with Economies of Scale, Endogenous Degree of Industrialization, and Transaction Costs Example 5.4: The Sachs and Yang Model (1999). Following MSV, we assume that the set of consumption goods produced by the industrial sector is a continuum with mass m. Each of L consumer-worker-owners has the same CES utility function. Her decision problem is: Max: u = [∫0m x(j)ρdj]1/ρ, s.t. ∫0m p(j)x(j)dj = I = (π+w) where j∈[0, m] is an industrial good, x(j) is the quantity of good j consumed, and p(j) is the price of good j. Each consumer endowed with one unit of labor has income I, which consists of dividend earning π and wage income w. Labor is assumed to be the numeraire, so that w = 1. Ownership of all firms is equally shared by all consumers. As in the MSV model, p(j) = 1 for all j in equilibrium. Hence, the optimum quantity demanded of good j is the same for all j. Using the symmetry, the solution to the consumer’s decision problem can be found as follows: x = I/m. The total market demand is: (5.30)

Xd = IL/m = (Π+L)/m,

Π = πL,

where Π is total dividend earning, which is equal to total profit. We now consider the production of x. For each industrial good, there are two available technologies. The modern one exhibits economies of scale, and the traditional one displays constant returns to scale.

158

Because of the existence of the traditional technology, the labor prices of all industrial goods are always 1, so that the quantity demanded is the same for all industrial goods. The production function of the modern sector producing good j is: (5.31)

xj = (Lj-Fj)/b ,

F0 = δ, Fj = γj > δ for j ∈ (0, m]

where xj is the quantity supplied, Lj is the amount of labor allocated to the production of the industrial good, and Fj is the fixed production cost of good j. We assume that the fixed cost differs across modern sectors and that the industrial goods are indexed according to their fixed costs. Industrial good 0 has the smallest fixed cost δ, which is a very small positive number, industrial good m has the largest fixed cost γm, and for j ∈ (0, m], Fj = γj ∈ (δ, γm]. Here, γ can be considered as a general production condition parameter. As γ decreases, the fixed costs for any modern sector j decrease. A large value of Fj implies that the modern sector j needs a high investment in fixed costs before a positive output can be produced. Hence, index j can be considered as an index of capital intensity of the modern sectors. We assume further that there is a variable transaction cost for each modern firm. The transaction condition differs across countries. The transaction cost incurred by a modern firm in country i is: (5.32)

Ci = cixj,

c1 = s,

ci = μi > s for i = 2, 3, …, M,

where i = 1, 2, …, M is an index of countries, s, a very small positive number, is the transaction cost coefficient for country 1, and xj is the output level of modern sector j, which is the same in any country and in any sector, as we have shown. The specification implies that two factors determine the transaction cost coefficient: a general transaction condition μ, and a country-specific transaction condition represented by index i. For a larger i, the transaction cost coefficient ci is larger. A country's geographical condition and institutional and cultural tradition determine its ranking index i. For any given i, the transaction cost coefficient ci decreases as μ decreases. A decrease in μ can be caused by worldwide changes in transportation technology or institutions. We may consider country 1 as the most developed country and country M as the most underdeveloped country. The profit of firm j in country i is: (5.33)

πij = xj -Lj-cixj = (1-μi-b)xj-γj

where xj = Xd/(1-ci) is determined by the market clearing conditioin and demand function given in (5.30). Total dividend earning is equal to total profit of n active modern firms: (5.34)

Π = ∫0nπijdj

where n ∈[0, m] is endogenously determined. Plugging this expression for total dividend earning into (5.30), total market demand for the good produced by modern firm j can be found as: (5.35)

xj = (Π+L)/m 159

where the number of all industrial goods is m, and the number of active traditional sectors is m–n. (5.33) - (5.35) nicely captures the feedback loop between income, demand, and production conditions. It also captures the idea of big push industrialization. If the transaction cost is 0, then as more modern firms operate (i.e., n increases), dividend earning and income increase and demand increases, which makes more modern firms profitable. Hence, as population size reaches a threshold level, the equilibrium number of modern sectors, n, jumps from 0 to its upper bound m. But in our model, transaction costs counteract the positive feedback between the extent of the market and economies of scale that can be exploited, so that industrialization may occur gradually as the transaction conditions are improved. Inserting (5.35) into (5.33), then inserting the resulting expression into (5.34), we can conduct integration and then express total income Π+L as a function of n: (5.36)

Π+L = (L-0.5γn2)m/[m-αn(1-b-μi)]

where L-0.5γn2 > 0 and m-αn(1-b-μi)] > 0 are required by positive income. We now consider the zero profit condition for the most capital-intensive active modern sector n. Letting j equal n in (5.33) and πn = 0, we get the zero profit condition, πn = (1-b-μi)xj-γn = 0. Inserting the demand function, given in (5.35), into the zero profit condition for the marginal active modern firm generates another expression of Π+L: (5.37)

Π+L = γmn/(1-b-μi)

where 1-b-μi > 0 is required by positive income. (5.36) and (5.37) together generate the following equation, which gives the equilibrium number of active modern firms n as a function of parameters γ, μ, L, b, i. (5.38)

f (n, α, γ, μ, L, b, i) = An2-bn+D = 0

where A ≡ 0.5αγ[1-b/(1-μi)], B ≡ γm, D ≡ αL[1-b/(1-μi)] are positive. The graph of this quadratic equation of n in the first and fourth quadrants of the n-f coordinates is a convex curve cutting the vertical axis above the horizontal axis, since f(0) = D > 0, f ' (0) = -B < 0, f ''(n) = 2A > 0. The unique minimum point n = B/2A > 0 of this curve is given by f '(n) = 0. Hence, this curve may have two cutting points on the right half horizontal axis, which defines two equilibria, given by f(n*) = 0. The two solutions of f(n) = 0 are called n1 and n2, respectively, with n2 > n1. Hence, we can see that f ' (n1) < 0 and f ' (n2) > 0 for a convex curve with the unique minimum point that is below the horizontal axis. But we can show that for a positive income, ∂f/∂n = (α/n)[1-b/(1-μi)](0.5γn2-L) < 0 must hold, since positive income in (5.36) requires 1-b/(1-μi) > 0 and 0.5γn2-L 0,

dn/dμ = -(∂f/∂μ)/(∂f/∂n) < 0, 160

dn/db = -(∂f/∂b)/(∂f/∂n) < 0,

dn/di = -(∂f/∂i)/(∂f/∂n) < 0

where ∂f/∂n = (α/n)[1-b/(1-μi)](0.5γn2-L) < 0and ∂f/∂γ < 0 if (5.38) holds, ∂f/∂b, df/di, ∂f/∂μ < 0, ∂f/∂L > 0. (5.39) implies that there is substitution between transaction conditions and population size in promoting industrialization. For a given μ, a larger population size generates a higher degree of industrialization. For a given L, better general transaction conditions generate a higher degree of industrialization. dn/di < 0 implies that the degree of industrialization is lower for a country with the larger transaction cost coefficient, which implies a larger i. This implies that a large country may have a low degree of industrialization if its transaction conditions are very bad. The general equilibrium in country i is summarized as follows: (5.40)

px = 1, Xd = α(Π+L)/m, Lx = ∫0n{[bα(Π+L)/(1-c)m]+γj}dj = [bα(Π+L)n/(1-c)m]+0.5γn2 R ≡ Lx/L, u = mα(1-ρ)/ραα[θ(1-α)]1-α[(Π/L)+1], (Π/L)+1 = γmn (1-μi)/α(1-b-μi)L, and n is given by (5.38)

where u is per capita real income (i.e., equilibrium utility level), (Π/L)+1 is per capita income in terms of labor, Lx is the amount of labor allocated to all active modern firms, and R ≡ Lx/L is the income share of the modern sector. Differentiating u in (5.40) and using (5.38) and (5.39), it can be shown that: du/dL > 0, and du/dμ < 0, dR/dL > 0, dR/dμ < 0, dn/dL > 0, dn/dμ < 0, dn/db < 0, d(m-n)/dL = -dn/dL < 0, d(m-n)/dμ = -dn/dμ > 0. It is straightforward that the number of active traditional sectors m-n decreases as the population size increases and/or as transaction conditions are improved. Hence, the duality of economic structure is endogenized. The comparative statics can be summarized in the following proposition. Proposition 5.2: As population size increases and/or as general transaction conditions are improved, the equilibrium number of active modern sectors, the degree of capital intensity of active modern firms, productivity, and per capita real income increase. For a given general transaction condition and population size, the country with the better country-specific transaction condition has a higher degree of industrialization than do other countries. Suppose general transaction conditions are very bad in the initial time. Then no modern firm operates in any country. As time goes by, general transaction conditions are improved, so that some modern firms operate in the country with the smallest transaction cost coefficient c1 = s. But other countries are not industrialized. As general transaction conditions are further improved, those countries with a slightly larger transaction cost coefficient start industrializing, and the number of active modern firms in each of the industrializing countries increases. As general transaction conditions are further improved, those countries with the worse transaction conditions are eventually industrialized. This process goes on until all countries and all sectors in each country are industrialized. 161

In this model, not only each modern firm's decision to be active depends on the number of active modern firms, but the equilibrium number of active modern firms is also determined by such decisions. The general equilibrium mechanism simultaneously determines the interdependent variables. Sachs and Yang (1999) have extended this model to the case with many countries. They have shown that not only each country's decision to participate in international trade is dependent on the network size of international trade and degree of industrialization in this network, but also that the network size is determined by all countries’ decisions of participation in the network. Kelly (1997) specifies the time dimension and introduces uncertainty to the transaction condition for setting up a trade connection. His model has endogenized the evolution of the degree of market integration. But this kind of model generates the scale effect. It predicts that productivity goes up if and only if the average size of the firm increases. Empirical evidence in Liu and Yang (2000) rejects the type II scale effect. Also, the National Research Council (1986) and Dasgupta (1995) reject the type I scale effect predicted by this model. As Krugman (1995, p. 21) noted, this kind of model cannot explain the transfer of benefit of economies of scale between sectors through price mechanism and industrial linkages, since prices of all goods are always constant. Although empirical evidence has rejected scale effects predicted by the models in this chapter, there is a lot of empirical evidence that confirms the positive effects of transaction efficiency on economic development and structural changes. This prediction is verified by historical evidence documented in North (1958) and North and Weingast (1989), and by empirical evidence provided in Barro (1997), Easton and Walker (1997), Gawaartney, Lawson, and Block (1996), Frye and Shleifer (1997), Gallup and Sachs (1998), and Sachs and Warner (1995, 1997). North shows that the continuous fall of ocean freight rates significantly contributed to early economic development in Europe. He and Weingast show that it was the institution (i.e., constitutional monarch and parliamentary democracy) established after the English Glorious Revolution (1688) that ensured the credible commitment of the British government to the constitutional order and that significantly reduced endogenous transaction costs caused by rent seeking, corruption, and state opportunism. Hence, economic development could take off in the UK in the 18th and 19th century. Barro uses a data set of one hundred countries in 1965-1990 to establish a positive effect of an index of rule of law, which affects transaction conditions on growth rates of per capita real GDP. Easton and Walker use cross country data to show that growth performance is positively affected by an index of economic freedom. Frye and Shleifer use survey data from Poland and Russia to establish a negative correlation between growth performance and government’s violation of private property rights. Gallup and Sachs use cross country data to show that the geographical conditions that affect transportation efficiency of a country have a very significant impact on per capita income. Sachs and Warner use a data set of 83 countries in 1965-1990 to establish a positive correlation between growth performance and indices of openness and quality of institutions that affect transaction conditions. Krugman (1995) argues that the ideas of external effects of industrial linkage, circular causation, and big push industrialization should be formalized by models with economies of scale. The general equilibrium models with economies of scale in this

162

chapter have successfully captured the general equilibrium flavor of the ideas. But they are not so successful in standing the empirical test because of their emphasis on economies of scale.

Key Terms and Review Relationships between circular causation, big push industrialization, network effects of industrial linkages, the notion of general equilibrium High development economics and different ways to formalize it Why various scale effects are rejected by empirical evidences? Differences between the models of labor surplus, the equilibrium models with economies of scale, and the Smithian models of division of labor Differences between the DS models of monopolistic competition and the MSV models of economies of scale

Further Reading Early ideas on big push industrialization, balanced vs. unbalanced industrialization, linkage externality: Rosenstein-Rodan (1943), Fleming (1955), Nurkse (1952), Scitovsky (1954), Myrdal (1957), Hirschman (1958), Sheahan (1958), Sutcliffe (1964), Streetern (1956), Krugman (1992, 1995); Dual structure: Ranis (1988), Lewis (1955), Fei and Ranis (1964); Formal general equilibrium models of structural changes and dual economy with economies of scale: Ciccone and Matsuyama (1996), Krugman and Venables (1995), Baldwin and Venables (1995), Puga and Venables (1998), Gans (1998), Matsuyama (1991), Yang (1994), Weitzman (1994), Wong and Yang (1994, 1998), Yang and Heijdra (1993), Dixit and Stiglitz (1977), Ethier (1982), Krugman (1979, 1980, 1981, 1995), Murphy, Shleifer, and Vishny (1989), Kelly (1997), Sachs and Yang (1999); Cheap talk to solve coordination problems: Matsui (1991), Bhaskar (1995), Blume, Kim, and Sobel (1993), Kim and Sobel (1995), Mailath (1998); Empirical evidence against scale effects: Liu and Yang (2000), National Research Council (1986), Dasgupta (1995); Empirical evidence for the positive relationship between development performance and transaction efficiency: Gallup and Sachs (1998), Sachs and Warner (1995, 1997), North (1958), North and Weingast (1989), Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997).

Questions 1. To what extent can the models in this chapter formalize the Smith theorem, which states that the extent of the market is determined by transportation efficiency and that the division of labor is limited by the extent of the market? 2. Discuss the differences between the development implications of transaction costs in the Ricardian model and the Smithian model and that in the models in this chapter. 3. According to the argument of infant industry (see, for instance, Scitovisky 1954), if there are economies of scale, externalities of linkage, and learning by doing, a tariff to protect the infant sector from international competition will improve social welfare and speed up industrialization. Use the models in this chapter to assess the argument in connection with the effect of population size and transaction condition on prices of goods with economies of scale in production. 163

4. Consider the model in example 5.1. Assume that there are job shifting costs, so that an individual who has just changed jobs is not as productive, at least for a time, as is a person who has not changed jobs. Suppose that the oil crisis has suddenly reduced transaction efficiency. Analyze what will happen to the equilibrium network size of division of labor and the equilibrium number of goods. Then discuss the possible effects on short-run unemployment, which is called by some economists (such as Friedman) natural unemployment and by other economists structural unemployment. 5. Many development economists (for instance, Myrdal, 1957) believe that high-growth rates of population impede economic development in the less developed countries. But Schultz (1974) argued that in a free market system, individuals’ rational decisions will take care of population growth. Hence, the negative effect of population growth on economic development must be associated with deficient institutions in less developed economies. For instance, an egalitarian institution of land allocation in the absence of private ownership and free trade of land in China creates incentives for a high birth rate of farmers. Discuss the two different views in connection to the models in chapters 4 and 5 and the empirical evidence that there is a positive correlation between population density and development performance in those countries with favorable geographical conditions for transportation and that there is a negative correlation between the two variables in those countries with unfavorable geographical conditions (see chapter 2). 6. In the model in example 5.2, as transaction efficiency is improved, the production functions of some new goods emerge from the evolution of division of labor. This looks like endogenous technical progress. Analyze the difference between this approach to explaining endogenous technical progress, which is dependent on a large size of market network and on the merging of separate local business communities into an increasingly integrated market, and the neoclassical approach to explaining technical progress by investment, which is independent of the evolution of the network size of division of labor. 7. Rosenstein-Rodan (1943) argues that an investment is likely to be unprofitable in isolation, but profitable if accompanied by similar investments in many other industries. Hirschman (1958) argues that an industry creates a backward linkage when its demand enables an upstream industry to be established at least at minimum economic scale. The strength of an industry’s backward linkage is to be measured by the probability that it will, in fact, push other industries over the threshold of profitability. This is called the effect of backward linkage. Forward linkage is also defined by Hirschman as involving an interaction between scale and market size. It involves the ability of an industry to reduce the costs of potential downstream users of its products and thus, again, to push them over the threshold. Use the models in this chapter to formalize these vague ideas about industrialization and economic development. 8. Nurkse (1952) proposed a concept of virtuous circles of development, which implies that demand and supply of different sectors are interdependent. Use the general equilibrium model in this chapter to formalize his vague idea. Scitovsky (1954) drew a clear distinction between technological and pecuniary external economies and made the point that, in competitive equilibrium, it is actually efficient to ignore pecuniary external effects. (Pecuniary external effects are those interdependencies between endogenous variables that are registered in price signals.) Use the concept of general equilibrium to analyze how interactions between selfinterested decisions in the market take into account the benefit of economies of scale and interdependencies between sectors. Most of these early development economists did not mention economies of scale. Use the model in chapter 4 to analyze why the network effect of industrial linkage can exist in the absence of economies of scale. 9. Fleming (1955) argues that the “horizontal” external economies of Rosenstein-Rodan are less important than the “vertical” external economies. Horizontal external economies relate to interdependency between the different sectors at the same link of a roundabout production chain, while vertical external economies relate to interdependency between different links. Use

164

the distinction between the DS model and the Ethier model to formalize the distinction between vertical and horizontal economies. You may relate your analysis to the model in chapter 12, which endogenizes the number of industrial links in a roundabout production chain. 10. Draw the distinction between dual economy in the Ricardian model in chapter 3, in the Ethier model, in labor surplus model of Lewis, and in the Sachs and Yang model. More dual structures will be predicted by the models in chapters 6, 11 and 12. Compare all the different definitions of dual economy. 11. If big push industrialization is beneficial to all firms, under what conditions can private firms use the financial market to organize big push industrialization, just as businessmen in Hong Kong did after WWII? 12. How can the coordination problem of industrialization in the MSV model be avoided by cheap talk, industrial associations, and other business practices in the absence of government interventions? How can we refine the notion of equilibrium and develop new research approaches to avoid the multiplicity of equilibria and to increase the predictive power of the models (see chapter 9)? 13. Specify the market clearing condition for labor in example 5.1 and use Walras’ law to check if the solution of equilibrium in example 5.1 is correct. (Hint: Do not forget transaction costs in terms of labor, tnpx, when you specify the market clearing condition for labor.)

Exercises 1. Interpret the utility function in example 5.1 as a production function of the final consumption good (or agricultural good). Each consumer’s utility equals the quantity of this good consumed. Interpret t as a sales tax rate of the consumption good. xi is intermediate good i employed to produce the consumption goods. Suppose that the government sales tax rate for intermediate goods is s and all tax revenue is evenly distributed among workers producing the intermediate goods. Work out the general equilibrium and its comparative statics. Will the equilibrium relative output and relative price of the industrial and agricultural sectors change as relative tax rates t and s change? Use this model to analyze the government’s discriminatory tax policy against the agricultural sector and the dual structure in the economic development process. 2. (Yang and Heijdra, 1992) Delete the equality condition between marginal revenue and marginal cost in example 5.1. Then all endogenous variables can be expressed as a function of the number of goods, n, using zero profit condition and demand functions of consumers. Suppose a central planner maximizes a consumer’s utility with respect to n. Then a Pareto optimum value of n can be solved. Compare this Pareto optimum value of n with the equilibrium value, and analyze under what condition it is greater or smaller than the equilibrium value one for production functions Xj = (Lj - a)/b and Xj = Lja, respectively. Nobody gains from the distortions in a monopolistically competitive market. Analyze why such distortions occur in a decentralized market. In your opinion, how can such distortions be avoided? 3. Assume that the economy in example 5.2 is initially in equilibrium. An oil crisis reduces transaction efficiency from k1 to k2, so that the equilibrium number of goods decreases. Assume that as the equilibrium shifts, there is a job shifting cost when individuals change jobs, so that those who lose their jobs are not as competitive as those who do not change jobs. Thus, unemployment will take place. Compute the unemployment rate caused by the oil crisis. 4. Replacing the production function in example 5.1 with Xj = Lja, solve for equilibrium and its comparative statics. If the DS formula for the own price elasticity of demand, 1/(1-ρ), is used in this new model, what is going to happen? If the production function is still Xj = (Lj - a)/b,

165

5.

6.

7.

8.

9.

10.

11.

12.

what is the solution based on the DS formula for the own price elasticity of demand? Analyze the results based on the DS formula in comparison with the results based on the YH formula. (Wong and Yang, 1994) Suppose that in the DS model in example 5.1, the tax rate t is imposed on sales rather than on consumption. Solve for equilibrium and its comparative statics. Then replace the production function with Xj = Lja and solve for equilibrium and its comparative statics. Analyze the sensitivity of the results to the specification of who is paying the transaction costs and to the specification of production function. Suppose that in example 5.1, parameter a, b, t, or M changes. Show that the equilibrium average size of firms and labor productivity of each good in the DS model will change in the same direction in response to each of these changes in parameters. Use your analysis to establish the claim that the DS model will be rejected if data show a negative correlation between changes in the average size of firms and changes in productivity. Use data to test the hypothesis generated by the DS model. Assume that in a simplified version of the model in example 5.2, each consumer’s utility function is u = yz where y and z are two consumption goods. There is no transaction cost other than government tax. The government imposes a consumption tax on goods y and z. The tax revenue is evenly distributed among manufacturers of goods z and x. Solve for equilibrium and its comparative statics. What are the effects of the tax on economic development and structural changes? Consider another version of the MSV model, in which each consumer maximizes her total discounted utility over two periods. U = [∫01x1γ(q)dq]θ/γ+β[∫01x2γ(q)dq]θ/γ, subject to the budget constraint ∫01x1γ(q)dq + ∫01x2γ(q)dq = L+ β*(L+nπ), where β is a subjective discount factor, β* is the equilibrium discount factor, 1/(1-θ) is the intertemporal elasticity, 1/(1-γ) is the elasticity of substitution between goods, n is the number of active modern firms, π is profit of each active modern firm, and the wage rate in each period is assumed to be 1. Each good q in the first period must be produced using a constant returns to scale technology, converting one unit of labor into one unit of output. Each sector q has a potential monopolist who can invest F units of labor in period 1 and then produce α > 1 units of output per unit of labor in period 2. Each modern firm maximizes its total discount profit over two periods π = [β*(α-1)y2/α] F. It will operate if this total discount profit is positive. Identify the parameter subspace within which there are two equilibria, one of which is n = 0 and the other is n = 1. Calculate the relative income share of the modern to traditional sector in the Sachs and Yang model. Identify if it increases or decreases as the transaction cost coefficient c decreases or as population size L increases. Suppose the variable cost coefficient b decreases or the fixed production cost F decreases. What will happen to the equilibrium degree of industrialization n? Use this model to explain industrialization and the evolution of dual structure of the economy. Specify the market clearing condition for labor in example 5.4 and show that Walras' law holds in this model. (Hint: do not forget transaction costs in terms of labor incurred to each active modern firm.) Show that the equilibrium in the Sachs and Yang model is not Pareto optimal. Is the equilibrium degree of industrialization higher or lower than the Pareto optimum one? What causes the distortions and how they can be reduced? Extend the Sachs and Yang model in example 5.4 to the case with intermediate goods. Assume that consumers' utility functions are U = yαz1-α and the production functions for goods y and z are y = [∫0m x(j)ρdj]β/ρLy1-β and z = Lz, respectively, where y is the manufactured consumption good, z is food, x(j) is the quantity of intermediate good j, and Ly and Lz are the respective amounts of labor allocated to the production of goods y and z. The production function is the same as in example 5.4. Solve for the equilibrium and its comparative statics.

166

13. Why are the equilibria in the DS model, Ethier model, and Sachs and Yang model unique? Why there are multiple equilibria in the MSV model? 14. Suppose that the government imposes a tax on sales of goods produced from traditional technology with constant returns to scale example 5.3. What are the effects of the tax rate on economic development and dual structure? 15. Specify a general equilibrium model of Lewis’ theory (1955) with the following features. In an economy with two goods, the agricultural good is produced out of labor with decreasing returns to scale technology, and the industrial good is produced out of labor and capital with constant returns to scale technology. There are two periods. In period 1, all profit is used to produce the capital good used in period 2. A unit profit in terms of labor can be converted to a unit of capital available in the next period. Suppose the discount rate is zero and a central planner maximizes a representative consumer’s total utility in two periods. If there is an institutional wage lower than the market wage in the agricultural sector, then absorption of surplus labor from the agricultural sector by the industrial sector takes place in the development process. Compare the development mechanism in this model with those in the models of economies of scale in this chapter. 16. Specify a general equilibrium model of the Fei-Ranis model (1964) with the following features. An institutional wage in the agricultural sector is higher than its market level, generating labor surplus. An exogenous increase of productivity in the industrial sector starts the process that absorbs labor surplus. Compare this model with the models in this chapter. 17. Assume that the Ethier model in example 5.2 is asymmetric. The production functions for intermediate goods are the same as in example 5.4 and the number of intermediate goods is a continuum. Solve the asymmetric Ethier model and compare its comparative statics with that in examples 5.2 and 5.4.

167

Chapter 6: Coexistence of Endogenous and Exogenous Comparative Advantages and Patterns of Development and Trade 6.1. Underdevelopment and Dual Structure with Underemployment If we introduce endogenous comparative advantage into the Ricardian model in chapter 3, introduce exogenous comparative advantage into the Smith-Young model in chapter 4, or introduce differences in transaction conditions between countries into the models of highdevelopment economics in chapter 5, we can develop more realistic models to explain development and trade phenomena. This kind of model can predict dual structure in economic development and a trade pattern in which a country exports goods with exogenous comparative disadvantage, if this disadvantage is dominated by endogenous comparative advantage. Inframarginal comparative statics can be used to predict the emergence, evolution, and disappearance of dual structure. In addition, the models can be used to analyze development strategies and trade policies that relate to the literature of import substitution and export-led industrialization. Lewis (1955) noted development implications of dual structure of commercialized versus noncommercialized sectors and evolution of commercialization. But he could not find the right way to model the evolution of division of labor, which is associated with the reallocation of resources from the noncommercialized and self-sufficient sector to the commercialized modern sector. He did not know how to use the general equilibrium model with increasing returns to describe the evolution of dual structure, nor could he command an inframarginal analysis of division of labor. Hence, he used neoclassical marginal analysis of a model with constant returns to scale and disequilibrium in labor market to investigate the development implications of evolution in division of labor. Ranis (1988, p. 80) emphasized that the guiding principle of organizational dualism is "commercialized" versus "noncommercialized," rather than "agricultural" versus "nonagricultural." Also, the notions of disequilibrium and institutionally rigid wages are not essential in this analysis. Chenery (1979) used market disequilibrium to explain structural changes in order to avoid a general equilibrium analysis of structural changes. Recently, three kinds of equilibrium models have been developed to analyze dual structure and the underdevelopment phenomenon. Khandker and Rashid (1995) and Din (1996) have developed general equilibrium models of dual structure in which the wage rate that is higher than market clearing level is still exogenously fixed. In the emerging literature of formal models of high development economics, equilibrium models with economies of scale are used to predict the evolution of dual structure (see Krugman and Venables 1995, 1996, and Fujita and Krugman 1995). The equilibrium models with endogenous geographical location of economic activities of Krugman and Venables (1995), Puga and Venables (1998), and Baldwin and Venables (1995) attribute the emergence of dual structure to the geographical concentration of economic activities in economic development that marginalizes peripheral areas. Kelly (1997) develops a dynamic general equilibrium model that predicts the spontaneous evolution of a dual structure between the modern sector with economies of scale and the 168

traditional sector with constant returns technology. As transaction conditions are sufficiently improved, the level of division of labor increases and dual structure disappears. In the growing literature of endogenous specialization, inframarginal analysis of the Smithian models with endogenous and exogenous comparative advantages is used to explain the emergence, evolution, and disappearance of dual structure. This literature pays more attention to the effects of the evolution of individuals’ levels of specialization and the coexistence of exogenous and endogenous comparative advantages on the emergence and evolution of dual structure. In this literature, dual structure not only implies unequal distribution of gains from trade between developed and less developed countries, which relates to underdevelopment phenomenon, examined in chapter 3, or a division between the industrial and agricultural sectors, examined in chapter 5, but also implies a dual structure between the commercialized sector, which is involved in international trade, and self-sufficient individuals who appear to be in underemployment in a less developed economy. In sections 6.2, 6.3, and 6.4, we use a Smithian model with endogenous and exogenous comparative advantage to illustrate how dual structure can be analyzed using the third kind of general equilibrium models. In section 6.5, we then use an extended Krugman-Venables model with economies of scale to illustrate how dual structure can be analyzed using the second kind of general equilibrium model. In section 6.6, this model is used to analyze import substitution, export-led industrialization, and coordination problems of the industrial linkage network. In these two kinds of models, evolution of dual structure is treated as an equilibrium phenomenon in the absence of an ad hoc disequilibrium wage rate. Also, the coexistence of increasing returns and ex ante differences between individual decision makers are common features of these two kinds of models of dual structure.

Questions to Ask Yourself when Reading the Chapter What are the differences between dual structure of the industrial and agricultural sectors, dual structure with unequal distribution of gains from trade, and dual structure between commercialized and self-sufficient sectors? What are the differences between dual structure caused by disequilibrium in the labor market and dual structure in the transitional stage of evolution of division of labor? What are the effects of coexistence of endogenous and exogenous comparative advantages on the emergence, evolution, and disappearance of dual structure? What are the effects of coexistence of economies of scale, industrial linkages, and differences in transaction conditions between countries on the emergence, evolution, and disappearance of dual structure? What are underdevelopment and dual structure with underemployment, and under what condition do they occur in the development process?

169

6.2 A Smithian Model with Dual Structure in the Transitional Stage of Economic Development Example 6.1: A Smithian model with endogenous and exogenous comparative advantages (Sachs, Yang, and Zhang 1999). Consider a world consisting of country 1 and country 2, each with a measure Mi (i=1, 2) of consumer-producers. The set of individuals is a continuum. The individuals within a country are assumed to be identical. The utility function for individuals in country i is: (6.1)

ui = (xi+kixid)β(yi+kiyid)1-β

where xi, yi are quantities of goods x and y produced for self-consumption, xid, yid are quantities of two goods bought from the market, and ki is the transaction efficiency coefficient in country i. The transaction cost is assumed to take the iceberg form: for each unit of goods bought, a fraction 1-ki is lost in transit; the remaining fraction ki is received by the buyer. The production functions for a consumer-producer in country i are: (6.2a) (6.2b)

x1 + x1s = L1xb, x2 + x2s = aL2x,

y1 + y1s = L1y, y2 + y2s = L2yc,

where xis, yis are respective quantities of the two goods sold by a person in country i, Lij is the amount of labor allocated to the production of good j by an individual in country i, and Lix + Liy = B > 1. For simplicity, we assume that B = 2. It is assumed that a, b, c > 1. This system of production functions and endowment constraint displays economies of specialization in producing good x for an individual in country 1 and in producing good y for an individual in country 2. It exhibits constant returns to specialization for an individual in country 1 to produce good y and for an individual in country 2 to produce good x. But an individual in country 2 has higher productivity in producing good x than an individual in country 1 has in producing good y. Suppose that b = c = 2. If all individuals allocate the same amount of labor to the production of each good, then an individual in country 1 has the same average labor productivity of good x as an individual in country 2 has in producing good y. But the average labor productivity of good x for an individual in country 2 is higher. This is similar to the situation in a Ricardian model with exogenous comparative advantage. Country 1’s productivities are not higher than country 2’s in producing all goods, but country 1 may have exogenous comparative advantage in producing good y. But if an individual in country 1 allocates much more labor to the production of x than an individual in country 2, then her productivity is higher than that of the latter. Similarly, if an individual in country 2 allocates at least as the same amount of labor of an individual in country 1 to the production of good y, her productivity of good y will be higher. This is referred to as endogenous comparative advantage, since individuals’ decisions on labor allocation determine the difference in productivity between them. But an individual in country 1 has no endogenous comparative advantage in producing good y and an individual in country 2 has no endogenous comparative advantage in producing good x, since respective productivities never change, independent of their labor allocation.

170

There are three configurations from which the individuals can choose:

country 1 country 2 (1) Structure AA

country 1 country 2 (2) Structure AD

country 1 country 2 (3) Structure DA

country 1 country 2 (6) Structure CP-

country 1 country 2 (5) Structure CP+

country 1 country 2 (4) Structure PC+

country 1 country 2 (7) Structure PC-

country 1 country 2 (10) Structure CC+

country 1 country 2 country 1 country 2 (8) Structure CD+ (9) Structure DC+

country 1 country 2 (11) Structure CC-

country 1 country 2 (12) Structure CD-

Figure 6.1: Dual Structure in Economic Development

171

Self-sufficiency. Configuration A, where an individual produces both goods for selfconsumption. This configuration is defined by: xi , yi > 0, xi s = xi d = yi s = yi d = 0, i = 1, 2 . Specialization in producing good x. Configuration (x/y), where an individual produces only x and sells x in exchange for y, is defined by: s d d s x i , x i , y i > 0, x i = y i = y i = 0 .

Specialization in producing good y. Configuration (y/x), where an individual produces only y and sells y in exchange for x, is defined by: s d d s y i , y i , x i > 0, y i = x i = x i = 0 . There are thirteen feasible structures that may satisfy market clearing and other conditions for a general equilibrium. Structure AA, as shown in panel (1) of Fig. 6.1, is an autarky structure, where individuals in both countries choose self-sufficiency (configuration A). Structure AD, shown in panel (2) of Fig. 6.1, is asymmetric between the two countries: all individuals in country 1 choose autarky configuration A, while some individuals in country 2 choose configuration (x/y) and others choose configuration (y/x). Hence, there are domestic division of labor and related domestic trade in country 2, but no international division of labor and related international trade. Structure DA is symmetric to structure AD: country 1 has domestic division of labor and country 2 is in autarky. This structure involves a type 1 dual structure between countries. Structure PC+, shown in panel (4) of Fig 6.1, involves a type 2 dual structure between the two countries as well as in country 1. Some individuals in country 1 choose configuration (x/y), the rest of the population choose autarky, and all individuals in country 2 choose configuration (y/x). There is a dual structure between professional individuals choosing (x/y) and self-sufficient individuals in country 1, despite their ex ante identical characteristics. The professional individuals in country 1 are involved in international trade with country 2. Structure CP+ is symmetric to structure PC+. Structure PC-, shown in panel (6) of Fig. 6.1, is the same as structure PC+, except that professional individuals in country 1 choose configuration (y/x) instead of (x/y) and individuals in country 2 choose configuration (x/y) instead of (y/x). Structure CP- is the same as structure CP+, except that individuals in country 1 choose configuration (y/x) instead of (x/y) and professional individuals in country 2 choose configuration (x/y) instead of (y/x). Structure DC+, shown in panel (9), is the same as structure PC+, except that those individuals choosing autarky in country 1 in structure PC+ choose configuration (y/x) instead in structure DC+. Hence, in structure DC+ all individuals completely specialize, but country 1 is involved in both domestic and international trade, whereas country 2 is involved only in international trade. Also, country 1 exports good x and country 2 exports good y. Structure DC- is the same as structure DC+, except that country 1 exports good y instead of good x and country 2 exports good x instead good y. Structure CD+, shown in panel (8) of Fig. 6.1, is symmetric to structure DC+: country 1 has only international trade, whereas country 2 has both international and domestic trade, and country 1 exports good x and country 2 exports good y. Structure CD- is the same as CD+, except that country 1 exports good y instead of x, and country 2 exports good x instead of y.

172

Structure CC+, shown in panel (10) of Fig. 6.1, is international complete division of labor between two countries, in which all individuals in country 1 choose configuration (x/y) and all individuals in country 2 choose configuration (y/x). Structure CC- is symmetric to structure CC+: all individuals in country 1 choose configuration (y/x) and all individuals in country 2 choose configuration (x/y).

6.3. General Equilibrium and Its Inframarginal Comparative Statics

According to Zhou, Sun, and Yang (1998), a general equilibrium exists and is Pareto optimal for the Smithian models with endogenous and exogenous comparative advantages in this chapter under the following assumptions. The set of individuals is a continuum, and preferences are strictly increasing and rational. Both local increasing returns and constant returns are allowed in production and transactions. Also, they have proved that the set of equilibrium allocations is equivalent to the set of core allocations. The definition of equilibrium is the same as in chapters 3 and 4. We will follow the twostep approach to inframarginal analysis developed in chapters 3 and 4. For simplicity, assume that M2 + M2 = 1, M1 = M2 = 0.5, and β = 0.5. Let the number (measure) of individuals in country i choosing configuration (x/y) be Mix, that choosing (y/x) be Miy, and that choosing A be MiA. In the first step, we consider a structure. Each individual’s utility maximizing decision is solved for the given structure. The utility equalization condition between individuals choosing different configurations in the same country and the market clearing condition are used to solve the corner equilibrium relative price of traded goods and number (measure) of individuals choosing different configurations. According to the definition, a general equilibrium is a corner equilibrium in which all individuals have no incentive to deviate, under the corner equilibrium relative price, from their chosen configurations. Hence, in the second step, we can plug the corner equilibrium relative price into the indirect utility function for each constituent configuration in this structure, then can compare corner equilibrium values of utility across configurations. The total cost-benefit analysis yields the conditions under which the corner equilibrium utility in each constituent configuration of this structure is not smaller than any alternative configuration. This system of inequalities can thus be used to identify a subspace of parameter space within which this corner equilibrium is a general equilibrium. With the existence theorem of general equilibrium proved by Zhou, Sun, and Yang (1998), we can completely partition the parameter space into subspaces, within each of which the corner equilibrium in a structure is a general equilibrium. As parameter values shift between the subspaces, the general equilibrium will discontinuously jump between structures. The discontinuous jumps of structure and all endogenous variables are inframarginal comparative statics of general equilibrium. We now take the first step of the inframarginal analysis. As an example, we consider structure CP+. Assume that in this structure, M2y individuals choose configuration (y/x) and M2A individuals choose autarky in country 2, where M2y + M2A = M2 = 0.5. M1 = 0.5 individuals in country 1 choose configuration (x/y). Since all individuals in the same country are ex ante identical in all aspects, the maximum utilities in configurations A and

173

(y/x) must be the same in country 2 in equilibrium. Marginal analysis of the decision problem for an individual in country 2 choosing autarky yields the maximum utility in configuration A: U2A = (a2c+1γ)0.5, where γ ≡ cc/(c+1)c+1. Marginal analysis of the decision problem for an individual in country 2 choosing configuration (y/x) yields the demand function x2d = 2c-1/p, the supply function y2s = 2c-1, and the indirect utility function U2y = 2c-1(k2/p)0.5. The utility equalization condition U2y = U2A yields p ≡ px/py = k22c-3/aγ. Similarly, the marginal analysis of the decision problem of an individual choosing configuration (x/y) in country 1 yields the demand function y1d = 2b-1/p, the supply function x1s = 2b-1, and the indirect utility function U1x = 2b-1(k1p)0.5. Inserting the corner equilibrium relative price into the market clearing condition for good x, M1x1s = M2yx2d, yields the number of individuals selling good y, M2y = 0.5 k2/23-caγ, where M1 = 0.5 by assumption. Indirect utility functions for individuals choosing various configurations in the two countries are listed in table 6.1. Table 6.1: Indirect Utility Functions

Indirect utility functions Configurations (x/y) (y/x) b-1 0.5 Country 1 u1x = 2 (k1p) u1y = (k1/ p)0.5 0.5 Country 2 u2x = a(k2p) u2y = 2c-1(k2/p)0.5 where α ≡ bb/ (1+b)b+1, γ ≡ cc/ (1+c)c+1.

A u1A = (2b+1αγ)0.5 u2A = (2c+1aγ)0.5

Following this procedure, we can solve for the corner equilibrium in each structure. The solutions of all corner equilibria are summarized in Table 6.2. Then we can take the second step to carry out a total cost-benefit analysis for each corner equilibrium and to identify the parameter subspace within which the corner equilibrium is a general equilibrium. Consider the corner equilibrium in structure CP+ as an example again. Table 6.2: Corner Equilibria

Structure Relative price of Numbers of individuals choosing x to y Various configurations AA M1A = M2A = 0.5 AD 2c-1/a M1A = 0.5, M2x = M2y = ¼ 1-b DA 2 M2A = 0.5, M1x = M1y = ¼ 3-b PC+ 2 α/k1 M2y = 0.5, M1A =0.5(1- k12c-3/α), M1x = 0.5k12c-3/α CP+ 2c-3k2/γa M1x = 0.5, M2A =0.5(1- k22b-3/γa), M2y = 0.5k22b-3/γa CP2c+1γ/ak2 M1y = 0.5, M2x =0.5k22-c-1/γ, M2A = 0.5(1-k22-c-1/γ) CC+ 2c-b M1x = M2y = ½ c-1 CD+ 2 /a M1x = 0.5, M2y = (1+2b-1/a)/4, M2x = (1-2b-1/a)/4 CD2c-1/a M1y = 0.5, M2x = 0.25+2-c-1, M2y = 0.25-2-c-1 In this structure, M1 individuals choose configuration (x/y) in country 1, and in country 2, M2y individuals choose configuration (y/x) and M2A individuals choose autarky. For an individual in country 1, equilibrium requires that her utility in configuration (x/y) is not smaller than in configurations (y/x) and A under the corner equilibrium relative 174

price in structure CP+. Also, equilibrium requires that all individuals in country 2 are indifferent between configurations (y/x) and A and receive a utility level that is not lower than in configuration (x/y). In addition, this structure occurs in equilibrium only if M2y∈(0, 0.5). All the conditions imply: u1x ≥ u1y,

u1x ≥ u1A,

u2A = u2y ≥ u2x, M2y∈(0, 0.5),

where indirect utility functions in different configurations and corner equilibrium relative price are given in Tables 1 and 2. The conditions define a parameter subspace: k1k2 ≥ 26-b-caαγ, k2 ∈ (24-b-caγ, Min{4γ, aγ23-b}), a < 24-b-c, k1 > Max{24-b-caα, α23-c}, where α ≡ bb/ (1+b)b+1 and γ ≡ cc/(c+1)c+1. Within this parameter subspace, the corner equilibrium in structure CP+ is the general equilibrium. Following this procedure, we can do total cost-benefit analysis for each structure. The total cost-benefit analysis in the second step and marginal analysis of each corner equilibrium in the first step yields inframarginal comparative statics of general equilibrium, summarized in Table 6.3. From this Table, we can see that the parameter subspace for structure DC+, DC-, or CC- to occur in general equilibrium is empty. Table 6.3: General Equilibrium Structure: Inframarginal Comparative Statics k1∈ (0, 4α)

k1∈ (4α, 1)

k2∈(0, 4γ)

k2∈(4γ, 1)

b+c-2

a2b-1 DA

k2∈(aγ2 , aγ23-b) CP+ 3-b k2>aγ2 CC+ 4-b-c

k2>aγ2

4-b-c

CP+

a>2 k1k2 < αγ2b+c+2/a AA

k1k2 > αγ2b+c+2/a CP-

k2 2b+c-2 k1< α2b+c/a AD k1∈ (α2b+c/a, 4α)

CD+

CD-

a>2

b-1

3-c

k1>α2 CC+ a2b-1

DA k2> γ2b+c/a CD-

CDCC+

CD+

where α ≡ bb/ (1+b)b+1, γ ≡ cc/ (1+c)c+1. C stands for complete specialization in a country, D stands for the domestic division of labor in a country, A stands for autarky in a country, P stands for the partial division of labor where the population in a country is divided between autarky and specialization, subscript + stands for a pattern of trade in which

175

country 1 exports good x and imports good y, and subscript – stands for a trade pattern in which country 1 exports good y and imports good x. Hence, structure AA involves autarky in both countries, structures AD and DA involve autarky in one country and division of labor in the other, structures PC and CP involve complete specialization in one country and coexistence of autarky and complete specialization in the other. The country with the lower transaction efficiency in this structure appears to be underdeveloped in the sense that it receives none of the gains from trade, and the income differential between it and the other country with higher transaction efficiency increases as a result of a shift of equilibrium from autarky to this structure. Also, ex ante identical individuals in the less developed country in this structure are divided between a professional occupation that trades with the foreign country and those who are selfsufficient and not involved in commercialized production. These self-sufficient individuals appear to be in underemployment, since they cannot find a job to work for the market. All individuals completely specialize in structures CD and CC. But CC involves complete specialization of both countries in the absence of domestic trade, whereas CD involves complete specialization in country 1 and domestic division of labor in country 2. Fig. 6.1 illustrates the equilibrium structures. 1 We say that the level of division of labor increases if the occurrence of letter A or P decreases or the occurrence of letter D or C increases in a structure. Recall from chapters 3 and 4 that endogenous comparative advantage is the productivity difference between individuals that is caused by individuals’ labor allocations, and exogenous comparative advantage is the productivity difference between individuals that is independent of their labor allocation. Since in this model, marginal and average productivity never change as labor allocation alters for a production function with constant returns to scale, these definitions imply that in this model endogenous comparative advantages come from economies of specialization, and exogenous comparative advantages come from exogenous difference of production conditions with constant returns. Parameter b represents the degree of endogenous comparative advantage for a person in country 1 producing good x since, as b increases, increases in productivity become more responsive to an increase in the amount of labor allocated to the production of x. Similarly, c represents the degree of endogenous comparative advantage for a person in country 2 producing good y. If b = c = 1, then country 2 has exogenous absolute and comparative advantage in producing good x and country 1 has exogenous comparative advantage in producing good y, since a > 1 in (2). This implies that a represents the degree of exogenous comparative advantage. With the definitions, we can now have a close examination of Table 6.3, which consists of four blocks. The northwest block is associated with low transaction efficiencies in both countries. The northeast block is associated with low transaction efficiency in country 1 and high transaction efficiency in country 2. The southwest block is associated with low transaction efficiency in country 2 and high transaction efficiency in country 1. The southeast block is associated with high transaction efficiencies in both countries. As parameter values move from the northwest toward the southeast, the occurrence of letter A, representing autarky, and letter P, representing partial division of 1

It can be shown that there are multiple equilibria in some razor edge cases with inequalities replaced by equalities. For instance, if 2b-1> a, 0 < k1 < 4α, k1 < aα24-b-c, and k2 = 4γ, multiple equilibria occur.

176

labor, decreases and the occurrence of letters D and C, representing complete division of labor, increases. Hence, as transaction conditions are improved, the level of domestic and international division of labor increases because of the trade off between economies of division of labor generated by endogenous and exogenous comparative advantages and transaction costs. If the transaction efficiency is low in one country and high in the other (northeast or southwest block), the country with the lower transaction efficiency has a dual structure (P) or in autarky (A) in a structure with asymmetric division of labor between countries (AD, DA, PC, or CP). If the transaction efficiencies are high in both countries, then complete division of labor occurs and dual structure disappears in equilibrium. Each block consists of three sections. If the degree of exogenous comparative advantage a is small compared to the degree of endogenous comparative advantage (b, c), each country exports the good with economies of specialization in production. This is denoted by subscript +. Otherwise, a country exports the good with constant returns and exogenous comparative advantage. From the table we can see that if b and c are sufficiently large, country 1 imports its good of exogenous comparative advantage, y. One of such cases is that structure CP+ occurs in equilibrium when k1∈(0, 4α), k2∈(0, 4γ), a < 2b+c-2, k1k2 > aαγ26-b-c, a>2b-1. In structure CP+, country 1 exports x and imports y, but country 1 has exogenous comparative advantage in producing y. All the results on evolution of division of labor, dual structure, and trade pattern are summarized in the following proposition, illustrated in Fig. 6.1 where large arrows indicate the direction of the evolution in division of labor. Proposition 6.1: As transaction efficiency increases from a very low to a very high level, the equilibrium level of domestic and international division of labor increases from complete autarky in both countries to the complete division of labor in both countries. In the transitional stage, two types of dual structure may occur. In a type 1 dual structure, the country with the lower transaction efficiency is in autarky, and the other has domestic division of labor and higher productivity and per capita real income. In a type 2 dual structure, the country with higher transaction efficiency completely specializes and obtains all the gains from trade, and the other country has a domestic dual structure between the commercialized sector and the self-sufficient sector (autarky) which appears to be in underemployment. The dual structures of the two types disappear as individuals in all countries are involved in international and domestic division of labor. Each country exports goods of exogenous comparative advantage if exogenous comparative advantage dominates endogenous comparative advantage in producing this good. Otherwise, each country exports goods with endogenous comparative advantage and economies of specialization in production.

The inframarginal comparative statics of general equilibrium can be used to establish two corollaries. The first is that the evolution in division of labor generated by improvements in transaction conditions will raise equilibrium aggregate productivity. In order to establish the above statement, we consider the aggregate PPF for individual 1 (from country 1) and individual 2 (from country 2). As shown in Fig. 6.2 where b = c = 2, the PPF for individual 1 is curve AB, and that for individual 2 is curve CD. In autarky, the two persons’ optimum decisions for taste parameter β∈(0, 1) are x1 = [4β/(1+β)]2, x2

177

= 2aβ/(2-β), y1 = 2(1-β)/(1+β), y2 = [4(1-β)/(2-β)]2. Let β change from 0 to 1; we can calculate values of Y = y1+y2 and X = x1+x2 as functions of β. The values of X and Y for different values of β constitute curve EGH in Fig. 6.2. The equilibrium aggregate production schedule in structure AA is a point on the curve, dependent on the value of β. But the aggregate PPF for the two individuals is the curve EFH. Since in structure CC, CD, or DC the equilibrium production schedule is point F, which is on the aggregate PPF, the aggregate productivity in a structure with the complete division of labor is higher than in structure AA. The difference between EFH and EGH can be considered as economies of division of labor.

Figure 6.2: Economies of Division of Labor Based on Endogenous and Exogenous Comparative Advantage

Following the same reasoning, we can prove that the equilibrium aggregate productivity in structure AD, DA, PC, or CP is lower than the PPF. Hence, proposition 6.1 implies that as transaction efficiencies are improved, the equilibrium level of division of labor and equilibrium aggregate productivity increase side by side. The second corollary is that deterioration of a country’s terms of trade and increase of gains received by this country from trade may concur. Suppose that the initial values of parameters satisfy k1∈(0, 4α), k2∈(0, 4γ), and k1k2 > aγα26-b-c, which implies, from Table 6.3, that we are considering the northwest block. Suppose that the initial value of k2 satisfies k2’< aγ23-c, so that the equilibrium structure is CP+ in which country 2 exports y and imports x, and its terms of trade, from Table 6.2, are 1/p = 2c-3 aγ/k2’. Now the value of k2 increases to k2”> aγ23-c, which implies, from Table 6.3, that the general equilibrium jumps from CP+ to structure CC+ in which country 2’s terms of trade, from Table 6.2, are 2b-c. It can then be shown that country 2’s terms of trade deteriorate as a result of the change in k2. But this shift of the equilibrium from CP+ to CC+ increases utility of each individual in country 2 from the autarky level. This has established the claim that the deterioration of a country’s terms of trade and an increase of gains that this country receives from trade may concur. There are other parameter subspaces within which changes in parameters may generate concurrence of the deterioration of one country’s terms of trade and an increase in its gains from trade.

178

Although an equilibrium in this model is always Pareto optimal, it generates interesting implications of economic development and trade for income distribution. It is straightforward that as the equilibrium jumps from a structure in which at least some individuals in a country are in autarky (structure AD, DA, PC, CP) to a structure in which all individuals are involved in trade and division of labor, then all individuals’ utilities in this country will be increased. Hence, immiserizing development never occurs for a less developed economy in our model, since all individuals in our model of endogenous specialization can choose occupation configurations, and they will not choose trade if autarky makes them better off. But the effects of trade and development on utility of an individual in the developed economy are not monotonic. As the equilibrium jumps from autarky to the partial division of labor (AD, DA, PC, or CP), the developed country gets all the gains from trade and development. But as the equilibrium jumps, say, from PC+ to CC+, it is possible that the utility of a person in the developed country may decline. It can be shown that this takes place within the parameter subspace in the southwest block in Table 6.3. This prediction is consistent with the fact, documented in Krugman and Venables (1995, pp. 857-58), that in the 1970s the general view was that the integration of world markets produced a rise in the living standards of rich nations at the expense of the poor. Now in the 1990s, it is believed that the rise of Third World manufacturing nations has had serious adverse impacts on developed economies. But according to our model, this reverse of the tide is just compensation to the less developed economies, which did not receive gains from trade in the early development stage. Also, in our model there exists some parameter subspace within which such immiserizing development never occurs. This is the case when the improvements in the transaction efficiency of the developed country keep pace with the improvements of the transaction efficiency of the less developed country.

6.4. Trade Pattern in the Presence of Both Endogenous and Exogenous Comparative Advantages and the Relationship Between Income Distribution and Development

Since the inframarginal comparative statics change with the specification of the system of production functions, we report the sensitivity analysis of our result. Example 6.2: A model with economies of specialization in one activity for all individuals. The system of production functions in (6.2) displays economies of specialization in producing good x by a person in country 1 and in producing good y by a person in country 2. We now assume that there are economies of specialization for all individuals in producing x, but constant returns prevail in the production of good y. Hence, the system of production functions in (6.2) is replaced by: y1 + y1s = L1y, x1 + x1s = L1xb, s c y2 + y2s = aL2y. x2 + x2 = L2x , Then the inframarginal comparative statics of general equilibrium are summarized in Table 6.4 and proposition 6.2. Proposition 6.2: As transaction efficiency is improved, the equilibrium level of division of labor and aggregate productivity increase. The country with lower transaction

179

efficiency and/or insignificant economies of specialization has a dual structure with underemployment in the transitional stage of economic development. If a country has endogenous comparative advantage and exogenous comparative disadvantage in producing a good, it exports this good when the former dominates the latter. Otherwise, it imports this good. In exercise 1, you are asked to replace the production functions in (6.1) with the one displaying economies of specialization for individuals in one country and constant returns for individuals in the other country. Then you can show that the essence of propositions 6.1 and 6.2 would not be changed. Table 6.4: Equilibrium Structure (Economies of Specialization in Producing One Good for All Countries)

k1 ∈ (0, 4α)

k1 ∈ (4α, 1)

k2∈(0, 4γ) a > 2c-b k1k2 < αγ2c-b+4/a

k1k2 > αγ2c-b+4/a

AA

CP+

k2γ22+b-c/a CP+

a < 2c-b k1 k2 < aαγ24+b-c AA k1 k 2 > aαγ24+b-c CPk2aγ22+b-c CP-

k2∈(4γ, 1) a > 2c-b 2c-b >1 k1 0, xij = yij = zij = 0. A consumer's decision yields demand functions for goods y and z. Each consumer supplies one unit of labor, and total supply of labor in country i is Mi. The zero profit condition for the firm producing z gives the price of good z in terms of labor in country i piz, The symmetry implies that quantities supplied or employed are the same for ni intermediate goods. The zero profit condition and a first order condition for the decision problem of the firm producing y yields the equilibrium relative quantity of labor and intermediate goods and an equation that determines the equilibrium piy/pix. Using the production and demand functions of y, the market clearing conditions for y and labor, and the first order conditions for the decision problem of the firm producing y, we can find the demand function for x. Using the DixitStiglitz formula for own price elasticity E = 1/(1-ρ), we can then work out the first order condition for the decision problem for the monopolist producer of an intermediate good. Then the zero profit condition for this firm yields the equilibrium ni. The local equilibrium and its marginal comparative statics in this structure are summarized as follows: p2z = 1, pix =b/ρ, wi = 1, p1z = 1/θ, β-1 β/ρ piy = (1-β) [a/(1-ρ)β] [(1-ρ)b/ρa]β (αMi)β (1-1/ρ), ni = Miβα(1-ρ)/a, u1 = [θ(1-α)](1-α)ααp1y-α, u2 = (1-α)(1-α)ααp2y-α, dpiy/dMi < 0, dni/dMi > 0, dui/dMi > 0 where i = 1, 2. The marginal comparative statics imply that as the population in an integrated market increases, the equilibrium price of final manufactured goods decreases and the equilibrium number of intermediate goods and per capita real income increase. Since total factor productivity of the final manufactured good is an increasing function of the number of intermediate goods, this productivity increases with population size, too. The result is similar to that in the Ethier model in chapter 5, except that we assume there is no transaction cost for domestic trade. 6.5.7. Local Equilibrium in Structure C Next, we consider structure C1 where x1, y1, z2, y12, x21 > 0, x12 = y21 = z12 = 0. The procedure to solve the corner equilibrium in this structure is the same as that for structure A, except that the markets for x, y, z are jointly cleared for both countries. The corner equilibrium in this structure is summarized as follows: p1z = 1/θ, p2z = t1ρ, p1x =b/ρ, p2x = t1ρb/ρ, w = t1ρ, p1y = (1-β)β-1β-β/ρ (b/ρ)β [(1-ρ)α(M1+ k1ρM2)/a] β (1-1/ρ), n1 = [(1-ρ)/a][M1(βα+1-α)-α(1-β)t1ρM2],

185

n2 = [(1-ρ)/a][M2α-(1-α)t1-ρM1], u1 = B(θk1)1-αt1-ρ(1-α)(M1+t1ρM2)αβ(1-ρ)/ρ,

u2 = Bt1ραk2α(M1+t1ρM2)αβ(1-ρ)/ρ

where B ≡ (1-α)(1-α)αα [(1-β)1-βββ/ρ(ρ/b)β]α[α(1-ρ)/a]αβ(1-ρ)/ρ. The differentiation of the solutions yields marginal comparative statics of the local equilibrium in structure C1. (6.4)

dni/dMi > 0, dni/dMj < 0, dn2/dt1 > 0, dn1/dt1 < 0, dn/dt1 > 0, if (1-α)M1/α(1-β)M2 > t12ρ, dn/dM1 > 0 iff t1>[(1-α)/αβ+1-α]1/ρ, dn/dM2 > 0, dw/dt1 > 0, dui/dMj > 0, dui/dki > 0, dui/dt1 > 0

where i, j = 1, 2 and n = n1 + n2 is the number of all intermediate goods available in the two countries. The marginal comparative statics of the local equilibrium imply that as the transaction condition in country 1 improves, the production of intermediate goods will shift from country 1 to country 2. This relocation of industrial production increases utility levels in the two countries, although the nominal income in country 2 relative to that in country 1, which is w, increases as well. The improvement of the transaction condition in country 2 has no effects on industrial structure and the location of industrial production, though it increases the utility of each individual in country 2. An increase in population size in country 1 will shift the production of producer goods from country 2 to country 1. But an increase in the population size in country 2 has the opposite effect on location of industrial production. However, an increase in population size in either country will raise per capita real income in both countries. As n1 or n2 tends to zero, the production of all intermediate goods becomes concentrated in country 2 or 1. A careful examination of the local equilibrium solutions in structure C1 yields the following conditions for such concentration: (6.5)

n1 = n and n2 = 0 if t1 < ta ≡ [M1(1-α)/M2α]1/ρ n1, n2 ∈ (0, n) if t1 ∈ (ta, tb), where tb ≡ [M1(αβ+1-α)/M2α(1-ρ)]1/ρ n2 = n and n1 = 0 if t1 > tb,

where ta< tb always holds. The marginal comparative statics of the local equilibrium in structure C1 are summarized in the following proposition. Proposition 6.3: If the transaction efficiency of intermediate goods is very low in country 1, country 2 specializes in producing the agricultural good in the absence of industrialization. The production of all final and intermediate manufactured goods is located in country 1. As the transaction condition is improved in country 1, country 2 starts industrialization, which relocates the production of intermediate goods from country 1 to country 2. The smaller the population size of country 1 relative to country 2, the faster the relocation process. Per capita real incomes in both countries increase as a result of the relocation, although the wage rate in country 2 increases compared to that in country 1. The wage difference between the two countries converges to 0 as transaction cost tends to 0. The per capita real income in country 1 is more likely to be higher than in country 2, the greater the income share of the final manufactured good, and/or the greater the elasticity of substitution between intermediate goods, and/or the higher the relative transaction

186

efficiency of country 1 to country 2. An increase in the population size of a country will move the production of intermediate goods to this country from the other country, increasing per capita real income in this country. The local equilibrium in structure C2 is symmetric to that in C1. Hence, a similar proposition can be obtained from the comparative statics of that local equilibrium. 6.5.8. Local Equilibrium in Structure D We now consider structure D0, in which country 1 produces final goods y and z and n1 intermediate goods. It exchanges the intermediate goods for n2 intermediate goods produced by country 2, which self-provides goods y and z as well. Hence, for this structure we have xi, yi, zi, xij > 0, yij = zij = 0. The local equilibrium in this structure is summarized as follows: w is given by f = M1 + t1ρ/(1-ρ) [M2w-ρ/(1-ρ)-M1w-1/(1-ρ)-M2w-(1+ρ)/(1-ρ) t2-ρ/(1-ρ)] = 0 p2z = 1, p1x =b/ρ, p2x = wb/ρ, p1z = 1/θ, ρ/(ρ-1) ρ/(1-ρ) ρ/(1-ρ) 1/(1-ρ) β β -t2 )/(1-t2 w )] [M1t11/(ρ-1)+M2wρ/(ρ-1)]-β/ρ p1y = A(M1/t1) [(t1 β ρ/(ρ-1) ρ/(1-ρ) ρ/(ρ-1) 1/(1-ρ) β -t2 )/(t1 w -1)] [M1t21/(1-ρ)+M2wρ/(ρ-1)]-β/ρ p2y = wAM2 [(t1 ni = β(1-ρ)Mi/a, u2 = (1-α)1-ααα (p2y/w)-α u1 = [θ(1-α)]1-αααp1y-α, where A ≡ (1-β)β-1αβ[a/(1-ρ)β]β/ρ[(1-ρ)b/aρ]β. The market clearing conditions for intermediate goods and the first order conditions for producers of good y in the two countries require: w∈(t1ρ, t2-ρ) where t1ρ< t2-ρ always holds. It is obvious that w converges to 1 as t1 and t2 tend to 1. The differentiation of the solutions yields: dw/dt1 = -(∂f/∂ t1)/(∂f/∂w) > 0, dw/dt2 = -(∂f/∂ t2)/(∂f/∂w) < 0 where ∂f/∂t1 > 0, ∂f/∂t2 < 0, ∂f/∂w < 0. The result implies that relative per capita nominal income of country 2 to country 1 increases as the transaction condition in country 1 improves or as the transaction condition in country 2 worsens. Similar results can be obtained for the relationship between per capita real income in a country and the transaction conditions in the two countries. It can be shown that: (6.6a)

du1/dt1 = (∂u1/∂t1)+(∂u1/∂w)(dw/dt1) < 0, du2/dt2 = (∂u2/∂t2)+(∂u2/∂w)(dw/dt2) < 0

where dw/dt1 > 0, dw/dt2 < 0, ∂u1/∂w < 0, ∂u2/∂w > 0, ∂u1/∂ t1 < 0, ∂u1/∂t2 < 0, ∂u2/∂t2 < 0. Other marginal comparative statics in this structure are: (6.6b)

dui/dMi > 0, dui/dMj > 0, dni/dMi > 0, dni/dρ < 0, dni/da < 0.

187

The Kuhn-Tucker condition for a producer of good y indicates that the first order derivative of profit with respect to the quantity of an imported intermediate good is always negative if the transaction efficiency coefficient is zero in this country. Hence, the equilibrium will jump to another structure if t is sufficiently close to 0 in either country. If 1-ti is interpreted as the import tariff rate in country i and all tariff revenue is exhausted by the bureaucrats who collect it, then the marginal comparative statics in (6.6) imply that each country has an incentive to impose tariff, which increases per capita real income in the home country. Proposition 6.4: As the population size in either country or import tariff rate increases in a country, the per capita real income in that country increases. Also, the number of intermediate goods produced in a country increases with its population size. The wage difference between the two countries converges to 0 as transaction cost tends to 0.

The local equilibrium in structure D1 is: w is given by f = αβM1-(1-α)wM2-αβt1ρ/(1-ρ)w-1/(1-ρ)M1 + w-ρ/(1-ρ)[(1-α+αβ)M2t1ρ/(1-ρ)+ (1-α)M2 t2-ρ/(1-ρ)-(1-α+αβ)M2w-(1+ρ)/(1-ρ) t1ρ/(1-ρ)t2-ρ/(1-ρ)] = 0 p2z = 1, p1x =b/ρ, p2x = wb/ρ, p1z = 1/θ, ρ/(ρ-1) ρ/(1-ρ) ρ/(1-ρ) 1/(1-ρ) β β -k2 )/(1-t2 w )] [M1t11/(ρ-1)+M2wρ/(ρ-1)]-β/ρ p1y = A(M1/t1) [(t1 β ρ/(ρ-1) ρ/(1-ρ) ρ/(ρ-1) 1/(1-ρ) β -t2 )/(t1 w -1)] [M1t21/(1-ρ)+M2wρ/(ρ-1)]-β/ρ p2y = wAM2 [(t1 n1 = [αβM1-(1-α)wM2](1-ρ)/a, n2 = (1-α+αβ)M2(1-ρ)/a, u2 = (1-α)1-ααα (p2y/w)-α u1 = [θ(1-α)]1-αααp1y-α, where A ≡ (1-β)β-1αβ[a/(1-ρ)β]β/ρ[(1-ρ)b/aρ]β. The market clearing conditions for intermediate goods and the first order conditions for producers of good y in the two countries require: w∈(t1ρ,t2-ρ) where t1ρ< t2-ρ always holds. The local equilibrium in structure D2 is symmetric to that in D1. Marginal comparative statics in structure D1 or D2 are similar to that in D0. 6.5.9. Local Equilibrium in Structure E The local equilibrium in structure E1 is: p1x =b/ρ, p2x = wb/ρ, w = p2z = t1ρ, p1z = 1/θ, p1y = (1-β)β-1β-β/ρ(b/ρ)β[(1-ρ)α(M1 +M2t1ρ)/a]-β(1-ρ)/ρ p2y = (1-β)β-1β-β (b/ρ)β[(1-ρ)αM2/a]-β(1-ρ)/ρ n1 = [αβM1-(1-β)α t1ρM2](1-ρ)/a, n2 = αM2(1-ρ)/a, u2 = B(M1+t1ρM2)αβ(1-ρ)/ρk2αt1αρ u1 = θ1-αB(M1+t1ρM2)αβ(1-ρ)/ρ where B ≡ αα(1-α)1-α [(1-β)1-β(ρ/b)βββ/ρ]α[α(1-ρ)/a]αβ (1-ρ)/ρ. The marginal comparative statics in this structure are:

188

(6.7)

dui/dMi > 0, dui/dMj > 0, dui/dt1 > 0, du2/dk2 > 0 dni/dMi > 0, dn1/dM2 < 0, dn1/dt1 < 0.

The local equilibrium in structure E2 is symmetric to that in E1. The marginal comparative statics in the two structures are summarized in the following proposition. Proposition 6.5: As transaction efficiency and population size increase in either country, per capita real incomes in both countries increase. The number of intermediate goods produced in a country increases with the population size in that country. The number of intermediate goods produced by a country importing intermediate goods decreases with the population size in the other country and with the transaction efficiency coefficient in the first country.

6.5.10. Local Equilibrium in Structure F The local equilibrium in structure F1 and its marginal comparative statics are: (6.8)

p1x =b/ρ, p2x = wb/ρ, w = p2z = t1ρ, p1z = 1/θ, β-1 β -β/ρ p1y = (1-β) (b/ρ) β [(1-ρ)α(M1+t1ρM2)/a] p2y = (1-β)β-1β-β (b/ρ)β[(1-ρ)M2/a]-β(1-ρ)/ρ n2 = M2(1-ρ)/a, n1 = [αβM1-(1-αβ)t1ρM2](1-ρ)/a, ρ 1-α αβ(1-ρ)/ρ , u2 = B(M1+t1ρM2)αβ(1-ρ)/ρt1ρk2. u1 = θ B(M1+t1 M2) dui/dMi > 0, dui/dt1 > 0, du2/dk2 > 0 dni/dMi > 0, dn1/dM2 < 0, dn1/dt1 < 0

where B ≡ αα(1-α)1-α [(1-β)1-β(ρ/b)βββ/ρ]α[α(1-ρ)/a]αβ (1-ρ)/ρ. The local equilibrium in structure F2 is symmetric to that in F1. The marginal comparative statics in the two structures are consistent with proposition 6.5.

6.6. General Equilibrium and Inframarginal Comparative Statics

Inserting the local equilibrium values of prices into (6.3), we can partition the parameter space of twelve dimensions (θ, b, a, ρ, M1, M2, α, β, t1, t2, k1, k2) into subspaces, within each of which a local equilibrium is the general equilibrium. This analysis needs the equilibrium value of the domestic price of some good in a country that does not produce this good in some structure. But we can calculate the shadow price of this good in this country from the first order condition of a firm, assuming that firm is active in producing this good. This analysis yields the following inframarginal comparative statics of general equilibrium: (6.9a) The local equilibrium in structure A is the general equilibrium if either k1 and t1 or k2 and t2 are sufficiently small. (6.9b) Suppose that M1 is not too small compared to M2 and that k2 and t1 are not too small. 189

(6.9b-I) The local equilibrium in structure C1 is the general equilibrium if t1ρ < k1/θ. (6.9b-II) The local equilibrium in structure E1 is the general equilibrium if t1ρ ∈(k1/θ, 1/θk2). (6.9b-III) The local equilibrium in structure F1 is the general equilibrium if t1ρ >1/θk2. (6.9c) Suppose that M1 is close to M2 and t1 is close to t2. (6.9c-I) The local equilibrium in structure D0 is the general equilibrium if k1 < θt1ρ and k2 < t2ρ/θ (6.9c-II) The local equilibrium in structure D1 is the general equilibrium if k2 > 1/θt1ρ. (6.9c-III) The local equilibrium in structure D2 is the general equilibrium if k1 > θ/t2ρ. (6.9d) Suppose that M2 is not too small compared to M1 and that t2 and k1 are not too small. (6.9d-I) The local equilibrium in structure C2 is the general equilibrium if t2ρ < θk2 (6.9d-II) The local equilibrium in structure E2 is the general equilibrium if t2ρ∈(θk2, θ/k1). (6.9d-III) The local equilibrium in structure F2 is the general equilibrium if t2ρ > θ/k1. Here, we have used the upper and lower bound of the local equilibrium value of w to find sufficient conditions for Di to occur in equilibrium, since the local equilibrium value of w in Di cannot be solved analytically. But these conditions may not be necessary. Hence, the parameter subspace (6.9c) is not completely partitioned. In other words, the inframarginal comparative statics state that three factors determine trade patterns: exogenous technological comparative advantage (its degree is represented by θ); endogenous comparative advantage (its degree is represented by 1/ρ which is the degree of economies of variety of producer goods as well); exogenous comparative advantages in transactions, which relate to relative transaction efficiencies of final and intermediate goods in country 1 compared to these in country 2 (ki/kj, ti/tj, ki/ti, kj/tj) and the absolute level of transaction efficiency. Here, we consider economies of variety of producer goods to be equivalent to endogenous comparative advantage since two countries have the same production conditions in producing y and x (i.e. no exogenous comparative advantage exists between them in producing y and x) and the equilibrium total factor productivity and variety of producer goods positively relate to 1/ρ. If the absolute level of transaction efficiency is low for all goods, autarky is equilibrium. As transaction efficiency is improved, the general equilibrium jumps from autarky to a structure with trade. It is the interplay between exogenous and endogenous comparative advantage in production and transactions that determines to which structure the equilibrium will jump. In order to understand the complicated comparative statics, we take a three-step analysis. We first consider inframarginal analysis between structures, then marginal analysis for each structure. For inframarginal analysis, we first compare cases (6.9b), (6.9c), and (6.9d), then compare between different structures in each case. The comparison of the cases indicates that when transaction conditions of intermediate goods are similar in the two countries, each country exports and imports intermediate goods, that is, structure D occurs in equilibrium. Otherwise, the country with the better transaction condition of intermediate goods imports such goods. This is case (6.9b) or (6.9d). Case (6.9b), in which only country 1 imports intermediate goods, is more likely to occur in equilibrium than case 190

(6.9d), in which country 2 imports intermediate goods, if the transaction efficiency of intermediate goods relative to that of final goods is higher in country 1 than in country 2 and/or if the population size in country 1 is larger. We now take the second step. We consider case (6.9b) first. Suppose that the transaction condition and exogenous comparative advantage change in the following way. k1 decreases and/or k2 increases, and/or θ (degree of exogenous comparative advantage) increases, and t1 increases over three periods of time. Hence, in period 1, k1> t1ρθ, which implies that country 1's transaction efficiency of final goods is high, its transaction efficiency of intermediate goods is low, and exogenous comparative advantage is not significant. Therefore, the local equilibrium in structure C1 is the general equilibrium (see (6.9b-I). In this structure, country 1 imports z and x and country 2 imports y. Then, these parameters change: k1 decreases, θ increases, and/or t1ρ increases such that in period 2, t1ρk2θ < 1 < t1ρθ/k1. Hence, the equilibrium jumps to structure E1, where country 1 no longer imports the final good z (see (6.9b-II)). In period 3, k2 increases, and/or t1ρ, θ further increase, such that k2θt1ρ > 1. Then the equilibrium jumps to structure F1, where country 2 imports one more final good z (see (6.9b-III)). This implies that as the degree of exogenous comparative advantage increases and as country 2's relative transaction efficiency of importing final and intermediate goods increases compared to that for country 1, the equilibrium trade pattern shifts to increase country 2's imported final goods compared to country 1. Also, the equilibrium trade pattern shifts from exporting goods with exogenous comparative disadvantage in production to exporting goods with exogenous comparative advantage. Repeating this analysis for other cases, we can obtain similar results. In summary, if exogenous and endogenous comparative advantages in production and transactions go in the same direction, then a country exports its comparative advantage goods. If it has endogenous comparative advantage in production and exogenous comparative advantage in transactions, but exogenous comparative disadvantage in production for exporting a good, then it will export this good if the advantage dominates the disadvantage. Otherwise, it imports this good. In other words, a country exports a good with net comprehensive endogenous and exogenous comparative advantage in production and transactions. It will use substitution between trade of different types of goods to avoid trade with low transaction efficiency. Putting together marginal comparative statics for structure C, given in (6.4), and inframarginal comparative statics, given in (6.9), we can see that if the local equilibrium in structure C1 is the general equilibrium, then the conditions for dn/dt1 > 0 and dn/dM1 > 0, given in (6.4), are satisfied. Hence, dn/dt1 > 0 and dn/dM1 > 0 hold if structure C1 occurs in equilibrium. All marginal and inframarginal comparative statics are summarized in the following proposition. Proposition 6.6: (1) If transaction efficiencies for all goods are low, then autarky structure is equilibrium, in which no international trade occurs though the number of intermediate goods, productivity, and per capita real income in each country, increases with population size. As transaction efficiency is improved, the equilibrium jumps to a structure with trade. In an equilibrium trade pattern, a country exports goods with net endogenous and exogenous comparative advantages in production and transactions. It exports a good if its endogenous comparative

191

advantage in production and exogenous comparative advantage in transactions outweigh its exogenous comparative disadvantage in producing this good. Otherwise, it imports this good. Each country will exploit the substitution between trades of different types of goods to avoid trading goods that are associated with low transaction efficiency. (2) If a country exports the agricultural good and imports the final manufactured good (structure C), then as the transaction efficiency of intermediate goods in the other country increases from a very low to a high level, this country shifts from specialization in producing the agricultural good to exporting increasingly more intermediate goods. Changes in relative population size will shift the production of producer goods to the country with increased relative population size. Improvements in transaction conditions of final goods benefit both countries, too. Improvements in transaction conditions and increases in population size raise per capita real incomes in both countries and raise the total number of producer goods in the whole economy. (3) If a country specializes in producing producer goods (structure E or F occurring in equilibrium), an increase in population size and/or in transaction efficiency in either country raises per capita real income. But an increase in a country's transaction efficiency or in population size in the other country will relocate the production of producer goods from the former country to the latter. (4) If the two countries trade producer goods (structure D occurring in equilibrium), then an increase in the transaction efficiency in a country may reduce its per capita real income, although increases in population size may have positive effects on industrialization and per capital real income. This implies that the government in each country may have an incentive to impose a tariff (reduces transaction efficiency for importing goods) to improve terms of trade and raise home residents' per capita real income.

6.7. Comparison with Conventional Wisdom Based on the Models with CRS

In this section, we compare the analysis of patterns of trade and economic development in example 6.3 with the wisdom in the conventional theories of trade and economic development. We first compare the result from example 6.3 with the core theorems of neoclassical trade theory, and then compare it with neoclassical development economics based on the models with constant returns to scale (CRS). We first compare the result from example 6.3 with the HO theorem. It is interesting to see that our comparative statics may generate a prediction that is empirically equivalent to rejecting the HO theorem. If we interpret intermediate goods as capital or producer goods, then empirically, the aggregate output level of intermediate goods in our model can be considered to be the total value of capital. With this interpretation, good y is capital intensive and z is labor intensive (i.e., z needs no capital goods for production). Hence, as the number of intermediate goods endogenously increases in response to improvements in transaction condition or to population growth, the capital intensity of good y increases. There is no reason that the country producing a lot of capital goods must export good y in our model. Hence, it is perfectly reasonable that from empirical observation, a country producing a lot of capital goods exports labor-intensive goods z and imports capital-intensive goods y. This analysis is consistent with the proposition

192

made by Bhagwati and Dehejia (1994), that as increasing returns and intermediate goods are introduced, the neoclassical core trade theorems may not hold. Next, we compare our results with the SS theorem. Using the results in subsections 6.5.7 - 6.5.10, it can be shown that if structure C, E, or F occurs in equilibrium, we have: d(pix/wi)/dti = 0 and d(piy/piz)/dti < 0 d(pix/wi)/dMi = 0 and d(piy/piz)/dMi < 0 d(pix/wi)/dMj = 0 and d(piy/piz)/dMj < 0. Also, if structure D occurs in equilibrium: d(pix/wi)/dtj = 0 and d(piy/piz)/dtj < 0 d(pix/wi)/dMi = 0 and d(piy/piz)/dMi < 0 d(pix/wi)/dMj = 0 and d(piy/piz)/dMj < 0. All these marginal comparative statics imply that as relative prices of goods and inputs change in response to changes in parameters, the direction of the changes of relative prices are inconsistent with the SS theorem. Here, the final manufactured good y is capital intensive and the agricultural good is labor intensive. As the relative price of the two final goods decreases in response to changes of transaction conditions, the relative price of capital goods to labor does not change. It is well known that the SS theorem does not hold outside of the diversification cone. Hence, if we consider inframarginal comparative statics that involve discontinuous jumps of equilibrium across structures, then the SS theorem can be easily invalidated. The SS theorem has been used to show that tariff can be employed to redistribute income toward the scarce factor. But common sense is inconsistent with the prediction of the SS theorem. Common sense says that as tariff increases in a country that exports capital-intensive goods and imports labor-intensive goods, labor will marginally benefit. But this tariff has foregone opportunity to increase productivity by expanding the trade network. Hence, it is the net effect that determines if labor can benefit from the increased tariff. Our model substantiates this common sense. From (6.9b), we can see that if k2 and t1 are large, structure C1 occurs in equilibrium. Assume that country 1 is the US and country 2 is Taiwan. Now, the government in the US increases the import tariff rate, so that t1 decreases. Its inframarginal effect is to make the equilibrium jump to autarky. From subsections 6.5.6 and 6.5.7, we can see that the relative wage rate of the US to Taiwan is 1/t1ρ >1 in C1, and is 1 in autarky. Hence, the inframarginal effect of the tariff increase is to reduce the relative wage in the US. But the marginal effect of a decrease in t1 is to raise the relative wage rate in the US, since d(1/w) = d(1/t1ρ)/dt1 < 0. Also, from subsection 6.5.7, the terms of trade of the US p1y/p2z marginally increase as t1 decreases (or as tariff rate in the US increases). These are the positive marginal effects of this tariff increase on terms of trade and wage rate in the US. But it generates negative marginal effect by reducing trade and productivity gains that can be exploited. The net marginal effect of this tariff increase is represented by resulting changes in per capita real incomes (equilibrium utility). From (6.4), it is obvious, this net marginal effect is negative, since per capita real income decreases as a result of the tariff increase in the US (du1/dt1,

193

du2/dt1 > 0). If we take into account the negative inframarginal effect of the tariff increase, which reduces the relative wage rate of the US, the total net effect of the tariff increase is to hurt labor in the US. We can conduct a similar analysis for other structures C, E, and F to obtain similar results. It is interesting to see that in this example, labor in the US benefits from a decrease in tariff rate, even if this tariff reduction marginally deteriorates the US’s terms of trade. This is because productivity gains from the expanded network size of trade (an increase in the number of traded intermediate goods n) may outweigh the negative effect of deteriorated terms of trade. The analysis of structure D suggests that the net marginal effect of a tariff increase in the US is positive (u1 increases as t1 decreases), though it marginally deteriorates terms of trade p1x/p2x and relative wage 1/w. But total net marginal and inframarginal effect could still be negative. It is straightforward from the local equilibria in C, D, E, and F that the factor price equalization does not hold in general since the equilibrium value of w is not 1 in general, though it tends to 1 as transaction costs go to 0. Hence, transaction costs explain the difference in factor prices between the countries. As transaction conditions are improved, the factor price tends to be equal for a given structure. A generalized FPE theorem may then be considered that as transaction conditions are improved, factor prices tend to be equalized. But inframarginal comparative statics (jumps of equilibrium between structures) will invalidate the generalized FPE theorem. For instance, as k2 increases, the equilibrium may jump from D0 to C1, which may cause an increase in the difference in wage rates between the two countries. It is easy to see that the RY theorem may not hold in this example. But it is not appropriate to directly compare the comparative statics with the core trade theorems in the HO model because of different specifications of model structures. Hence, we should pay more attention to the distinct features of comparative statics of the model in example 6.3, which are summarized in propositions 6.3 - 6.6. The effects of changes in transaction conditions on the number of traded goods and intermediate goods (degree of industrialization), productivity, per capita real income, and on discontinuous jumps of trade patterns are much more important than their effects on the structure of relative prices. Not much regularity of comparative statics that relate to changes of structure of relative prices stands out in general in example 6.3. Anything is possible, even if a specific model is explicitly specified. The regularity of comparative statics that relates to price structure is not only model specific, but also trade-structure specific (or parametersubspace specific). Hence, it is inconsequential to try finding the counterparts of the SS theorem and RY theorem in the model with economies of scale. We now consider a comparison between our comparative statics and conventional wisdom in development economics. We first consider the development trap, then the relationship between industrialization, income distribution, and evolution of dual structure, and finally, development strategy. Assume that food z is a necessity and its minimum per capita consumption must not be smaller than 1 for subsistence. Suppose all labor is allocated to the production of z. Then per capita output, and therefore per capita consumption, of z is θi, which is not greater than 1 if and only if θi ≤ 1. Hence, for a value of θi small enough to be close to 1, the equilibrium number of intermediate goods must be at its minimum value 1. In other

194

words, each intermediate good is not individually a necessity for the production of the final manufactured good y, and therefore labor must be concentrated in the production of food, rather than dispersed in producing many intermediate goods if productivity of food is very low. If transaction efficiency for international trade is also very low, then importing food is not an optimum choice. Therefore, a country with very low transaction efficiency and low productivity of agricultural goods will be locked in the development trap associated with autarky structure A, where the number of available producer goods is very small, productivity of the final manufactured goods is low, and trade dependence and per capita income is low. This provides a formal equilibrium theory that predicts empirical evidence in chapter 2 that tropical regimes are in development trap due to unfavorable geographical conditions that cause low agricultural productivity. It is not difficult to show that as transaction conditions are improved, the relative output of industrial goods x and y to the agricultural good z increases, though the income share of industrial goods is always a constant, regardless of the degree of industrialization. Here, industrialization relates to an increase in the number of intermediate goods and to a decrease of price of final manufactured goods (which is associated with an increase in the total factor productivity of final manufactured goods). As industrialization continues, changes in the difference in per capita real income between countries do not have much general regularity. Suppose structure C1 occurs in equilibrium. Then from subsection 6.5.7, we can see that per capita real income in country 1 is higher than in country 2 if and only if (θk1)1-αt11ρ-α > (k2t2)α. Suppose this inequality holds, and the difference in per capita real income between the two countries increases with θ and k1 and decreases with k2 and a. Its relationship with t1 is ambiguous. Hence, there are many determinants of the relationship between trade and inequality of income distribution between countries. Suppose industrialization and increases in trade are driven by improvements in transaction conditions. The relative change speed of transaction conditions in the two countries affects changes in the difference in per capita real income between the two countries. There is no monotonic correlation, nor is there a simple, inverted U-curve between the difference and trade, which increases with transaction efficiency and industrialization. If marginal comparative statics in other structures and inframarginal comparative statics are considered, our conclusion will be strengthened: little general regularity of the relationship between inequality and economic development and related trade exists. This prediction is supported by recent empirical evidence in Ram (1997) and Deininger and Squire (1996) which show that no monotonic correlation between inequality of income distribution and economic development exists. We now consider the implications of comparative statics for development strategies. Again, we may take country 1 to be the US and country 2, Taiwan. Suppose transaction efficiency for international trade in the initial period of time is very low in both countries, then autarky occurs in equilibrium. Assume further that the US has quite a large autarky equilibrium number of intermediate goods (quite a high degree of industrialization) due to their relatively large population size, and that Taiwan is in the development trap. Now we consider the two cases. In case (a), Taiwan is in the development trap due to low relative productivity of the agricultural sector (bad climate conditions and limited arable land). In case (b), Taiwan’s relative productivity of the agricultural sector is high, but its population size is too small.

195

Assume that in period 2, transaction efficiency for international trade is slightly improved. The equilibrium will jump to structure F1 for case (a), since (6.9a) and (6.9b-III) indicate that for a large θ (country 2’s relative productivity of the agricultural good is low) as transaction conditions are slightly improved, the equilibrium jumps from autarky to F1. For case (b), as transaction conditions are improved, the equilibrium jumps from autarky to structure C1, since (6.9b-I) indicates that for a small θ (country 2’s relative productivity of the agricultural good is high), structure C1 is more likely to occur in equilibrium. Suppose that the slight improvement in transaction conditions is not enough to ensure t1 > ta, so that n2 = 0 as shown in (6.5). This implies that Taiwan completely specializes in producing and exporting the agricultural good (without industrialization), though it can gain from exogenous comparative advantage in production. In period 3, Taiwan has several options, dependent on the transaction cost coefficient or tariff rate in the US, which is 1-t1. Suppose 1-t1 decreases over time due to liberalization reforms or a preferential tariff rate to Taiwan in the US. Then Taiwan starts industrialization. The production of intermediate goods relocates from the US to Taiwan, increasing per capita real incomes in both countries and the relative wage rate in Taiwan (see (6.4) and (6.5)). This shift from C1 with a small n2 to C1 with a large n2 looks like an export oriented development pattern pursued by Taiwan in the 1960s - 1980s. The driving forces of this industrialization are the open-door policy of the US (an increase in t1 and k1, see (6.4) and (6.9b-I)) and Taiwan’s liberalization and internalization policy (a large k2, see (6.9b)). In the literature of development economics, structure C1 with a small n2 is sometimes called the development pattern of dependence (see Myrdal 1957, Nelson 1956, Palma 1978, for instance). But if k2 is small compared to t1 and t2 because of a high tariff of imported final goods and a low tariff of imported producer goods in Taiwan, then the equilibrium will jump from C1 with a small n2 to D0 as Taiwan lowers its import tariff of producer goods. This policy regime is just like the import substitution strategy carried out in Taiwan in the 1950s (see, for instance, Balassa 1980, Chenery, Robinson, and Syrquin 1986, Meier 1989, pp. 297306, and Bruton 1998). The jump from C1 with a small n2 to D0 is just like an import substitution process. The difference between export-oriented and import substitution development patterns lies in the fact shown in propositions 6.3 - 6.5, that all countries have incentives to raise import tariff rates in structure D0, which will reduce per capita real incomes in both countries, while in structure C, E, or F, both countries have incentives to reduce tariff rates. In other words, if a government manipulates their tariff structure to pursue structure D (import substitution), D itself will justify a more distorted tariff structure which impends economic development. Hence, this distorting tariff policy could generate a particular type of development trap. In the absence of such a distorting tariff, structure D may occur naturally in equilibrium as a consequence of certain patterns of endogenous and exogenous comparative advantages in production and transactions. Since utilities of both countries increase with transaction efficiencies in structures C, E, and F, liberalization and internationalization policy is easier to carry out in these structures. This explains why an export-oriented development pattern is more successful than the pattern of import substitution. But the notion of import substitution is inaccurate, since this pattern of trade and development relies on increases in imported intermediate goods, though it promotes domestic production of final manufactured goods.

196

Another interesting difference in development patterns is between structure E1 or F1 and structure E2. F1 indicates that the less developed country (country 2) imports final goods and exports parts and components of the final manufactured goods. Taiwan does not export automobiles, but exports a lot of parts and components of automobiles and computers. In structure E2, the less developed country imports intermediate goods and exports final manufactured goods, similar to Hong Kong’s development pattern in the 1970s and 1980s. However, if E1 or F2 occurs in equilibrium in the absence of government intervention, which of them actually takes place is determined by natural endogenous and exogenous comparative advantage in production and transactions. It is counterproductive to pursue a particular one by using tariff policy. Any improvements in transaction efficiencies will promote productivity progress and increase per capita real income, regardless of which one, E or F, occurs in equilibrium. The Krugman-Venables model and the model in example 6.3 predict type II scale effects (productivity of manufactured goods goes up if and only if the average size of manufacturing firms increases). The type II scale effects are rejected by empirical evidence provided by Liu and Yang (2000). There are two ways to avoid the scale effects. One is to specify local economies of scale. This makes the algebra very complicated due to feedback loops between positive profit and consumers' demand functions. The other way is to develop the Smithian models with intermediate goods and firms, which are presented in chapter 12.

Key Terms and Review Dual structure between the industrial and agricultural sectors, dual structure with unequal distribution of gains from trade, and dual structure between commercialized and self-sufficient sectors Dual structure caused by disequilibrium in labor market vs. dual structure in the transitional stage of evolution of division of labor Effects of coexistence of endogenous and exogenous comparative advantages on the emergence, evolution, and disappearance of dual structure Underdevelopment and dual structure with underemployment Why may the deterioration of terms of trade of a country and increases in gains that country receives from trade may concur? Effects of economies of scale, industrial linkages, and differences in transaction conditions between countries on the evolution of dual structure and on income distribution Immiserizing development Coordination problems of the industrial linkage network caused by multiple equilibria Type II scale effect Relationship between inequality of income distribution, economic development, trade, and evolution in division of labor

Further Reading Smithian models with both endogenous and exogenous comparative advantages: Gomory (1994), Liu (1999), Cheng, Liu, and Yang (2000), Zhou, Sun, and Yang (1998); Existence theorem and first welfare theorem in a general class of Smithian models: Sun, Yang, and Yao (1999), Zhou,

197

Sun, and Yang (1998); Underdevelopment: Bauer and Yamey (1957), and Kindleberger (1958), Myrdal (1957), Nelson (1956), Palma (1978); Dual economy and structural changes: Ranis (1988), Lewis (1955), Fei and Ranis (1964), Chenery (1979, 1986), Khandker and Rashid (1995), Dixit (1968); Equilibrium models of dual economy and economies of scale: Din (1996), Murphy, Schleifer, and Vishny (1989), Gans (1998), Kelly (1997), Fujita and Krugman (1995), Baldwin and Venables (1995), Puga and Venables (1998), Krugman and Venables (1995); Deteriorated terms of trade: Sen (1998), Cypher and Dietz (1998), Kohli and Werner (1998), Morgan (1970); Variable returns to scale: Young (1991), Panagariya (1983), Kemp (1991); Empirical evidence for the coexistence of exogenous and endogenous comparative advantage: Gallup and Sachs (1998), Sachs and Warner (1995, 1997); Development strategy of import substitution and export substitution: Hirschman (1968), Krueger (1984), Balassa (1980), and Bruton (1998); Unequal distribution of gains from trade and deteriorated terms of trade: United Nation’s Economic Commission for Latin America (ECLA) (1950), Spraos (1983), Sapsford (1985), Singer (1984), Kravis and Lipsey (1981), Emmanuel (1972), Bacha (1978), Smith and Toye (1979), Alizadeh (1984), Thirwal (1986), Evans (1987); Positive correlation between inequality and growth: Banerjee and Newman (1993), Lewis (1955), Palma (1978), Li and Zou (1998), Grossman (1998), Murphy and Welch (1991), Borjas, Freeman, and Katz (1992), Karoly and Klerman (1994), Sachs and Shatz (1995); Negative correlation between inequality and growth: Alesina and Rodrik (1994), Galor and Zeira (1993), Thompson (1995), Fei, Ranis, and Kuo (1979), Aghion, Caroli, and Garcia-Pendosa (1999), Frank (1977), Balassa (1986); Immiserizing growth: Bhagwati (1969), Sachs, Yang, and Zhang (1999a); Inverted U-curve for inequality and per capita income: Kuznetz (1955), Krugman and Venables (1995); Fluctuation of inequality: Ram (1997), Jones (1998, p. 65), Deininger and Squire (1996); Survey of the relationship between inequality, trade, and economic development: Cline (1997), Jeffrey Williamson (1998), Burtless (1995).

Questions 1. Gallup and Sachs (1998) have found empirical evidence that different geographical conditions are responsible for development performance differences between countries. Those countries located in temperate zones and having better geographical conditions for transportation have better long-term development performance. Use the model with endogenous and exogenous comparative advantages in examples 6.1 and 6.3 to explain the empirical evidence. 2. There are several different definitions of dual economy. Lewis (1955) and Fei and Renis (1964) take dual economy as a structure with division of population between the modern industrial sector and the traditional agricultural sector. In chapter 3, we consider a structure with unequal incomes between two groups of ex ante different individuals as a dual structure. Compare the dual structure in example 6.1 to these definitions and discuss the effects of the coexistence of endogenous and exogenous comparative advantage on dual structure. Relate your discussion to the notions of underemployment and underdevelopment. 3. Emmanuel (1972), Bacha (1978), Smith and Toye (1979), Prebisch (1988), Frank (1995), and Alizadeh (1984) argue that international trade transfers wealth from the poor countries to the rich ones. Use the models in this chapter to assess the argument. 4. John Stuart Mill (1848) emphasized the importance of “the tendency of every extension of the market to improve the processes of production.” He argued that “a country which produces for a larger market than its own can introduce a more extended division of labour, can make greater use of machinery, and is more likely to make inventions and improvements in the processes of production.” Use the models in this chapter to formalize his ideas. 5. United Nations, Department of Economic Affairs (1950, pp. 7, 13-24) and Lewis (1952, p.118) argued, based on the measurement of prices of the United Kingdom’s commodity terms of

198

trade or the terms of trade between primary products and manufactured products, that international market forces have transferred income from the poor to the rich nations through deterioration in the terms of trade of less developed countries. Meier (1989, pp. 390-92) argues that this does not provide a sufficiently strong statistical foundation for any adequate generalization about the terms of trade of poor countries. The import-price index conceals the heterogeneous price movements within and among the broad categories of foodstuffs, raw materials, and minerals; no allowance is made for changes in the quality of exports and imports; there is inadequate consideration of new commodities, and the recorded terms of trade are not corrected for the substantial decline in transportation costs. The introduction of new products and qualitative improvements have been greater in manufactured products than in primary products, and a large proportion of the fall in British prices of primary products can be attributed to the great decline in inward freight rates. Even if it were true that the less developed country experienced a secular deterioration in their commodity terms of trade, this deterioration may have been caused by productivity progress in the export sector. Hence, as long as productivity in export industries is increasing more rapidly than export prices are falling, the single-factoral terms of trade (commodity terms corrected for changes in productivity in producing exports) may increase and the country’s real income can rise despite the deterioration in the commodity terms of trade. Use the model in example 6.1 to formalize this analysis. 6. Many economists argued that the deterioration of terms of trade for less developed countries hinders economic development in these countries. Other economists try to find empirical evidence for or against the fact that terms of trade for developing countries have been worsening, or to measure adverse effects of the worsening terms of trade on economic development. (See, for example, Morgan 1970, and Kohli and Werner 1998). Sen (1998) reports that from 1990 to 1995, Thailand’s GDP increased by 49%, its export price increased by 18%, and its import price by 21%. During the same period, Singapore’s GDP increased by 49%, its export price decreased by 18%, and its import price decreased by 9%. Use the model in example 6.1 to explain this fact. 7. Murphy, Shleifer, and Vishny (1989) show that if income distribution is very unequal, so that a limited market will adversely affect economic development Compare this theory on the relationship between dual structure and economic development to the Smithian mechanism for economic development in example 6.1. 8. Lewis (1955) argues that an exogenously fixed wage rate that is higher than the market clearing level generates a labor surplus in the traditional agricultural sector. As capital accumulates in the modern industrial sector over time, marginal productivity of labor relative to capital in the industrial sector increases, so that this sector can absorb surplus of labor and grow at no cost of the agricultural sector. Compare this mechanism of development and dual economy to the Smithian mechanisms in examples 6.1 and 6.2. Find empirical evidence to test one against the other of the two mechanisms. 9. Chenery (1986, pp. 13-32) used models with disequilibrium and changes of tastes to explain structural changes in an economy. According to him, “Given imperfect foresight and limits to factor mobility, structural changes are most likely to occur under conditions of disequilibrium; this is particularly true in factor markets. Thus a shift of labor and capital from less productive to more productive sectors can accelerate growth.” Use the equilibrium models in this and previous chapters to explain structural changes and dual structure, and discuss the differences between the two approaches. Which of them is analytically more powerful, and why? 10. Chenery (1986) emphasized the effects of changes on the demand side on structural changes in the economic development process. For instance, he argued that changes in preferences and in income alter the expenditure share of agricultural goods. Other economists pay more attention to effects of changes in the supply side on structural changes. For instance, changes in technology alter the income share of industrial output. Use the general equilibrium analysis

199

in this text to explain why the separation between demand and supply analyses is inconsistent with the notion of general equilibrium. For example, income is determined by productivity and network size of division of labor, which are in turn determined by the extent of the market, which relates to aggregate income. Also, use models in this chapter to explain why economic structure may change endogenously in the absence of changes in production functions and in preferences. 11. Lewis (1955) uses a model with disequilibrium in the labor market to analyze dual structure. Use the approach developed in chapter 13 to specify a formal dynamic general equilibrium model with constant returns to scale technology in two sectors. One of the sectors needs capital and labor as inputs, and the other sector needs only labor as input in production. Show that in the absence of exogenous technical changes and of disequilibrium in labor market, the equilibrium relative size of the two sectors can evolve over time. Use this example to discuss the effects of economists’ limited capacity in managing general equilibrium models on the economic thinking in the 1950s and 1960s. 12. Lewis (1955) considered economic development and structural changes as a process of transformation of the traditional sector with a low degree of exchanges to a modern sector with a high degree of exchanges. Use the models in this chapter to formalize his conjecture. 13. Compare the policy implications of the model in example 6.1 with the view that underdevelopment is caused by the exploitation of less developed economies by capitalist developed economies (Myrdal 1957, Nelson 1956, Palma 1978). 14. Use the inframarginal comparative statics in Table 6.3 to analyze a recent debate on competitiveness. Show that a country with low transaction efficiency cannot receive gains from trade in the transitional stage of economic development. Verify the following statements. From the northwest block of Table 6.3, we can see that if the degree of economies of specialization in country 1, b, which negatively relates to α, is small relative to c, which negatively relates to γ, or k1< α23-c, then structure PC is the equilibrium where this country is in an inferior position in the transitional stage. If c is small relative to b, or k2 < aγ23-b, structure CP occurs in equilibrium, where country 2 is in an inferior position in the transitional state. You may interpret absolute level of transaction efficiency and degree of economies of specialization for a country in producing a good as degree of competitiveness. 15. Compare the model of dual economy in example 6.1 with the Ethier model of dual economy in example 5.2 and the Sachs and Yang dual economy model in example 5.4. 16. Compare the model of dual economy in example 6.1 with the model in example 6.3, analyze empirical implications of the differences, and design a method to test the two types of models of dual economy against data. 17. Use the model in example 6.3 to show that the notions of import substitution and export substitution may be misleading. Use this model to analyze welfare effects of industrial and trade policies. 18. Some economists argue that imperialism and colonialism are detrimental for economic development since they deter expansion of a variety of industrial sectors in the less developed country. Use the models in this chapter to assess this statement. Draw the distinction and connection between division of labor, diversity of professional occupations, and individuals' specialization in your analysis. 19. Compare Taiwan's development pattern, which does not promote domestic production of automobiles, but promotes exports of components and parts produced by many small companies, with South Korea's development pattern, which promotes domestic production of automobiles and other final manufactured goods. Use the extended KV model in example 6.3 to assess the effects of the two different development patterns. 20. Use the extended KV model in example 6.3 to comment on the following statements: "Any industrial and trade policies are harmful for economic development and exploitation of gains from trade." "Industrial and trade policies can be used to enhance a developing country's

200

performance of trade and development and thereby significantly enhance welfare of this country." 21. Use the model in example 6.3 to analyze the differences between three types of coordination problems of the industrial linkage network. The first two types are caused by multiplicity of equilibria. One of them involves interest conflicts between the countries (in a Recardo model with dichotomy between pure consumers and firms). The other does not (the MSV model in example 5.3). The final type is caused by a particular kind of distortions in the equilibrium models of monopolistic competition that are not beneficial to any decision makers (in the DS model in example 5.1 and the Ethier model in example 5.2. Also see example 2 in chapter 5). 22. Hirschman (1958) argues that forward (to downstream sectors) and backward (to upstream sectors) linkages to the sectors with economies of scale in production are more important than terms of trade for a developing country to gain from trade. Use the models in this chapter to formalize this idea. 23. Some economists argue (see Meier 1989, pp. 381-93) that if income elasticity of demand for goods exported by a developing country is low, export-led industrialization may not benefit the economic development of that country. Compare the general equilibrium analysis with this analysis of demand. Why is the marginal analysis of demand often very misleading? Some economists argue that the demonstration effects of international trade will increase the desire for consumption and reduce saving and investment. This will be detrimental for economic development. Use the model in example 6.3 to show that as the taste parameter for imported final manufactured goods increases in country 1, economic development may be speeded up in structure C1. 24. Ram (1997), Jones (1998, p. 65), and Deininger and Squire (1996) have found empirical evidence that inequality fluctuates as an economy develops. Yang and Zhang (1999, see exercise 12) specify different types of individuals in each country in example 6.1 and show that inequality of income distribution fluctuates as different groups are sequentially involved in an increasingly higher level of division of labor. Use that model to explain the empirical evidence. 25. Discuss the effect of a change in analytical framework on interpretation of empirical observation in connection with the following statement of Albert Einstein: "It is quite wrong to try founding a theory on observable magnitudes alone. … It is the theory which decides what we can observe" (quoted in Heisenberg, 1971, p. 31). 26. Why is marginal analysis not enough for managing the model in example 6.3?

Exercises 1. Following the method to draw Fig. 6.2, draw individual PPFs, the aggregate production schedule for autarky, and the aggregate PPF in the model in example 6.2. Show that there are economies of division of labor in this model. 2. Suppose that b = c = 2 in example 6.1. Show that inframarginal comparative statics are given by the following table.

0 < k2 ≤ 16/27

0 < k1 ≤ 16/27 k1k2< k1k2 > 4a(2/3)6 6 4a(2/3) k k2’, k2’∈(4a/27, 16/27), k1∈(16/27, 1), a < 4, k2”∈(16/27, 1) and if k2’< 8/27, then as k2 increases from k2’ to k2”, country 2’s terms of trade deteriorate. Meanwhile, each individual's utility in country 2 increases from autarky level to a higher level. 4. If we assume that there are economies of specialization only for individuals in country 1 in producing two goods, whereas constant returns prevail in country 2 in producing the two goods, the system of production functions is then: x1 + x1s = L1xb, y1 + y1s = L1yc, s x2 + x2 = aL2x, y2 + y2s = L2y Draw individual PPFs, the aggregate production schedule for autarky, and the aggregate PPF. Show that the inframarginal comparative statics of general equilibrium are given in the following table. k1∈ (0, 4θ)

k2< 1 a>2b-c k1k2 < θ2bc+2 /a

b-c

k1k2 > θ2b-c+2/a

a>2b-1 a2b-1 a2 where θ ≡ bbcc/(b+c)b+c.

a aθ2c-b+2 PC+

k2 a2c-b

k2 = 1 a>2b-c a>2b-1

aθ2b+1/a CC-

AD k1> θ2c-b+2/a

a>2b-1

a t. In other words, each type a person has higher transaction efficiency than each type b person. Also, we assume that in country 2, k2 = k. This implies that country 2 is a developed country which has better transaction conditions. Country 1 is a less developed country, where some residents (who might be urban or coastal residents) have the same transaction condition as in a developed country, but the rest of the population have a lower transaction efficiency. The production conditions are the same for all individuals in the same country, but different between the countries. Hence, the production functions for a type i consumer-producer are xj + xjs = Ljxc, yj + yjs = Ljy, j = a, b. x2 + x2s = L2xc, y2 + y2s = rL2y, where xis, yis are respective quantities of the two goods sold by a type i person, Lis is the amount of labor allocated to the production of good s (= x, y) by a type i person, and Lix + Liy = 2. It is assumed that r, c > 1. Solve for equilibrium and its inframarginal comparative statics. Show that as transaction conditions are improved, the level of division of labor increases and inequality of income distribution fluctuates. 12. (Yang and Zhang, 1999) Assume that in the developed country, there are also two types of individuals. Show that as more individuals are sequentially involved in the division of labor, some individuals achieve a higher level of specialization before others do. This increases inequality. As the latecomers catch up, inequality decreases. As the leading group goes to an

203

even higher level of specialization, leaving the other behind, inequality increases again. Show how such a ratcheting process generates the fluctuation of inequality. 13. Prove that in the model in example 6.3, the following structures cannot occur in equilibrium for ki ∈(0, 1): A structure in which each country produces y, z, x, and one of them exports y, x and the other exports z, x; A structure in which each country produces all goods, and imports and exports all goods cannot occur in equilibrium. (Clue: use the first order conditions for the decision problems of consumers in two countries to show that equilibrium requires k1k2 = 1 which contradicts ki∈(0, 1).) 14. (Puga and Venables, 1998) Suppose that in example 6.3, the production function for the agricultural sector is a Cobb-Douglas function of labor and land. Solve for local equilibria in all possible market structures. Use the model to analyze effects of geographical concentration of industrial production on dual structure. 15. Introduce tariff into the KV model to analyze the effects of trade policy on development pattern. Assuming that the two governments can choose between Nash tariff game and Nash tariff negotiation, as in the Ricardian model in chapter 3, what policy regime will occur if structure D takes place in equilibrium? 16. Consider the model in example 6.3. Prove that in the structure in Fig. 6.3(b) cannot occur in equilibrium. (Clue: use the market clearing conditions to show that equilibrium requires x11 = k1x21, x12 = k1(k1k2)ρ/(1-ρ)x22, x11+x12= x1, x21+x22= x2, which contradicts ki∈(0, 1)), where xij is the amount of an intermediate good produced in country i and sold in country j.) 17. Show that the corner equilibrium in structure C2 is: w = k2-ρ, p1z = 1, p2x = bw/ρ, p1x = b/ρ, β-1 -β/ρ β -ρ p2y = (1-β) β (b/ρ) k2 [(1-ρ)α(M2+ k2ρM1)/a] β (1-1/ρ), n1 = [(1-ρ)/a][M1β- (1-β)k2-ρM2], n2 = [(1-ρ)/a][M2αβk2-ρ-(1-α)βM1], u2 = Bk21-α-ρ p2y-α, u1 = B k1αp2y-α, where B ≡ (1-α)(1-α)αα. Prove a proposition for this structure similar to proposition 6.3. 18. In the original version of the KV model, the transaction cost for the agricultural good is 0 and transaction conditions for industrial goods y and x are the same in the two countries. Prove that for this version of the KV model, the local equilibrium in structure in Fig. 6.3(b) is indeterminate, the equilibrium n1 and n2 are indeterminate, and equilibrium values of xij yij, and zij are indeterminate. 19. Assume that in the KV model, country 1's total productivity of good y is θ>1. Solve for local equilibria in all possible structures and their comparative statics. Then compare your results with the results in example 6.3. 20. Use the model in example 6.3 to formalize Chenery and Meier’s idea that exporting final manufactured and importing intermediate goods can be a development pattern, which may evolve to the pattern exporting producer goods.

204

Chapter 7: Structural Changes, Trade, and Economic Development

7.1. Endogenous Trade Theory and Endogenous Number of Consumer Goods Smith explained domestic and international trade by individuals’ decisions in choosing their levels of specialization. Hence, the rationale for both international and domestic trade is the same: economies of division of labor. But within the neoclassical framework, the dichotomy between pure consumers and firms implies that the rationale for domestic trade differs from that for international trade. Domestic trade is essential for pure consumers even if comparative advantage, economies of scale, and difference in tastes between individuals are absent, since pure consumers do not produce and will die from starvation in the absence of domestic trade between them and firms. However, international trade will not take place if these elements are not present, since each country has firms, or each country is a consumer-producer. Therefore, neoclassical trade theory cannot explain why and how international trade emerges from domestic trade. The first purpose of this chapter is to use a Smithian model to illustrate the intimate relationship between economic development, trade, structural changes, and evolution of division of labor. This model explains international and domestic trade by individuals’ decisions in choosing their levels of specialization, and explains the emergence of international trade from domestic trade by evolution in division of labor and evolution in endogenous comparative advantage between ex ante identical individuals. Since the number of goods in the models in this chapter is a parameter or a variable instead of a specific number, structural changes and their relationship with evolution of division of labor and economic development can be more thoroughly investigated. In section 7.2, we specify a Smithian model with endogenous specialization and the number of goods as a parameter. In section 7.3, individuals’ decisions in choosing their patterns of specialization and resource allocation are solved. Then inframarginal comparative statics of the decisions are analyzed in section 7.4. Section 7.5 is devoted to the analysis of general equilibrium network of division of labor. Then inframarginal comparative statics of general equilibrium are used to analyze many concurrent phenomena of structural changes as different aspects of economic development. Section 7.5 analyzes how international trade emerges from domestic trade. In section 7.6, we combine the approach of endogenizing individuals’ levels of specialization with the approach of endogenizing the number of all available goods to investigate the role of the development of division of labor in accounting for the emergence of new goods. More than two centuries ago, Josiah Tucker (1755, 1774) noted that the development of division of labor creates the conditions for the emergence of new goods. Casual observations indicate that in an autarchic society without much division of labor, the variety of available goods is small, whereas in a developed economy with a high level of division of labor and specialization, the variety of available goods is large. Does this positive correlation between specialization and variety of available goods

205

happen by coincidence? Or is it generated by some economic mechanism that is essential for understanding economic development? We may have a guess. Assume that there are economies of specialization, transaction costs, and economies of consumption variety or economies of complementarity between consumption goods because of individuals’ preferences for diverse consumption. Assume further that the calculation cost of the optimum decision increases with the number of consumption goods and accordingly counteracts the economies of consumption variety. Therefore, there are several trade offs among four elements: economies of specialization, transaction costs, economies of consumption variety, and management costs of consumption variety. The efficient trade offs are, of course, dependent on the parameters of transaction efficiency, the degree of economies of consumption variety, the management cost of consumption variety, and the degree of economies of specialization. For a sufficiently low transaction efficiency, each person has to choose autarky. The narrow scope for trading off among economies of specialization, economies of consumption variety, and management cost of consumption variety, due to each individual’s limited time endowment in autarky, may force individuals to produce a few goods. It would not be feasible in autarky for individuals to self-provide the cars, trains, airplanes, computers, television sets, telephones, and various detergents. However, as transaction efficiency is improved, the scope for trading off economies of specialization against transaction costs is enlarged, so that the level of division of labor is increased. The increased division of labor enlarges the scope for trading off economies and diseconomies of consumption variety, so that each individual’s level of specialization and the number of available consumption goods can be simultaneously increased through a higher level of division of labor between specialists who produce different goods. Thus, in a Smithian model with the CES utility function, the number of consumption goods and the level of division of labor can be simultaneously endogenized if a trade off between economies and diseconomies of consumption variety is specified in addition to the trade off between economies of specialization and transaction costs. The endogenization of the number of goods is associated with the endogenization of emergence of new goods, which is considered by many economists as endogenous technical progress. If transaction efficiency is low, then the production functions of some goods cannot be seen in equilibrium. As transaction efficiency is improved, the production functions of new goods emerge from a greater scope for trading off economies of specialization against transaction costs and economies of consumption variety. Hence, in our model of endogenous specialization and endogenous number of goods, productivity progress is associated with the emergence of the production functions of new goods. This view of endogenous technical progress differs from the conventional view that attributes technical progress to investment in research and development. According to our view of endogenous technical progress, investment in R&D alone is not sufficient for emergence of new goods and related new production functions. It is essential for the emergence of new goods that the size of the network of division of labor and the related extent of the market are sufficiently large to create the condition for the commercialization of new technology. A sufficiently high transaction efficiency is therefore essential for a large size of the network of division of labor. In section 7.9, we consider a model with endogenous level of specialization in trading activities. If individuals are allowed to choose levels of specialization in trading activities

206

and if there are economies of specialization and transaction costs in the trading activities, then transaction efficiency is endogenously determined by the level of division of labor between production and transactions and within the professional trading sector. Hence, the level of division of labor is determined by transaction efficiency, which is determined by the level of specialization in the trading sector, and which is in turn determined by the efficient trade off between economies of specialization in the trading sector and transaction costs of the transaction services. Therefore, we can use a Smithian model to explain the equilibrium level of division of labor and productivity by transaction conditions of transaction services, and investigate effects of institutions and government policies on economic development via their effects on transaction conditions of transaction services. In this general equilibrium model, transaction efficiencies, the network size of division of labor, the extent of the market for transaction services, the level of division of labor within the transaction sector, the emergence of professional middlemen, productivity, and per capita real income are interdependent. The notion of general equilibrium is powerful for figuring out a development mechanism that simultaneously determines all of them. Finally, section 7.10 presents the Becker-Murphy model with the trade off between economies of specialization and coordination costs, which can explain evolution of division of labor by improvements of coordination efficiency in the absence of increases in population size.

Questions to Ask Yourself when Reading this Chapter Why can fixed learning costs generate economies of division of labor? What are the differences between the neoclassical and Smithian theories of demand? What are the differences between neoclassical trade theory and Smithian trade theory? Why does evolution in division of labor generate concurrent increases in the following variables: the degree of commercialization, trade dependence, the degree of interpersonal dependence, the extent of the market, the number of types of markets, productivity, the extent of endogenous comparative advantage, the degree of diversity of economic structure, individuals’ levels of specialization, the degree of production concentration, and the degree of market integration? How does international trade emerge from domestic trade? Why is endogenous comparative advantage a more important determinant of trade dependence and economic development than exogenous comparative advantage? Why does the development of division of labor create conditions for a greater consumption variety and the emergence of new goods? What are development implications of the emergence of professional middlemen?

7.2. A Model of Economic Development with Fixed Learning Costs Example 7.1: A Smithian trade model with fixed learning cost (Yang 1996). As in the previous chapters, we assume that the set of consumer-producers is a continuum of mass M.

207

The set of consumer goods is either a finite set {1, 2, …, m} or a continuum with mass m. As shown by Zhou, Sun, and Yang (1998), the assumption of a continuum of goods is not essential for the existence of equilibrium in this kind of models though it may simplify the algebra of a symmetric model by avoiding an integer problem. If the set of goods is considered as a continuum, then symbols for summation ∑ and multiplication ∏ should be viewed as integration. If the set of goods is finite, then all derivatives with respect to the number of goods in the first order condition for maximization should be considered as the approximation of the first order condition for an integer programming. The self-provided amount of good i is xi . The amount of good i sold in the market is xis . The amount of good i purchased in the market is xid . The transaction cost coefficient for a unit of goods bought is 1-k. Thus, kxid is the amount an individual obtains when she purchases xid . The amount c d consumed of good i is thus xi ≡ xi + kxi . The utility function is identical for all individuals: (7.1) u = Π i =1 m x i c The system of production for each consumer-producer is: (7.2a) xi p ≡ xi + xis = Max { Li − A, 0} i = 1, …, m

∑L

(7.2b)

i

i

=1

p

where xi is the output level of good i, Li is an individual’s level of specialization in producing good i, and A is a fixed learning and training cost in producing each good. This system of production displays economies of specialization for each individual in producing each good. For Li > A, the average labor productivity, (xi+xis)/Li = 1-(A/Li), increases with an individual’s level of specialization in producing good i, Li . Houthakker (1956) uses a graph to illustrate the development implications of the fixed learning cost. A similar graph in Fig 7.1 shows that economies of division of labor exist for the production condition defined in (7.2) with m = 2. An individual's transformation curve is EFGH in Fig 7.1. The aggregate transformation curve for the two persons when each of them produces two goods, with no division of labor, is segment DI. The aggregate transformation curve for the division of labor, which implies at least one person producing only one good, can be obtained in the following way. Suppose that an individual (she) produces only good 1. Her output level is represented by the vertical line HK. Assume that the other individual (he) can choose any production configuration, so that his transformation curve is still EFGH. By moving the individual transformation curve horizontally to the right by distance 1-A, the aggregate transformation curve for the two individuals can be then obtained as KBJL. Suppose now, alternatively, that she produces only good 2 instead of good 1, while he can still choose any production pattern. Now the aggregate transformation curve is MCAK. Therefore, in the simple two-good-twoperson case, the aggregate transformation curve for the division of labor, where at least one individual produces only one good, is MCAKBJL.

208

Figure 7.1: Economies of Division of Labor Generated by Fixed Learning Costs

It is obvious that the aggregate transformation curve for the division of labor is higher than the aggregate transformation curve for autarky, even if the two persons are ex ante identical or even if exogenous comparative advantage is absent. This is because each individual’s total learning cost is 2A if she produces both goods and her total learning cost is reduced to A if she produces only one good. That is, her time for production increases from 1-2A to 1-A as she reduces the number of goods produced from two to one. Hence, the total learning cost for the economy with two individuals is 4A in autarky, 3A for partial division of labor (segment CA and BJ), and 2A for complete division of labor (point K) in an economy with two individuals. The economies of division of labor are represented by the difference between the transformation curve for the division of labor, MCABJL (which is also the PPF), and the transformation curve for autarky, DI. In section 7.6, we shall show that as transaction efficiency is improved, the equilibrium aggregate production schedule jumps from line DI to point K, generating economic development. Charles Babbage (1832, pp. 170-74) noted this phenomenon more than a century ago, pointing out that the division of labor can save on fixed learning cost by avoiding duplicated learning and training. Becker (1981), Barzel and Yu (1984), and Rosen (1983) have formalized the idea that division of labor can increase the utilization rate of a fixed learning and training investment. Tamura (1992) and Yang (1996) have explored the general equilibrium implication of fixed learning cost for the endogenization of individuals’ levels of specialization. The economies of division of labor are, of course, generated by endogenous comparative advantage. When ex ante identical individuals choose different levels of specialization in an activity, a specialist endogenously acquires a higher productivity than a novice. Consider the two-person-two-goods example in Fig. 7.1, where the two individuals choose complete division of labor. If person 1 specializes in producing good 1 (accordingly choosing L1 = 1), her labor productivity in that good is Max{( L1 -A)/L1,0}= 1A. For person 2, specializing in good 2 (and thus choosing L1 = 0), labor productivity in good 1 is Max{( L1 -A)/L1, 0}=Max{- ∞, 0}=0. The difference in productivity between the specialist and novice is endogenous comparative advantage.

209

The following story may provide intuition for economies of division of labor generated by fixed learning cost. Suppose there are two individuals: a professor (he) and a secretary (she). If they do not have division of labor, then each of them must engage in both research and secretarial support work. The first type of work needs education at the Ph.D level, while the second type of work needs education in a secretarial school. Hence, each of them must get two types of education to do the two kinds of jobs. If the professor specializes in research and the secretary specializes in secretarial work, the professor can avoid the cost of training at secretarial school and the secretary can avoid the cost of training for a Ph.D. For each of them, the utilization rate of the investment in specialized learning increases as they spend more time in their specialties. The benefit of division of labor can be reaped by both of them. The secretary is able to begin working several years earlier than she could if she were in school during those years, so that her lifetime income is increased. Similarly, specialization increases the professor’s productivity in research and in the utilization rate of his learning investment in a Ph.D program, and reduces his total fixed learning cost. Economies of division of labor based on fixed learning cost are more ubiquitous than they seem, since fixed learning cost can be caused by a trial-and-error process that is common in all production activities. The next section investigates how the market sorts out the efficient trade off between transaction costs and economies of division of labor based on the fixed learning cost. 7.3. How Are Demand and Supply Functions Determined by Individuals’ Levels of Specialization?

It can be shown that the Wen theorem (see theorem 5.1 in section 5.2, chapter 5) is applicable to the model in this chapter. Hence, an individual does not simultaneously buy and sell the same good; nor simultaneously buy and self-provide the same good; and she sells at most one good. This implies that the decision configuration of each consumerproducer who sells good i satisfies the following conditions: s d xi > 0 , xi > 0 , xi > 0 , Li > 0 (7.3) x r = x r = Lr = 0 , x r > 0 , ∀r ∈ R , d

s

x j , L j > 0 , x j = x j = 0 , ∀j ∈ J s

d

where R is the set of n-1 goods that are purchased from the market, and J is the set of m-n non-traded goods. In words, the conditions imply the following propositions: for each good i that is sold, its self-provided quantity, its quantity for sale, and the level of specialization in producing it are positive, while its quantity purchased is 0; for each good r that is sold, its self-provided quantity, its quantity for sale, and the level of specialization in producing it are 0, while its quantity purchased is positive; for each non-traded good j, its selfprovided quantity and the amount of labor allocated to produce it are positive, while its quantities sold and bought are 0. According to these conditions, the decision problem of an individual selling good i can be specified as follows: Max: ui = x i c Π r ∈R x r c Π j ∈J x j c = x i Π r ∈R kx r d Π j ∈J x j p

s

s.t. xi ≡ xi + xi = Max { Li - A , 0},

(production function for good i)

x jc = x j p ≡ x j = Max { L j - A , 0 }, ∀j ∈ J (production function for good j)

210

Li + ∑ j∈J L j = 1

(endowment constraint for time)

p ixis = ∑ r∈R pr xr d

(budget constraint) where pi is the price of good i, xr ≡ kxr and xic ≡ xi are respective quantities of goods r and i c

d

s

that are consumed, xi , xi , x r d , Li , x j , L j , and n are decision variables. Having inserted s

all constraints into ui , we can express ui as a function of Li , L j , xi , x r d , and n. One of all xr can be eliminated using the budget constraint, and one of all L j can be eliminated using the endowment constraint for time. Hence, we can convert the original constrained maximization problem to a non-constrained maximization problem: (7.4) Max: ui = xi c x c s Π r x r c Π j x j c = xi kx s d (Π r kx r d )( Lt − A) Π j ( L j − A) where

s

xi = xi = Max { Li - A , 0 }- xi c

s , r ∈ R, s ≠ r x s d = ( pi x i s − ∑ r p r x r d ) / p s t, j ∈ J, t ≠ j Lt = 1 − Li − ∑ j L j The first order conditions for problem (7.4) are: d ∂u i / ∂x r = 0 (7.5a) (7.5b) (7.5c)

∂u i / ∂x i = 0 ∂ui / ∂L j = 0 s

(7.5d) ∂u i / ∂Li = 0 (7.5e) ∂u i / ∂n = 0 Since (7.5a) and (7.5d) hold for all r ∈ R and for all j ∈ J , they can be used to prove that p r x r is the same for any r ∈ R and that x j is the same for any j ∈ J . Using this result, all d

first order conditions yield: (7.6)

xis = (n-1)[1-(m-n+1)A]/m Li = A+n[1-(m-n+1)A]/m Lj = [1+(n-1)A]/m, xi = xj = [1-(m-n+1)A]/m, d s xr = pir xi /(n-1) = pir[1-(m-n+1)A]/m, ∀ r ∈ R

where pir ≡ pi / pr . As shown in chapter 4, the neoclassical supply function in (7.7a) is independent of prices because of the unitary elasticity of substitution of the Cobb-Douglas utility function in this model. Inserting the solution into (7.4) yields the indirect utility function: (7.7)

ui = αβ = ui (n, A, k , pir ) ,

where α ≡ {[1 − (m − n + 1) A] / m}m , β ≡ (kpi )n −1 (Π r ∈R pr −1 ) . (7.6) and (7.7) are neoclassical optimum decisions for a given level of specialization. The new classical decision sorts out resource allocation for a given level of specialization. Here, an individual’s level of specialization in producing the good sold is uniquely determined by the number of traded goods n.

211

In (7.7), [1 − (m − n + 1)A] m is per capita output of each good, where 1 − (m − n + 1) A is each person's amount of time allocated for production after total fixed learning cost (m − n + 1)A is deducted. This amount of time is allocated to produce m-n non-traded goods and one good that is sold in exchange for n-1 goods purchased. Hence, this amount is ultimately used to obtain m consumption goods. Since marginal labor productivity of each good is 1, the total output of m goods produced out of the amount of time is 1 − (m − n + 1) A . Thus, per capita consumption of each good, which equals per capita

output of each good, is [1 − ( m − n + 1) A] m . As the number of traded goods n increases, the total learning cost incurred in producing m-n non-traded goods (m − n )A will be reduced, so that the amount of time available for production increases and, therefore, per capita consumption of each good increases. α in ui can be considered as the product of the per capita consumption amounts of each and every good, which is an increasing function of n, while n determines an individual’s level of specialization. kn-1 in β decreases as n increases, since k is between 0 and 1. β can then be considered as a term through which utility is reduced by an increase in the number of transactions and related transaction costs. Since the Smithian optimum decision sorts out the optimum level of specialization that relates to n, the Smithian optimum decisions are given by (7.6)-(7.7) and the following condition: (7.8)

(∂u

i

∂α )( dα / dn) = −(∂ui ∂β )(dβ dn)

Since n can represent an individual’s level of specialization in the symmetric model, the left-hand side of the equation is the marginal utility of an increase in an individual’s level of specialization. The right-hand side is marginal transaction cost in terms of utility loss caused by an increase in an individual’s level of specialization. Hence, (7.8) implies that the optimum level of specialization is determined by equality between marginal benefit of specialization and marginal transaction cost. This law of optimum level of specialization was first proven by Yang (1984) and then confirmed by Becker and Murphy (1992, see example 7.4). Plugging the optimum value of n, given by (7.8), back into (7.6)-(7.7) yields the optimum resource allocation. Hence, (7.6)-(7.8) give the complete optimum decisions, which sort out optimum organization, which in turn relates to the optimum productivity and economic development, as well as optimum resource allocation. Since n-1 is the number of each individual's trade partners, the optimum level of specialization determines the optimum network size of each person's trade partners. However, this is an impersonal networking decision since each person does not care about who are her partners. She cares only about how many partners she has. Impersonal network decision is associated with price taking behavior. It should be noted that although (7.8) looks like a marginal condition for an interior solution, it is only an approximation of realistic inframarginal analysis. Strictly speaking, when the set of goods is finite rather than a continuum, we need integer programming to solve for the optimum integer n. As n jumps between the integers, all endogenous variables discontinuously jump. More importantly, if the model is asymmetric, we must use marginal analysis to solve for many corner equilibria, and then use total benefit-cost analysis to identify the general equilibrium from among them. If a symmetric model is assumed, a 212

decision to choose one from many configurations, and a procedure to identify one from many corner equilibria, turns out to be equivalent to choosing a value of n. There are two integer values of n, n1 and n2, such that n1 < n' < n2, where n' is the value of n that is given by (7.8). The optimum value of n* of the integer programming is determined by Max {u(n1), u(n2)}. But for a large value of m, n' is a good approximation of n*. In this text, we will use n' to represent n* in all symmetric Smithian models. Since all of n traded goods are produced only if all occupations generate the same utility level for the ex ante identical individuals, the inframarginal analysis between configurations establishes the utility equalization conditions: (7.9)

u1 = u 2 = u 3 = L = u n

(7.8) and (7.9) are completely symmetric between configurations selling different goods. Hence, they hold at the same time if and only if (7.10)

p i = p r ∀i, r = 1,2, L , n

and n is the same for all individuals. Using the information about the equilibrium relative prices of traded goods and the equilibrium number of traded goods, each individual’s optimum decision can be solved as follows: (7.11)

n = m + 1 − (1 / A) − [m / ln(kp ir )] Li = [1 − (ln kpir ) −1 + ( A − 1)mA] /(− ln kpir ) xi = A[m − (1 / A) − (m / ln kp ir )] /( − ln kp ir ) s

xi = x j = − A /(ln kpir )

j∈J

x r = p ir A /( − ln kp ir ) ∀r ∈ R d

u i = (kpir ) m −(1 / A) −( m / ln kpir ) [1 + (1 / A) + (m / ln kpir )] / m where pir ≡ pi / pr is the price of a good sold in terms of a good purchased. Since the optimum values of all decision variables are no longer functions of n, we call them Smithian optimum decisions, which differ from the neoclassical optimum decisions in (7.7). The distinction between the neoclassical decisions and the Smithian decisions formalizes Young’s idea that demand and supply are two sides of specialization. The optimum decisions that generate individuals’ demand and supply are ultimately determined by the optimum level of specialization, which is determined by n in a symmetric model.

7.4. Inframarginal Comparative Statics of the Optimum Decisions

As discussed in chapter 4, marginal comparative statics differ from inframarginal comparative statics of the optimum decisions. From the neoclassical optimum decisions in (7.7), you can see that the level of specialization Li and the neoclassical supply function are independent of relative prices. But the optimum level of specialization and the Smithian

213

supply function are dependent on prices. The distinction between the decisions before and after the level of specialization is chosen was first noted by Stigler (1951) and received attention later from Rosen (1978). Suppose that parameters m, A, and k are fixed. Differentiation of the Smithian optimum decisions with respect to the relative price pir yields: (7.12a)

dn / dp ir > 0

(7.12b) (7.12c)

dx i / dp ir > 0

(7.12d)

dx i / dp ir < 0

dLi / dp ir > 0

s

dxi / dp ir = dx j / dp ir > 0 d

where (7.12b) is called the law of supply, and (7.12d) is called the law of demand. Certainly, the comparative statics of the Smithian optimum decisions differ from the comparative statics of the neoclassical optimum decisions given in (7.7). The distinction between the marginal and the inframarginal comparative statics of the optimum decisions highlights the point that we cannot really understand demand and supply if we do not understand individuals’ decisions in choosing their levels of specialization. The neoclassical demand and supply functions and their marginal comparative statics for a given value of n are only a half-way house. Since the choice of n determines productivity, there is an intimate relationship between inframarginal analysis of demand and supply and the analysis of economic development.

7.5. How is the Level of Division of Labor in Society Determined in the Market?

Assume that the numbers of individuals selling goods i and r are respectively Mi and Mr. The total market supply of good i is M i x i s . The market demand for good r by individuals selling good r is M r xi . The total market demand for good i is then Σ r∈R M r xi . The market clearing conditions are thus: d

(7.13)

d

M i xi = Σ r∈R M r x i , s

d

i=1,2, . . ., n

This system comprises n equations. One of them is independent of the other n-1 due to Walras’ law. The n-1 equations and the population equation Σ i M i = M determine the numbers of individuals selling n traded goods. The market clearing conditions, together with the utility equalization condition (7.9), yield the final solution of the general equilibrium: (7.14)

Li = A + A[1-m(lnk)-1][1-m-1-(Am)-1-(lnk)-1], xis = A[m-(1/A)-(m/lnk)]/(-lnk), xi = xrd = xj = -A/lnk, ∀ r∈R, ∀ j∈J pir = 1, Mr = M/n, for r = 1, ..., n ui = kn-1{[1-(m-n+1)A]/m}m

214

n = m+1-(1/A)-(m/lnk) where i = 1, 2, . . ., n. The equilibrium value of utility can be considered as the absolute price of labor. We call ui(n) in (7.14) the Smithian utility function, which is a function of the number of traded goods that relates to an individual’s level of specialization and the level of division of labor for society. The Smithian utility function differs from the indirect utility function, since the former is not a function of prices, whereas the latter is a function of the prices of traded goods. Usually, we can work out the analytical expression of the Smithian utility function only for a completely symmetric model. For asymmetric models, we can only work out the corner equilibrium per capita real income in each structure, where the level and pattern of division of labor, equivalent to n here, is exogenously fixed. Then a total benefit-cost analysis can sort out the equilibrium level and pattern of division of labor. The absolute price of labor is associated with the equilibrium levels of division of labor and productivity. But the relative prices of traded goods, and the relative numbers of individuals choosing different configurations, are determined by relative tastes and relative production and transaction conditions. A corner equilibrium for a given n sorts out resource allocation, relative prices, and numbers of different specialists, while the general equilibrium sorts out the absolute price of labor and the levels of division of labor and productivity. Hence, in a Smithian model, a corner equilibrium sorts out problems of resource allocation and a general equilibrium sorts out problems of economic development. Now we assume that individuals’ residential locations are exogenously given. They reside at vertices of a grid of triangles with equal sides, as shown in Fig. 7.2. In order to save transaction costs, each individual will trade first with those closest. But as the number of each individual’s traded goods increases, she will trade with those who are further away. Because of symmetry, the number of traded goods, n, is the same for all individuals and for society. Thus, there is a local business community around each individual. The members of the local community are trade partners of the individual who sells a good to, and buys a good from, each of them. Therefore, for n traded goods, each individual has n-1 trade partners, while there are n members of the community. If the local communities do not overlap, then M individuals will be divided among N = M/n local communities. If the local communities overlap, N is the number of producers of each traded goods, and can be considered as a measure of the fragmentation of the economy, since there is no trade between individuals who sell the same good or choose the same configuration (occupation). We may say that structure B has a higher level of division of labor than structure A, if the levels of specialization of all individuals are higher in B than in A and the number of distinct configurations in B is larger than in A. Later, we shall show that in the model, each individual’s optimum level of specialization is an increasing function of her number of traded goods n. Also, the number of traded goods is positively related to the number of distinct configurations in a structure. Hence, n represents the level of division of labor for the symmetric model.

215

Figure 7.2: Evenly Dispersed Residence Location of Individuals

According to the first welfare theorem proved by Zhou, Sun, and Yang (1998), a general equilibrium with consumer-producers in this chapter (which is different from the Arrow-Debreu model with dichotomy between consumers and firms) is Pareto optimal. For a given value of n, a corner equilibrium is allocation efficient, while the general equilibrium is both allocation efficient and organization efficient. Here, organization efficiency is associated with the efficient productivity that balances the trade off between productivity gains from the division of labor and transaction costs. Hence, organization efficiency is a central notion for the analysis of problems of economic development. Two points need more attention. It is not difficult to show that the second order condition for the optimum n is satisfied, that is, the second order derivative of ui in (7.4) with respect to n is negative. Also, it can be shown that the partial derivative of ui with respect to n is always negative for any positive n if k is sufficiently close to 0. According to the Kuhn-Tucker theorem, this implies that the equilibrium level of division of labor will be its minimum value, n = 1, which means that the number of goods purchased n-1 = 0 (autarky), if k is sufficiently close to 0. The second point to note is the problem of multiple equilibria. Because of symmetry, which bundle of goods is to be traded is indeterminate in equilibrium. Hence, n combinations of m factors generate many general equilibria with the same per capita real income and the same value of n, but with different bundles of traded goods (type I multiplicity of equilibrium). There are still more possible general equilibria, since who specializes in producing which good is indeterminate, too. Exchanges of choices of configurations between each pair of different specialists will generate more general equilibria with the same value of n and the same per capita real income, but with different choices of configuration by each individual (type II multiplicity of equilibrium). Finally, the case in which the number of traded goods for society does not equal each individual’s number of traded goods may incur more general equilibria with the same per capita real income (type III multiplicity of equilibrium). Fig. 7.3a shows an example of the case where individual 1 sells good 1 to individual 2, who sells good 2 to individual 3, who sells good 3

216

to individual 1. Each individual in this structure trades two goods, but the whole society trades three goods. For the symmetric model, the equilibrium in this structure generates the same per capita real income as does the structure in Fig. 7.3b.

(a) Different individuals trade different bundles of goods

(b) All individuals trade the same bundle of goods

Figure 7.3: Multiple General Equilibria

For the symmetric static model, the two types of structures have symmetric properties of equilibrium, except that in the case of Fig. 7.3(a) the number of traded goods for an individual is smaller than that for society. Since the comparative statics of general equilibrium are easier to handle for those structures with an equal number of traded goods for each individual and for society, we focus on this type of structure. A slight difference in tastes or in production and transaction conditions between different goods will rule out type I and type III of multiplicity of general equilibrium. A slight difference in taste and/or production and transaction conditions between individuals will rule out type II multiplicity of general equilibrium. 7.6. Inframarginal Comparative Statics of General Equilibrium and Many Concurrent Development Phenomena

Since choosing a structure of division of labor is also choosing a certain network of transactions, many economic phenomena can be generated by inframarginal comparative statics of the general equilibrium as different aspects of the size and structural features of the network of division of labor. These structural changes are generated by a coherent mechanism of economic development. Hence, we first examine the change in the equilibrium level of division of labor, n, in response to changes in transaction efficiency, k, and in fixed learning cost, A. Differentiation of the equilibrium value of n in (7.14) yields: (7.15)

dn * / dk > 0

dn * / dA > 0

This implies that the equilibrium level of division of labor increases as transaction efficiency is improved or as fixed learning cost increases. This formalizes the Smith theorem that division of labor is dependent on the extent of the market (Smith 1776,

217

chapter 3 of book I) and that the extent of the market is determined by transportation conditions (Smith 1776, pp. 31-32). Total differentiation of the equilibrium level of per capita real income in (7.14) yields: (7.16a)

du / dk = (∂u / ∂n)( dn / dk ) + (∂u / ∂k ) = ∂u / ∂k > 0

where the first order condition for the optimum level of specialization ∂u / ∂n = 0 is used. (7.16) is referred to as the envelope theorem, which states in words that the total derivative of the optimum value of the objective function with respect to a parameter equals the partial derivative of the objective function with respect to the parameter at the optimum values of the endogenous variables. Application of the envelope theorem to u in (7.4) with respect to parameter A yields: (7.16b)

du / dA = ∂ u / ∂ A < 0 .

(7.16) implies that there are two different ways to increase the equilibrium level of division of labor. The first is to improve transaction efficiency and the second is to increase the fixed learning cost of each activity. The first approach increases while the second decreases per capita real income as they raise the level of division of labor. You may relate the first method to the development of an efficient banking system, the improvement of the legal system, government liberalization policies, and urbanization, all of which reduce the transaction cost coefficient 1-k. You may relate the second method to a stiff licensing fee and other entry barriers that decrease per capita real income and increase the equilibrium level of division of labor.

(a) Autarky

(b) Partial division of labor

(c) Complete division of labor

Figure 7.4: Exogenous Evolution in Division of Labor

Fig. 7.4 gives an intuitive illustration of the inframarginal comparative statics of general equilibrium where the number of goods is assumed to be 4. The lines denote goods flows. The small arrows indicate the directions of goods flows. The numbers beside the lines signify the goods involved. A circle with the number i denotes a person selling good i. Panel (a) illustrates the case of autarky, where each person self-provides 4 goods, due to an extremely low transaction efficiency. Panel (b) shows how an improvement in transaction efficiency leads to partial division of labor, where each person sells one good, buys one good, trades two goods, and self-provides three goods. Panel (c) shows how a very high

218

transaction efficiency results in complete division of labor, where each person sells and self-provides one good, buys three goods, and trades four goods. If we suppose that the transaction efficiency coefficient k continuously and exogenously evolves from 0 to 1, then the inframarginal comparative statics of general equilibrium predict that the equilibrium level of division of labor will evolve as illustrated in Fig. 7.4. This exogenous evolution in division of labor differs from the exogenous evolution of productivity and per capita real income generated by an exogenous change in the total factor productivity parameter in the Solow model (1956), which is a state equation that does not involve individual decision-making. In our model the exogenous evolution in division of labor is based on individuals’ decisions in choosing their levels of specialization and on interactions between those decisions. The evolution of division of labor will generate economic development associated with jumps of productivity from a low level to a high level in the absence of changes in production conditions (production functions and endowment constraint). Making a close examination of Fig. 7.1 in connection to Fig. 7.4, you can see that as transaction efficiency is improved, the general equilibrium jumps from the aggregate transformation curve DI to MCAKBJL. The novelty of the Smithian model is that it can predict many phenomena of structural changes, some of them seemly contradictory to each other, as different aspects of a coherent development mechanism. Let us now examine the phenomena one by one.

219

Concurrent increases in each person’s level of specialization, degree of commercialization, trade dependence, and decrease in the degree of self-sufficiency as results of an increase in the level of division of labor. Each individual’s level of specialization, Li is given in (7.7) and (7.14). It is not difficult to see that (7.17)

dLi / dk = ( dLi / dn)( dn / dk ) > 0 ,

where dLi / dn = [1 − (m − 2n + 1) A] / m > [1 − (m − n + 1) A] / m > 0 . The last inequality can be obtained by inserting the equilibrium value of n into the expression of the derivative. dn/dk > 0 is given by (7.16a). In this simple model, the amount of labor allocated to producing a good can be considered as the price of the good in terms of labor. Hence, the equilibrium value of Li is a measure not only of each individual’s level of specialization, but also of the value, in terms of labor, of all goods that she purchases, which equals her income from the market. The total value of consumption, including self-provided consumption and consumption from the market, in terms of labor is 1. Thus, the ratio of consumption purchased to total consumption, which is called the degree of commercialization, is Li/1 = Li. Also, trade dependence can be defined by total trade volume divided by total income, including commercialized and self-provided income. It is not difficult to see that the degree of trade dependence equals two times the degree of commercialization in the simple model, since trade volume equals double commercialized income. (7.17) implies that the degrees of commercialization and trade dependence increase as an improvement in transaction efficiency raises the level of division of labor. (1- Li ) /1 = 1-Li is the degree of selfsufficiency, which is defined as the ratio of the value of self-provided income in terms of labor to total income in terms of labor. Thus, (7.17) shows the negative relationship between the degree of self-sufficiency and transaction efficiency, and the level of division of labor. The extent of the market and the level of division of labor are two sides of the same coin (Young, 1928). Let E denote the extent of the market; then E equals the product of population size and per capita aggregate demand. An individual’s aggregate demand is the total demand of that individual for all traded goods. Market aggregate demand is the sum of all individuals’ aggregate demand for all traded goods. It is what we call the extent of the market and it differs from total market demand for a particular good. Total market demand for a good is a microeconomic or disaggregated concept, while market aggregate demand is a macroeconomic concept, which relates to the level of division of labor and the related size of the market network. From (7.7) and (7.14), the extent of the market can be calculated as follows. (7.18)

E = M xis = M (n − 1)[1 − (m − n + 1)A ]/m

dE / dk = ( dE / dn)( dn / dk ) > 0

(7.15) and (7.18) imply that the equilibrium extent of the market and the equilibrium level of division of labor increase concurrently as transaction efficiency is improved. Smith (1776) proposed the conjecture that the level of division of labor is determined by the 221

extent of the market, which is in turn determined by transaction efficiency. Some economists have misinterpreted this as meaning that division of labor is determined by the size of an economy (population size or resource size). Young (1928) criticized this interpretation. According to him, the extent of the market is determined not only by population size, but also by per capita effective demand, which is determined by income, which is determined by productivity, which is in turn determined by the level of division of labor. The interdependence between the level of division of labor and the extent of the market is analogous to the interdependence between prices and quantities demanded and supplied. The notion of general equilibrium is a powerful vehicle to sort out the mechanism that simultaneously determines the interdependent endogenous variables. In the Smithian general equilibrium model, the equilibrium level of division of labor and the equilibrium extent of the market are two sides of the equilibrium size of the market network. They are simultaneously determined by transaction efficiency. The driving force of the mechanism is, of course, the trade off between economies of division of labor and transaction costs. In chapter 14, we shall use dynamic general equilibrium models to show that a dynamic mechanism may generate endogenous evolution in division of labor in the absence of exogenous changes in parameters. Productivity progress. s The labor productivity of traded and non-traded goods, xi / Li and x j / L j , can be worked out from (7.14). It can be shown that (7.19)

d ( x i s / Li ) / dk > 0 ,

d ( x j / L j ) / dk > 0

This implies that labor productivity of each good increases as the level of division of labor is raised by improvements in transaction efficiency. This formalizes Smith’s thought that productivity progress and national wealth are generated by evolution in division of labor and that the development implications of division of labor should be at the core of mainstream economics. Hence, if we formalize classical economic thought about the development implications of division of labor within the Smithian framework, then trade theory, which is concerned with trade dependence, and development economics, which is concerned with productivity progress, are two aspects of the core of economics. The development implications of evolution of division of labor can be better appreciated by looking at Fig. 7.1, which shows that as division of labor evolves, the equilibrium production schedule will discontinuously jump to be closer to the PPF. Evolution in endogenous comparative advantage. We define the extent of endogenous comparative advantage as the difference in productivity of a good between its sellers and its buyers. Since in our model the buyer of a good stops producing it, her labor productivity of that good is zero. But a seller’s labor productivity of the good increases as transaction efficiency is improved, as indicated in (7.19). Hence, the extent of endogenous comparative advantage increases as improvements in transaction efficiency drive division of labor to evolve. This has formalized Smith’s idea that the difference in productivity between a specialist and a novice is a consequence, rather than the cause, of division of labor. Development of diversity of economic structure and of interpersonal dependence. From the foregoing comparative statics of general equilibrium, you can see that when individuals choose autarky, all individuals’ configurations of production and consumption 222

are the same, and their productivities in all activities are the same; thus, there is no diversity of economic structure. As improvements in transaction efficiency drive division of labor to evolve, the number of distinct occupation configurations and kinds of markets increases. As the degree of self-sufficiency falls, each pair of different specialists shares a progressively smaller number of common self-provided production activities, so that the degree of difference between each pair of individuals choosing different configurations increases. We define the degree of diversification by reference to the degree of this difference and the number of different traded goods, n. We define the degree of interpersonal dependence as the number of trading partners for each individual, which is n - 1. Hence, both the degree of diversification of economic structure and the degree of interpersonal dependence increases as division of labor evolves. Increases in the degree of production concentration and in the degree of market integration. In the symmetric model, the number of producers of each traded good is N = M/n, where M is population size and n is the number of traded goods. The number of separate local business communities is also N = M/n. The degree of production concentration can then be defined as 1/ N= n /M. The degree of market integration can also be defined by 1/N. Hence, the degrees of production concentration and market integration increase as improvements in transaction efficiency raise the equilibrium level of division of labor n. Changes in industrial structure. If good 1 is the agricultural good, and other goods are industrial goods, then the model predicts structural changes, which look like an increase in employment share of the industrial sector and a decrease in employment share of the agricultural sector. If transaction efficiency is low, autarky is the general equilibrium where each individual selfprovides agricultural and industrial goods. This looks like a traditional agricultural society where all individuals are farmers. As transaction efficiency is improved, some individuals become professional farmers and others become professional manufacturers of industrial goods. But the number of professional farmers is much smaller than the number of all individuals producing agricultural goods in autarky. Hence, this looks like a structural change that transfers labor from the traditional agricultural sector to the industrial sector. In essence, this is a process of evolution of division of labor in which each individual’s level of specialization increases, natural agents who used to self-provide everything for themselves become different specialist producers, and new professions emerge. These are the structural changes and economic development in which Smith was interested. Evolution of degree of information asymmetry. In the Walrasian model, it is assumed that each individual does not know the others' utility and production functions, endowments, and transaction conditions. She does not even know the distribution functions of the characteristics of others. Since all individuals are ex ante identical in our model and each of them has exactly the same ex post production and consumption pattern in autarky equilibrium, then each of them actually knows all the detailed production and consumption plans of each of the others if autarky occurs in equilibrium. As transaction conditions are improved, the equilibrium level of division of labor increases. The population is divided between different occupations. All individuals choosing the same occupation have the same ex post production, trade, and consumption pattern, which is different from those of other occupations. Hence, each individual actually knows 1/n information about detailed production, trade, and consumption plans of n

223

occupations. This implies that in a Walrasian model of endogenous specialization, the equilibrium degree of information asymmetry increases as division of labor evolves. 1 The inframarginal comparative statics of general equilibrium can be summarized in the following proposition. Proposition 7.1: As transaction efficiency is improved, the level of division of labor increases. The following concurrent phenomena are different aspects of the evolution in division of labor. Each individual’s level of specialization, productivity, and trade dependence increases. The degree of commercialization, the extent of endogenous comparative advantage, the degrees of production concentration and market integration, and the degree of diversity of economic structure all increase. The number of traded goods, the number of markets, and the degree of information asymmetry increase, while the degree of self-sufficiency falls. This process transfers the traditional agricultural economy, where everybody self-provides everything to a modern economy with a high level of division of labor between professional farming and industrial manufacturing.

Compared to structural changes analyzed by Chenery (1979) and Kuznetz (1966), the Smithian model predicts more structural changes, such as increases in the degree of market integration, degree of commercialization, extent of the market, extent of endogenous comparative advantage, degree of production concentration, and degree of structural diversity. More importantly, this model predicts comovement of all of the structural changes, rising productivity, and increasing per capita real income. This prediction implies that all of the endogenous variables are simultaneously determined by a general equilibrium mechanism. It does not make sense to explain some of them by others of them. Hence, regression of structural variables, such as the income share of the industrial sector or expenditure share of food consumption, on income may establish correlation, rather than a one-way causation chain, between the variables. The Smithian model in this chapter explores a coherent general equilibrium mechanism that explains all of the development phenomena by transaction conditions. Preliminary empirical works that relate to this hypothesis can be found from Barro (1997), North (1958), North and Weingast (1989), Gallup and Sachs (1998), Sachs and Warner (1995), Easton and Walker (1997), Gwartney, Lawson, and Block. (1996), Frye and Shleifer (1997), and Yang, Wang, and Wills (1992). They use indices of freight fee (North), quality of institution (Sachs and Warner), rule of law (Barro), economic freedom (Easton and Walker, and Gwartney, Lawson, and Block ), and violation of private property (Frye and Shleifer), or an index of transaction efficiency in specifying and enforcing property rights (Yang, Wang, and Wills) to approximate transaction conditions.

7.7. Emergence of International Trade from Domestic Trade

Now we use our model to address the questions: Why and how does international trade emerge from domestic trade and what is the distinctive contribution of the Smithian 1

According to Hurwicz (1973), the Walrasian model has more information asymmetry than in most game models with information asymmetry, and the Walrasian equilibrium can efficiently utilize information in society with minimum information that each agent knows.

224

framework to trade theory? Suppose there are one hundred countries in the world and the population size of each country is ten million. Assume further that the number of goods m and the population size of the world are both one billion, and that transaction efficiency is infinitesimally greater for trade within the same country than for trade across countries. Then our theory tells a story of trade as follows. If transaction efficiency is extremely low, then autarky for each person is equilibrium, and therefore, domestic and international trade are not needed. If transaction efficiency is improved such that the equilibrium n=1,000, then 10,000 local markets emerge from the division of labor in each country. The equilibrium number of business communities is M/n where M is the population size of the economy and n is the number of traded goods as well as the population size of a local business community. Each member of a local business community sells one traded good to the other 999 individuals and buys one traded good from each of them. Under the assumption that trade occurs first with those closest, there is no trade between the local communities and therefore a national market does not exist. Suppose that transaction efficiency is further improved such that n*=10,000,000. Then the national market emerges from the higher level of division of labor, but international trade does not exist. As n* increases to 100 million due to an improvement in transaction efficiency, such as that caused by the invention of the steam engine, the world will be divided into ten common markets. In each of these, ten countries have an integrated market and international trade emerges from domestic trade, but no trade occurs between the ten common markets. However, if transaction efficiency becomes extremely high, then an integrated world market will emerge from the complete division of labor. The difference between this story and the Dixit-Stiglitz model with economies of scale in example 5.1 is obvious. For the Dixit-Stiglitz, international trade instead of autarky is always the equilibrium in the absence of government intervention. But for our model, autarky for each individual or for each country may be the equilibrium in the absence of government intervention. If there are many goods, many different types of individuals in each country, and many countries in the Ricardo model in chapter 3, emergence of international trade from domestic trade can be explained by transaction conditions, too. But the Ricardo model with many goods and many different types of individuals is extremely difficult to manage. In particular, endogenous comparative advantages in the Smithian model can be endogenously determined by individuals’ decisions, whereas exogenous comparative advantages in the Ricardo model and HO model are not affected by decisions. Hence, the Smithian model is referred to by Smythe (1994) as the theory of endogenous trade. 7.8. Comovement of Division of Labor and Consumption Variety

This section uses a new classical model with an endogenous number of consumer goods and fixed learning costs to illustrate the general equilibrium mechanism that simultaneously determines the network size of division of labor, the number of traded goods, and the number of all goods (including non-traded ones). Example 7.2: A Smithian model with the CES utility function (Yang, 1996). The production functions and time endowment constraint for each consumer-producer are the same as in the previous sections. 225

xi ≡ xi + xi = Max{li − A,0}i = 1,2,L,m p

(7.20)

s

Σ im=1 l i = 1 ,

li∈[0, 1] p

where li is an individual’s level of specialization in producing good i, xi is the output s

level of good i, xi is the amount of good i self-provided, xi is the amount of good i sold, and A is a fixed learning cost in producing each good. Different from the previous sections, m, the number of consumption goods, is each individual’s decision variable rather than a given parameter. Each individual’s utility function is: (7.21)

V = (1-cm)u,

1

u = [Σ im=1 ( x i ) ρ ] ρ c

where xi ≡ xi + kxi is the amount of good i that is consumed, xi is the amount of good i that is purchased, and k is the transaction efficiency coefficient. Following the method introduced in example 4.2, we can calculate the elasticity of substitution between any pair of consumption goods as 1 (1 − ρ) . Since there is an inverse relationship between the elasticity of substitution and the degree of economies of complementarity, and a positive relationship between the elasticity of substitution and parameter ρ , we can use 1 /ρ to represent the degree of economies of complementarity between each pair of consumption goods, or the degree of economies of consumption variety. Taking account of the Wen theorem and the budget constraint, each consumer-producer’s decision problem is c

d

d

1

⎤ ⎡ ui = ⎢ x i ρ + ∑ ( kx rd ) ρ + ∑ x j ρ ⎥ r ∈R j ∈J ⎦ ⎣ s s.t. x i + x i = Max{Li − A, 0}, x j = Max{L j − A, 0}∀j ∈ J (production function)

(7.22)

Max:

ρ

Vi = (1 − cm)ui ,

Li + Σ j∈J L j = 1

(endowment constraint)

pixis = Σ r∈R pr xr d

(budget constraint) s

d

where pi is the price of good i, and x i , x i , x r , Li , x j , L j ,n , m are decision variables. Each decision variable can be zero or a positive value. R is the set of goods purchased and J is the set of non-traded goods. We assume that the calculation of the optimum decision will generate more disutility as the number of the first order conditions for the optimum decision increases with the number of consumption goods m. This disutility is referred to as the management cost of consumption variety. Let c be the management cost coefficient of a particular consumption good, measured as a fraction of utility that is lost. The total management cost of m consumption goods in terms of the fraction of utility that is lost is then cm . This implies that the fraction of utility that is ultimately enjoyed from the consumption of m goods is (1 − cm ) . From the decision problem, the individual’s level of specialization, her demand and supply functions, and her indirect utility function can be solved as follows.

226

(7.23)

Li = {( n − 1)[1 − A(m − n)] + K } /[n − 1 + (m − n + 1) K ] xi = (n − 1)[1 − A(m − n + 1)] [n − 1 + K (m − n + 1)] s

xi = x r = x j = K [1 − A(m − n + 1)] [n − 1 + K (m − n + 1)],∀r ∈ R, ∀j ∈ J d

n = 1 + {( A − c)(1 − K ) + ρ[ A − (1 − K 2 ) 2 ]} cA(1 + ρ)(1 − K ) m = [ A + cρ(1 − K )] c(1 + ρ) Vi = (1 − cm)(akpi p r )[1 − A(m − n + 1)][n − 1 + K (m − n + 1)](1−ρ) ρ ρ (1−ρ )

where K ≡ ( p r kpi ) is a decreasing function of pi and k and an increasing function of pr , good i is sold and good r is purchased. Note that the demand and supply functions in (7.23) are neoclassical demand and supply functions if n is exogenously given, but are Smithian demand and supply functions if n is endogenized. In exercise 5, you are asked to work out the own price elasticity of the neoclassical and Smithian demand and supply functions, and to examine the differences between these functions. The utility equalization and market clearing conditions V1 = V2 =LVn M i xi = Σ r∈R M r xi for all i = 2, 3, …, n s

d

yield n-1 relative prices of n traded goods and n-1 relative numbers of individuals selling different goods. All of the relative prices and relative numbers are 1 because of symmetry. Note that we have not used the market clearing condition for good 1, since it is independent of the other n-1 market clearing conditions. The equilibrium numbers of individuals selling different traded goods can be solved from the market clearing conditions and the population equation Σ i M i = M . The equilibrium values of the relative prices of traded goods and of the numbers of individuals selling different traded goods are pi p r = 1 , M i = M r = M n,

r, i = 1, 2, 3, …, n r, i = 1, 2, 3, …, n

Inserting the equilibrium values of the relative prices of traded goods into the optimum decision (7.23) yields the equilibrium values of the endogenous variables. Let K ≡ ( p r kp i ) ρ (1− ρ ) = k ρ ( ρ −1) in (7.23). Then (7.23) becomes the equilibrium values of an individual’s optimum decisions. Differentiation of the equilibrium values of the number of consumption goods m and the number of traded goods n (which represents the level of division of labor) with respect to transaction efficiency k and the management cost coefficient of consumption variety c yields the main results of the inframarginal comparative statics of general equilibrium.

227

(7.24a) (7.24b) (7.24c) (7.24d)

dn* dk > 0, dn* dc < 0 dm* dk > 0, dm* dc < 0, dm dρ < 0, d(m * − n * ) dk < 0, d (m * − n * ) dc > 0, d (cm * ) dk > 0 , d (cm * ) dc < 0 ,

where cm * is the fraction of utility that is lost because of the management costs of consumption variety. It is an interesting result that total management cost cm * increases as the management cost coefficient c decreases. This implies that management cost as a proportion of real income increases as management efficiency is improved. (7.24a, b) implies that the equilibrium number of traded goods (or the level of division of labor), n, and the equilibrium number of all consumption goods, m, increase concurrently as transaction efficiency, k, and/or management efficiency, 1/c, is improved. (7.24c) implies that n increases more quickly than m does, so that the number of traded goods will eventually equal the number of all consumption goods, that is, all goods are eventually involved in the division of labor as transaction efficiency and/or management efficiency are continuously improved. Let us now consider the second order conditions for the interior solutions of n and m. Recalling the second order condition for a non-constrained maximization problem from, for instance, Chiang (1984), we know the solutions given by the first order conditions are maximization solutions if the following conditions are satisfied. (7.25a) (7.25b)

∂ 2V ∂n 2 < 0, ∂ 2V ∂m 2 < 0, (∂ 2V ∂ n 2 )(∂ 2V ∂ m 2 ) − (∂ 2V ∂n∂ m) > 0.

where m and n are valued at their equilibrium values. Let pi p r = 1 in (7.23); then differentiation of V with respect to n and m indicates that (7.25a) holds when n and m equal their equilibrium values. But for pi p r = 1 and the equilibrium values of m and n, (7.25b) holds if and only if (7.26)

f (k ,ρ) ≡ k − [ρ (1 + ρ − ρ 2 )](1+ρ) 2ρ > 0

where ∂ f ∂ρ < 0 . This implies that the second order condition holds only if the degree of economies of consumption variety (or of complementarity between consumption goods), 1/ρ, is sufficiently great in comparison with transaction efficiency. If economies of consumption variety are not significant, then the equilibrium m takes on one of two corner values, either n = m or m = ∞ . Since m = ∞ is incompatible with the endowment constraint, the general equilibrium entails n = m if economies of consumption variety are not significant, or if the second order condition is not satisfied. If n = m, then the results in (7.24) become irrelevant. For this case, in order to determine the general equilibrium and its comparative statics, we should first let m = n in each individual’s decision problem, and then solve for each individual’s optimum decision. It can be shown that if (7.26) does not hold, or if economies of consumption

228

variety are not significant in comparison to transaction efficiency, then the general equilibrium and its inframarginal comparative statics are given as follows. (7.27)

m * = n * = [(1 − ρ ) c]+ ρ (1 − k ρ (ρ −1) ) dm * dk > 0 ,

d m * dc < 0 .

(7.24), (7.26), and (7.27) together yield the following proposition. Proposition 7.2: As transaction efficiency k and/or management efficiency 1/c are improved, the equilibrium level of division of labor, n, and the equilibrium number of all consumption goods, m, increase concurrently, with the former increasing more quickly than the latter, so that all goods are eventually traded and the complete division of labor will be achieved. If economies of consumption variety are not significant in comparison to transaction efficiency, the number of traded goods always equals the number of all consumption goods. They simultaneously increase as transaction efficiency and management efficiency are improved. In addition, all concurrent development phenomena listed in proposition 7.1 take place as different aspects of the evolution in division of labor.

(a) Autarky, n=1, m=2

(b) Partial Division of Labor with n=2, m=3

(d) Complete division of labor with n = m = 4

(c) Complete division of labor with n = m = 3

Figure 7.5: Emergence of New Technology and New Consumption Goods

Fig. 7.5 gives an intuitive illustration of the inframarginal comparative statics of general equilibrium. The difference between the development mechanism in this chapter

229

and that in chapter 5 is as follows. In the Smithian model, there is not a scale effect. The population size plays a very passive role: the number of occupations cannot excess the population size. Compared to the Dixit-Stiglitz model and Ethier model, the model in this chapter has endogenized individuals’ levels of specialization and degree of market integration. Hence, the following structural changes can be predicted as different aspects of economic development: increases in the degree of commercialization and in the extent of endogenous comparative advantage, and a decrease in each individual’s degree of selfsufficiency. If transaction efficiency is very low, a large population size will be divided into as many separate local communities as do not trade with each other, and productivity and per capita real income will be very low in such an economy (for instance, in prereform India). As transaction efficiency is improved, separate local communities merge into an increasingly more integrated market, thereby generating economic development. Sachs and Warner (1995) use cross country data to establish a positive correlation between economic development, trade dependence, the degree of openness, and quality of institution that affect transaction conditions. Gallup and Sachs (1998) use cross country data to show that geographical conditions, such as population share in coastal regions, have significant impacts on per capita income in a country. The empirical evidence supports the theoretical models in this chapter. 7.9. Emergence of Professional Middlemen and Trade Pattern

Example 7.3: A Smithian model allowing for specialization in trading a particular good. In the previous sections, specialization in trading activities is not allowed, so that transaction efficiency is exogenous. In order to explore this issue, we now specify a new model as follows. Max: u=[x+(rx+kx rxd)xd][ y+(ry+ky ryd)yd][z+(rz+kz rzd)zd] s.t. x+xs = Max{0, Lx -a}, y+ys = Max{0, Ly -a}, z+zs = Max{0, Lz -a}, (production function) rx+rxs = Max{Lrx- a, 0}, ry+rys = Max{Lry -a, 0}, rz+rzs = Max{Lrz - a, 0} (transaction condiiton) Lx+Ly+Lz+Lrx+Lry+Lrz = 1 (endowment constraint) prx(rxs-rxd)+ pry(rys-ryd)+prz(rzs-rzd)+px(xs-xd)+py(ys-yd)+pz(zs-zd)=0 (budget constraint) where a is a fixed learning or training cost in each production and transacting activity, transacting services r for different goods are distinguished by subscript i (i=x,y,z), Lri is labor allocated to the production of transaction service in delivering good i, ki is the transaction efficiency coefficient for delivering transaction service for good i, and pri is the price of the transaction service in delivering good i. In this model, although transaction efficiency for goods is endogenized, the transaction efficiency coefficient for transaction services, ki, is exogenously given. Hence, we can use ki to explain all endogenous variables through comparative statics analysis of general equilibrium. Following the two-step approach, we can solve for the corner equilibria in 5 structures: A (autarky), P (partial division of labor in production, where two goods are traded), PT

230

(partial division of labor in production and transactions, where two goods and transaction services for the two goods are traded), C (complete division of labor in production where three goods are traded), and CT (complete division of labor in production and transactions where all goods and transaction services for all goods are traded), as shown in Table 7.1. Table 7.1: Corner Equilibria in Five Structures

Structure Relative price

A

C

PT

CT

pi / pj =1

py /px = pz /px = 1

pri / prj = pi / pj = (ki/kj)1/4; pi / pri = [44(1-2a)/55]1/3

pri/prj = (ki/kj)1/6 pi /pj = (kj/ki)1/6 pi /pri = 5(1-a)1/5/66/5

(1-3a)4 ÷44

(1-3a)5 ÷55

(1-2a)13/3(kikj).5÷ (55/348/3)

(1-a)27/5(kxky kz)2/3÷ (53612/5) where pri is the price of transaction service for good i. Because of symmetry, which goods are traded is indeterminate in structures P and C. Each middleman in the two structures in example 7.3 only provides transaction service for one good. Comparisons between per capita real incomes in the five types of structures indicate that structures P and C cannot be equilibrium structures. If transaction efficiency of transaction service is sufficiently low, autarky is the general equilibrium, whereas if that efficiency is sufficiently high the general equilibrium is the complete division of labor in production and transactions (structure CT) involving three types of middlemen. Each type of middleman completely specializes in producing transaction services for one type of good. If the transaction efficiency of transaction service ki is neither too large nor too small, then the general equilibrium is structure PT, where only two goods are traded and transaction services for delivering each of the two goods are provided by middlemen. As indicated in Table 7.1, the per capita real income for this structure is uPT = (1-2a)13/3(kikj)0.5/55/348/3, where ki and kj are the transaction efficiency coefficients of transaction services for goods i and j, respectively. Hence, the corner equilibrium that trades the two goods with the larger transaction efficiency coefficients of transaction services generates a greater per capita real income. This, together with the Yao theorem, imply that if not all goods are traded in the general equilibrium, those will be traded that have the larger transaction efficiency coefficients for transaction services. Also, Table 7.1 shows that the relative price of the two traded goods in the corner equilibrium trading only two goods is Real income

(1-3a)3 ÷ 27

P

pi/pj = (ki/kj)1/4 where ki/kj is the relative transaction efficiency of transaction services for the two goods. Our results about the implications of relative transaction conditions for trade pattern are summarized as follows. Proposition 7.3: The general equilibrium includes as traded goods those with larger transaction efficiency coefficients of transaction services if not all goods are traded. The higher the transaction efficiency of transaction service for a good, the higher the equilibrium price of this good in terms of other goods. As transaction efficiency for transaction services is improved, the general equilibrium evolves from autarky to the partial division of labor 231

between production and transactions, followed by the complete division of labor between production and transactions. This result implies that those goods that involve inferior transaction conditions may be excluded from the network of division of labor and related trade. Even if such a good is involved in trade, its equilibrium price will be lower than that of other goods with the same production and consumption conditions. This explains why the market price is lower for those houses that are subject to government rent and trade restrictions than for other similar houses that can be freely traded. This also explains why there is no market for some goods. For instance, no market exists for clear air because of the extremely low transaction efficiency in trading this. In many textbooks, the absence of such markets is exogenously given. But in our models, this is endogenously determined by the trade off between positive network effects of division of labor and transaction costs. In chapters 9 and 10, the existence of markets for different goods is endogenized by specifying more complicated trade offs among endogenous transaction costs, exogenous transaction costs, coordination reliability of the network of division of labor, and economies of division of labor. Because of economies of specialization assumed in our models, the inframarginal comparative statics of equilibrium also imply that productivities and equilibrium quantities produced and consumed are greater for the traded goods with the higher transaction efficiency of transaction services than for the non-traded goods, even if production and consumption conditions are exactly the same for the two types of goods. This explains why the income share of the sectors manufacturing automobiles, refrigerators, and computers can dramatically increase despite the fact that they do not generate direct use value for final consumption. These sectors specialize in producing goods that can be used to improve transaction efficiency, so that they can promote the division of labor in all sectors. This, in turn, enlarges the market for all goods, including those produced by these sectors.

7.10. Trade off Between Economies of Specialization and Coordination Costs

Example 7.4: The Becker-Murphy model of endogenous specialization (1992). Consider a production team consisting of n ex ante identical agents. This team undertakes a continuum of activities with mass 1 to produce good y. The production function of y is (7.28a)

Y = Mins∈[0, 1] Y(s),

where Y(s) is the contribution of activity s to the final output Y. The Leontief relationship between Y and Y(s) implies that each activity is essential for obtaining the final output. Each team member has a production function in activity s (7.28b)

Y(s) = AThθ(s)Tw1-θ(s)

where Th(s) is her total amount of time devoted to acquiring activity-specific skills and Tw(s) is time devoted to the production in activity s. Each agent is endowed with one unit of time. This implies that if each agent disperses her limited time among many activities, duplicated investment in acquiring activity specific skills will generate inefficient

232

aggregate output. Hence, in an efficient team, each team member specializes in a certain range of activities that are different from other members' activities. Suppose that the number of agents in the team is n; then each member undertakes a range of activities with measure 1/n. Therefore, (7.28b) is the production function of the agent who specializes in activity s as well as the team's aggregate production function in this activity. Let each agent's total amount of time allocated to learning and production in each activity be T(s). Then each person's time endowment constraint is (1/n)T(s) = 1, where 1/n is her range of activities. This implies that T(s) = n. Hence, each agent will maximize (7.28b), subject to the time endowment constraint Th(s) + Tw(s) = T(s) = n. The optimum solution of this decision problem, together with the production function (7.28a), yields (7.29)

Y* = B(n) ≡ Anθθ(1-θ)1-θ.

Hence, the optimum aggregate final output of the team is an increasing function of the team size n. But a larger team size generates greater coordination cost. Assume that the coordination cost in terms of final output among team members is (7.30)

C(n),

C'(.)>0, C"(n)>0,

Then the optimum team size can be determined by maximizing the net output B(n)-C(n). The first order condition is (7.31)

dB(n)/dn = dC(n)/dn

that is, the marginal benefit of division of labor equals the marginal coordination cost. Here, 1/n is the scope of each team member's activities and n can be interpreted as each team member's level of specialization as well as the level of division of labor within the team. Suppose C(n) = cn2. The efficient team size given by (7.31) is n = α/2c, where α ≡ Aθθ(1-θ)1-θ. This result implies that even if the population size for the society is fixed, the level of division of labor increases as the transaction condition is improved (c decreases). Suppose the population size is M. Then for a very large c, the efficient team size n = α/2c is small, so that the economy is divided into a large number (M/n) of separated teams. There is no connection between the teams. As c decreases, the efficient team size increases and the separate teams merge into an increasingly integrated coordination network. As Becker and Murphy (1992) indicate, the relationships between the members within the same team could be either relationships within a firm or market relationships between firms. Dynamic versions of this model of endogenous specialization can be found from Tamura (1991, 1992).

Key Terms and Review Economies of division of labor generated by fixed learning cost Differences between the decision rules in choosing the optimum resource allocation for a given configuration and the decision rules in choosing the optimum configuration of specialization

233

Differences between neoclassical and Smithian demand and supply functions Relationship between resource allocation and relative prices of traded goods vs. relationship between the level of division of labor and the absolute price of labor Young theorem: demand and supply are two sides of the division of labor; the extent of the market and the level of division of labor are two sides of the same coin Extent of the market and the distinction between total market demand for a good and aggregate demand (the extent of the market or the thickness of the market) Difference between effects of an increase in transaction efficiency and an increase in fixed learning cost on the level of division of labor Mechanism that generates the following concurrent phenomena: increases in the degree of commercialization, in trade dependence, in the degree of interpersonal dependence, in the extent of the market, in the number of types of markets, in productivity, in the extent of endogenous comparative advantage, in the degree of diversity of economic structure, in individuals’ levels of specialization, in the degree of production concentration, and in the degree of market integration Mechanism generating the Linda pattern of trade Relationship between evolution of division of labor, an increase in consumption variety, and emergence of new goods Economies of consumption variety Differences between the Smithian and neoclassical approaches to endogenizing the number of goods and the degree of market integration?

Further Reading Smithian models with endogenous specialization: Houthakker (1956), Chu (1997), Chu and Wang (1998), Lio (1997, 1998), Sun (1999), Wen (1997), Yang and Y-K. Ng (1993, ch. 5), Smith (1776), Yang (1991, 1994), Yang and S. Ng (1998), S. Ng (1995), Rosen (1983), Becker (1981), Becker and Murphy (1992), Barzel and Yu (1984), Young (1928); Models with endogenous number of goods: Dixit-Stiglitz (1977), Krugman (1979, 1980), Ethier (1981); Smithian models with endogenous number of goods: Yang and Shi (1992), Yang and Y-K. Ng (1993, ch. 8), Yang (1996), Sun and Lio (1996); Emergence of professional middlemen: Yang (1991), Carter (1995), Bolton and Dewatripont (1994), Yang and Ng (1993, chapter 6).

Questions 1. In the early part of this century, Ford pioneered the use of mass production techniques featuring production lines. The new method of management and production substantially reduced the prices of automobiles and drastically increased demand and supply of automobiles. This made the US the first country “on the wheelers.” Not only did the income share of the automobile industry and related sectors drastically increase, but also many new specialized sectors emerged from the better transportation conditions provided by cheap automobiles. (For instance, the supermarket might not survive market competition in the absence of cheap automobiles.) Many economists call this phenomenon “economies of scale and economies of scope” (Chandler 1990). However, Young claimed that the notion of economies of scale misses the phenomenon of division of labor, and in particular misses the qualitative aspect of division of labor. Use the notion of positive network effect of division of labor and the trade off between economies of division of labor and transaction costs to explain the phenomenon. Discuss the implications of the production line, the geographical concentration of production of automobiles, the standardization of parts, and the division of labor between manufacturing and Ford's dealer franchise network for reducing coordination costs (a type of transaction cost)

234

2.

3.

4.

5.

6.

7.

8.

and for increasing the efficient level of division of labor within the automobile industry. Then analyze the implications of cheap automobiles for an increase in the level of division of labor for society as a whole and for the extent of the market for automobiles. Use the notion of general equilibrium to figure out the mechanisms that simultaneously determine all of these interdependent phenomena. Use Marshall’s idea that a finer division of labor in production creates more scope for the division of labor in management to explain the emergence of Taylor’s scientific approach to management from mass production and industrialization. How does the market simultaneously determine the demand and supply of management services as two aspects of the division of labor between production and management? The Smithian model in example 7.1 explains structural changes as evolution of division of labor, in which self-sufficient individuals transform into increasingly more professional individuals as the number of professional occupations increases. If the increase in employment share of the tertian sector is interpreted as the increase in employment share of the professional transaction sector as in North (1986), can you use the Smithian models in this chapter to explain this data as evolution of division of labor? Reprocess data according to your theory (for instance, counting all sectors that relate to the production of automobiles and computers as part of the transaction sector) and then test your theory against empirical observations. Many economists cite the Smith theorem, that division of labor is dependent upon the extent of the market, to argue that population size determines the extent of the market, which determines the level of division of labor. Use the Young theorem to critically assess the statement. Young argued that the approach that separates the analysis of demand from the analysis of individuals’ decisions in choosing their levels of specialization is misleading. The Young theorem (1928, p. 539, p. 534) consists of three statements: (a) Not only is the level of division of labor dependent upon the extent of the market, but also the extent of the market is determined by the level of division of labor, so that the extent of the market and the level of division of labor are two sides of the same coin; (b) Demand and supply are two aspects of division of labor from a general equilibrium view; (c) The securing of increasing returns depends on the progressive division of labor. Use the new classical models in this chapter to explain the Young theorem. Smith claimed that the extent of the market is determined by transportation efficiency (1776, pp. 31-32) and that the division of labor is limited by the extent of the market (1776, chapter 3 of book I). Use the models in this chapter to formalize the Smith theorem in connection to the Young theorem. In ancient Europe and China there was a debate about the role of commerce in comparison to production in determining the wealth of a nation. One side in the debate argued that commerce is nonproductive, and thus makes no positive contribution to the wealth of a nation. Hence, commerce should be restricted. The other side argued that commerce is a driving force of economic development which positively contributes to the wealth of the nation. Use the Smithian models in this chapter, and the notion of the general equilibrium network of division of labor, to assess the views. Transaction costs in the Smithian models can be interpreted as costs caused by unpunctual delivery of traded goods and unpunctual transmission of information. It follows that, the development of the watch, the refrigerator, the automobile, the computer, the Internet, the inventory facility, and the standardization of goods and services have very important influences on the general equilibrium network size of division of labor. Use statistical data on the income shares of all sectors that are directly and indirectly related to transaction conditions to verify this theory. Consider the Smithian model with an endogenous number of consumption goods in example 7.2. Assume that there are job shifting costs, so that an individual who has just changed jobs is

235

not as productive, at least for a time, as a person who has not changed jobs. Suppose that the oil crisis has suddenly reduced transaction efficiency. Analyze what will happen to the equilibrium network size of division of labor and the equilibrium number of goods. Then discuss the possible effects on short-run unemployment, which is called by some economists (such as Friedman) natural unemployment and by other economists structural unemployment. Analyze the intimate relationship between the equilibrium network size of division of labor before such a shock and the unemployment rate after the shock. (You may start from the two extreme cases: (a) Before the shock, the equilibrium is autarky; (b) Before the shock, the equilibrium is the complete division of labor, where each person produces only one good and completely depends upon the market for other goods.) 9. It is said that specialization should be restricted because this conflicts with diversification, which is good for society. Marx and other economists argued that specialization makes individuals dull and bored, which is uncivilized thing to do to people, so that specialization should be restricted. Japanese managers of companies emphasize the diversified experience of their employees rather than specialization. In contrast, American managers have paid more attention to specialization since Taylor’s scientific approach to management was developed. Similarly, American universities emphasize the diversity of undergraduate education, while fine specialization occurs at the level of graduate education. In contrast, the German technical training system and the Russian tertiary education system introduce specialization at quite early stages of education. Analyze these cases to identify the conditions for different efficient balance points between specialization and diversification. Draw the distinction between the following two kinds of economies of diversity in your analysis. One is the economies of variety of inputs, which is considered in this chapter and in chapters 18 and 19. The diversity of each person’s inputs and the specialization of each person’s output can increase side by side as the network size of division of labor evolves, as shown in this chapter and in chapters 18 and 19. The other type of economies of diversity is a certain technical complementarity between activities in which a person engages. For instance, a person’s teaching experience of economics may help her research in economics. This kind of technical complementarity is not considered in this chapter. Do some thought experiments about the possible general equilibrium implications of this kind of technical complementarity in the new classical framework. You are referred to Rosen (1983) for the analysis of the trade off between economies of specialization and this type of economies of technical complementarity. 10. Many economists use the notion of economies of scope to describe diseconomies of specialization. Use an example similar to the following one to illustrate that the notion of economies of scope may be misleading. In the example, there are two firms A and B. A hires 3 employees who all engage in exactly the same 3 activities. B hires 10 workers. Each of them engages in an activity that is distinct from the activities of the others. B has a larger scale of operation as well as a greater scope of activities than A. But a higher productivity of B than A may be due to a higher level of specialization of each worker in B and a higher level of division of labor in B than in A. Use your example to illustrate why the Herfindal index, which uses the output share of a sector, a city, or a region as a measure of the level of specialization, is misleading. According to this index, many large American cities, such as Los Angeles, Chicago, San Francisco, and New York have lower levels of specialization than Albany, Gary, and Norfolk (see Diamond and Simon 1990, pp. 180-183). But from casual observation, we can perceive that the four large cities certainly have a much higher level of division of labor than the three small cities, because of their higher degree of diversity of occupations as well as the higher levels of specialization of many professionals. This is verified by Baumgardner’s (1988b) empirical evidence that individuals in a larger city are more specialized than those in small towns. 11. In the Smithian model in example 7.2, as transaction efficiency is improved, the production functions of some new goods emerge from evolution of division of labor. This looks like

236

endogenous technical progress. Analyze the difference between this approach to explaining endogenous technical progress, which is dependent on a large size of market network and on the merging of separate local business communities into an increasingly integrated market, and the neoclassical approach to explaining technical progress by investment, which is independent of the evolution of the network size of division of labor. 12. Yang, Wang, and Wills (1992) have tested the concurrent evolution of the degree of commercialization (one aspect of division of labor) and per capita real income, generated by improvements in a transaction efficiency index, which is determined by institutional changes, against China’s data. Find other ways to test the theory developed in this chapter. For instance, you may test concurrent evolution in commercialization and in the number of available goods or concurrent evolution in commercialization and in the degree of market integration and production concentration. 13. Casual observations suggest that individuals in a very developed and highly commercialized economy are often frustrated by the disutility caused by management of a great variety of goods and services. Use the statistical data of cases of psychosis caused by complexity in managing a great variety of goods in a highly commercialized society to test the theory developed in example 7.2. 14. Design a method to test the model in example 7.2, which predicts a neutral role of population size in promoting per capita real income, vs. the DS model with transaction costs in example 5.1, which predicts a positive effect of population size on per capita real income against empirical data. The former has endogenized the degree of market integration and the latter has not. Design a statistical approach to test the comovement of all concurrent phenomena of structural changes predicted by the models in this chapter. 15. From our daily experience, we can perceive that coordination costs for specialization are increasingly more significant as specialization is increased. For instance, an expert on the Russian military system can provide professional knowledge that nobody else can provide. But the value of her professional knowledge is very low in peace time (though she may become a star in TV shows when there is a possibility of War between Russia and the US). Smith noted the trade off between coordination costs and economies of division of labor. Becker and Murphy have formalized the trade off in a decision model (See example 7.4). How does the market sort out the efficient balance of this trade off? How should you find the efficient trade off when you choose your professional career? 16. Use the Smithian models in this chapter to explain the Linder pattern of trade, which suggests that trade volume between ex ante similar developed countries is much greater than that between ex ante different developed and less developed economies. Discuss the difference between the Smithian way and Krugman’s way (using the D-S model) to explain the Linder pattern of trade. 17. Many development economists compare cases of India, Bangladesh, some African countries, and the East Asian experience in the 19th century, with the development experience of Western Europe in the 18th and 19th centuries to argue that population growth has negative effects on economic development. Hence, they say, birth control is essential for economic development. Other economists use the early development experience of the US, Australia, and New Zealand, and the development experience of Hong Kong and Japan in the 20th century, to argue that population size has a positive effect on economic development. Use the Smithian models in this chapter to assess the two types of opinions in relation to the effects of transaction conditions on economic development. 18. Rosenberg and Birdzell (1986, p. 168) find that “The agricultural revolution came after 1880 (increased use of fertilizers, machines, improved seeds, improvements in methods of cultivation and animal husbandry) as a consequence of improved transportation, the development of regional specialization in agriculture.” Use the model in this chapter to explain this historical fact.

237

19. Mokyr (1993, p. 31) indicates that “Many authors maintain that the challenge imposed by resource scarcities stimulates invention. Thus the deforestation of Britain is alleged to have led to a rise in timber prices, thus triggering Britain into adopting a novel and ultimately far more efficient set of techniques using fossil fuels.” Use the model in exercise 13 to analyze the conjecture. Under what conditions does the frightening forecast of crises due to an energy shortage and a population explosion make sense, and under what conditions is the forecast nonsense? 20. In the model in exercise 14, the transaction efficiency coefficient k is equivalent to “public goods.” According to Pigou and Samuelson, the output level of public goods is not Pareto efficient in the Walrasian regime with no government intervention. Use the Chu model to assess under what condition this claim is wrong in relation to the following facts. Early economic development in the US in the last century was driven by the development of infrastructure. But the infrastructure (canals, railways, and early freeways) was developed largely by private companies. The development of freeways by private companies in Malaysia is much more successful than in China, where the government monopolizes the construction of freeways. According to Coase (1960), the market and the private sector are able to take care of so called “public goods,” and Pigou and Samuelson’s notion of distortion being caused by externality and public goods is misleading. Use the Chu model to assess Coase’s view. 21. Kremer (1993) argues that population density has a positive effect on long-run economic growth. But Jones (1981, p. 232) provides historical evidence of the negative effect of population density on early economic development in India, China, the Ottoman empire, and Europe in 1500-1800. Use the model in this chapter to analyze the opposite opinions. 22. Many development economists argue that mainstream economics on the function of the market is not applicable to developing countries because of the nonexistence of many markets in these countries. Use the models in this chapter to show that if classical mainstream economics about development implication of division of labor is formalized, its core purpose is to explain the emergence of markets and the evolution of marketization. Hence, the development experience of 18th and 19th century Britain in improving transaction conditions becomes applicable to currently developing countries.

Exercises 1. Let the equilibrium number of traded goods in the model in example 7.1, n ≥ 1 . Then identify the parameter space within which the solution given by the first order condition is relevant. If the parameter values are not within this subspace, what is going to happen to general equilibrium and its inframarginal comparative statics? Do the same analysis for the case of n ≤ m . Check the second order condition for maximizing utility with respect to n and discuss the feature of the general equilibrium when the second order condition is not satisfied. 2. (Siang Ng, 1995) Consider the model in example 7.1 with m=3. Suppose that there are two countries. Each of them has M citizens and transaction efficiency k differs from country to country, so that utility equalization may not hold between countries. Solve for the general equilibrium and analyze under what condition international trade emerges from domestic trade. Suppose k is the same between the two countries, but is larger for domestic trade than for international trade. Identify the condition for international trade emerging from domestic trade and trade pattern. 3. Suppose there are two countries and only two goods in the model in example 7.1. The utility function is u = (x c )α (y c )1−α . The population size for each country is M. Identify the condition for international trade to emerge from domestic trade.

238

4. Show that the Nash bargaining equilibrium in example 7.1 or 7.2 is the same as the Walrasian equilibrium. 5. Work out the own price elasticities of the neoclassical and Smithian demand and supply functions in example 7.2, and examine the differences between them. 6. Suppose that the government taxes sales of goods at rate t and then equally distributes the tax revenue among individuals in the model in example 7.1. Solve for the general equilibrium and its inframarginal comparative statics, and analyze the implications of the tax for the equilibrium network size of division of labor and other related variables. p a 7. (Yang and Shi, 1992) Assume that the production function in (7.1) is xi = li ,a > 1 . Solve for the general equilibrium and its inframarginal comparative statics. Check the second order condition where the equilibrium number of traded goods is n∈(1, m), and analyze the implications of the second order condition. Then work out the general equilibrium and inframarginal comparative statics when the second order condition is not satisfied. 8. Introduce the externality of pollution caused by consumption of cars into the model in example 7.3. Suppose that the government taxes the consumption of cars (for example, through a value tax on gas) and then evenly distributes the tax revenue among all consumerproducers. What is the optimum tax rate that efficiently trades off organization efficiency, which may be reduced by the tax, for allocation efficiency, which may be increased by the tax? 9. Assume that in the model in example 7.2, transaction efficiency k = 1, but the government imposes a tax rate t on each dollar of sales, then equally distributes the tax revenue among all individuals. Solve for general equilibrium and its comparative statics. Analyze the implications of the tax for the equilibrium network size of division of labor and number of available goods. 10. Assume that in example 7.3, transaction service is not good-specific, so that transaction service for one good is the same as that for another good. Solve for the inframarginal comparative statics of general equilibrium. In some developing countries, such as China, the government monopolizes both the wholesale and the retail network. The government uses the licensing system and other regulations to deter free entry of private businessmen into trading businesses, in particular into importing, exporting, and wholesale businesses. Use your answer to analyze the effects of such institutions and regulations on economic development. 11. Assume that the economy in example 7.2 is initially in equilibrium. An oil crisis reduces transaction efficiency from k1 to k2, so that the equilibrium number of goods decreases. Assume that as the equilibrium shifts from a corner equilibrium to another corner equilibrium, there is a job-shifting cost when individuals change jobs, so that those who lose their jobs are not as competitive as those who do not change jobs. Thus, unemployment will take place. Compute the unemployment rate caused by the oil crisis. 12. (Lio, 1998) Each ex ante identical consumer-producer’s utility function is: V = ∑i=1mln(xI+ xid)+βlnH, where xi, xid , and k have the same meanings as in example 7.1. H = 1- L is the amount of time allocated for leisure, L is the amount of time allocated for the production of goods, and β is a parameter representing the desire for leisure. It is assumed that the total amount of available time for each individual is 1, so that the production functions and the endowment constraint for time are xI+xid = Max{0, lI-a}, i = 1, 2, …, m, ∑i=1m lI ≡ L, L + H,= 1. Solve for the comparative statics of general equilibrium. Show that as transaction efficiency k or the degree of desire for leisure β increases, the equilibrium level of division of labor n, productivity, and per capita demand from the market, which equals per capita supply xid increase. Lio (1996) finds empirical evidence that productivity, per capita real income, and leisure time increase, while working time for self-provided consumption decreases as division of labor evolves. Why do productivity and the level of division of labor increase as the degree of desire for leisure increases? Assume the utility function is of CES. Will your result change? (Hint: see Lio.) 239

13. (Wen, 1996) Consider an economy with M ex ante identical consumer-producers. Each individual’s utility is specified as a function of the quantities of two goods that are consumed, u = (x+kxd) (y+kyd), where all variables have the same meanings as in example 4.1. Each individual has the following production functions for the two consumption goods. x+xd = Max{0, (lx-a)(sx-b)}, y+yd = Max{0, (ly-a)(sx-b)}, where li is the individual’s level of specialization in producing good i, si is the amount of primary resource allocated to produce good i, a is a fixed learning cost in producing a good, and b is a fixed amount of the resource that is essential for the production of each good. ly+ly = 1 and sy+sy = s0 where s0 is each individual’s initial endowment of the resource, which can be considered as coal, iron ore, or land. Solve for the inframarginal comparative statics of general equilibrium, and show that as per capita endowment of the resource s0 decreases due to population expansion or depletion of the resource, the equilibrium level of division of labor and productivity increases. Explain why labor surplus caused by population expansion, and an energy crisis caused by the depletion of energy, can increase the level of division of labor and productivity under good transaction condition. (Hint: work out the critical value of k that divides autarky and the division of labor, as a function of s0, then show that the derivative of this critical value with respect to s0 is negative.) 14. (Chu, 1997) Consider an economy with M ex ante identical consumer-producers, where transaction efficiency k is determined by the level of specialization in producing transaction infrastructure. For an individual who does not produce infrastructure, the decision problem is: Max: u = ( x + kx d )( y + ky d ) s.t.

y + ys = 1− α Lx + L y = 1

(production function of y) (endowment constraint of time)

1 ⎪⎧1 − M k if M k > 1 k=⎨ ⎪⎩k 0 if M k ≤ 1

(transaction condition)

p x x s + p y y s = p x x d + p y y d + pk

(budget constraint)

where x and y are respective quantities of two goods that are self-provided, xd and yd are respective quantities of the two goods purchased from the market, xs and ys are respective quantities of the two goods sold, and Li is the individual’s level of specialization in producing good i. k is the transaction efficiency coefficient, which is an increasing function of the number of individuals producing infrastructure, Mk. If the number is 0, that is, no professional infrastructure sector exists, then k = k0 . xd (i = x, y) is the price of good i, and pk is a fee for the use of infrastructure paid by each individual. It is assumed that individuals compete for the rights to construct the infrastructure in an auction. The bidder who collects the lowest per capita fee will get the rights. If no infrastructure exists, that is, Mk = 0, then p k is irrelevant and k = k 0 . For an individual choosing to be a specialist in the infrastructure sector, her decision problem is: Max: u = kx d ky d s.t.

p x x d + p y y d = p k ( M x + M y ) / M k where

( M x + M y ) / M k is the ratio of the number of specialists producing goods to those producing infrastructure, so that p k ( M x + M y ) / M k is the earnings that an infrastructure specialist receives from the production of infrastructure. Because of the assumptions that individuals are ex ante identical and that a competitive bidding process determines distribution of the rights to produce infrastructure, the earnings must be the same between the infrastructure specialists. Solve for the inframarginal comparative statics of general equilibrium, and show that the level of division of labor between the production of goods and the production of infrastructure is more likely to be higher if the population size M is larger. Use your result to formalize

240

Boserup's idea (1975) that the per capita investment cost of a canal system, a railway network, a freeway network, an airport system, and other infrastructure decreases with the population density, so that a high population density may be favorable for evolution in division of labor and economic development. Why can a competitive bidding procedure for rights to develop infrastructure, plus free choice of occupation configurations, avoid distortion in producing infrastructure (public goods)? (Hint: the corner equilibrium Mk is implicitly given by an equation. Use the envelope theorem and the implicit function theorem to show that the corner equilibrium utility in the structure with specialists producing infrastructure is greater as the population size M increases.)

241

Chapter 10: Transaction Risk, Property Rights, Insurance, and Economic Development

10.1. Uncertainties in Transactions and the Economics of Property Rights Mokyr (1993, pp. 40-58, 158-162,) provides historical evidence that one of the major conditions for the British Industrial Revolution in 1760-1830 was well specified and enforced private property rights. As he summarizes (pp. 56-58), “The specific form of government that had emerged in Britain created an environment that was more conducive to economic development than elsewhere. Most important, the right to own and manage property was truly sacrosanct, contrasting sharply with the confiscations and conscriptions on the Continent during the French Revolution and Napoleonic era. Personal freedom – with some exceptions – was widely accepted in Britain. … Nowhere in the world was property perceived to be more secure than in Britain.” North (1981, pp. 158-62) states: “It was better specified property rights (not the same thing as laissez faire) which improved factor and product markets … The resultant increasing market size induced greater specialization and division of labor, which increased transaction costs. Organizational changes were devised to reduce these transaction costs and had the consequence of radically lowering the cost of innovating at the same time that the increasing market size and better specified property rights over inventions were raising the rate of returns on innovating. It was this set of developments which paved the way for the real revolution in technology.” Mokyr (1993, p. 44) concurs with him: “Property rights in innovation (patents and trademarks), better courts and police protection, and the absence of confiscatory taxation are examples of how the same phenomenon could raise the rate of innovative activity and capital accumulation.” North and Weingast (1989) survey the institutional changes that occurred in Britain in the wake of the Glorious Revolution of 1688, in which wealth holders increased their grip on power, and the government was put on a sound fiscal footing and committed itself to respect the existing distribution of property rights. They point to secure contracting and property rights as a precondition for specialization and impersonal exchange. Mokyr (1993, p. 45) also indicates: “By taxing according to prespecified and well-understood rules, and by gradually abandoning the Tudors’ and Stuarts reliance on monopoly rights as a source of crown revenues, the post-1689 regime continued a trend that had begun long before and was certainly well established by the Restoration of 1660.” On the other hand, confiscatory taxation in France was regarded by Mokyr (1993, p.44) as an obstacle of economic development. Violation of private entrepreneurs’ property rights by the Chinese government during Ming and Qing dynasties is considered by Mokyr (1990, p. 238), by Fairbank (1992), and by Baechler (1976, p. 82) as detrimental for China’s economic development. Yang, Wang, and Wills have also found empirical evidence for the relationship between economic development, evolution of division of labor, and better specified and enforced property rights. In this chapter, we use Smithian models of endogenous network size of division of labor to study the intimate relationship between economic development, enforcement of 323

property rights, and insurance. In section 10.2, we first introduce a transaction risk into each transaction in a model of endogenous specialization. This will generate a trade off between economies of division of labor and reliability of a larger network of transactions required by the finer division of labor. Since aggregate transaction risk is an exponential function of the number of transactions, the transaction risk that may be caused by unsecured property rights is a much more important detriment to economic development than tangible transportation costs. The problem of coordination reliability of division of labor is important in our daily decision making process. It is because of this problem that many individuals do not want to specialize in a particular activity. As an individual increases her level of specialization, she becomes more dependent on other specialists whose produces are essential for her consumption and production. Since the division of labor is associated with an inputoutput network which involves a series connection of many individual specialists, the whole network may fail to work if one of the links in the series connection fails to work. Therefore, the aggregate risk of coordination failure of the network of division of labor increases more than proportionally as the level of specialization and division of labor increases. In the Soviet-style centrally planned economy of China, a firm was reluctant to specialize in an activity and tried to self-provide many services, such as setting up its own kindergarten, primary school, and cafeterias, and the self-provision of many intermediate goods and services. This reflected the high risk of coordination failure resulting from restrictions on free trade. In 1994, one of the 115 automobile companies in China assembled less than 100,000 cars annually and self-provided 80-90% of their intermediate goods (see Lardy, 1998a). In the relatively free market system of the US, in contrast, there are only four automobile companies assembling cars. Each of them produces more than one million cars annually and less than 40% of its intermediate goods (Webster et al. 1990). Recent economic development in the US is associated with the boom in franchise networks, which features a finer division of labor between specialized production of entrepreneurial ideas by franchisers and specialized production of tangible services by franchisees. This feature of economic development in the US is based on more reliable enforcement and protection of rights to intangible entrepreneurial knowledge, such as those included in operations manuals and reputation. The trade off between economies of division of labor and coordination reliability implies that taking a higher aggregate risk for coordination failure may be efficient so long as economies of division of labor that can be exploited outweigh the increased aggregate risk. If an improvement in the transportation condition enlarges the scope for trading off economies of division of labor against the aggregate transaction risk, the efficient aggregate transaction risk and productivity may increase side by side. Such a higher efficient aggregate risk for coordination failure may be associated with an episode such as the Great Depression in 1930 and the Asian financial crisis in 1997. In the 1920s, as a result of successful industrialization in Western Europe and the US, a large network of domestic and international division of labor was developed. While on the one hand, this high level of division of labor raised productivity and created historically unprecedented prosperity, on the other hand, it significantly increased the risk of coordination failure of the network of division of labor. In that network, many very specialized sectors are connected in a series, so that it might fail to work when one of the

324

professional sectors, such as the banking sector, fails to work, resulting, for example, in the Great Depression and mass unemployment. In other words, the greater risk for an economic crisis caused by the higher risk of coordination failure is endogenously and efficiently chosen by individuals, just as we choose the higher risk of being killed when we decide to drive on the freeway by efficiently trading off the cost of doing so against the benefit. Hence, the relationship among economic development, coordination reliability, and property rights is much more sophisticated than the statement that better enforced property rights are conducive to economic development. In particular, if the risk of coordination failure for each transaction can be reduced by inputting resources, that risk then becomes an endogenous decision variable. The risk of coordination failure of division of labor can be reduced by allocating resources to the specification and enforcement of contractual terms at the cost of rising exogenous transaction costs in specifying and enforcing property rights. We may consider the welfare losses caused by the risk of coordination failure as anticipated endogenous transaction costs caused by the opportunistic behavior examined in chapter 9. Thus, we have a trade off between the exogenous transaction costs of specifying and enforcing property rights and endogenous transaction costs. We can then see that the efficient trade off between endogenous and exogenous transaction costs in the market place may involve imperfect specification and enforcement of property rights. A monthly ticket for a train or bus is an example that illustrates the implications of this trade off. A monthly ticket does not well specify the correspondence between the riding fee and the amount of transport services (number and distance of rides) provided, and it may encourage inefficient travel that generates endogenous transaction costs. However, it involves much lower exogenous transaction costs in collecting payment for each ride than many single ride tickets. Another example is the arrangements for financing construction of a bridge. There are different ways to finance a bridge. One is for the government to use tax revenue to finance the construction of the bridge. Under this arrangement, some individuals who never use the bridge are compelled to pay the tax while others pay no more for frequent use of the bridge. This will generate distortions, which are endogenous transaction costs, so that, relative to the Pareto optimum, the output of the former type of individuals is too little compared to that of the latter type of individuals. However, this arrangement does not involve many exogenous transaction costs in collecting fees from the users of the bridge. The other way is to allow a private company to construct the bridge and to collect fees from the users of the bridge. This method avoids endogenous transaction costs at the expense of the exogenous transaction costs of collecting fees. The most efficient method is the one with the minimum sum of the two types of transaction costs. If the exogenous transaction costs that are saved by financing the bridge through government taxes outweigh the endogenous transaction costs that are generated by the tax arrangement in comparison to the arrangement without the tax, then government finance can be used to promote division of labor and economic development, or to play a role in rectifying “market failure.” Otherwise, the government tax may generate “government failure” and restrict the market from fulfilling its function. In many less developed countries, the government does not know how to use public finance to develop the infrastructure that promotes evolution of division of labor and related urbanization and economic development. On the other hand, in the Soviet style centrally planned

325

economies, the governments extended public finance to the degree that the market could not play its role in the development process. The two extreme cases illustrate that it is not easy to find the efficient trade off between endogenous and exogenous transaction costs. One more example of the trade off between endogenous and exogenous transaction costs in relation to coordination reliability is provided by a comparison of a piece rate wage system vs. an hourly wage. If the quantity and quality of the job to be done can be precisely measured, the piece rate wage can be used to well specify and enforce contractual terms and thereby reduce the risk of coordination failure of the network of division of labor. However, precise measurement of the quantity and quality of the job may involve prohibitively high exogenous transaction costs. If these exogenous transaction costs are taken into account, an hourly wage with more vague contractual terms and with low exogenous transaction costs may be more efficient than a piece rate wage, despite the fact that the former generates much higher endogenous transaction costs than the latter. The trade off between exogenous and endogenous transaction costs is referred to by Mirgrom and Roberts (1992, pp. 277, 377) as the trade off between influencing cost and distortions cased by rigid rules reducing employees’ activities to influence the decisions of a manager. We will consider the relationship between this interesting trade off and economic development in section 10.3. In that section, we will also consider one of the market mechanisms that can reduce the risk of coordination failure of a large network of division of labor. This mechanism employs competition between peer specialist suppliers to provide so called parallel connections to the incumbent supplier that can significantly reduce the risk of coordination failure. But it involves cost for a buyer to keep in touch with many potential peer suppliers. Hence, there is a trade off between the costs in deepening the incumbent trade relationship and the costs in broadening potential trade relationships, in addition to the trade off between economies of division of labor and all kinds of transaction costs. The implications of this trade off for economic development will be investigated in section 10.3. Another institution that can be used to reduce the risk of coordination failure of a large network of division of labor is insurance. In section 10.4, we shall use a model of endogenous specialization to show why insurance can promote division of labor and economic development. Then, the trade off between risk sharing and incentive provision is specified in section 10.5 to investigate the function of incomplete insurance in reducing endogenous transaction costs caused by moral hazard and in promoting economic development. Since incentive provision is associated with well specified and enforced property rights, we have a trade off between the positive effect of insurance on the reliability of the network of division of labor and the negative effect of insurance on the precise enforcement of property rights. This trade off implies that development implications of property rights are much more complicated than many economists have realized. The disappointing development performance of Russia and Eastern Europe in the early 1990s illustrates this point. The Soviet Union mimicked the pattern of industrialization in the capitalist economies by developing a high level of division of labor through a central planning system. Each state or republic in the Soviet Union, or in the communist block of Eastern Europe, was required to specialize in a particular sector. For instance, the Ukraine specialized in producing grain, Czechoslovakia specialized in producing locomotives, and Bulgaria

326

specialized in producing fruit and vegetables. On the one hand, this high level of division of labor generated quite impressive development performance in the 1930s and in the 1950s. But on the other hand, it also significantly reduced the coordination reliability of the non-commercialized network of division of labor. A system of complete insurance was developed to reduce coordination failure of the large network of division of labor, while generating pervasive moral hazard. In a Soviet style economic system, there is complete insurance for each employee of a state enterprise. She can obtain complete medical insurance, she will never lose her job (a complete unemployment insurance), and she will receive a pension no matter what happens to her job, to her health condition, or to the enterprise that hired her (a complete insurance for pension payment). Also, each state enterprise is insured by the government through the soft budget constraint against all kinds of risk in business operation. In China, such complete insurance is referred to as the “iron rice bowl.” It generates a great deal of endogenous transaction costs associated with moral hazard on the one hand, and provides complete insurance that may maintain a reasonable coordination reliability of the network of division of labor on the other. In Russia’s reforms in the early 1990s, this form of complete insurance was abolished when an alternative insurance system was yet to be developed in the market. Hence, a breakdown of an enterprise, a sector, or of a link between two states generated spectacular coordination failure of the whole network of division of labor, resulting in the disappointing development performance of the Russian economy in the 1990s. The trade off between the positive and negative effects of insurance relates to the trade off between economic reforms requested by IMF and the insurance mechanism associated with IMF financial assistance which was requested by South Korea and other Asian countries during the 1997 financial crisis. According to Radelet and Sachs (1998), a harsh push for reforms may exacerbate the panic and the crisis. Because of the trade off between economies of division of labor and coordination reliability, no reforms can completely eliminate the risk of such a financial crisis. A certain insurance mechanism is essential for mitigating the damage caused by an unavoidable crisis. On the other hand, moral hazard caused by complete government insurance of the banking system was one of the causes of the crisis. Hence, too soft terms of insurance and related financial assistance are not efficient either. It is not easy to find the efficient balance of the trade off. The trade offs between risk sharing and incentive provision, and between endogenous transaction costs caused by imprecise enforcement of property rights and exogenous transaction costs in enforcing property rights, relate to public policies in handling so called externality and public goods. In the conventional literature of externality and public goods represented by Pigou (1940), externality and non-exclusivity of public goods are exogenously given and the role of the government in rectifying the market failure is the focus of the analysis. In the literature of the economics of property rights and endogenous externality, represented by Barzel (1989), Cheung (1983), Coase (1960), Hart (1995), Milgrom and Roberts (1992), and O. Williamson (1985), the above trade offs are used to endogenize the degree of externality, while the role of a variety of institutions, ownership structures, and contractual arrangements in sorting out the efficient trade offs is the focus of the analysis. In this chapter we use Smithian general

327

equilibrium models with transaction risk to formalize the notion of endogenous externality and to explore its implications for economic development.

Questions to Ask Yourself when Reading this Chapter What is the trade off between endogenous and exogenous transaction costs? What is the trade off between transaction costs in deepening incumbent relationships and transaction costs in expanding potential relationships? What are the implications of the trade off between positive network effects of division of labor and reliability for economic development? Why can competition in the market substitute for precise specification and enforcement of property rights in promoting economic development? How does the market sort out the efficient degree of competition, the efficient degree of vagueness in specifying and enforcing property rights, and the efficient level of division of labor? What are the effects of transaction risk and the degree of risk aversion on the equilibrium network size of division of labor and economic development? Why can insurance promote division of labor and economic development? Why will complete insurance and moral hazard generate endogenous transaction costs?

10.2. Economic Development and the Trade off between Economies of Division of Labor and Coordination Reliability We use an extended version of the model in example 7.1 to formalize North’s idea about the intimate relationship between economic development and secured property rights. The model is exactly the same as in example 7.1, except there is a transaction risk in each transaction. The story behind the algebra runs as follows. In each transaction, there is a risk of delivery failure, which can be considered as a risk of losing property rights. A Cobb-Douglas utility function implies that utility is zero if the amount of any goods consumed is zero. Hence, if an individual purchases n-1 goods and the risk of delivery failure of each good is 1-r, then the total risk for her to receive 0 utility is (1-r)n-1. As transportation efficiency is improved, the scope for trading off economies of division of labor against transportation costs and transaction risk is enlarged, so that the equilibrium network of division of labor and the related extent of the market expand, productivity increases, and the efficient aggregate risk of coordination failure increases. If the risk of coordination failure for each transaction is reduced due, for example, to more secured property rights, the extent of the market, the network size of division of labor, and productivity will rise too. However, if the direct positive effect of the higher reliability of each transaction on the aggregate reliability of the network of division of labor is outweighed by its indirect negative effects through increasing the number of transactions, the aggregate reliability decreases. Otherwise, the equilibrium and efficient aggregate reliability of network of division of labor will increase.

328

Example 10.1: A simplified version of the Yang-Wills model (1990). Consider an economy with M ex ante identical consumer-producers. The decision problem for a person selling good i is: (10.1)

Max: s.t.

Vi ≡ Eui = uiP + 0(1-P) ui = xi (kxrd )n −1 x jm −n

(expected utility) (utility function)

P = rn-1 (reliability of n-1 transactions) s xi+xi =Max{li-α, 0}, xj=Max{lj- α, 0} (production function) li + (m − n)lj = 1 (endowment constraint of time) p i xi = (n − 1) p r x r s

d

(budget constraint)

where xi, xj, xis, xid, li, lj, n, P are decision variables, r and k are parameters, pi is the price of good i. V = Eui is the expected utility, which is a weighted average of ui and 0, where the weights are P and 1- P, respectively. Let us examine the difference in specification between this model and the model in example 7.1. The Cobb-Douglas utility function ui is the same as in example 7.1. We have used the symmetry of that model, that is, tastes and production and transaction conditions are the same for all goods. Hence, the amounts of goods purchased, xrd, are the same for all r, the amounts of self-provided goods, xj, and the amounts of labor allocated to the production of non-traded goods, lj, are the same for all j. However, coordination reliability of division of labor P, which is the probability that all goods purchased are received, is new. 1-r is the probability that the individual fails to receive a good from a purchase contract. We assume that the failure of a seller to deliver the good to the buyer is an event that is independent of the failure of any of the other goods. The risk of coordination failure may be caused by traffic accidents or other stochastic events. That risk may also be caused by opportunistic behavior, as discussed in chapter 9. For this case 1-r can be interpreted as the anticipated risk of coordination failure caused by opportunism. In the alternating offer bargaining game of example 9.12, where players compete for the advantage of the first mover, there is a probability at which mutually beneficial gains to trade cannot be realized. The risk of coordination failure 1-r in this chapter can be interpreted as that probability as well. Therefore, r is the probability that the buyer receives the good and P = rn-1 is the probability that she receives all n-1 goods purchased. 1-P is the probability that she fails to receive at least one of all goods that she buys. Since for the Cobb-Douglas utility function an individual’s utility is zero if the quantity of any good consumed is zero, a consumerproducer will receive 0 utility at probability 1-P and receives ui at probability P. The production functions in (10.1) are the same as in example 7.1. α is a fixed learning cost in each activity, li and lj are respectively the levels of specialization in producing the traded good i and the non-traded goods j. The budget constraint in (10.1) is also the same as in example 7.1. Assume that prices are sorted out through a Nash bargaining mechanism, which generates the same utility between ex ante identical individuals who have the same disagreement point. As shown in chapter 9, this establishes the utility equalization conditions which, together with the market clearing conditions, will generate the same equilibrium as in a Walrasian regime. The equilibrium has equal prices of all traded

329

goods and an equal number of sellers for each traded good, N = M/n, because of symmetry. With these results, the equilibrium values of decision variables can be solved as follows. (10.2) For any i = 1,2 L , n xi = xrd = x j = [1 − α (m − n + 1)] m ∀r ∈ R , j ∈ J

xis = (n − 1)[1 − α (m − n + 1)] m li = α + (n /m )[1 − α (m − n + 1)] P = rn-1 V ≡ Eu i = {1 − α (m − n + 1) / m}m (kr ) n −1 n = m+1-(1/α)-[m/(lnk+lnr)] The inframarginal comparative statics of the general equilibrium are: (10.4a) dn/dr > 0, dn/dk > 0, (10.4b) dP/dr = (∂P/∂r)+ (∂P/∂n)(dn/dr) < 0, if and only if (∂P/∂r) < |(∂P/∂n)(dn/dr)| (10.4c) dP dk = (dP dn)(dn dk ) < 0 (10.4d) dV dr = ∂ V ∂ r > 0 , dV dk = ∂V ∂ k > 0. (10.4e) dli dr = (dli dn)(dn dr ) > 0 , dli dk = (dli dn)(dn dk ) > 0,

(10.4f) dxis dr = (dxis dn)(dn dr) > 0 , dxis dk = (dxis dn)(dn dk ) > 0 (10.4g) dN dr = (dN dn)(dn dr) < 0 , dN dk = (dN dn)(dn dk ) > 0 (10.4a) implies that the equilibrium level of division of labor increases as the reliability of each transaction increases, or as the anticipated risk of coordination failure of each transaction caused by endogenous transaction costs falls. (10.4b) implies that as the reliability of each transaction rises, total reliability P would fall if the negative effect of the increase in r, (∂P/∂n)(dn/dr), outweighs its positive effect, ∂P/∂r. Otherwise, total reliability rises. Here, (∂P/∂n) < 0 and (dn/dr) > 0. Since 1-P can be considered as aggregate risk of coordination failure caused by anticipated endogenous transaction costs, (10.4b) can be interpreted in another way. It means that total endogenous transaction costs in terms of the aggregate risk increase as the endogenous transaction cost, 1-r, for each transaction falls, if the positive effect of the fall on the total endogenous transaction costs through its impact on the number of transactions outweigh its direct negative effect on total endogenous transaction costs. Otherwise, total endogenous transaction costs decrease with the endogenous transaction cost for each transaction. Because of the connection between total endogenous transaction costs and the degree of softness of the budget constraint, this result implies that the budget constraint may become increasingly softer as the endogenous transaction cost for each transaction falls. (10.4c) implies that as the exogenous transaction cost coefficient, 1-k, is reduced, or as transaction efficiency k rises, total anticipated endogenous transaction costs 1-P, or the aggregate risk of coordination failure, increase (or aggregate reliability P falls). This is because as exogenous transaction efficiency is improved, the benefit of increasing division of labor rises in comparison to increasing endogenous and exogenous transaction costs, so that total endogenous transaction costs may increase to the degree that the increased endogenous transaction costs are outweighed by the increased economies of division of labor that are exploited.

330

(10.4d) means that as the endogenous transaction cost for each transaction falls (or as the coordination reliability for each transaction rises), or as exogenous transaction efficiency is improved, expected real income V goes up. We have used the envelope theorem to get this result. (10.4e) and (10.4f) imply that as the reliability of each transaction r rises, or as exogenous transaction efficiency k is improved, each individual’s level of specialization and per capita trade volume go up. Because of economies of specialization, the result implies that labor productivity of each traded good goes up and the degree of selfsufficiency falls. (10.4g) implies that as the reliability of each transaction r goes up (or as the anticipated endogenous transaction cost for each transaction falls), or as exogenous transaction efficiency is improved, the number of sellers of each traded good, which represents the degree of competition, goes down. This results in a fall of aggregate reliability and a rise in total anticipated endogenous transaction costs. Since an increase in r can be caused by more secured property rights, this model formalizes North’s conjecture (1981) about the implications of more secured property rights for economic development, evolution of division of labor, and expansion of the market. If the transaction risk is introduced into the model with the CES utility function in example 7.2, then North’s idea about the intimate relationship between the extent of the market, secured property rights, and emergence of new goods can be formalized. However, our formal model predicts the possible increase in total endogenous transaction cost and aggregate risk of coordination failure as a result of improved transportation conditions (k or r is increased). This prediction invalidates the belief that more secured property rights and improved transaction conditions will always reduce the risk of coordination failure that results in economic crises like the Great Depression in 1930 and the Asian financial crisis in 1997. A high risk of coordination failure can be interpreted as a risk of mass unemployment as all individuals will be forced to choose autarky when coordination of the division of labor breaks down. Hence, it is possible that more secured property rights promote economic development, on the one hand, and increase the aggregate risk of economic crisis, on the other. The devastating consequence of the Great Depression was a major reason that communism spread in many countries after World War II. But in the long run, the striking development performance difference between the capitalist system and the Soviet style system shows that the cost of economic development caused by the greater risk of coordination failure associated with a large network of division of labor may be worthwhile to pay. From the experience of the recent Asian financial crisis, we may appreciate more about the trade off between the positive effect of evolution of division of labor on economic development and its effect on the risk of coordination failure. A more general version of the model with endogenous r can be found in Yang and Wills (1990) or in Yang and Ng (1993, chapter 9). The endogenization of r is a feature of the economic literature on the trade off between economies of division of labor and coordination reliability that distinguishes this literature from the engineering literature on reliability.

331

10.3. Endogenization of Coordination Reliability in Each Transaction and Substitution between Competition and Better Enforced Property Rights

If probability for coordination failure in each transaction can be reduced by inputting resources into specification and enforcement of contractual terms and property rights, then there is a trade off between endogenous transaction costs caused by imprecise enforcement of property rights and exogenous transaction costs incurred in the enforcement. In addition, there are two ways to reduce risk of coordination failure or to reduce the endogenous transaction costs in each transaction. The first is to allocate more resources to reducing the risk of coordination failure of each incumbent transaction. The second is to allocate more resources to cultivating more potential relationships, which are in parallel connection with an incumbent relationship. This will increase the number of parallel connections for each incumbent transaction and reduce the risk of coordination failure of the transaction. In other words, extensive connections with many potential partners yield competitive pressure on the incumbent partner, so that the individual can turn to one of the potential partners when the incumbent one fails to deliver what the person needs. Mathematically, the total risk of coordination failure of each transaction is (1-r)N when there are N potential trade partners and each of their deliveries is realized with probability r. Then total reliability of each transaction P = 1-(1-r)N can be raised either by reducing the risk of coordination failure with the incumbent partner, 1-r, or by increasing the number of potential partners, N. Note that r is between 0 and 1 and P increases as r or N increases. For a nontrivial transaction cost in keeping a potential relationship, there is a trade off between costs in deepening incumbent relationships and costs in broadening potential trade connections. Hence, each buyer’s efficient number of potential sellers of a good with whom she keeps in touch may be smaller than the number of all sellers of the good in the market. This section uses a Smithian model to formalize this trade off in addition to the trade off between economies of division of labor and all kinds of transaction costs. The story behind the algebra runs as follows. In an economy, there are many ex ante identical consumer-producers who can choose their levels of specialization. In addition to the trade off between economies of specialization and transportation costs, there are trade offs between economies of specialization, transaction risk, and transaction costs in reducing such risk, and between transaction costs in deepening incumbent trade relationships and transaction costs in broadening potential trade connections. If an individual pays higher exogenous transaction costs in specifying and enforcing property rights and related contractual terms, the welfare loss caused by the risk of coordination failure 1-r of each transaction can be reduced. Hence, 1-r becomes an individual’s decision variable. From our experience of litigation (did you ever have such an experience?), an increase in legal service fees paid to lawyers, a form of exogenous transaction costs, can raise the probability that our property rights are well protected. The damage caused by infringement of property rights can be considered a form of endogenous transaction costs. There is a trade off between exogenous and endogenous transaction costs. The question of how the efficient trade off between the two kinds of transaction costs can be achieved is the central question in the economics of property rights and institutional economics.

332

For instance, in a Soviet style economy, the exogenous transaction costs associated with legal service fees are trivial. The income share of lawyers’ earnings is very low. But endogenous transaction costs are extremely high, because property rights are not well specified and enforced, individuals have no incentive to work hard, and the patterns of division of labor and resource allocation are distorted. Such endogenous transaction costs are not easy to measure directly. They can be indirectly measured from the long-run development performance. In the US, the opposite situation prevails: exogenous transaction costs and the national income share of lawyers’ earnings are high, whereas endogenous transaction costs are low because of much better specified and enforced property rights. In the US, individuals are more willing to work hard because of the much lower distortions in information transmission. The inframarginal comparative statics of general equilibrium generate the following interesting results. As the parameter that represents efficiency in specifying and enforcing property rights is increased, the equilibrium level of division of labor and per capita real income go up. But two types of changes in transaction reliability may take place in response to improvement in specification and enforcement efficiency. Individuals can either divert resources from specification and enforcement to raising the level of division of labor in production, or allocate the resources that are saved by the more effective specification and enforcement of rights to raising the degree of precision of the specification and enforcement of property rights in each transaction. These two responses are to some extent substitutes in raising per capita real income. If the first generates a greater net benefit than the second, an improvement in specification and enforcement efficiency will generate a lower reliability of each transaction and thereby a higher aggregate risk of coordination failure when it promotes division of labor and economic development. If the second method is better, then an improvement in specification and enforcement efficiency will raise the level of division of labor and the reliability of each transaction, meanwhile generating a higher or a lower aggregate risk of coordinate failure. Its effect on the aggregate risk of coordination failure is parameter value dependent, since the positive effect of an increase in the number of transactions on the aggregate risk may or may not outweigh the negative effect of an increase in the reliability of each transaction. For a large value of the cost coefficient for deepening the incumbent relation relative to the cost coefficient for widening potential relations, “classical contracts” with many potential trading partners (similar to perfect competition) may occur at equilibrium. For a small value of the deepening cost coefficient, “relational contracts” without potentially alternative trading partners may occur at equilibrium As shown in Yang and Wills (1990), in the model with endogenous risk of coordination failure of each transaction, if the transportation efficiency coefficient (which differs from the exogenous transaction efficiency coefficient in specifying and enforcing each contract) is increased, the equilibrium levels of division of labor, productivity, and per capita real income all rise, while the equilibrium degree of reliability of each transaction and the degree of competition decrease. The inframarginal comparative statics of the general equilibrium explore very complicated relationships among the endogenous transaction costs of each transaction, exogenous transaction costs in specifying and enforcing property rights, exogenous transportation costs, aggregate endogenous transaction costs, and the level of division of labor. These sophisticated relationships

333

imply that it is not efficient to eliminate entirely the aggregate endogenous transaction costs that relate to distortions. The idea of eliminating all endogenous transaction costs is too naïve to be realistic because it cannot explain why an hourly wage, which has a lower degree of precision in specifying and enforcing property rights than a piece rate wage, becomes more common than the piece rate wage as division of labor (commercialization) evolves. It is impossible for the government to identify the efficient trade offs among so many conflicting forces. It requires a laissez-faire regime, which allows individuals to choose freely among various structures of division of labor, institutions, and contractual arrangements to sort out the efficient trade offs. The restriction of free choices among occupations and institutional configurations and interference with free pricing will paralyze the functioning of the market in sorting out the efficient trade offs. Mokyr (1993, pp. 47-48) indicates that one of the main conditions for the Industrial Revolution in Britain in 1760-1830 was the British government’s de facto laissez-faire policy. He states: “Compared with Prussia, Spain, or the Hapsburg Empire, Britain’s government generally left its businessmen in peace to pursue their affairs subject to certain restraints and rarely ventured itself into commercial and industrial enterprises. Seventeenth-century mercantilism had placed obstacles in the path of all enterprising individuals, but British obstacles were less formidable than those in France. More regions were exempt, and enforcement mechanisms were feeble or absent. One such enforcement mechanism, widely used on the Continent, was the craft guild, yet by the time of the Glorious Revolution of 1688, the craft guild in Britain had declined into insignificance … During the heyday of the Industrial Revolution, even social-overhead projects that in most other societies were considered to have enough public advantages to warrant direct intervention of the state were in Britain left to private enterprise. Turnpikes, canals, and railroads were built in Britain without direct state support; schools and universities were private. Even the less invasive forms of state support, like the policies of William I of Orange in the Low Countries or the Saint-Simonians in France during the Second Empire, were notably absent in Britain. Until the end of the 19th century, the British government clearly was reluctant to invade what it considered to be the realm of free enterprise. The general consensus among historians today is that the regulations and rules, most of them relics from Tudor and Stuart times, were rarely enforced. The central government was left to control foreign trade, but most other internal administration was left to local authorities. Internal trade, the regulation of markets in labor and land, justice, police, county road maintenance, and poor relief were all administered by local magistrates. Although in principle these authorities could exercise considerable power, they usually elected not to. By ignoring and evading rather than altogether abolishing regulations, Britain moved slowly, almost imperceptibly toward a free-market society.” According to Coase (1960), even lighthouses, which are usually used in textbooks as a typical example of public goods, were built by the private sector in Britain. Example 10.2: An equilibrium model with a trade off between deepening the incumbent relationship and broadening potential relationships. The model is the same as in example 7.1 except that there are only two consumption goods and each buyer has a risk of failing to receive the good she buys. The risk may be caused by a transportation accident when the good is delivered, or by some anticipated opportunistic behavior. If

334

each of M ex ante identical consumer-producers chooses autarky, then there is no risk of coordination failure. An individual’s decision problem in autarky is (utility function) Max: U = xy s.t. x = lx − α (production function of x) y = ly − α (production function of y)

lx + ly = 1

(endowment constraint of time)

where x, y, lx, and ly are decision variables. The per capita real income in this structure is UA = [(1-2α)/2]2. The decision problem for a specialist producer of good x is U x = xy d P Max: (utility function) s.t. x + x s = lx − α (production function) s d (budget constraint) px x = py y (labor cost of public relationship) lc = cN (labor cost for each incumbent relation) ls = sr (endowment constraint of time) lx + lc + ls = 1 N (total coordination reliability) P = 1 − (1 − r) d s where x , y ,x ,lx ,lc ,ls , N ,r , P are decision variables. c is the cost coefficient for the specialist producer of x to keep in touch with a seller of y. This may be interpreted as a cost of making a phone call to a potential seller to inquire about prices and availability of goods, or as a cost of cultivating a relationship with the seller. A restriction on the free choice of trade partners, such as those institutional arrangements in a Soviet style economic system which prohibit individuals from trading land and capital goods, will increase c to a very large value, so that the optimum choice of N will be at its minimum, 1. Hence, N represents the endogenous degree of competition and lc is the total labor cost of broadening potential trade connections. s is the cost coefficient for the specialist producer of x to increase by 1% the degree of reliability of the incumbent relationship. This can be interpreted as the costs of specifying and enforcing contractual terms with the incumbent partner. Hence, ls is the total labor cost in deepening the incumbent relationship. Uncertainties in trade may make the number of suppliers of a good an important determinant of the risk of coordination failure from the complex exchange interdependencies associated with the division of labor. To reduce such risk, a buyer of a good may maintain relationships with many suppliers, or alternatively she may increase the precision of the terms stipulated in a contract with the incumbent supplier. The former method of reducing a risk of coordination failure relates to transaction costs in delimiting rights to contracting, or ls, and the latter relates to transaction costs in specifying and enforcing the terms of a contract, or lc. If we draw the distinction between rights specified in a contract and rights to contracting, we may specify a tradeoff between the two kinds of transaction costs and the substitution between increasing competition, which relates to lc, and increasing accuracy in specifying and enforcing the terms of a contract, which relates to ls. An example is the decision problem faced by an assistant professor who holds a tenure track position. For her given ability and effort and the quality of the match with her incumbent employer, it is uncertain whether the employer will grant tenure to the employee

335

even if she is qualified, and whether the employee will meet the terms of the contract even if the employer treats her fairly. To reduce the risk of being treated unfairly, the employee may spend time negotiating and enforcing the terms of the contract. Alternatively, she may spend time keeping in touch with potential alternative employers in order to reduce the risk of losing her job. Similarly, the employer may hire several tenure track employees for one tenured position, or spend resources specifying and enforcing the terms of a contract. The question is: what is the efficient balance of the tradeoff between the two alternative uses of resources to reduce the total risk of coordination failure? The efficient balance is crucial for the determination of the efficient level of division of labor that balances, in turn, the tradeoff between economies of specialization and various transaction costs. The tradeoff between the two kinds of transaction costs relates to the tradeoff, described by Williamson, between relational costs incurred in mitigating the hazards of opportunism and transaction costs incurred in stipulating detailed contingent contracts (O. Williamson, 1985). The public relations cost function, and the specification and enforcement cost function of each incumbent relationship in this section, formalize Williamson’s idea. It will be clear later that for a small value of the relation cost coefficient, “classical contracts” with many potential trade partners (similar to perfect competition) may occur at equilibrium. For a large value of the relation cost coefficient, “relational contracts” without potentially alternative trade partners may occur at equilibrium. Also, the trade off between the two kinds of transaction costs relates to the trade off between the distortions caused by imprecise contractual terms and bargaining costs in sorting out precise contractual terms, investigated by Milgrom and Roberts (1992, chapter 7). Milgrom and Roberts use this trade off to explain why the piece rate wage is replaced by the monthly wage and why some promotion rules according to seniority can restrain excessive bargaining and “influencing activities” at the cost of incentive provision. Each buyer of good y receives y d that she orders from a seller of y. She keeps in touch with N sellers of y and can turn to one of them if the incumbent seller fails to deliver the good according to the timing and quality that she requires. The reliability of each seller is r, or each seller has a risk of coordination failure 1-r. Hence, the total risk of the buyer failing to receive good y when she keeps in touch with N incumbent and potential sellers is (1-r)N, or her aggregate reliability to receive yd is P = 1- (1-r)N. You may interpret P as the probability that the transaction efficiency coefficient is 1 and 1-P = (1-r)N as the probability that the transaction efficiency coefficient is 0. The solution of the decision problem yields not only demand and supply functions for x and y, but also the optimum number of potential partners, N, with whom a buyer should keep in touch, the optimum risk of coordination failure of each relationship 1-r, and the optimum aggregate coordination reliability P or optimum aggregate risk of coordination failure 1-P. The decision problem for a specialist producer of y is symmetric to that for a specialist producer of x. (utility function) Max: Uy = yxdP s.t. y + ys = Max{0, ly -α} (production function of y) s d (budget constraint) pyy = pxx (labor cost of public relationship) lc = cN (labor cost of each incumbent relation) ls = sr (endowment constraint of time) ly + l c + l s = 1 N (aggregate coordination reliability) P = 1- (1-r)

336

where y, xd, ys, ly, lc, ls, N, r, P are decision variables. Structure D is a division of M individuals between the two professions. Using the symmetry of the model, we can show that the corner equilibrium relative price of two goods px/py = 1 and the corner equilibrium numbers of two types of specialists are Mx = My = M/2 in structure D. Also, in the corner equilibrium, the number of trade partners with whom each individual keeps in touch, N, the reliability of the incumbent relationship, r, and the labor allocation between broadening potential relationships and deepening the incumbent relationship are all the same for the two types of specialists. The corner equilibrium N and r are determined by the first order conditions (10.5a) 2c[1- (1-r)N] = -(1-cN-sr-α) (1-r)Nln(1-r) (10.5b) N = -s(1-r)ln(1-r)/c There are multiple solutions of (10.5). Also, (10.5) does not apply to the several possible corner solutions of r and N. Hence, an analytical solution of the comparative statics of the corner equilibrium cannot be obtained. Table 10.1 reports part of the computer simulation results of the comparative statics of the corner equilibrium reliability of each transaction, r, the number of trade partners with whom each person keeps in touch (degree of competition), N, and aggregate reliability P in structure D. It shows that if s is sufficiently small, then the corner equilibrium value of r is 1, its maximum, so that the equilibrium values of N and P are 1 too; if c is too large, the corner equilibrium value of N is 1, its minimum; as s increases relatively to c, the corner equilibrium value of r falls and the corner equilibrium value of N increases. This implies that as the cost of deepening the incumbent relationship increases in comparison to that in broadening potential relationships, the equilibrium degree of competition, N, increases and the equilibrium degree of reliability for the incumbent relationship, which relates to the degree of precision of contractual terms, decreases. A decrease in the transaction cost coefficient in broadening potential relationships, c, has the opposite effects, decreasing the equilibrium degree of competition and increasing the reliability of the incumbent relationship. The per capita real income in the structure with the division of labor is (10.6)

UD = [(1-α-lc-ls)/2]2[1-(1-r)N]

where r = ls/s and N = lc/c are given by the labor cost functions in deepening the incumbent relationship and in broadening potential relationships, respectively. ls and lc are each individual’s decision variables. Applying the envelope theorem to (10.6), we can show that (10.7)

dUD/ds = ∂UD/∂s < 0 and dUD/dc = ∂UD/∂c < 0. Table 10.1: Equilibrium Reliability and Degree of Competition

C

α

s 0.01 ≥0.02 0.01 ≥0.02

≤0.05 0.1 0.1 0.2 0.2

r 0.1 0.1 0.1 0.1 0.1

337

N 1 0.69 1 0.43 1

P 1 4 1 6 1

1 0.991 1 0.966 1

0.01 0.02 0.03 0.04 ≥0.05

0.3 0.3 0.3 0.3 0.3 ≥0.4

0.1 0.1 0.1 0.1 0.1 0.1

0.33 0.46 0.57 0.69 1

8 5 4 3 1 1

0.959 0.954 0.966 0.97 1 r

Since per capita real income in autarky is independent of s and c, (10.7) implies that as s or c falls, it is more likely that the corner equilibrium in structure D will be Pareto superior to that in autarky. According to the Yao theorem in chapter 4, this implies that as s and/or c falls, the general equilibrium will jump from autarky to the division of labor.

(a) Autarky

(b) Division of labor with N = 1

(c) Division of labor with N = 2

Figure 10.2: Different Degrees of Competition in Equilibrium

Fig. 10.2, where population size M = 4, gives an intuitive illustration of different patterns of equilibrium market structure. In panel (a), large transaction cost coefficients for deepening the incumbent relationship and for broadening potential relationships generate autarky as the general equilibrium. In panels (b) and (c), falling transaction cost coefficients make the division of labor the general equilibrium. But in panel (b), a large transaction cost coefficient for broadening potential relationships, c, relative to the transaction cost coefficient for deepening the incumbent relationship, s, generates the equilibrium N = 1 in an economy with 4 individuals, so that the economy is fragmented into two separate local communities. There is division of labor and transactions within each of the local communities, but no interactions between the communities. In panel (c), a small transaction cost coefficient for broadening potential relationships relative to the transaction cost coefficient for deepening the incumbent relationship generates the equilibrium N = 2, so that each individual has one incumbent trade partner and keeps in touch with another potential partner to put pressure on the incumbent one. The economy is integrated as one market, though this degree of integration is not necessary for all incumbent trade relationships. Dashed lines denote possible trade between potential trade partners when the incumbent suppliers fail to deliver goods. This model shows that there are two functions of the market. One is to execute exchanges. The other is to keep the pressure of competition on individuals in order to reduce the risk of coordination failure in exchanges. The second function may require a local market size that is larger than required to complete all realized exchanges, because each individual may keep in touch with some potential trade partners in order to put pressure on

338

the incumbent trade partners, thereby reducing the risk of coordination failure. If the number of goods is m rather than 2, and population size is greater than 4, then the following point will be clearer. The size of the market network that relates to potential trade partners may be greater than the network size of realized trade connections. For instance, in the model with many goods and large population size, if the equilibrium number of traded goods is 3 due to a low transaction efficiency, then three individuals can constitute a local community where each of them sells one good to and buys one good from each of the other individuals. But each individual may keep in touch with half of the population in the economy in order to put pressure on each of her incumbent trade partners to reduce the risk of coordination failure. The empirical works of Barro (1997), Sachs and Warner (1995, 1997), and Frye and Shleifer (1997) cited in chapter 7 provide strong support of the theory developed in this chapter. Yang, Wang, and Wills (1992) have tested this theory against the data set of rural China in 1979-1987. The empirical studies show that the reforms in rural China during this period significantly improved transaction efficiency in specifying and enforcing peasants’ rights to use, to transfer, and to appropriate earnings from goods, labor, land, and other assets. The institutional changes raised the level of division of labor, measured by the degree of commercialization in an extensive household survey, and per capita real income. The results of the model in this section differ from the conventional wisdom of market failure, which does not explain why markets do not exist for some commodities, for example, clean air and intangible entrepreneurial ideas. Our model formalizes Cheung's argument (1970, 1983) that the determination of contractual forms is a matter of the degree of vagueness in specifying and enforcing property rights, or, in less illuminating words, the degree of externality. In particular, if there are many goods, and transaction conditions differ across goods, it can be shown that markets exist only for those goods with better transaction conditions in specifying and enforcing property rights. Eliminating all externalities is not efficient because of the costs of specifying and enforcing exclusive rights to property. The efficient extent of externality will balance the trade off between the welfare loss caused by the absence of markets and the costs of specifying and enforcing the property rights required for markets. Hence, the absence of the market for some goods is a consequence of the efficient trade off between economies of division of labor and various transaction costs. Externality caused by the absence of the market is efficiently and endogenously determined in the market. The difference between the externalities in buying a pound of oranges and buying clean air is a difference of degree rather than a difference of substance. When people buy oranges, there are externalities resulting from vagueness in weighing oranges and in estimating their quality (Barzel, 1982). However, the equilibrium degree of vagueness in specifying and enforcing property rights is much lower for oranges than for clean air because there is much greater efficiency in specifying and enforcing property rights to oranges than to clean air. Since the degree of market competition (related to N) is endogenized in our model, the degree of involvement of a particular exchange in the market is endogenized. Hence, for those goods associated with a small equilibrium value of the number of potential trade partners, N, we may say that the exchange relationship has a low degree of marketization. This implies that our models can be used to explain why some non-market exchange relationships exist in a society when transaction costs in keeping extensive connections with potential trade partners are very high. As shown by Mauss (1925), individuals in a

339

primitive society rely on such non-market and individual specific exchange relationships to develop division of labor. Trade in such a primitive society is conducted via individual specific exchanges of gifts. Such non-market exchanges are very common in many developing countries, where efficiency in keeping extensive market connections is very low. Efficiency in specifying and enforcing property rights is determined by both the legal system and technical conditions. For example, low efficiency in specifying and enforcing property rights in pre-reform Russia and China can be attributed to a legal system that restrained free trade in labor, land, and capital, while low efficiency in specifying and enforcing property rights to clean air is due to the high cost of the technology used to measure pollution. The following examples provide intuition behind the models in sections 10.2 and 10.3. Example 10.3: Trade off related to the institutions of the library and the university. The institution of the university can be used to improve efficiency in specifying and enforcing rights to knowledge. Faculty members' rights to the knowledge that is sold to students is specified and enforced via wage contracts between a university and the staff members and the tuition payments to the university by students. Transaction efficiency is lower when teachers collect payment from students individually than when teachers receive payment from students through the university. The improvement in efficiency in specifying and enforcing the rights to knowledge that is associated with the emergence of a university will promote division of labor between the producers of knowledge (faculty members) and future producers of other goods (students) and between different specialist teachers. However, monthly wage contracts are more common between universities and their teaching staff than between students and private tutors who usually charge an hourly fee. If property rights are more vaguely specified and enforced in a monthly wage contract than in an hourly fee contract, the above example implies that an increase in the division of labor caused by a lower exogenous transaction cost of the institution of the university is associated with a more vague specification and enforcement of property rights as long as the benefits from the higher level of division of labor outweigh the cost caused by the higher level of vagueness of contracts. Further, the emergence of the institution of the university promotes the division of labor between the professional management of books (library) and the users of books (teachers and students). The emergence of professional libraries increases the vagueness in specifying and enforcing rights to the knowledge generated by books. Before professional libraries were established, an individual had to buy a book if she wanted to utilize the knowledge in that book, since it was not easy to borrow many different books from other individuals. She can more easily borrow a book without any payment to the author of the book since libraries emerged. Even if students' tuition includes a payment for using a university library, the payment is not proportional to the frequency of book use, and the payment does not go to the authors of the books. This implies that rights to authors' knowledge are more vaguely specified and enforced in a library system than in a book market without the institution of the library. However, the system with libraries will be the equilibrium as long as the benefits generated by division of labor between professional libraries and other sectors outweigh the utility loss generated by the higher level of vagueness in specifying and enforcing the rights to intellectual property.

340

Nevertheless, a new institutional arrangement that charges for each use of a book in a library could be combined with copyright laws to increase the level of division of labor and decrease the level of vagueness in specifying and enforcing rights to intellectual property at the same time, if magnetic cards and a computer system were effectively employed to monitor and collect the required payments. Such arrangements emerged in some Northern European countries in the 1980s. Intuitively, it would seem that the slight improvement in transaction efficiency due to the emergence of professional libraries increases both the equilibrium level of division of labor and the equilibrium degree of vagueness in specifying and enforcing property rights, because this slight improvement is insufficient to allow both an increase in the level of division of labor and a decrease in vagueness at the same time. By contrast, the emergence of a system that charges for each use of a book, together with copyright laws, magnetic cards, and the computer system, will significantly improve transaction efficiency in specifying and enforcing authors' rights to knowledge in books, so that the level of division of labor increases and the degree of vagueness in specifying and enforcing property rights decreases, resulting in a significant increase in productivity and welfare. Here, the distinction should be drawn between nonexclusivity and nonrivalry of goods when we analyze endogenous externality. Nonrivalry is a technical characteristic. It implies that use of a good by a person does not prevent another person from using the same good. In other words, a good is non-rival if its production and/or consumption involves only fixed costs but no variable costs. A TV program is a non-rival good, since the cost of its production and consumption does not increase with the number of its viewers. There is only a fixed production cost of the TV program. Hence, non-rivalry implies significant increasing returns. This does not necessarily imply non-exclusivity, which is determined endogenously by institutions. If transaction efficiency in specifying and enforcing property rights to a good with non-rivalry is very high, then in equilibrium, individuals will choose to well specify and enforce property rights, so that non-rivalry does not cause externality. The following example illustrates the point. Example 10.4: Non-rivalry and non-exclusivity of TV programs. A TV program is a nonrival commodity. When a person watches a TV program at her home, it does not prevent others from watching the same program at their homes. The number of viewers of the same program can be very large. If the owner of the copyrights of the TV program had very low costs of monitoring the consumption of the TV program at each person’s home, she could extract a fee for each viewing of the program by each person. If somebody refused to pay, she could take legal action against him. But in reality, we never see such institutional arrangements, not because it is impossible, but because the monitoring costs are prohibitively high. Hence, the efficient trade off between the transaction costs in specifying and enforcing property rights and the distortions caused by imprecise specification and enforcement will result in free TV programs. This implies that TV programs are endogenously chosen as nonexclusive commodities. The non-exclusivity implies externality and related distortions. However, the degree of externality is endogenously chosen by individuals and the invisible hand (interactions between self-interested behaviors). The functioning of the market in handling distortions caused by externalities is much more sophisticated than described by neoclassical marginal analysis. For the case of the TV

341

program, there is a multilateral trade among three parties: the owner of the copyright of the program, the viewers of the program who are buyers of other tangible goods, and the sellers of the tangible goods. A one way trading chain may reduce the distortions caused by the nonexclusivity of the TV program. The sellers of the tangible goods make money by selling the goods to viewers of the TV program. The producer of the TV program makes money from selling advertising time to the sellers of the tangible goods, while the viewers obtain utility from freely viewing the program. This one way trade triangle generates distortions by forcing viewers to watch advertisements that they may not want to see. But it saves on exogenous transaction costs for the producer of the TV program to collect payment from the viewers, thereby reducing the externalities caused by the nonexclusivity of the TV program. Compared to the cable TV system, the open TV system generates more distortions because of the inaccurate correspondence between the amount of payment of reviewers and the quantity of TV programs consumed by them and by forcing viewers to see something that they do not like. The cable TV system causes much less endogenous transaction costs of this kind. But the open TV system saves on exogenous transaction costs caused by deploying cable and collecting fees. As discussed in chapter 10, the market will efficiently trade off economies of division of labor against endogenous and exogenous transaction costs to determine the efficient degree of externality. If the total endogenous and exogenous transaction cost is nearly the same between the open TV system and the cable TV system, they may coexist in a competitive market.

342

10.4. Why Can Insurance Promote Economic Development? In chapter 9, we learned the concepts of risk aversion and moral hazard. Let us review these concepts before developing new models utilizing them. In the presence of uncertainty, a decision maker maximizes expected utility. The institution of insurance can be used to pool risk together. Hence, in an economy with a very large population, each individual can receive utility at the weighted average of contingent states. If the decision maker’s utility function is strictly concave, she prefers the value of the utility function at the weighted average of contingent states, which can be provided by insurance that pools risk, to the weighted average of utility values at contingent states. Therefore, a strictly concave utility function implies that an individual prefers an outcome with insurance to outcomes with uncertainty. In other words, she is risk averse. If individuals have different degrees of risk aversion, they can all gain from trading in risk. An individual who is more risk averse than another can sell risk to the latter and both of them can be better off. This can be considered as the former buying insurance from the latter. The neoclassical model of principal-agent in example 9.1 can be considered as a model with insurance where the agent buys insurance from the principal. The principal plays the role of an insurance company. That model shows that complete insurance will generate moral hazard if the principal cannot detect the agent’s effort devoted to reducing risk. The efficient contract between the principal and agent entails incomplete insurance. That is, the payment to the agent is contingent: it is higher when the outcome is good than when the outcome is not good. In sections 10.4 and 10.5, we investigate further the relationship between insurance, division of labor, and endogenous and exogenous transaction costs. The story in this section runs as follows. Assume that there are risks in transactions in the model in example 7.1. In each transaction, transaction efficiency k takes on a great value at probability θ and a small value at probability 1-θ. The transaction risk may be caused by traffic accidents or by opportunistic behavior that takes place with a probability as shown in example 9.13 of chapter 9. Moreover, we assume that all consumer-producers are risk averse to the same degree, or they have ex ante identical strictly concave utility functions. In the model, there is a trade off between economies of division of labor and coordination reliability, in addition to a trade off between economies of division of labor and exogenous transaction costs. If an insurance company collects a premium from each individual and compensates her in the event of low transaction efficiency, each individual will have the weighted average of the two levels of transaction efficiency for certain by pooling risk. Such an institution of insurance will certainly promote division of labor and productivity progress if all individuals are risk averse. It will promote many other structural changes associated with evolution in division of labor, discussed in chapters 4, 7, and 8. More interestingly, the improved transaction conditions enlarge the scope for trading off economies of division of labor against transaction risk, so that the equilibrium and efficient aggregate risk of coordination failure increases. Also, a decrease in the risk of coordination failure for each transaction may increase the efficient aggregate risk of coordination failure for the same reason. This story is formalized in the following example.

343

Example 10.5: The Lio Model (1998). The structure of the model is similar to the one in example 7.1 except that transaction efficiency k is a random variable. The decision problem for each consumer-producer selling good i is specified as follows. 1

(10.8)

E ui = E {x i Π r ∈R ( k r x r d ) Π ∈J x j } ρ (expected utility)

Max:

s.t. xi + xi = li − α ,x j = lj − α s

(production functions)

li + (m − n)lj = 1

(endowment constraint)

pixis = (n − 1)pr xr d

(budget constraint) where xi is the amount of good i self-provided, is the amount of good r purchased, kr is the transaction efficiency coefficient for good r, R is the set of n-1 goods purchased, J is the set of m-n non-traded goods, n is the number of traded goods, xj is the self-provided amount of non-traded good j, xis is the amount of good i sold, li and lj are respective levels of specialization in producing goods i and j, and pi and pr are respective prices of good i and r. It is assumed that each individual is endowed with one unit of non-leisure time. α is the fixed learning cost in each production activity. We will see later that parameter ρ > 1 relates to the degree of risk aversion. The larger the value of ρ, the more risk averse is the individual, since a larger value of ρ implies a more concave utility function. The endowment constraint and the budget constraint in (10.8) are obtained using the symmetry. The difference between this decision problem and the one in example 7.1 is characterized by the transaction efficiency coefficient. ⎧k H with θ (10.9) kr = ⎨ ⎩k L with 1 - θ xrd

where θ∈(0, 1) is the probability that transaction efficiency is high, k H > k L , r∈R. That is, there is transaction risk. It is not difficult to see that a special case of the Lio model for ρ = 1, kL = 0 is the model in example 10.1. θ here is equivalent to r in example 10.1. Inserting all constraints into the utility function, the constrained maximization problem in (10.8) can be converted to a non-constrained maximization problem. (10.10a)

Max: Eui = WP, P ≡ E(∏r∈Rkr)1/ρ

where xis, li, and n are decision variables, P can be interpreted as the aggregate reliability, or 1-P can be interpreted as the aggregate transaction risk, and 1 s s (10.10b) W ≡ {(li − α − xi )[xi /(n − 1)]n −1 [(1 − li )/(m − n) − α ]m − n } ρ . Also, it can be shown, using symmetry, that pi / pr = 1 in equilibrium. The procedure to solve for xis and li is the same as in chapter 7. But the procedure to solve for n differs, since the solution of equilibrium n relates to the aggregate transaction risk E(∏rkr)1/ρ. Let us have a close look at this term. The number of kr is n-1. Suppose that s of them take on value k H and n-1-s of them take on value kL, while s can take on value from 1 to n-1. Here, kH takes place with probability θ and k L takes place with probability 1-θ. Therefore, the n-1 of kr follows a binomial distribution. The probability for n-s of kr to take on value kH and for s-1 of kr to take on value kL is

344

(10.11) Ps = Cns−−11θ n − s (1 − θ ) s −1 where Cns−−11 is s-1 combinations of n-1 elements. Following a binomial formula, it can be shown that (10.12)

P = E ( Π r ∈R k r )

1

ρ

(

= Σ ns =−11 Ps k Hn− s k Ls−1

( n −1) / ρ H n −1

=C θ k +C n −1 +[C n −1 (1 − θ ) k L n −1

0 n −1

1 n −1 (n −1)/ρ

θ

n−2

)

1

ρ

(1 − θ ) k H( n − 2 )/ ρ k L1/ ρ + L

]

1/ρ

= [θ k H + (1 − θ )k L1/ρ ]n −1 where Ps is given by (10.11) and the final equality in (10.12) is given by the binomial formula. Having inserted (10.12) into (10.10), we can express E ui as a function of li, xis, and n. Letting the derivatives of Eui with respect to the three variables equal 0 yields the solutions for the corner equilibrium values of all endogenous variables when insurance is absent. li = [n + α (n 2 − m n + m − n)]/m (10.13) lj = [1 + α (n − 1)]/m x i = x r d = x j = [1 − α (1 + m − n)] / m , n = (1 −

1

α

) + m{1 − 1 / ln[θ k H

1

ρ

x i s = (n − 1) x i / n

+ (1 − θ ) k L ρ ]}

Eu = {[1 − α (1 + m − n)] / m} ρ [θ k H m

1

1

ρ

+ (1 − θ ) k L ρ ] n −1 1

1/ρ

P = [θ k H + (1 − θ )k L1/ρ ]n −1 Differentiation of the corner equilibrium values of the endogenous variables with respect to parameters ks (s = H, L), θ, ρ yields the comparative statics of the corner equilibrium with no insurance. (10.14a) dn /dks > 0 , dn /dθ > 0 , dn /dρ < 0 (10.14b) dli / dk s > 0 , dli / dθ > 0 , dli / dρ < 0

(10.14c)

d[ M (n − 1) x r d ] / dk s > 0 , d[ M (n − 1) x d ] / dθ > 0

d[ M (n − 1) x r ] / dρ < 0, dE u /dks > 0 , dE u /dθ > 0 (10.14d) (10.14e) dP/dks = (∂P/∂ks)+ (∂P/∂n)(dn/dks)< 0, and dP/dθ = (∂P/∂θ)+ (∂P/∂n)(dn/dθ)< 0 where (n-1)xrd = xrs is each individual’s aggregate purchase volume and M(n-1)xrd = Mxrs is the aggregate demand for all goods in the market, which is the extent of the market. As in chapter 8, we have used the envelope theorem to obtain (10.14d). To obtain (10.14e), we have used the solution of n, given in (10.13), and the fact that αm 1. A comparison between Eu in (10.13) and Eu in (10.18) indicates that an individual 1/ ρ gets f(Ek)=[ θ k H + (1 − θ )k L ]1/ρ if she is insured, and she gets Ef(k) = θ k H1/ ρ + (1 − θ ) k L

346

if she is not. Since for a strictly concave function f(k), the value of the function at the weighted average of two contingent transaction efficiencies is greater than the weighted average of the values of the function at the two contingent transaction efficiencies, (10.18) is certainly greater than the expected utility in the absence of insurance. (Recall the discussion of this in section 9.2 of chapter 9.) The first order conditions for maximizing (10.18) are exactly the same as those for (10.10), except for the first order condition for the equilibrium n. These conditions yield the corner equilibrium with insurance. li ′ = [n ′ + α (n ′ 2 − mn ′ + m − n ′)] / m l ′ = [1 + α (n ′ − 1)] / m j

(10.19)

x i ' = x r d ' = x j ' = [1 − α (1 + m − n ′)] / m , n ′ = (1 −

1

α

x i s ' = (n ′ − 1) x i '/ n ′

) + m{1 − 1 / ln[θ k H + (1 − θ ) k L ]} m

(n ′ − 1)

E u ′ = {[1 − α (1 + m − n ′)]/m } ρ [θ k H + (1 − θ )k L ] n −1

P’ = [θ k H + (1 − θ )k L ]

ρ

ρ

Primes of the variables denote corner equilibrium values with insurance. The differentiation of the corner equilibrium values of the endogenous variables with respect to parameters k ,θ ,ρ indicates that the comparative statics in (10.14) hold for the case with insurance. A comparison between the corner equilibrium in (10.13) and that in (10.19) indicates (10.20a) (10.20b)

Eu’ > Eu, Mxis’ > Mxis n’ > n, li’ > li, P’ > P, dEu’/dθ < 0 dn’/dks > 0, dn’/dθ > 0, dEu’/dks > 0, dP'/dks < 0, dP'/dθ < 0

. This implies that the expected utility with insurance is greater than that with no insurance. Applying the Yao theorem, it can be shown that all individuals will choose insurance in a general equilibrium. The corner equilibrium with no insurance is not a general equilibrium. (10.20) implies also that the level of division of labor for society, individuals’ levels of specialization, productivity, aggregate coordination reliability of the network of division of labor, and the extent of the market are all greater in the corner equilibrium with insurance than that in the corner equilibrium with no insurance. The complete insurance in this model is equivalent to the complete insurance in a Soviet style economy. But in this model, it is assumed that the risk of low transaction efficiency is exogenously given, independent of the effort devoted to reducing such risk. Hence, complete insurance does not generate the endogenous transaction costs that are associated with moral hazard. But we know that complete insurance in a Soviet style economy indeed generates tremendous endogenous transaction costs and moral hazard problems. In the next section, we will endogenize the risk of a low transaction efficiency and investigate the relationships between the level of division of labor, incomplete insurance, and complete insurance that generate moral hazard and endogenous transaction costs.

347

10.5. Economic Development and Endogenous Transaction Costs caused by Moral Hazard

Example 10.6: A simplified version of the Lio model (1996) with endogenous transaction costs caused by complete insurance. The difference between the two Lio models in this section and in the preceding section relates to the probabilities of different levels of transaction efficiency. Those probabilities are exogenously given in the last section, whereas here they are endogenously determined by an individual’s effort devoted to reducing the risk of low transaction efficiency. It is also assumed that this effort level is not observable to others or not verifiable in court when a dispute occurs, so that moral hazard may arise. Since the model with endogenous specialization and with moral hazard is much more difficult to manage than a model with endogenous specialization alone or with moral hazard alone, we assume that there are only two goods in this section. Hence, each ex ante identical consumer-producer’s decision problem is (10.21) Max: E u = E[ln( x + kx d ) + ln( y + ky d )] s.t. x + x s = lx − α , y + y s = ly − α

lx + ly + e = 1

(expected utility function) (production functions) (endowment constraint)

k = k H with probability 2 3 ⎫ ⎬ if e = 1/3 k = k L with probability 1 3 ⎭

(effect of effort on

k = k H with probability 0⎫ ⎬ if e = 0 , i= x, y k = k L with probability 1 ⎭

transaction risk)

px x s + p y y s = px xd + p y yd

(budget constraint)

where it is assumed that k H > k L . Variable e is the level of effort devoted to reducing the risk of a low transaction efficiency. It can be considered as effort devoted to transporting goods carefully or to protecting the goods from being stolen. For simplicity, we assume that there are only two levels of such effort. The high level of effort e =1/3 generates a low probability of low transaction efficiency ( k = k L ) and the low level of effort e = 0 causes low transaction efficiency for sure. Hence, the risk of low transaction efficiency is determined by the level of effort devoted to reducing transaction risk. Since the utility function is strictly concave in the quantities of the two goods consumed, all individuals are risk averse to the same degree. Also, an increase in the effort level devoted to reducing transaction risk will reduce the amount of labor allocated to the production of goods and thereby reduce income and utility. Hence, each individual has an incentive to choose the low level of effort in reducing transaction risk if complete insurance is available. This implies that complete insurance will generate moral hazard if the division of labor is chosen. From the point of view of an insured, the insurance company cannot observe her effort level if she is completely insured. Her optimum decision is thus to choose the lowest level of effort. The insurance company will go bankrupt if every one of the insured behaves similarly. Hence, the insurance company will provide an incomplete 348

insurance to restrain moral hazard. Suppose that each consumer-producer chooses premium π for a given policy of the insurance company, c. Then, the insurance company chooses the policy for a given π according to the incentive compatibility condition. The second step to sort out the insurance contract terms is equivalent to choosing a parameter β for a given π. The definition of β is given as follows. (10.22)

β = (2 /3)π /(1 /3)(c − π ) ≥ 1

where 1/3 is the probability of a low transaction efficiency and 2/3 is the probability of a high transaction efficiency, the denominator is the insurance company’s expected net payout in the event of a low transaction efficiency and the numerator is its expected premium earnings in the event of a high transaction efficiency. Since β is uniquely determined by c for any given π, choosing π for a given c is equivalent to choosing β for a given c. If β = 1, then the expected payout net of premium is the same as the expected premium, so that insurance is complete. If β > 1, the expected net payout is smaller than the expected premium, so that insurance is incomplete and the insured must take part of transaction risks. Hence, parameter β describes the completeness of the insurance contract for each transaction. Using the definition of β, we can express the insurance company’s payout net of premium in the event of low transaction efficiency as a function of β and π as well. We thus have (10.23)

c − π = 2π / β

Applying the Wen theorem to the model, there are 6 structures that we must consider. The first is autarky, denoted as A. In this structure, there is no trade or transaction risk, so that it is easy to solve for the corner equilibrium in this structure. The second class of structures features division of labor, but with no insurance, denoted as Bi, i = L, M, H. There are three structures in this class. In structure BL, there are two types of specialist producers of the two goods and they choose the low level of effort in reducing transaction risk, that is e = 0. In structure BM, the specialist producers of one good choose the high effort level e = 1/3 and the specialist producers of the other good choose e = 0. Because of symmetry, the outcome is unaffected by which specialist producers choose e = 0 and which choose e = 1/3. In structure BH, both specialist producers of the two goods choose e = 1/3. The third class of structures features division of labor with insurance, denoted Ci, i = L, M, H. Structure CL features complete insurance and e = 0. Since it is assumed in (10.21) that the probability of the low transaction efficiency is 1 if e = 0, the uncertainty disappears for this case, so that the insurance company cannot survive. This implies that the corner equilibrium for this structure does not exist. In structure CM with the division of labor and insurance, one type of specialist producers chooses e = 1/3 and the other type of specialist producers chooses e = 0. Structure CH features division of labor, incomplete insurance, and e = 1/3 chosen by all individuals. Let us first consider structure CH. In this structure, the decision problem for a specialist producer of good x is:

349

(10.24) Max: E u x = ln x + ln y d + (2 3 )ln(k H − π ) + (1 3 )ln(k L + c − π ) s.t. x + x s = 1 − α − e , e = 13 (production condition)

px x s = p y yd

(budget constraint)

We can use (10.22) and (10.23) to eliminate c, then solve for the optimum x , x s , y d . Inserting the solution back into (10.24) yields (10.25) Max: E u x = ln(p x / p y ) + +2 ln[(2 − 3α )/6]+ (2 3 )ln(k H − π ) + (1 3 )ln[k L + (2π /β )] Each specialist in x chooses premium π to maximize E u x for a given β. The optimum premium is (10.26) π = (1 3 )(k H − β k L ) Inserting (10.26) back into (10.25) yields the expected indirect utility function for a specialist in x. (10.27a) E u x = ln( p x / p y ) + 2 ln(2 − 3α ) + ln(2 k H + βk L ) − 3 ln 3 − (ln β / 3) − 2 ln 2 Following the same procedure, we can solve for the expected indirect utility function for a specialist in y. (10.27b) E u y = ln( p y / p x ) + 2 ln(2 − 3α ) + ln(2 k H + βk L ) − 3 ln 3 − (ln β / 3) − 2 ln 2 The expected utility equalization condition E u x = E u y determines the corner equilibrium relative price of the two traded goods in structure CH, that is, px/py = 1. The market clearing condition Mxxs = Myxd and the population equation Mx + My = M, together with the corner equilibrium relative price, determines the corner equilibrium numbers of the two types of specialists Mx = My = M/2. An insurance company will choose β according to the incentive compatibility condition. This condition implies that the insured has a higher expected utility when she chooses e = 1/3 than when she chooses e = 0. Following the approach to calculating the expected indirect utility function, we can work out the expected indirect utility function for a specialist in x to choose e=0. For this case, k = kL will occur for sure, so that the effect on the utility of the expected payout net of premium is ln(kL + c - π). After elimination of c - π using (10.23), the expected indirect utility function for a specialist in x who chooses e = 0 is: (10.28) E u x = ln(p x / p y ) + 2 ln[(1 − α )/2]+ ln(2 kH + βk L ) − ln 3 − ln β Incentive compatibility implies that (10.27a) is not smaller than (10.28), that is, the expected utility for a high effort level in reducing transaction risks is not lower than that for a low effort level. This inequality sets up a constraint for β. β > [3(1 − α ) / (2 − 3α )] 3 (10.29) Further, a positive π implies kH > kH - π = (2kH/3) +(βkL/3), where we have used (10.26). This sets up another constraint on β. β < k H /k L (10.30) The two constraints on β imply that structure CH with insurance is equilibrium only if k H /k L > [2(1 − α )/(1 − 2α )]6 (10.31)

350

If this condition does not hold, the set of candidates for the equilibrium structure comprises only A, BL, and BH. If this condition is satisfied, the set comprises A, BL, BH, and CH. Following the procedure used in solving for the corner equilibrium in structure CH, we can solve for all corner equilibria in the 7 structures, which are summarized in Table 10.2. Table 10.2: Expected Real Incomes in 7 Structures

Equilibrium structure A BL BM BH CL CM CH

Expected corner equilibrium per capita real income 2ln[(1-2α)/2] 2ln[(1-α)/2] + lnkL ln(2-3α) + ln(1-α) - 2ln2 +(lnkH /3)+ (2/3)lnkL - ln3 2ln(2-3α) -2ln6 + (2/3)lnkH + (lnkL/3) No corner equilibrium exists ln[(2-3α)/3]+ln(1-α)-2ln2+0.5{lnkL-(lnβ/3)+ ln[(2kH/3)+(βkH/3)]} 2ln(2-3α)-2ln6+ln[(2kH/3) +(kLβ/3)] - (lnβ/3)

Using the Table, it can be shown that E u(BM) < Eu(BL), if Eu(BM) > Eu(BH). This implies that either Eu(BM) < Eu(BH) or Eu(BM) < Eu(BL). According to theorem 5.1, it follows that structure BM cannot be an equilibrium structure. Similarly, we can prove that BH can be an equilibrium structure only if 2 2 2 ⎛ 1 − 2α ⎞ ⎛ 1 − 2α ⎞ 3 3 (10.32) ⎟ k H− 2 ⎟ > kL > 3 β ⎜ ⎜ ⎝ 2 − 3α ⎠ ⎝ 1−α ⎠ which holds only if [(2-3α)/3(1-α)]2 > 3β2/3 where β > 1. It is obvious that this 1 . Therefore, BH cannot be an equilibrium structure. inequality does not hold for α ∈ (0,) Following a similar line of reasoning, it can be shown that BL cannot be an equilibrium structure if kH/kL > [3(1-α)/(2-3α)]3. Taking into account all of the relevant information, comparisons of expected real incomes in all structures yield the general equilibrium and its inframarginal comparative statics, as summarized in the following table. Table 10.3: General Equilibrium and Its Inframarginal Comparative Statics

kH/kL > [3(1-α)/(2-3α)]3 kH/kL < [3(1-α)/(2-3α)]3 kL[(1-2α)/(1-α)]2 2kH+βkL < γ 2kH+βkL > γ A BL A CH 3 1− 2α 2 1/ 3 where γ ≡ [3 ( 2 − 3α ) β ] , A is the autarky structure, BL is the structure with the division of labor and with no insurance, where individuals choose the low effort level in reducing transaction risks, CH is the structure with the division of labor and incomplete insurance where individuals choose the high effort level. We need an additional assumption to determine the equilibrium terms of insurance or the equilibrium degree of incompleteness of insurance. Suppose that the market for insurance is competitive and the management cost for an insurance contract is b; then the

351

expected profit for each insurance contract is π - (c/3) - b = 0. Free entry and competition will drive the profit down to 0. Hence, the equilibrium insurance contractual terms can be determined by the zero profit condition and equations (10.22), (10.23), (10.26). After manipulation of the equations, it can be shown that the equilibrium contractual terms are given by the following equations. β is given by f( β , b, kH, kL) ≡ 2(β-1)( kH - βkL) - 9b = 0, π = (c/3)+b. c = 3b(2+β)/2(β-1),

Then the equilibrium level of division of labor, endogenous transaction costs, and productivity are explained by the insurance management cost coefficient b. In this model, the efficient balance point (or efficient degree of incompleteness of insurance, β) of the trade off between incentive provision and risk sharing is determined by the insurance management cost coefficient, c, the degree of risk that relates to 1-θ, kH/kL, and ρ. Because of the connection between the degree of insurance completeness and the degree of softness of the budget constraint, the trade off between risk sharing and incentive provision is equivalent to the trade off between risk sharing and the softness of the budget constraint. This trade off has many more general implications for the analysis of the relationship between economic development and institutions. From the experience of the Asian financial crisis in 1997, we can see that it is not easy to identify the efficient balance point of the trade off. When the IMF emphasized the reforms of the financial market as a precondition for financial assistance for alleviating the damage of the crisis, it paid more attention to incentive provision in reducing the risk of a bad outcome. When the Korean and Indonesian governments asked for prompt financial assistance from the IMF, they emphasized risk sharing. The bargaining between the two sides was to find the efficient balance of the trade off between incentive provision and risk sharing. Table 10.3 implies that if the two values of transaction efficiency are sufficiently small, the general equilibrium is autarky where there is no market or transaction risk. As kH and kL increase, the general equilibrium jumps to the division of labor with transaction risks. When the ratio kH/kL is not great, or the gains from a high effort in reducing risk of a low transaction efficiency are not great, insurance cannot survive moral hazard. Hence, the division of labor is not associated with insurance and individuals choose the low effort level in reducing transaction risk (structure BL). When the gains are significant, insurance emerges from the division of labor and individuals choose the high effort level in reducing transaction risk (structure CH). Next, we show that for kH/kL > [3(1-α)/(2-3α)]3, insurance can promote division of labor and productivity progress. Comparisons between corner equilibrium expected real incomes in structures A, BH, and CH, given in Table 10.2 yield the following results. Eu(BH) > u(A) iff μ1 ≡ kH2/3kL1/3 > μ0 ≡ [3(1-2α)/(2-3α)]2 Eu(CH) > u(A) iff μ2 ≡ (2kH + βkL)/3β1/3 > μ0 A close examination of μ1 and μ2 yields (10.33a) μ 2

β →kH / kL

= μ1 and

(10.33b) ∂μ2 / ∂β < 0 if β < k H / k L and ∂μ2 / ∂β > 0 if β > k H / k L

352

(10.33b) implies that μ2 reaches its minimum at β = kH /kL. This, together with (10.33a), implies that μ2 > μ1. This implies that Eu(BH) < u(A) and Eu(CH) > u(A) if μ0∈(μ1, μ2). In other words, structure CH with insurance is better than autarky, which is in turn better than structure BH with no insurance if μ0∈(μ1, μ2). This establishes the proposition that incomplete insurance in CH may promote division of labor and productivity progress. Next, we show that such incomplete insurance cannot eliminate the endogenous transaction costs caused by moral hazard, though it does reduce such endogenous transaction costs. To substantiate this claim, it suffices to prove that the corner equilibrium in structure CH is not locally Pareto optimal. It is easy to show that the corner equilibrium expected real income in CH increases as β tends to 1. Indeed, the local Pareto optimum for the division of labor can be calculated as the corner equilibrium in CH with β = 1. The locally Pareto optimum real income for the division of labor is (10.34)

V = 2ln(2-3α)-2ln6-ln3+ln(2kH+βkL)-[(lnβ)/3] and V > u(A) iff μ3 ≡ (2kH + kL)/3 > μ0.

A comparison between μ3 and μ2 indicates that μ3 > μ2. This implies that V is always greater than u(A) whenever Eu(CH) is greater than u(A). But for μ0 ∈ (μ2, μ3), V > u(A) > Eu(CH). Hence, if the effort level in reducing transaction risks is observable, complete insurance can be given only to those who choose the high effort level, so that moral hazard is eliminated and the expected real income is higher than that in structure CH, which is associated with β > 1. In other words, the corner equilibrium in structure CH is not locally Pareto optimal. However, the Pareto optimum is not a feasible utopia when CH is the general equilibrium structure. It is interesting to note three different cases of endogenous transaction costs caused by moral hazard. (1) Suppose kH/kL > [3(1-α)/(2-3α)]3 and μ0∈(μ2, μ3), which imply that the general equilibrium structure is A and the Pareto optimum is the division of labor with complete insurance and with no moral hazard. Hence, the division of labor and related welfare gains cannot be realized because of the positive equilibrium endogenous transaction costs. This kind of endogenous transaction costs is called type I endogenous transaction costs, which are associated with the Pareto inefficient equilibrium levels of division of labor and productivity and number of transactions. (2) Suppose kH/kL > [3(1-α)/(2-3α)]3 and μ2 > μ0, which implies that the general equilibrium structure is CH that is not Pareto optimal. Hence, the equilibrium resource allocation is not efficient (i.e., the relative quantity and relative price of the two goods are not efficient) because of the endogenous transaction costs caused by moral hazard, despite the efficient equilibrium level of division of labor. This kind of transaction costs is called type II endogenous transaction costs. (3) Suppose kH/kL [(1-2α)/(1-α)]2, which imply that the equilibrium structure is BL that is not Pareto optimal and has a low effort level in avoiding transaction risk. Hence, moral hazard generates endogenous transaction costs that are associated with a low effort level in avoiding transaction risk, despite the Pareto efficient level of division of labor. This is referred to as type III endogenous transaction costs.

353

(4) Suppose kH/kL > [3(1-α)/(2-3α)]3 and μ0>μ3> μ2, which imply that the equilibrium structure is A that is Pareto optimal. Assume now that transaction efficiency is improved such that μ0∈(μ2, μ3). This implies that the general equilibrium jumps from structure A to structure CH and the equilibrium endogenous transaction costs increase from 0 to a positive level. In other words, concurrent increases in endogenous transaction costs, in productivity, and in the level of division of labor may take place as a result of reduced exogenous transaction costs (improved transaction efficiency). We call this kind of endogenous transaction costs that emerge from reduced exogenous transaction costs and increased productivity type IV endogenous transaction costs. Type I and III transactions are similar to X inefficiency, which causes a low productivity or a low effort level. But type I transaction cost causes organizational inefficiency (Pareto inefficient level of division of labor) while type III and type II endogenous transaction costs result in allocative inefficiency. Type IV endogenous transaction cost is due both to a higher productivity, which can be used to afford increased endogenous transaction costs, and to moral hazard. These results on endogenous transaction costs substantiate Coase’s conjecture (1960) that if there exist endogenous transaction costs, the interactions between self-interested individuals will sort out the contractual arrangements that maximize economies of division of labor net of endogenous and exogenous transaction cost, rather than minimize a particular type of transaction cost. If the trade off between measuring the cost of effort level and moral hazard is introduced into the model with the trade off between incentive provision and risk sharing, the story will be much more realistic and complicated. Milgrom and Roberts (1992, p. 336) survey several models that have the two types of trade offs. In one of the models, promotion according to seniority can reduce influencing (rent seeking) cost in a firm, encourage continuous accumulation of firm-specific human capital, and provide risk sharing between the employee and the employer. But it will cause endogenous transaction costs associated with inaccurate measurement of effort levels and prevent the realization of productivity enhancing labor mobility. The effects of a promotion scheme according to performance are opposite. Hence, the efficient promotion criteria must efficiently trade off one against the others among incentive provision, risk sharing, employment stability (or its reciprocal, labor mobility), and measurement costs. Example 10.7: Application of the models in examples 10.5 and 10.6 to the analysis of the Asian financial crisis in 1997. There are two opposite views of the Asian financial crisis in 1997. According to one of them, the financial crisis was caused by moral hazard associated with cronyism and complete insurance of loans provided by the government. The other view (Radelet and Sachs, 1998a, and Stiglitz, 1998) holds that as the network of trade expands, aggregate risk of coordination failure inevitably increases even if moral hazard is not that serious. Hence, policy missteps and hasty reactions by the governments and by international organizations may miss the efficient balance of the trade off between insurance and incentive provision. For instance, the overemphasis of the financial reform programs which reduce moral hazard when insurance should receive more attention added to the virulence of the banking panics. We can apply the models in examples 10.5 and 10.6 to assess this view. According to (10.14e) and (10.20b), it is obvious that even if moral

354

hazard is absent, the aggregate risk of coordination failure 1-P increases as transaction conditions are improved or as the risk of coordination failure for each transaction decreases. This is because as the risk of coordination failure for each transaction reduces, the scope for trading off economies of division of labor against aggregate risk is enlarged, so that individuals can afford a higher risk. Hence, choosing a higher aggregate risk of coordination failure is associated with economic development generated by evolution of division of labor, and it is efficient. This explains why a more successful developed economy has a higher risk of having an episode like the Great Depression than a less developed economy. This is why Radelet and Sachs call the 1997 Asian financial crisis a “crisis of success.” The higher risk is efficiently chosen, just like choosing the higher risk of being killed by driving on the freeway. This implies that moral hazard is not the whole of the story. This is why more moral hazard generated by complete insurance in China and in the Soviet Union does not necessarily imply more risk of the financial crisis. The model in example 10.6 indicates that the efficient way to handle the Asian financial crisis is to efficiently balance the trade off between incentive provision in reducing the risk and risk sharing, rather than paying too much attention to one of them. If the time lag between financial decisions and economic fundamentals is considered, we may have another trade off between the strong incentive created by sensitive feedback of financial decisions to market shocks and the stability of the financial market. Financial reforms may increase the sensitivity of the feedback mechanism. But too-sensitive feedback may make overshot more likely to occur. Sometimes, too-sensitive feedback may generate overreactions that create a financial crisis. Aghion, Bacchetta, and Banerjee (1998) develop such a cobweb model. See also example 19.5 for a Smithian model with such a trade off. Policy making is to identify the efficient balance of the trade offs between insurance provision and moral hazard and between strong incentive and stability.

Key Terms and Review Trade off between endogenous and exogenous transaction costs Trade off between exogenous transaction costs in deepening the incumbent relationships and exogenous transaction costs in expanding potential relationships Implications of the trade off between economies of division of labor and various transaction costs in addition to the above two trade offs for economic development Externality, public goods Relationships between non-rivalry, non-exclusivity, and public goods Difference between Pigou’s marginal analysis of the distortions caused by externalities and public goods, and inframarginal analysis of endogenous transaction costs and endogenous externality Substitution between competition in the market and precise specification and enforcement of property rights Why may not perfect competition and perfectly specified and enforced property rights be efficient if the trade offs among various endogenous and exogenous transaction costs and economies of division of labor are taken into account?

355

Connection between the softness of the budget constraint and vagueness in specifying and enforcing property rights Market mechanism to sort out the efficient degree of competition, the efficient degree of vagueness in specifying and enforcing property rights, and the efficient level of division of labor Relationship between risk aversion and a strictly concave utility function Measure of degree of risk aversion Effects of transaction risk and the degree of risk aversion on the equilibrium network size of division of labor and economic development Effect of insurance on the equilibrium network size of division of labor and economic development Complete insurance, moral hazard, incomplete insurance, and endogenous transaction costs What are the features of a Soviet style economic system with complete insurance? Why does it generate extremely high endogenous transaction costs? Why would productivity decline sharply if the complete insurance system was abolished before a developed market for insurance was available?

Further Reading Trade off between different kinds of transaction costs: Cheung (1969, 1970, 1983), Milgrom and Roberts (1992), Yang and Y-K. Ng (1993, ch. 10, 11), Yang and Wills (1990), Yang, Wang, and Wills (1992), Williamson (1975, 1985), Monteverde and Teece (1982); Economics of property rights: Barzel (1989), Demsetz (1967, 1988), Demsetz and Lehn (1985), Furubotn and Pejovich (1974), Manne (1975), North (1981), North and Weingast (1989); New political economy models with endogenous stealing: Marcouiller and Young (1995), Skaperdas (1992); Soft budget constraint: Kornai (1980, 1991), Qian (1994); Theory of reliability: Shooman (1968), Sah and Stiglitz (1986, 1988, 1991), Sah (1991), Bazovsky (1961), Lange (1970), Blanchard and Kremer (1997), Kremer (1993). Historical evidence about the relationship between property rights and economic development: Macfarlane (1988), Baechler, Hall, and Mann (1997), Pipe (1999), Jones (1981), Baechler (1976), Rosenberg and Birdzell (1986), and Mokyr (1990, 1993), Landes (1998); Empirical evidence for the relationship between better enforced property rights and economic development: Barro (1997), Sachs and Warner (1995, 1997), Yang, Wang, and Wills (1992), Frye and Shleifer (1997); Insurance and economic development: Lio (1996, 1998), Dixit (1987, 1989); Risk and insurance: Mas-Colell, Whinston, and Green (1995, chs. 6, 13, 14), Varian (1993, ch. 8), Milgrom and Robert (1992); General equilibrium models of moral hazard: Legros and Newman (1996), Laffont and Tirole (1986), Helpman and Laffont (1975), Kihlstrom and Laffont (1979); Economic crisis and development: Sachs (1986d, 1987, 1989), Radelet and Sachs (1998a).

Questions

1. The automatic traffic light system can be used to save on the costs of hiring traffic policemen for manual control of traffic lights. But it causes endogenous transaction costs as well. The automatic traffic light system is not as flexible as a manually controlled system, so that it quite often wastes drivers’ time in waiting for a green light. Technically, an ultrasound system for monitoring traffic conditions at each cross point can be used to reduce such endogenous transaction costs at the exogenous transaction costs of buying the ultrasound system. Discuss under what conditions (for instance, the salary of a policeman is low in a developing country, or technical progress could significantly reduce the price of the ultrasound system) acceptance of the endogenous transaction

356

2.

3.

4.

5.

6.

costs caused by the automatic traffic light system is efficient. Why is the term “externality” misleading for addressing endogenous transaction costs? Before the patent laws were first introduced in Britain (Statute of Monopolies, 1624), the invention of new technology involved substantial endogenous transaction costs in trading intellectual property. The patent laws significantly reduced such endogenous transaction costs at the cost of increasing the distortions caused by monopoly. A discussion on benefits and costs of the patent laws for the Industrial Revolution can be found from Mokyr, 1993, pp. 40-48. Why are the terms “externality” and “spread-over effect” that are used to describe such endogenous transaction costs misleading? In the earliest postal system in Britain, postal fees were accurately calculated according to the weight and post distance of the mail in order to reduce the endogenous transaction costs caused by an inaccurate correspondence between fee and service provided. Analyze why that postal system was replaced with an inaccurate measurement of the correspondence between fee and service based on postage stamps and mailboxes. Why is the term “externality” misleading for describing the various transaction costs involved in the postal system? Holmstrom and Roberts (1998, pp. 80-81) examine the difference between contractual arrangements in the US and Japan. In the US: When products were outsourced, the design was typically done by the automaker, with the drawings being provided to the suppliers. This pattern is what Williamson's hold-up stories would predict, for the investment in design is highly specific and probably cannot be protected fully by contracts; thus, external suppliers will not make such relationship-specific investments for fear that they will be held up by buyers after their investments are in place. In stark contrast, it is normal practice for Japanese auto firms to rely on their suppliers to do the actual design of the products supplied. The design costs are then to be recovered through the sale price of the part, with the understanding that this price will be adjusted in light of realized volumes. A second contrast: the traditional US practice has been that physical assets specific to an automaker's needs are owned by the automaker. This clearly applies in the case of internally procured items, but it also holds in cases where the assets are used by the external supplier in its own factory. In Japan, in contrast, these specific investments are made by the supplier, who retains ownership of the dies. This would seem to present the automaker with temptations to appropriate the returns on these assets, once the supplier has made the relationship-specific investment. Moreover, because the Japanese auto manufacturers typically have a very small number of suppliers of any part, component or system, the supplier would also seem to be in a position to attempt opportunistic renegotiation by threatening to withhold supply for which there are few good, timely substitutes. The Japanese pattern is directly at odds with transaction cost theory. Meanwhile, the divergence in ownership of the dies between the two countries presents problems for Hart, Grossman, and Moore's attempts to explain ownership allocation solely in terms of providing incentives for investments. Use the model in example 10.2 to explain the difference between contractual arrangements in Japan and US in connection to Williamson's theory of asset specificity and Hart's theory of incomplete contract (example 9.15). (Cheung, 1970, Barzel, 1982) Oranges can be grouped in a very fine or a rough way. One of the two extremes is to price each orange precisely according to its quality (taste, color, and size). The other is to set up the same price for all oranges of different quality. In reality, grouping and pricing of oranges is in between the two extremes. Apply the models in this chapter to analyze how the efficient degree of precision in measuring oranges is determined in the market place. Why is the existence of externality caused by the imprecise measurement of the quality of oranges efficient in the free market system? Use the model of endogenous “externality” to formalize Coase’s and Cheung’s criticisms of Pigou’s welfare analysis of externality and public goods. According to Cheung (1970, 1983) and Coase (1960), so called externality is endogenously chosen by individuals in efficiently trading

357

off between endogenous and exogenous transaction costs, and if exogenous transaction costs in specifying and enforcing property rights are counted, keeping a certain degree of “externality” may be efficient. Also, inframarginal analysis across different structures of property rights is more appropriate than Pigou’s marginal analysis of quantities and prices for a given economic structure. In other words, discontinuous jumps between corner solutions should be taken into account for a general equilibrium analysis of the trade off between the benefits of trade and all kinds of transaction costs. 7. Marshall (1989, p. 241) described the relationship between the network of division of labor, transaction conditions, and the development of new machinery as follows. “The development of the organism, whether social or physical, involves an increasing subdivision of functions between its separate parts on the one hand, and on the other a more intimate connection between them. Each part gets to be less and less self-sufficient, to depend for its well-being more and more on other parts, so that any disorder in any part of a highly developed organism will affect other parts also. This increased subdivision of functions, or ‘differentiation,’ as it is called, manifests itself with regard to industry in such forms as the division of labour, and the development of specialized skill, knowledge and machinery; while ‘integration,’ that is, a growing intimacy and firmness of the connections between the separate parts of the industrial organism, shows itself in such forms as the increase of security of commercial credit, and of the means and habits of communication by sea and by road, by railway and telegraph, by post and printing-press.” Interpret the models in this chapter in connection to this description. 8. Mokyr (1990, p. 267) indicates: “Small firms do not guarantee competitiveness. If firms are catering to a small enough market (that is, if transport costs are sufficiently high), even a single artisan could be a monopolist. Moreover, competitive industries can devise cushioning mechanisms that mitigate the sharp edges of competition and eventually make the industry behave as a monopolist in some respects. The guild system, although not set up for that purpose, clearly carried out that task in Europe for many centuries.” Use the models in this chapter to substantiate the conjecture on the relationship between the degree of competition and transaction efficiency. 9. If the capital market is not developed, a government postal system can be used to develop the market for postal services. Why may the government postal system generate greater endogenous transaction costs than the market for private postal services if the capital market is developed? Some economists use the notion of network externality to justify a government monopoly in the market for postal services. Why may this notion be misleading? 10. The comparative statics of the equilibrium model in examples 10.2 can be used to identify the impact of the improvements in two kinds of transaction efficiency: efficiency in delimiting rights to contracting and efficiency in specifying and enforcing the terms of a contract. For instance, an improvement in transaction efficiency in delimiting rights to contracting may increase buyers' dependence on competition between peer suppliers of a good, and reduce the equilibrium degree of precision in specifying and enforcing the terms of a contract. An improvement in efficiency in stipulating and enforcing a contract may have contrary effects, so that a buyer of a good will increase the precision of a contract rather than maintaining contact with many potential suppliers of this good. Meanwhile, improvements in efficiency of either kind may enhance the equilibrium level of division of labor, trade dependence, and productivity. This model can also be used to analyze the structure of property rights in a Soviet style economy. Economists in socialist countries and comparative system economists are now realizing that equivocation in delimiting property rights under a state ownership system is a much more serious problem than distorted prices in a socialist economy. Many Chinese economists believe the more precisely delimited property rights are better. Use the distinction between efficiency in delimiting rights to contracting and efficiency in specifying and enforcing the terms of a contract to comment on that view.

358

11. Restrictions that exist on the trading of labor, land, and capital in a Soviet style economy will substantially reduce transaction efficiency in delimiting rights to contracting, thereby restricting institutional development and economic growth. Under such restraints, the scope for people to balance the two types of transaction costs is very limited. Use the model in example 10.4 to analyze the difference between a state-run enterprise in a socialist country and a government owned firm in a free enterprise system, and the difference between a state-run enterprise in a socialist country and a private firm in a free market. 12. The Chinese government and Taiwanese government use government revenue to develop the freeway system, while in Malaysia the major freeway system is developed by the private sector. Use the models in this chapter to analyze the relative advantage of the two ways of developing infrastructure. 13. Use the models in this chapter to analyze the financial crisis in East Asia in 1997. 14. Yang, Wang, and Wills use meticulous documentation of institutional changes in China to estimate sub-indices of transaction efficiencies in specifying and enforcing rights to use, transfer, and appropriate earnings from land, goods, labor, and financial assets. Then the 12 sub-indices are used to estimate a comprehensive transaction efficiency index over 9 years. A regression of the per capita real income on the degree of commercialization (a measure of the level of division of labor) and the transaction efficiency index, and a regression of the degree of commercialization on the index, show a significant positive relationship between per capita real income, the level of division of labor, and transaction efficiency in specifying and enforcing property rights. Derive more empirical implications, and find more empirical evidence for the theories developed in this chapter. 15. Use the models in this chapter to analyze the function of the stock market in providing incomplete insurance for entrepreneurial activities and its development implications. 16. In many less developed societies, individuals allocate a lot of resources to the deepening of personal trade relationships to increase the reliability of exchanges. They do not rely on broad impersonal market connections to secure transactions (see, for instance, Mauss, 1925). Use the model in example 10.2 to explain this phenomenon. North (1970) argues that the development of impersonal exchanges is essential for reducing transaction costs and for economic development. Use the models in this chapter to analyze the conditions for the development of impersonal exchanges. 17. Analyze the functions of unemployment insurance, medical insurance, and other insurance in increasing the network size of division of labor and productivity. 18. The Soviet style economic system provides complete insurance for those specializing in different professions in the state sector. That complete insurance generates tremendous endogenous transaction costs because of moral hazard on the one hand, but is an essential condition for the operation of a large network size of division of labor on the other. Explain, using the models in this chapter, why the Russian economy drastically declined in the 1990s after the complete insurance system had been abolished. 19. Analyze why the framework of consumer-producers and the notion of the positive network effect of division of labor are essential for exploring the productivity implications of insurance. 20. Use the models of insurance in this chapter to explain the impact of the development of the insurance sector on the success of British commerce and the wealth of the nation in the 18th century. 21. Use empirical data to test the concurrent evolution of division of labor and the income share of insurance, which are used to accommodate the increasing risk of coordination failure of a larger network of division of labor. 22. A survey of Economist (1998, September 5-11 issue, pp. 4-7) has found that the probability that a motorist gets in a traffic jam is higher in a city with faster upgrading of its transportation infrastructure. Use the theory in this chapter about the trade off between the benefit of

359

expanding the network and the reliability of the network to explain why aggregate reliability declines as transaction conditions are improved. 23. The model in example 10.6 shows that in a Smithian model of endogenous specialization, moral hazard, division of labor, and productivity may increase side by side as transaction conditions are improved. Hence, the distortions caused by moral hazard in a developed country might be more than in a less developed country, despite higher productivity in the former. Use this result and other models in this chapter to comment on the claim made by some development economists that mainstream economics is not applicable to developing countries, because the nonexistence of many markets in the developing countries creates many more distortions than in the developed countries. 24. Use the models in this chapter to analyze the division of labor in producing books and related ideas, and the role of copy-right laws and their enforcement in promoting the division of labor. 25. Endogenous transaction costs caused by interest conflicts in economic development, investigated in chapters 10 and 11 are treated in conventional development economics under rubrics “public goods”, “externality”, “market failure”, “inequality of income distribution.” Assess the differences between two approaches to studying obstacles of economic development.

Exercises 1. (Yang and Wills, 1990) Assume that q in the model of example 10.1 is endogenously determined by labor effort in reducing transaction risk. Solve for general equilibrium and its inframarginal comparative statics. 2. Mokyr (1993, p. 56) describes the trade off between the negative effect of taxation and its benefit to economic development via developing infrastructure that improves the transaction condition. In the 18th and 19th centuries, the British people were more heavily taxed than the French people, but a stable and prespecified tax rule was never allowed to become as arbitrary and confiscatory as in France. Tax revenue was used to develop the institutional and transportation infrastructure that significantly improved transaction conditions. Hence, in 1788, British GNP per capita was about 30% higher than that in France. Specify a tax rate on each dollar from sales of goods in the model of example 10.1. Assume that transaction reliability r is an increasing function of tax revenue. Use the extended model to explain the historical fact documented by Mokyr. Note that because of the trade off between the positive and negative effects of taxation, there is an optimum tax rate which maximizes per capita real income. 3. Assume that q in the model of example 10.1 differs from good to good and m=3. Solve for the general equilibrium and its inframarginal comparative statics. Use your results to analyze why a property that has the same consumption and production conditions as other properties, but involves more restrictions on its trading or has a greater transaction risk q, will have a lower market price if it is traded, and will not be traded if not all goods are traded in equilibrium. Apply the analysis to explore the welfare implications of a public housing program. Use the model to explain why, in many developing countries, government institutions, including government funded universities, are reluctant to buy all kinds of services from the market. They tend to have their own guest houses instead of buying professional hotel services for their guests, to have their own lawyers instead of buying professional law services from independent law firms, and so on. Analyze the implications of such a tendency to selfsufficiency for the equilibrium network size of division of labor and economic development. 4. Suppose good x in the model in example 10.4 is a producer good that is essential for the production of the consumption good y. Each consumer-producer’s utility is a function of the consumption amount of good y. There is no transaction uncertainty for good y. Solve for the

360

5.

6.

7.

8.

9.

general equilibrium and its inframarginal comparative statics. (Yang and Ng, 1993, chapter 11). (Holmstrom and Milgrom, 1991) The employer hires the employee to undertake two activities to generate profit. The employer's certain equivalent (see section 9.2 of chapter 9 for the definition of this concept) is P(e1, e2)-(α+β1e1+β2e2), where ei is the employee's effort level in activity i, βi is the incentive intensity coefficient for activity i, P(e1, e2) is the expected gross profit, and α+β1e1+β2e2 is the expected wage payment. Contingent wage payment is w = α+β1(e1+x1)+ β2(e2+x2), where xi ∼ N(0, σ) is a white noise in activity i and x1 and x2 are independent. The employee's certain equivalent wealth is α+β1e1+ β2e2-C(e1+e2)0.5rvar(β1x1+β2x2), where C(e1+e2) is the disutility of total effort, r is the employee's coefficient of absolute risk aversion, and var(β1x1+β2x2) = (β12+β22)σ. Find the optimum incentive intensity in each activity βi by maximizing the employer and employee's total certain equivalent wealth subject to the first order condition for maximizing the employee's certain equivalent wealth. Show that the trade off between balanced incentives for the two activities and the benefit of strong incentives for each activity generates the optimum incentive payment structure that entails much weaker incentives than in the conventional principal-agent model. Holmstrom and Milgrom use this model to show that the institution of the firm can use such a weak but balanced incentive contract to get a particular activity going, whereas this activity may not occur in the market without the firm. Discuss the difference between this model and the models in examples 8.1 and 9.15. Introduce stealing into the models in this chapter and assume that an individual can spend time in stealing the goods of trade partners in transactions. Also, each individual can spend time in protecting herself from theft. You may specify some stealing function, of which the right hand side is time spent stealing and the left hand side is goods that can be obtained without pay. Then you may specify a protection function on the negative relationship between the degree of theft and the effort spent protecting her property. Use such a model to explore the implications of endogenous stealing for the equilibrium network size of division of labor and economic development. Criminal laws penalize stealing much more than direct economic cost caused by stealing. For instance, according to criminal laws, theft can get a jail sentence of several years, in addition to the fine that covers the direct economic damage of the theft. Also, the moral code requires responsible individuals to do more than that suggested by a cold economic calculation of the cost and benefit of theft. What are the development implications of the criminal laws and moral code of respecting private properties? Assume that in the model of example 10.5 m=3 and α 1 > α 2 > α 3 . Solve for the corner equilibria with and without insurance, and for the inframarginal comparative statics. Analyze the development implications of insurance. Assume that in the model of example 10.5 m=3 and kH and kL differ from goods to goods. Solve for the corner equilibria with and without insurance, and for the inframarginal comparative statics. Analyze the implications for the trade pattern of the difference in transaction risk across goods. Assume that in the model of example 10.6 the utility function is 1 2

u = [(x + k x x d )(y + k y y d )]

Solve for the inframarginal comparative statics. 10. Assume that there is a management cost b for each insurance contract in the model in example 10.6 Free entry and competition drives the net profit of the insurance company to 0, or π − (c / 3) − b = 0 . Solve for the inframarginal comparative statics and analyze the implications of insurance for productivity and the network size of division of labor. 11. Develop a general equilibrium model, on the basis of example 10.6, to endogenize the emergence of professional insurance agents from the evolution of division of labor. You may

361

specify the economies of specialization in estimating transaction risk. Discuss the possible implications of the economies of specialization, which might be used to get some results that are contrary to some insurance models, which predict that the insured knows more about risk than the professional insurance company (adverse selection). 12. (Kremer, 1993) The production function for a neoclassical firm is y = kαqnnB, where y is the expected output level, k is the input level of capital, α∈(0, 1), q is the probability that a worker does a job meeting a quality requirement, or 1-q is the probability that this worker's job does not meet a quality requirement, n is the number of jobs that are essential for production, and B is a contribution parameter of each qualified job to output. Market wage is a function of q, which is positively related to the quality of workers hired. Hence, w = w(q). The interest rate is r. Suppose that good y is the numeraire. Specify the first order conditions for maximizing profit with respect to k and q and identify the market relationship between the wage rate and the quality of workers w(q) (Hint: insert the expression of the optimum k into the first order condition for the optimum q, then solve for the differential equation dw/dq = f(q)). 13. (Sah and Stiglitz, 1986) Consider two patterns of the decision making process in which a project is assessed by two decision makers. In pattern A (series connection), person 1 assesses a proposed project first. She accepts a proposal with probability p and rejects it with probability 1-p. A proposal that has been accepted by person 1 is then assessed by person 2, who accepts a proposal with p∈(0, 1). In pattern B (parallel connection), each person assesses each proposal independently of the other's assessment. Assume that 50% of the proposals are good and the others are bad (should be rejected). What is the probability that a good proposal is rejected (type I error) under each of the decision patterns? What is the probability that a bad proposal is accepted type II error) under each of the decision patterns? 14. Assume that reliability for each transaction r is a decreasing function of the number of potential partners, N (because the incumbent partner's loyalty decreases as a person keeps in touch with many potential substitutes for the incumbent) in example 10.2. Solve for inframarginal comparative statics again. Use your result to analyze why many franchise contracts include the clause that creates high cost for the franchisee to go away from the incumbent franchiser.

362

Part III: Urbanization and Industrialization

Chapter 11: Urbanization, Dual Structure between Urban and Rural Areas, and Economic Development

11.1. Why and How Cities Emerge from the Division of Labor Xenopnon (see Gordon, 1975, p. 41), William Petty (1683, p. 947), Adam Smith (1776, chs. 2, 3), and Alfred Marshall (1890, ch 9-10, book IV) recognized the intrinsic connection between division of labor and the emergence of cities. However, no general equilibrium analysis had been developed to explain the emergence of cities from the evolution of division of labor until the 1990s. There are two ways to explore the relationship between urbanization and division of labor. One is proposed by Yang (1991) and Yang and Rice (1994), with the accentuation of the endogenization of individuals’ levels of specialization and degree of market integration. The other is proposed by Fujita and Krugman (1995), with the emphasis on the endogenization of the number of goods and economies of scale. Yang’s model (1991) predicts that if all individuals reside together within a small area to form a city, then transaction efficiency can be improved by reducing the distance between each pair of trade partners, so that the level of division of labor and productivity can be raised. But since the logic of that model suggests that all individuals should reside together, it cannot predict the emergence of the dual structure between rural and urban areas. The story behind the Fujita-Krugman model runs as follows. There are trade offs between global economies of scale, the utility benefit of the consumption variety of manufactured goods, and transaction costs. Farming is land intensive, so farmers must have dispersed residences in the rural area. Manufactured goods are not land intensive, so manufacturers can reside together in the city. In addition, as the residences of manufacturers are concentrated in a city, there is a trade off between the reduction of transaction costs between urban residents and the increase in transaction costs between rural farmers and urban manufacturers. An increase in population size or in transaction efficiency will enlarge the scope for individuals to trade off among these conflicting forces, thereby increasing productivity, per capita real income, and consumption variety. The increase in the number of manufactured goods, an aspect of division of labor, will move the efficient balance of the trade offs toward a more concentrated residential pattern of manufacturers, making a city more likely to emerge. The benefit of concentrated residences of manufacturers is called type I economies of agglomeration. As the comparative statics of the general equilibrium model predicts, a decrease in the unit

363

transaction cost coefficient of agricultural goods or a larger population size will make a city more likely to emerge from a greater number of manufactured goods. But concurrent increases in the urban-rural land price differential, decreases in relative per capita consumption of land by urban and rural residents, the population size of urban residents as a share of total population, and increases of individuals’ levels of specialization cannot be predicted by the model. We shall study this model in section 11.2. Yang and Rice's model (1994) of endogenous specialization predicts the emergence of cities, and of the dichotomy between urban and rural areas, as consequences of the evolution of division of labor and individual specialization. The story behind the model may be outlined as follows. Suppose the production of food is land intensive. The production of many manufactured goods is not land intensive. There are economies of specialization in producing each good, and trade generates transaction costs. Hence, there is a trade off between economies of specialization and transaction costs. If transaction efficiency is low, individuals will choose autarky where no market and city exist. As transaction efficiency is slightly improved, the division of labor between partially specialized farmers and partially specialized cloth makers emerges as a consequence of the efficient trade off between economies of specialization and transaction costs. Since farming is land intensive and cloth making is not, farmers will have dispersed residences while each cloth maker will reside near a farm to reduce the transaction costs caused by division of labor. Hence, the low level of division of labor between farming and cloth making does not generate cities. As transaction efficiency is further improved, the division of labor between cloth makers, house builders, and furniture makers emerges in addition to the division of labor between farmers and manufacturers. The manufacturers can have dispersed residences or reside together in a city since their production is not land intensive. In order to save on the transaction costs caused by the division of labor and related transactions among manufacturers, they will reside in a city. Hence, a city and a dichotomy between urban and rural sectors emerge from a high level of division of labor between specialist manufacturers and between professional manufacturers and farmers. In this story, if different specialist manufacturers reside in the city, the transaction cost coefficient for trade between manufacturers (urban residents) is much smaller than that for trade between farmers (rural residents) and urban residents. This transaction efficiency differential, due to the different degrees of land intensity in agricultural and industrial production, is a driving force behind the emergence of the city from the division of labor. In the development of urbanization and division of labor, urban residents’ levels of specialization and productivity increase more quickly than rural residents’, since the short distance between each pair of urban residents ensures higher transaction efficiency in the urban area than in the rural area. The dual structure, in terms of differences in productivity and in commercialized income between the urban and rural areas, takes place in the transitional phase as the economy moves from a low to a high level of division of labor. However, free migration between areas and between occupations will equalize the per capita real incomes of urban and rural residents, despite the inequality of their per capita commercialized incomes. As transaction efficiency is continuously improved, the economy will evolve to a state of complete division of labor. Then the dual structure will disappear and productivity, the degree of commercialization, and

364

commercialized incomes will be equalized between the two areas. Section 11.3 uses a simplified version of the Yang-Rice model (1994) to formalize the story. Similar to the Fujita-Krugman model, the driving force of the story is type I economies of agglomeration, which look like externality of urbanization. There is another way to explain the relationship between urbanization and the evolution of division of labor in the absence of a differential of transaction efficiency between agricultural and industrial goods. This explains urbanization by exploring the general equilibrium implications of interactions between the positive network effects of the division of labor and the geographical concentration of transactions that are required by a particular network of division of labor. Because of the positive network effect of the division of labor, the geographical concentration of transactions required by a particular network of division of labor can save on transaction costs by reducing total traveling distance for each individual. Hence, urbanization can promote division of labor by concentrating a large network of transactions in a city to reduce transaction costs. The benefit of a geographical concentration of transactions is referred to as type II economies of agglomeration, which differs from the benefit of geographical concentration of manufacturers’ residences. Type II economies of agglomeration imply that individuals may come to the city to conduct their transactions even if they do not reside in the city, while type I economies of agglomeration can be realized only if individuals reside in the city. It is interesting to note the interdependence among equilibrium transaction efficiency, the equilibrium level of division of labor, and the equilibrium geographical pattern of transactions in this story. The concept of general equilibrium is a powerful vehicle in investigating the simultaneous determination of the interdependent variables. Section 11.4 will formalize the story of general equilibrium. In section 11.5, we extend this story to endogenize simultaneously the land price differential between the rural and urban areas, the level of division of labor, and the population density in the urban area. This is done by introducing the consumption level of land into the utility function. In addition to the trade off between economies of division of labor and transaction costs, there is a trade off between high transaction efficiency for urban residents and congestion in the city. Equilibrium is associated with the efficient trade off that generates the following phenomenon. As transaction efficiency is improved, division of labor evolves. This generates increasingly more significant economies of agglomeration (transaction efficiency increasing with the degree of geographical concentration of transactions), so that more individuals are willing to reside in the city. This bids up the land price of the urban area, resulting in a fall in the per capita consumption of land by urban residents compared to rural residents. The potential for the rise of land prices in the urban area is determined by the potential for the evolution of division of labor.

Questions to Ask Yourself when Reading this Chapter What is the relationship between the emergence and development of cities, the level of division of labor, and transaction efficiency?

365

Why do the different land requirements of agricultural and industrial production generate a dual structure between urban areas with a high population density and rural areas with a low population density? What are the effects of free migration and the absence of free migration on urbanization, evolution in division of labor, and economic development? Why are transaction efficiency, the geographical pattern of transactions, and the level of division of labor interdependent? How are they simultaneously determined in the marketplace? Why is the price of land in the urban area higher than in the rural area? What are the main economic determinants of the potential for the increase in urban land prices in the development process?

11.2. The Fujita-Krugman Model of Urbanization based on the Trade off Between Economies of Scale and Transaction Costs Example 11.1: A simplified version of the Fujita-Krugman model (1995). Consider an economy with N identical consumers, an agricultural good, and n manufactured goods, where n is endogenous. It is assumed that the manufacturing activity needs no land. Hence, the central point of the geographic area is a city where all NM manufacturers reside. Suppose that NA = N-NM farmers’ residences are evenly located around the city. The area of land that is employed is endogenously determined in this model. Each rural resident has the following decision problem. (11.1a)

Max: s.t.

uA = zA α [n(kxA)ρ](1-α)/ρ p zA+ nqxA = wA

(utility function) (budget constraint)

where p is the price of the agricultural good, q is the price of the manufactured goods, zA is the quantity of the agricultural good consumed by a rural resident, n is the number of manufactured goods, and xA is the amount of a manufactured good consumed by the rural resident. Each consumer is endowed with one unit of labor, so that the income of a rural resident equals the rural wage rate wA. k ∈(0, 1) is the transaction efficiency coefficient for the manufactured goods. We assume that there is no transaction cost for a rural resident to buy the agricultural good from the local rural market. Hence, transaction costs are incurred only in buying the manufactured goods. Note that we have used symmetry to justify equal prices and equal quantities of all manufactured goods consumed. Each urban resident has the following decision problem. (11.1b)

Max: uB = (tzB)α [nxBρ](1-α)/ρ s.t. p zB+ nq xB = wB

(utility function) (budget constraint)

where subscript B stands for variables for an urban resident and t ∈(0, 1) is the transaction efficiency coefficient for the agricultural good. If we assume that labor at the city is the numeraire, then wB = 1. We assume that there is no transaction cost for a urban

366

resident to buy manufactured goods from the local urban market. Hence, transaction costs are incurred for the urban resident only in buying the agricultural good. The demand functions and indirect utility function and own price elasticity of demand for a consumer of type i = A, B are: (11.2)

E = -(n-ρ)/(1-ρ)n zi = αwi/p , xi = (1-α)wi/qn, uA = αα(1-α)1-αn(1-α)(1-ρ)/ρ k(1-α)wA/ pαq1-α uB = αα(1-α)1-αn(1-α)(1-ρ)/ρ tαwB/ pαq1-α

where the own price elasticity of demand E is calculated using the Yang-Heijdra formula (see the expression 5.4 in chapter 5). The simple Leontief production function is assumed for the agricultural sector. So a units of labor and one unit of land are required to produce one unit of z. The zero profit condition in the agricultural sector yields (11.3)

p = a wA

Free migration between the urban and rural areas will establish utility equalization between the two areas. The condition uA = uB, together with (11.3), yields (11.4)

wA = tα/k1-α, wB = 1.

A linear production function with a fixed cost is assumed for manufacturing a nonagricultural good. Hence, the amount of labor to produce output Qi is f+bQi. A monopolistically competitive regime prevails in the market for any manufactured good. With the Yang-Heijdra formula for own price elasticity (see (5.4) in chapter 5), the conditions that marginal revenue equals marginal cost and zero profit yield (11.5)

nq(1-ρ) = (n-ρ)(q-b),

(1-α)(q-b)(NA wA + N- NA) = f nq

where NA is the number of farmers, NB = N-NA is the number of urban residents, and the equilibrium value of wA is given in (11.4). (11.4) and (11.5), together with the market clearing condition for labor or for the manufactured goods, can then be used to determine NA, q, wA, and n. The equilibrium total output level of the agricultural good, Z = zN, can be obtained by plugging the equilibrium price into the demand function, zi = αwi/p, where wi is given in (11.4). Therefore, the demand for labor from the agricultural sector is (11.6)

NA = aZ = a[(αNA/a)+ (α(N-NA)/awA)] or NA = αk1-αN/[(1-α)tα+αk1-α],

where wA = tα/k1-α is given in (11.4). Inserting (11.6) into (11.5) yields the equilibrium value of the number of manufactured goods, which can be considered as the degree of industrialization. (11.7)

n = ρ + (1-α)(1-ρ)tαN/[(1-α)tα+αk1-α]f.

367

Differentiation of (11.6) and (11.7) yields (11.8)

dn/dN > 0, dn/dt > 0, and d(NB/N)/dt > 0. dn/dk < 0, and d(NB/N)/dk < 0.

This implies that as the population size and/or the transaction efficiency for the agricultural good increase, the number of manufactured goods increases, or industrialization develops. Also, the comparative statics predict that as the transaction condition for the agricultural good is improved, the population share of urban residents increases, or urbanization develops. But the transaction efficiency for the manufactured goods has the opposite effects. The equilibrium land area employed for agricultural production is the same as the output level of the agricultural good z, which increases as the population size rises, as the transaction efficiency for the manufactured goods increases, or as the transaction efficiency for the agricultural good declines. Fujita and Krugman’s original model is slightly more complicated than the simplified version. They assume that transaction cost is an increasing function of the distance from the city, which is the middle point of a segment line. All farmers reside on the segment on the two sides of the city. Also, they have discussed the condition for more than one cities to emerge from the evolution of the number of manufactured goods. According to Baumgardner (1989), physicians in large cities are much more specialized than those in small towns. This empirical evidence is consistent with the conjecture of classical economists. But the Fujita and Krugman model cannot predict this phenomenon, since individuals’ levels of specialization are not endogenized in their model. Hence, we consider a model with endogenous specialization and endogenous emergence of cities from evolution of division of labor in the next section. 11.3. Emergence of the Dual Structure between Urban and Rural Areas from the Division of Labor Example 11.2: A simplified version of the Yang-Rice model. We consider a simplified version of the Yang-Rice model (1994) that has been solved by Monchi Lio. The model is similar to those in chapters 4 and 7. There are three goods, cloth (good 1), furniture (good 2), and food (good 3). Goods 1 and 2 are industrial goods requiring little land in production. Hence, the residences of producers of these two goods can either be dispersed over a large area or be concentrated in a small area. The production of good 3, food, is land intensive. The residences of the farmers must be dispersed over a large area. Though all M consumer-producers are ex ante identical, they can choose to specialize in producing different goods and their residence location pattern (far away from or close to neighbors). We call those individuals who choose to produce only industrial goods Ctype persons, and those who choose to produce agricultural goods R-type persons. The transaction cost coefficient for a unit of goods purchased is 1-K, or the transaction efficiency coefficient is K. But K differs between different types of persons and is dependent on individuals’ decisions concerning the geographic pattern of their residences. If C-type persons reside together within a small area, the transaction efficiency

368

coefficient K = k between a pair of C-type persons. The transaction efficiency coefficient K = r between a pair of R-type persons and K = s between a C-type person and an R-type person. We assume that k > s > r. The first inequality is easy to understand since the average distance between a pair of C-type persons who reside together is shorter than the average distance between an R-type person, who must occupy a quite large area of land, and a C-type person. Suppose an R-type person resides at the center of her farm, which has the shape of a circle with radius 1. Since a C-type person can minimize transaction costs by residing on the boundary of the farm if she trades with the farmer, the minimum distance between the R-type and C-type persons is 1. But the distance between two Rtype persons who reside at the respective centers of their farms with radius 1 is 2. This is why transaction efficiency is higher between an R-type person and a C-type person than between a pair of R-type persons, or why s > r. As in the previous chapters, each consumer-producer’s utility function is (11.9)

u = (x1+Kx1d) (x2+Kx2d) (x3+Kx3d).

Each consumer-producer has the following production functions and endowment constraint for working time. (11.10) x i + x i s = Max{li − α , 0}, l1 + l2 + l3 = 1 , α ∈(0,) 1 , li ∈[0,] 1, i=1,2,3. α is a fixed learning or training cost in producing a good, li is an individual’s level of specialization in producing good i, subscript i stands for good i, superscript s stands for the quantity sold (supplied), and superscript d stands for the quantity purchased (demanded).

(a) Autarky (b) Partial division of labor, no city, no market structure P2, no city

(c) Complete division of labor, structure D with cities

Figure 11.1: Emergence of Cities from Evolution of Division of Labor According to the Wen theorem, there are three types of configurations: Autarky (denoted A), as shown in Fig. 11.1(a), selling good i and buying good j, denoted (i/j), and selling good i and buying goods j and t, denoted (i/jt), There are six of the second type of configurations: (1/2), (2/1), (1/3), (3/1), (2/3), and (3/1), as shown in Fig. 11.1(b). There are three of the third type of configurations: (1/23), (2/13), and (3/12), as shown in Fig. 11.1(c).

369

Combinations of these configurations yield four structures. M individuals choosing configuration A constitute an autarky structure A. A division of M individuals between configurations (1/2) and (2/1) constitutes a partial division of labor structure P1. A division of the population between configurations (1/3) and (3/1) constitutes structure P2, as shown in Fig. 11.1(b). Since a structure based on configurations (2/3) and (3/2) is symmetric to structure P2, and yields the same per capita real income as P2, we omit it. A division of individuals between the other configurations (1/23), (2/13), and (3/12) constitutes the complete division of labor structure D, as shown in Fig. 11.1(c). Following the inframarginal analysis developed in the previous chapters, we can solve for the corner solutions in the eight configurations, as shown in Table 11.1. From the utility equalization and market clearing conditions, we can solve for the corner equilibria in the four structures, as shown in Table 11.2. Table 11.1: 8 Corner Solutions Confi Selfgura- provided Quantity tion xi = (1-3α)/3 A (1/2) x1=x3=(1-2α)/3

Level of Speciali zation

Supply

x1s =(1-2α)/3

x2d = p1x1s/p2

x2s =(1-2α)/3

x1d = p2x2s/p1

[(1-2α)/3]3rp2/p1

x1s =(1-2α)/3

x3d = p1x1s/p3

[(1-2α)/3]3sp1/p3

x3s =(1-2α)/3

x1d = p3x3s/p1

[(1-2α)/3]3sp3/p1

x1s =2(1-α)/3

xid = p1(1-α)/3pi xid = p2(1-α)/3pi xid = p3(1-α)/3pi

[(1-α)/3]3ksp12÷ p2p3 [(1-α)/3]3ksp22÷ p1p3 [(1-α)/3]3s2p32÷ p 2p1

(3/1)

x3=x2=(1-α)/3

(1/13)

x1 = (1-α)/3

(2/13)

x2 = (1-α)/3

l2 = 1

x2s =2(1-α)/3

(3/12)

x3 = (1-α)/3

l3 = 1

x3s =2(1-α)/3

(1/3) x1=x2=(1-2α)/3

Indirect utility function [(1-3α)/3]3 [(1-2α)/3]3rp1/p2

li = 1/3 l1 = (2-α)/3 l2 = (2-α)/3 l1 = (2-α)/3 l3 = (2-α)/3 l1 = 1

(2/1) x2=x3=(1-2α)/3

Demand

Comparisons of per capita real incomes in the four corner equilibria, together with the Yao theorem, yield the results shown in Table 11.2 about the general equilibrium and its inframarginal comparative statics. A comparison between structures P1 and P2 indicates that structure P2 always yields greater per capita real income than does P1. That is, under partial division of labor, it is impossible that two types of individuals exchange industrial goods and self-provide agricultural goods, since in this pattern of partial division of labor all individuals are of R-type (producing food), who have a larger transaction cost coefficient than between Rtype persons and C-type persons in structure P2. But structures P1 and P2 can exploit the same economies of division of labor (due to the symmetry of the model). Note that transaction efficiency between two R-type persons, r, is lower than that between a C-type person and an R-type person by assumption. Hence, the set of candidates for the equilibrium structure consists of A, P2, and D. 370

Table 11.2: Corner Equilibria in 4 Structures Structure A P1 P2 D

Relative price

Number of individuals selling different goods

p1/p2 = 1 p1/p3 = 1 p2/p1 = 1, p3/p1=(k/s)1/3

M1 = M2 = M/2 M1 = M3 = M/2 M1 = M2 = M/[2+(s/k)1/3] M3 = (s/k)1/3M/[2+(s/k)1/3]

Per capita real income [(1-3α)/3]3 [(1-2α)/3]3r [(1-2α)/3]3s [(1-α)/3]3(s4k2)1/3

Table 11.3: General Equilibrium and Its Inframarginal Comparative Statics k s Equilibrium structure

< k0 < s0

∈(s0, s1)

A

P2

> s1

> k0 < s2

> s2

D

A

D

where s0 ≡[(1-3α)/(1-2α)]3 < s1 ≡[(1-2α)/(1-α)]9/k2 iff k < k0 ≡ [(1-2α)4/(1-α)3(1-3α)]1.5, and s2 ≡[(1-3α)/(1-α)]9/4/k0.5. Comparisons of per capita real incomes across structure A, P2, and D indicate that P2 is better than A iff s > s0, D is better than P2 iff s > s1. A comparison between s1 and s0 indicates that s1 > s0 iff k < k0. This implies that for k < k0 the general equilibrium structure is A if s < s0, is P2 if s is between s0 and s1, and is D if s > s1. For k > k0, structure P2 is inferior to either A or D. Hence, A occurs in equilibrium if s < s2 and D occurs in equilibrium if s > s0. Note that in structure P2, no individual selling an industrial good produces the agricultural good, so that she can either reside far away from her trade partner-farmer or reside on the boundary of the farmer. She will choose the latter geographical pattern of residence to save on transaction costs. This implies that each partially specialized seller of an industrial good will reside next to a partially specialized farmer. Therefore, there is no city in structure P2, despite the division of labor between farmers and manufacturers of industrial goods. This establishes the statement that the division of labor is necessary, but not sufficient, for the emergence of cities. For structure D, the division of labor between completely specialized manufacturers of industrial goods 1 and 2 can be organized in such a way as to save on transaction costs by all specialist manufacturers residing in cities. If two manufacturers reside in a city, transaction efficiency is k between them. If they have dispersed residences, transaction efficiency is s, which is smaller than k. As transaction efficiency increases from a low to a high level, the general equilibrium evolves from autarky (A) to the partial division of labor between farmers and manufacturers of industrial goods (P2) where no cities exist, followed by the complete division of labor between specialist manufacturers of industrial goods and between professional farmers and the manufacturers (D). Cities emerge from this high level of division of labor between manufacturers of industrial goods and between farmers and the 371

manufacturers. Hence, a sufficient condition for the emergence of cities from the division of labor is a sufficiently high level of division of labor in producing industrial goods which are not land-intensive. Figure 11.1 gives an intuitive illustration of the story based on the formal model. Panel (a) is autarky where there are no transactions or cities, panel (b) is the partial division of labor without cities (P2), and panel (c) is the complete division of labor with cities, where two specialist manufacturers reside in a city denoted by the dashed circle. The geographical distance between the residences of the two manufacturers is much shorter than that between a manufacturer and a farmer. In panel (c) only a local community is used to illustrate structure D. In structure D, there are M/[2+(s/k)1/3] such local communities and M1 + M2 urban residents who are specialist manufacturers and M3 professional farmers, where the equilibrium values of Mi are given in Table 12.2. In each of the local communities, 2 manufacturers reside in a city and (s/k)1/3 farmers reside in the countryside. In order to save on transaction costs, individuals will trade with those closest. Hence, there is no trade between different local communities. In structure D there are M/[2+(s/k)1/3] cities. If we introduce many goods into the model, it is not difficult to show that the number of local communities and the number of cities decreases and the size of each city increases as continuous improvement in transaction efficiency raises the equilibrium level of division of labor. Yang and Rice (1994) extend the simple model in this section to the case with 4 goods and non-linear production functions. They draw the distinction between a dual structure between the urban and rural areas in terms of the differential of population density, and a dual structure between the urban and rural sectors in terms of the differential of level of specialization and productivity between the two sectors. They show that as transaction efficiency is improved, there will be a transitional stage of unbalanced division of labor as the economy evolves from a low level of balanced division of labor to a high level of balanced division of labor. During that stage, urban residents have higher levels of specialization and productivity, and higher levels of per capita commercialized income and commercialization. This is because in the transitional stage, the levels of specialization cannot be the same between rural and urban residents, while a higher level of specialization for urban residents generates a higher per capita real income than a higher level of specialization for rural residents because of the higher transaction efficiency for urban residents. However, free migration will ensure that per capita real incomes become the same between urban and rural residents despite their unequal commercialized incomes. As transaction efficiency is further improved, such a dual structure in terms of a differential in productivity and level of specialization will disappear as it is replaced by complete and balanced division of labor, where levels of specialization and productivity in the two sectors converge.

11.4. Why Can the Geographical Concentration of Transactions Improve Transaction Efficiency? The method to explain the emergence of cities from the evolution of division of labor in the preceding section relates to type I economies of agglomeration, which occur as manufacturers’ residences are concentrated, given farmers’ dispersed residences. The

372

other way to explain the emergence of cities from the evolution of division of labor relates to type II economies of agglomeration that are associated with the network effects of division of labor and the concentrated location pattern of transactions. If the geographical pattern of individuals’ residences is fixed and each pair of trade partners trade in the geographical mid-point of their residences, total travel distance and related cost will increase more than proportionally as the network of transactions required by a particular level of division of labor is enlarged. If all individuals conduct their transactions at a central place, the large network of transactions can be geographically shrunk and can be concentrated in that central place to significantly reduce the total travel distance of all individuals. The economies of agglomeration differ from economies of scale. Some economists call them positive externalities of cities. Indeed, they are generated by interactions between the positive network effects of division of labor and the effects of the geographical concentration of transactions. In other words, not only do the equilibrium topological properties (whether a person has a trade connection with another person) of economic organisms depend on the pattern of resource allocation (quantities of flows of goods and factors which are non-topological properties of economic organisms), but they also depend on the geographical properties of economic organisms (which are also non-topological properties of those organisms). One of the implications of the interplay between topological and non-topological properties of economic organisms relates to the potential for a rise in land prices in the urban area. If we do not understand this implication, we will not be able to explain why the price of land of Hong Kong, Tokyo, and Taipei has increased by more than forty times since the World War II. ?? The most important determinant of the land price of a city is the size of the network of division of labor that is associated with the city as its center of transactions. While that size is determined by transaction efficiency, this itself depends on the geographical pattern of transactions. The effect of the geographic pattern of transactions on transaction efficiency is in turn determined by the level of division of labor. Hence, transaction efficiency, the geographical pattern of transactions, and level of division of labor are interdependent and should be simultaneously determined in general equilibrium. The notion of general equilibrium is a powerful vehicle to explore a mechanism that simultaneously determines all of the variables. We first use a simple example to illustrate why the geographical concentration of transactions can improve transaction efficiency through the network effects of division of labor. Example 11.3: A general equilibrium model endogenizing the geographical pattern of transactions, transaction efficiency, and the network size of division of labor. Let us look at the case with n = 7 in Fig. 11.2. Panel (a) or (b) represents a local community with 7 traded goods in a symmetric model in chapter 7. 7 ex ante identical consumer-producers reside at 7 vertices of a grid of triangles with equal sides, which are represented by 7 points. The distance between each pair of neighbors is assumed to be 1. Due to symmetry, each individual sells a good to, and buys a good from, each of the other six individuals in equilibrium. In panel (a), each pair of individuals trades at the geographical middle point of their residences, which is represented by a small circle. In panel (b), all individuals go to the center of the local community, represented by the small circle, which is the residence of an individual, to trade with each other. Suppose that exogenous transaction costs are proportional to the travel distance of individuals in conducting the transactions

373

required by the division of labor. This assumption implies that there are increasing returns in transactions. Transaction costs are independent of the quantity of goods traded. You may imagine that within a certain quantity range of goods that you purchase, transportation cost is proportional to the quantity of gas that you use for your car, which is proportional to the driving distance but independent of the quantity that you buy. That is, your car is large enough to generate increasing returns in transportation. In the next section, this assumption is relaxed and variable transaction costs are specified as an increasing function of the quantity of goods traded. The relaxation will not change the essence of our result as long as increasing returns in transactions are sufficiently significant. Moreover, we assume that one unit of travel distance costs $1.

374

(a) Dispersed location of transactions

(b) Concentrated location of transactions

Figure 11.2: Dispersed vs. Concentrated Location Patterns of Transactions

375

Let us now calculate total transaction costs for the two geographical patterns of transactions. In panel (a), each of the six individuals residing at the periphery of the community has a farthest away trade partner. She travels to the center to trade with that partner, which is the middle point between them. She can trade with the person at the center by way of the trip. The travel distance for the return trip costs $2. She has two other neighboring trade partners. It costs her $1 to trade with each of them. The distance between her and each of the other two trade partners is √3. A return trip to the middle point between her and each of them is thus √3. Hence, it costs her $2√3 to trade with the two trade partners. Her transaction costs with six trade partners then total $(2+2+2√3) = $7.46. For the person at the center, transaction costs are zero, since all other individuals will trade with her at the center as they stop by there to trade with their farthest partners. In the geographical pattern of panel (b), all individuals not residing at the center bring their goods there to trade. Total transaction cost for each of them is $2. A comparison of transaction costs between panels (a) and (b) indicates that the geographical concentration of transactions can save on transaction costs if the size of the network of division of labor is sufficiently large. O. Williamson refers to the pattern of transactions in panel (b) as the pattern of the wheel, and that in panel (a) as the pattern of all channels. If the purpose of traveling is to obtain information about products, prices, and partners, then increasing returns to the geographical concentration of transactions will be more significant. However, if the geographical concentration of transactions (or exchanges) generates congestion problems for vehicles, and if new computer technology can significantly improve the transmission cost of information, then economies of geographical concentration of information exchange may generate a geographical concentration of information exchange, as occurs in the information superhighway, rather than a geographical concentration of the physical appearance of individuals and vehicles associated with the relevant exchanges. 1 If the fixed construction cost of highways is considered, the increasing returns in transactions will be more plausible. We may define a central marke place as a geographical location where many trade partners conduct transactions. This definition implies a corresponding geographical concentration of transactions. Geographically dispersed bilateral transactions are not associated with the market according to this definition. It can be shown that the market is not needed if the level of division of labor is low. Consider, for instance, a symmetric model in which there are two traded goods and a community of seven individuals. It can be shown that if the geographical pattern of transactions is such that each pair of trade partners trades at the midpoint between their residences, as shown in the case with n = 2 in Fig. 11.2, the transaction cost to each of them is only $1. But if all individuals go to the central marketplace to trade, as shown in Fig. 11.2, panel (b), for the case with n = 7, then each individual’s transaction cost is $2. This illustrates that for a low level of division of labor, geographically concentrated transactions will generate unnecessary transaction costs. Thus, the capacity of a geographically concentrated pattern of transactions to save on transaction costs depends on the level of division of labor. In other words, transaction efficiency is dependent not only on the geographical pattern of transactions, but also on 1

Quigley (1998) considers benefit from intra-city informational spillovers. Tabuchi (1998), by combining methods of Henderson (1974) and Krugman (1991), considers the trade off between type I economies of agglomeration and cost of intra-city congestion.

376

the level of division of labor. But, as shown in the previous chapters, the level of division of labor is itself determined by transaction efficiency. This interdependence among the level of division of labor, the geographical pattern of transactions, and transaction efficiency implies that the three variables are simultaneously determined in a general equilibrium environment. It is analogous to the interdependence between the prices and quantities of goods that are consumed and produced in the neoclassical general equilibrium model, where the optimum quantities of goods consumed and produced are dependent on prices, while the equilibrium prices are themselves determined by individual agents’ decisions on the optimum quantities. Now we introduce the geographical pattern of transactions into the Smithian model in section 7.2 of chapter 7 to illustrate how the level of division of labor, transaction efficiency, and geographical pattern of transactions are simultaneously determined in general equilibrium. From (7.14) in chapter 7, we can see that the level of division of labor, n, is a function of transaction efficiency k, that is (11.11)

n = m + 1 - (1/A) - (m/lnk)

where m is the number of all consumer goods and A is the fixed learning cost in each production activity. Assume now that (11.12)

k = β/d

where β is a parameter that reflects transportation conditions and d is the average traveling distance for each individual to trade with a trade partner, which obviously is related to the geographical pattern of transactions. For simplicity, we consider only the cases with n = 1, 2, 3, 4, 5, 6, 7. We first assume a given value of n, then for the given n, compare values of d for different geographical patterns of transactions as shown in Fig. 11.2. According to the Yao theorem, it can be shown that in equilibrium, individuals will choose a geographical pattern of transactions that has the lowest value of d in order to minimize transaction costs for any given n. Thus, we can use (11.3) and (11.4) to calculate the critical value of β that ensures that values of the level of division of labor, n, transaction efficiency, k, and geographical pattern of transactions, reflected by d, are consistent with each other in equilibrium. Let us start with n = 2 to use the iterative approach to solving for general equilibrium. As discussed previously and indicated in Fig. 11.2, where n = 2 each individual’s traveling distance d is 1 and transactions are dispersed at the midpoints between each pair of trade partners. Other geographical patterns generate longer traveling distances and higher transaction costs for this level of division of labor. For society as a whole with this level of division of labor, there are M/2 local business communities. If we define an urban area as a place where many transactions take place among many individuals at the residences of some of them, then there is no city associated with this pattern of transactions since all transactions are dispersed at many middle points of many pairs of trade partners. Here, the definition of an urban area overlaps with the definition of a central marketplace, but the distinction between them is that an urban area relates to the residences of some of the trade partners, while the definition of market is independent of individuals’ residences.

377

Inserting d = 1 into (11.12), then inserting (11.12) into (11.11), we can solve for the critical value of β for n = 2, which is β2 = e-mA/[1-(m-1)A], where A is the fixed learning cost in each production activity, m is the number of all consumption goods, and e ≅ 2.718 is the base of natural logarithm. The level of division of labor n is at least 2 if β ≥ β2. In order to solve for the critical values of other levels of division of labor, let us look at Fig. 11.2. The graphs in the left column represent those geographical patterns of transactions in which transactions take place at the middle points of each pair of trade partners, whereas the graphs in the right column represent those geographical patterns of transactions in which transactions take place at the center of all trade partners. The solid dots denote consumer-producers and the circles denote the locations where transactions take place. Here, we follow that assumptions that all individuals reside at the vertices of a grid of triangles with equal sides, and that the distance between each pair of neighbors is 1. Hence, the values of d for the different patterns of transactions that correspond to various levels of division of labor can be calculated from Fig. 11.2. All of the values of d, which are of course dependent on the geographical pattern of transactions as well as on the level of division of labor, are listed in Table 11.4.

Table 11.4: Interactions Between Geographical Patterns of Transactions, Transaction Efficiency, and Level of Division of Labor Level of division of labor n=2 n=3 n=4 n=5 n=6 n=7

d for dispersed transactions 1 2/(n-1) (5+√3)÷2(n-1) >2 >2 >2

d for concentrated transactions 1 2√3)÷2(n-1) (1+√3)÷2(n-1) 2÷(n-1) 2 2

Transaction Critical value of efficiency k for βn a given n

β 2β/√3 6β÷(1+√3) 2β 5β/2 β/3

emA/[(m-1)A-1] (√3/2) emA/[(m-2)A-1] (1+√3) emA/[(m-3)A-1]/6 (1/2)emA/[(m-4)A-1] (2/5)emA/[(m-5)A-1] (1/3) emA/[(m-6)A-1]

From Fig. 11.2, it can be seen that the best geographical pattern of transactions for n=2 is at the midpoints between each pair of trade partners, so that d = 1 for n=2. For n = 3, there are two geographical patterns of transactions to choose from. In one of them, each pair of partners trades at the geographical midpoint of their residences, so that all transactions in the economy take place at M places. In the other, all partners in a local community where each person trades with each of the other two go to the geographical center of their residences to conduct all transactions between them, so that all transactions in the economy are implemented at M/3 places. For the latter pattern, it is not difficult to use basic geometry to show that d = 0.5√3 2, and that the minimum value of d for any given n > 4 is 2. Table 11.5: General Equilibrium and Its Inframarginal Comparative Statics Transaction condition β Equilibrium structure n

β7

1

4

5

6

7

2

3

Inserting the minimum value of d for a given n back into (11.12) yields the values of transaction efficiency k for a given n, which are listed in column 4 of Table 11.4. Plugging these values of k back into (11.11), we can work out the critical values of β for n = 2, 3, 4, 5, 6, 7, which are listed in column 5 of Table 11.4. In fact, Table 11.4 has already given the general equilibrium and its inframarginal comparative statics, as summarized in Table 11.5. The Table shows that the general equilibrium is autarky if β < β2. If β ∈ (β2, β3) the general equilibrium is partial division of labor with n = 2, with the geographical pattern as shown in the left column of Fig. 11.2, and with the transaction efficiency k as shown by the entry of row n = 2 and column 4 in Table 11.4. If β ∈ (β3, β4) the equilibrium is the division of labor with n = 3, with the geographic pattern as shown in the right column of Fig. 11.2, and with the transaction efficiency k as shown in the entry of row n = 3 and column 4 in Table 11.4. If β ∈ (β4, β5), the general equilibrium is the division of labor with n = 4, with the geographic pattern as shown in the right column of Fig. 11.2, and with the transaction efficiency k as shown in the entry of row n = 4 and column 4 in Table 11.4. If β ∈ (β5, β6), the general equilibrium is the division of labor with n = 5, with the geographic pattern as shown in the right column of Fig. 11.2 for n = 5, and with the transaction efficiency k as shown in the entry of row n = 5 and column 4 in Table 11.4. If β ∈ (β6, β7), the equilibrium is the division of labor with n = 6, with the geographic pattern as shown in the right column of Fig. 11.2 for n = 6, and with the transaction efficiency k as shown in the entry of row n = 6 and column 4 in Table 11.4. If β > β7, the equilibrium is the division of labor with n = 7, with the geographic pattern as shown in the right column of Fig. 11.2 for n = 7, and with the transaction efficiency k as shown in the entry of row n = 7 and column 4 in Table 11.4. Here, cities emerge from the division of labor with n = 5, 6, 7 and the number of cities is M/n. Marketplaces coincide with locations of the cities, and the number of marketplaces is the same as that of cities. There is no market nor any cities in autarky. For n = 2, there are M/n = M/2 marketplaces with two trade partners for each, and no cities. For n = 3, 4, there are M/n marketplaces with n trade partners for each, and no cities exist. The inframarginal comparative statics of general equilibrium suggest again that the division of labor is a necessary but insufficient condition for the emergence of cities. For n = 2, 3, 4, there are division of labor and related marketplaces, but no cities. It is easy to see that the volume of trade that is executed in a marketplace or in a city increases with the equilibrium level of division of labor, which is determined by the transaction condition parameter β.

379

11.5. Simultaneous Endogenization of Level of Division of Labor, Location Pattern of Residences, Geographical Pattern of Transactions, and Land Prices Although the equilibrium model in the previous section simultaneously endogenizes the level of division of labor, transaction efficiency, and the geographical pattern of transactions, it has not endogenized the location pattern of individuals’ residences and the differential of land price between urban and rural areas, since we implicitly assume that d is the same for urban and rural residents. But the average traveling distance for necessary transactions d is much shorter for an urban resident than for a rural resident, since an urban resident can get all transactions done in the city where she resides without traveling around when all necessary transactions are concentrated in the city. In this section, we take into account the difference between traveling distances of urban and rural residents to develop a general equilibrium model with the endogenous geographical pattern of all individuals’ residences and the land price differential between the urban and rural areas. Example 11.4: (Sun and Yang, 1998) A Smithian equilibrium model with endogenous residences of individuals and endogenous land prices. Consider a Smithian model similar to that in example 7.1 of chapter 7. We assume that production, consumption, and transaction conditions are the same as in that example, except for the following two new features. Each consumer-producer’s utility is a function of the amount of land consumed by her and of whether the city as a center of transactions emerges from the division of labor. When a dual urban-rural structure occurs in equilibrium, the transaction efficiency coefficient is kA for those who reside in the city and k for those who reside in the rural area. The emergence of cities from a sufficiently high level of division of labor generates a transaction cost advantage for urban residents whose transaction cost coefficient is much smaller than that for rural residents. For simplicity, we assume that the relative transaction efficiency coefficient of urban and rural residents is a constant greater than one, (11.13) kA/k = λ > 1. If free migration between urban and rural areas is assumed, then the residential pattern must be endogenously determined rather than exogenously given. Free migration, together with the transaction cost advantage for urban residents and the positive contribution of land consumption to utility, generates a trade off between type II economies of agglomeration and per capita consumption of land in the urban area that will be reduced by the competitive bidding up of urban land prices. The balance of this trade off in the market will generate equilibrium location patterns of individuals’ residences and of transactions, while the efficient trade off between economies of specialization and transaction costs will determine the equilibrium network size of division of labor. Here, the location pattern of residences, the location pattern of transactions, the consumption pattern of land, the relative urban and rural land price, and the network size of division of labor are interdependent. Therefore, the concept of general equilibrium is a powerful vehicle for figuring out a mechanism that simultaneously determines all the interdependent variables.

380

It will be shown later that for n ≤ 2, the equilibrium location patterns of residences and transactions are trivial, that is, all individuals reside at vertices of the grid of triangles with equal sides, transactions take place at the midpoints between the residences of each pair of trade partners, and no cities exist. Hence, we first focus on the case with n>2 where cities emerge from the division of labor. Later, it will be shown that the equilibrium value of n is greater than 2 if and only if transaction efficiency k is sufficiently large. Denote the traded goods produced in the urban (or rural) area A-type goods (or Btype goods). Producers of A-type goods (B-type goods) have an incentive to reside in the urban (rural) area to save on commuting costs between their residences and their work places. Therefore, for each consumer-producer, the decision on residence location and occupation choice becomes independent: they choose to reside in the urban (rural) area if and only if they choose to produce A-type (B-type) goods. Thus, we can use symmetry to simplify the algebra significantly. Since all individuals’ choices of nA, nB, and n determine the network size of division of labor and the location patterns of residences and transactions, their optimum values must be obtained from inframarginal analysis. A value profile of nA, nB, and n is a structure. First, all individuals’ utility maximizing decisions are solved for the given values of nA, nB, and n. Then the market clearing conditions and utility equalization conditions are used to solve for a corner equilibrium for a given structure. For different value profiles of nA, nB, and n there are many corner equilibria. The general equilibrium is the corner equilibrium with the highest per capita real income. The symmetry of the model implies that we need to consider only two types of decision problems. For an urban resident producing an A-type good, the decision problem is (11.14) Max: u A = ( x A )( k A x Ad ) n A −1 ( kx Bd ) nB x mjA−n ⋅ R A s.t. xA+ xAs = Max{0, lA - α} (production function for a good sold) xjA = Max{0, liA - α} (production function for a non-trade good) lA+(m-nA)ljA = 1 (endowment constraint for working time) pA xAd (nA -1)+ pB nB xBd +rA RA = pA xAs +EA (budget constraint) where nA (nB ) is the number of traded goods produced by the urban (rural) residents and purchased by the individual; n ≡ nA + nB is the number of all traded goods that she purchases; xA is the quantity of the A-type good that she self-provides; xAs is the amount of the A-type good that she sells to the market; lA is her level of specialization in producing this good; xAd is the amount of the A-type good that she purchases from the market; xBd is the amount of the B-type good that she purchases from the market; xiA is the amount of a non-traded good that she produces and consumes; and ljA is the quantity of labor that she allocates to the production of a non-traded good. Symmetry implies that xAd is the same for nA -1 of A-type goods purchased, xBd is the same for nA-1 of A-type goods purchased, xBd is the same for nB of B-type goods purchased, and ljA is the same for m-n non-traded goods. pA and pB are respectively the prices of A-type and B-type goods. rA and rB are respectively the prices of land in the urban and rural areas. RA is the lot size of each urban resident’s house. EA = rAA/MA is the land rental, equally distributed to each urban resident, MA (MB ) is the number of urban (rural) residents. The decision variables are xA, xAs, lA, xjA, liA, xAd, xBd, RA, nA, and n. The choice of nA and n, which determines nB,

381

determines how many goods an individual has to buy from the market and how many goods she self-provides. The solution of the decision problem for the given values of nA, nB, and n in (11.14) is an individual’s resource allocation for a given organizational pattern. Standard marginal analysis is applicable to such resource allocation problems. It yields the demand and supply functions and indirect utility function as follows. (11.15a) xAs = {npA[1-(m-n+1)α] - (m-n+1)EA}/pA(m+1) lA = [pA(1+nα)+EA]/pA(m+1), (11.15b) xAd = {pA[1-(m-n+1)α]+EA}/pA(m+1) (11.15c) xBd = {pA[1-(m-n+1)α]+EA}/pB(m+1) (11.15d) RA = {pA[1-(m-n+1)α]+EA}/rA(m+1) m +1 k An −1 p A n B ⎧ E A + p A [1 − (m − n + 1)α ]⎫ uA = ( ) ⎨ (11.15e) ⎬ . m +1 rA p Am p B ⎭ ⎩ The optimum decision for a rural resident is symmetric to (11.15), that is, it can be obtained by exchanging subscripts A and B in (11.15). A corner equilibrium is determined by the market clearing conditions for land and goods, the utility equalization condition between urban and rural residents, and individuals’ optimum decisions for given values of nA, nB, and n. The land market clearing conditions are (11.16) MARA = A, MBRB = B. The market clearing condition for A-type goods (the traded goods produced in the urban area) yields np A [1 − (m − n + 1)α ] − (m − n + 1) E A M A ⋅ (m + 1) p A nA (11.17) p [1 − (m − n + 1)α ] + E B p [1 − (m − n + 1)α ] + E A M A = A ⋅ ⋅MB (n A − 1) + B (m + 1) p A (m + 1) p A nA The market clearing condition for B-type goods is not independent of (11.16) and (11.17) because of Walras’ law. The utility equalization condition yields

(11.18)

⎧ E + p A [1 − ( m − n + 1)α ]⎫ k ( A ) n −1 ⎨ A ⎬ k ⎩ E B + p B [1 − ( m − n + 1)α ]⎭

m +1

=

rA p A m −n ( ) . rB p B

(11.16)-(11.18), the population equation MA+MB = M, and the definitions EA ≡ rAA/MA and EB ≡ rBB/MB yield a corner equilibrium for a given structure defined by nA, nB, and n. 1

(11.19)

1− n

p ⎛ Bθ ⎞ n n ⎟ λ , p ≡ A = ⎜⎜ p B ⎝ A(1 − θ ) ⎟⎠ 1 + (n − 1)α l A = lB = m [ 1 − (m − n + 1)α ]θM [1 − (m − n + 1)α ](1 − θ ) M , rA = p A , rB = mA mB n M n M M A = A = θM , M B = B = (1 − θ ) M , n n

382

R A AM B A(1 − θ ) = = , R B BM A Bθ k n −1 (1 + f ) ⎛ θ ⎞ u A = A (1−θ ) n +1 ⎜ ⎟ Mf ⎝1 −θ ⎠

(1−θ ) n

⎧ [1 − (m − n + 1)α ]⎫ ⎬ ⎨ m ⎭ ⎩

1

m

θ n ⎤ n +1 ⎡A ) , θ ≡ nA/n, and a B-type good is assumed to be the where f ≡ ⎢ ⋅ λ n −1 ⋅ ( 1 − θ ⎥⎦ ⎣B numeraire. A general equilibrium has two components. The first consists of a set of relative prices of traded goods and two types of land, and a set of numbers of individuals choosing different configurations of occupation and residence, a pattern of individuals’ residences, and a location pattern of transactions that satisfies the market clearing and utility equalization conditions. The second component consists of each individual’s choice of nA and n, or n and θ, and each individual’s resource allocation that maximizes the decision maker’s utility. Following a similar procedure to that used to prove the Yao theorem in chapter 4, we can prove that the Yao theorem holds for the model in this section. Let us outline the proof. Because of the equal distribution of urban (rural) land among urban (rural) residents, we know that RA = A/MA and RB = A/MB. This implies that rjRj = Ej for j = A, B. Hence, the decision problem in (11.6) can be rewritten by deleting rARA and EA in the budget constraint and letting RA in the utility function equal a constant A/MA. The indirect utility function generated by the equivalent decision problem is m nB ⎧ [1 − (m − n + 1)α ]⎫ A n −1 ⎛ p A ⎞ ⎜ ⎟ u A ( p, N ) = k A ⎜ , ⎬ ⎟ ⎨ m ⎭ MA ⎝ pB ⎠ ⎩ where p ≡ pA/pB is the price of an A-type good in terms of a B-type good, N ≡ (n, nA, β) is a vector of decision variables. n and nA determine a person’s number and structure of traded goods and her network of trade partners and transactions. β relates to her choice of location of residence and transactions. The value of k is affected by β. Exchanging subscripts A and B, we can obtain a B-type person’s indirect utility function UB(p, N). Note that (11.20) ∂uA/∂p>0 and ∂uB/∂p uA(p”, N”) and uB(p”, N’) > uB(p”, N”). Since N’ at p’ is Pareto superior to N” at p” and utility equalization holds in each corner equilibrium, we have (11.21b) uA(p’, N’) > uA(p”, N”) and uB(p’, N’) > uB(p”, N”).

383

(11.21a) and (11.13b) together imply that at least one of the two inequalities in (11.13a) holds if at least one of the following two inequalities holds. (11.22a) uA(p”, N’) > uA(p’, N’) and (11.22b) uB(p”, N’) > uB(p’, N’). Because the functional forms on the two sides of each inequality in (11.22) are the same, and because of (11.20), (11.22) is equivalent to (11.23a) p” > p’ and (11.23b) 1/p” > 1/p’. It is obvious that one of the two inequalities in (11.23) must hold. Hence, at least one of the two inequalities in (11.21a) must hold, that is, either urban or rural residents have an incentive to deviate from the Pareto inefficient corner equilibrium network of division of labor (N”) under the Pareto inefficient corner equilibrium relative prices. Therefore, any Pareto inefficient corner equilibrium is not a general equilibrium. The Yao theorem is pivotal to the results in this chapter, since it establishes the claim that a decentralized market can fully utilize the economies of agglomeration (which look like externalities) and the network effects of division of labor by choosing the Pareto efficient pattern of individuals’ residences, the efficient location pattern of transactions, and the efficient network size of division of labor. This theorem also rules out multiple equilibria with different per capita real incomes, and shows that there is no coordination difficulty in a static general equilibrium model with network effects of division of labor and location pattern. 2 The very function of the market is to coordinate individuals’ decisions in choosing the pattern and size of the network of division of labor and in choosing the location patterns of residences and transactions in order to fully utilize the network effects and the economies of agglomeration. The maximization of uA in (11.7e) with respect to n for a given nB and the maximization of uB, which is symmetric with uA, with respect to n for a given nA, together with the market clearing and utility equalization conditions, will generate a corner equilibrium that is not the Pareto optimum corner equilibrium. This corner equilibrium is based on individuals' Nash strategies in choosing trade patterns (an A type individual's choice of n is dependent on a B type person's choice of nB). According to the Yao theorem, that Pareto inefficient corner equilibrium partly based on Nash strategies is not a Walrasian general equilibrium. Using the Yao theorem, we can prove the following proposition. Proposition 11.1: In a symmetric model, the economy is divided into M/n separate business communities. For n≤2, all individuals’ residences are evenly located and all transactions (if any) are evenly dispersed. For n>2 traded goods, all trade partners within a business community will choose to execute all transactions that are essential for the division of labor among them in the central marketplace of the community, even if some of them do not reside in the central marketplace. Proof It is trivial to prove the first statement since each person needs only n-1 trade partners and will incur unnecessary transaction costs to trade with other n-1 partners in 2

But because of indeterminancy about who specializes in which activity, which n out of m goods are traded, and which nA out n traded goods are produced in the urban area in equilibrium, we have multiple equilibria that generate the same per capita real income.

384

the symmetric model. Hence, n trade partners will form a local business community that does not trade with other local business communities. We now check whether residences are evenly located when the equilibrium value of n is not greater than 2, and whether the dual urban-rural structure emerges from n>2. Because all individuals are ex ante identical and have the same preferences for consumption of land, in equilibrium each person must consume the same amount of land in autarky, and the price of land must be the same everywhere, which means residences must be evenly located. For n=2, it is not difficult to show that residences are evenly located too, because the ex ante identical individuals have the same tastes for land consumption. There are two possible location patterns of transactions. The pattern in Fig. 11.2(a) involves trade at the midpoint between two trade partners’ residences, and pattern 11.2(b) involves trade at one person’s residence (city). For the latter case, the land price in the city is high enough to offset the transaction cost advantage of residing in the city. Hence, patterns (a) and (b) are equivalent. Let us assume that unequal land prices between the urban and rural areas generate infinitesimally small disutility for rural residents. Then (a) is Pareto superior to (b). According to the Yao theorem (a) instead of (b) will occur in equilibrium for n=2. For n = 3, simple arithmetic shows that a location pattern (ii) of transactions, with one person’s residence as a central marketplace, generates a lower total transaction cost than in (i) of panel (b), which generates a lower total transaction cost than in panel (a). Hence, a central marketplace will emerge from n=3, which implies in turn that the transaction cost advantage of residing at the central marketplace will generate a land price differential, which implies that per capita land consumption is unequal between urban and rural residents and their residences cannot be evenly located in equilibrium. For n = 4 in a symmetric model, the location pattern in (i) of panel (b) is better than that in (a). But in (i), two persons who reside more closely to the central marketplace certainly have a transaction cost advantage, so that the land price cannot be the same for all residential lots. This implies that the initial, even residential location of residences cannot be sustained in equilibrium, since that even pattern occurs only if the land price is the same for all localities. This implies that evenly dispersed residences cannot occur in equilibrium, so that the dual urban-rural structure, such as in (ii) where two persons reside in a city and the other two reside in the rural area with higher per capita consumption of land, may occur at equilibrium for n=4. Following the same reasoning, we can show that the dual urban-rural structure occurs in equilibrium if and only if n>2. Q.E.D. With the Yao theorem and proposition 11.1, we can solve for the general equilibrium by maximizing the corner equilibrium per capita real income given in (11.11) with respect to nA and nB. Since nA + nB = n, this is equivalent to maximizing per capita real income in (11.11) with respect to n and θ ≡ nA/n. The first order conditions for this problem yield: −1

(11.24)

⎡ A(1 − θ )λ ln ⎢ Bθ ⎣

(11.24b)

ln k +

n −1

1 ⎧ n −1 n +1 ⎫ ⎤ 1 ⎡ A(1 − θ )λ ⎤ ⎪ − 2 ⎪1 − θ +⎢ ⎥ + =θ ⎨ ⎥ ⎬ . Bθ ⎦ θ ⎣ ⎦ ⎪ ⎪ θ ⎩ ⎭

mα = −θ ln λ 1 − (m − n + 1)α

385

(11.24) determines the general equilibrium values of n and θ as functions of k, λ, α, m, A, B, which characterize the size and pattern of the network of division of labor and the location pattern of individuals’ residences and transactions. Note that the left-hand side of (11.16a) is an increasing function, while the righthand side is a decreasing function of λn-1A(1-θ)/Bθ, so that (11.24a) holds if and only if B θ λn −1 = ⋅ (11.25) . A 1−θ Differentiation of (11.25) yields ⎡ 1 ⎤ (11.26) [ln λ ]dn = ⎢θ (1 − θ ) ⎥dθ ⎣ ⎦ (11.26) implies that θ ≡ nA/n increases with n, or the number of traded goods produced in the urban area increases more than proportionally as the network size of division of labor n increases. Using (11.17) and (11.19), we can also show that the general equilibrium relative price (11.27) p = 1. It can be shown that the first order conditions in (11.24), together with the second order condition that requires a negative definite Hessian matrix (D2u(n, θ) < 0), leads to: −1

⎫ dn ⎧ mα 2 2 θ ( 1 θ )(ln λ ) (11.28) =⎨ − − ⎬ > 0. dk ⎩ [1 − (m − n + 1)α ]2 ⎭ The second order condition can be worked out as follows. Inserting (11.25) and (11.27) into the second order derivative of u* in (11.19) with respect to n and θ yields n(n + 2) ∂ 2u 1 =− ⋅ (11.29a) 2 2 ∂θ (n + 1) θ (1 − θ ) (11.29b) (11.29c)

∂ 2 u n(n + 2) = ⋅ ln λ ∂θ∂n (n + 1) 2 θ (1 − θ )(ln λ ) 2 ∂ 2u mα 2 = − + ∂n 2 (n + 1) 2 [1 − (m − n + 1)α ]2

The negative definiteness of the Hessian matrix D2u(n, θ) < 0 requires that (11.29a) and (11.29c) be negative and ∂ 2u 2 ∂ 2u ∂ 2u (11.29d) ⋅ −( ) >0. ∂θ∂n ∂θ 2 ∂n 2 (11.29a) and (11.29c) are negative and (11.29d) holds if mα 2 2 (11.30) 2 > θ (1 − θ )(ln λ ) . [1 − (m − n + 1)α ] Since (11.30) holds if and only if (11.28) holds, (11.28) holds if the second order conditions for maximizing U* with respect to n and θ are satisfied. Since kA = λ k where λ>1 is a constant, (11.28) implies also dn (11.31) >0 dk A

386

This implies that the number of traded goods for each individual, as well as for society as a whole, increases with transaction efficiency. (11.26), (11.28), and (11.31) imply dθ dθ (11.32) , >0 dk A dk where θ ≡ nA/n. This implies that the number of traded goods produced in the urban area increases more than proportionally as improvements in transaction conditions enlarge the equilibrium network of division of labor, n. (11.28), (11.31), and (11.32) summarize the comparative statics of the general equilibrium network size of division of labor and the equilibrium location patterns of residences and transactions because of the correspondence between choices of residences and occupations. Since all endogenous variables are determined by n and θ, the comparative statics of the general equilibrium values of other endogenous variables can be worked out by using (11.28), (11.31), and (11.32). Differentiation of all corner equilibrium values of the endogenous variables in (11.19), together with (11.28), (11.31), and (11.32), yields the comparative statics of general equilibrium. (11.33)

nA/nB = MA/MB = θ/(1-θ) increases with transaction efficiency k rA = [1-(m-n+1)α]θM/mA increases with transaction efficiency k rA/rB = Bθ/A(1-θ) increases with transaction efficiency k n increases with transaction efficiency k nA = θn increases with transaction efficiency k RA/RB decreases with transaction efficiency k li (an individual’s level of specialization in producing the good sold) increases with transaction efficiency k u* (per capita real income) increases with transaction efficiency k

To identify the positive effect of k on u* in (11.33), we have used the envelope theorem to u* in (11.19). Adapting the analysis of chapter 7, we can also show that the following concurrent phenomena are different aspects of the evolution in division of labor driven by exogenous improvements in transaction conditions. The degree of diversity of economic structure (which is defined by the number of different occupations), the differences between different occupations, and the number of markets for different goods, all increase. The number of transactions for each individual, trade dependence (which is defined by the ratio of trade volume to real income), interdependence among individuals of different occupations, the extent of the market (which is defined by per capita aggregate demand for all traded goods), and the degree of commercialization (which is defined by the ratio of the income from the market to total real income), all increase. The extent of endogenous comparative advantage (which is defined as the difference in productivity between sellers and buyers of traded goods) increases. The degree of market integration (which is defined by the reciprocal of the number of separate communities) increases as more separate local communities merge into fewer, increasingly integrated larger communities. The number of separate communities is also the number of cities in this model. Production concentration (which is defined as the reciprocal of the number of

387

producers of each traded goods) increases as per capita real income and productivity of each good increase. Now we consider the location patterns of residences and transactions that are associated with the general equilibrium values of division of labor, n = 1 and n = 2, respectively. If transaction efficiency k is sufficiently low, the transaction costs caused by a large network size of division of labor outweigh the positive network effects of the division of labor generated by the fixed learning cost in each activity, so that the general equilibrium level of division of labor n = 1. This implies that each individual’s number of goods purchased is n -1 = 0, or autarky is chosen. According to proposition 11.2, all individuals’ residences are evenly located. Each individual self-provides m consumption goods, and no market or cities exist, as shown in Fig. 11.3(a). Only four of M selfsufficient consumer-producers are represented by four circles. Only four of m selfprovided goods are represented by four lines. As transaction efficiency k is slightly improved, the equilibrium value of n increases to 2. Each pair of individuals will establish a local business community in which each trader sells one good to and buys one good from the other. In order to save on transaction costs, according to proposition 11.1, two trade partners meet at the midpoint between their residences to exchange goods 1 and 2. In order to maximize utility with respect to consumption of land, all individuals will reside at vertices of the grid of triangles with equal sides, so that the equilibrium price of land is equal for each residence. Hence, many local markets emerge from the low level of division of labor, but there is no central marketplace or city. All transactions are evenly dispersed at M/2 places, as shown in panel (b) where there is no division between the urban and rural areas. Only four of m goods are represented by lines and only four of M individuals are represented by four circles in (b). As transaction efficiency is further improved such that n > 2, then the central marketplace generates economies of agglomeration, according to proposition 11.2. In the symmetric model, each individual needs only n-1 trade partners. In order to save on transaction costs, n individuals will form a local business community where each person sells her produce to, and buys one good from, each one of other n-1 individuals. The good that she sells is different from the one sold by each of the other n-1 members of the community. All of the n members of the local community go to the central marketplace to trade with each other. As shown in Fig. 11.2c, nA of the n individuals reside at the central marketplace which is a city, and nB of the n individuals reside in the countryside. Population size of each local community is then n, and the number of such local communities is thus M/n. The urban land size of each local community is An/M and the rural land size of each local community is Bn/M because of the assumption of fixed respective total sizes of urban and rural areas. In panel (c) M/n separate local business communities are represented by 4 medium squares and cities are denoted by small squares. All transactions in a community are executed at the city. The graph under (c) illustrates the network of transactions of all n urban and rural residents that are executed at the city when n = m = 4 and M = 16. (a) Autarky without market and cities

(b) Low level of division with market and without cities

388

(c) Division of labor with market and M/n=4 cities

(e) Very high level of division of labor (d) High level of division of labor with with an integrated market and a city, M/n=2 cities and 2 separate communities M/n = 1 Figure 11.3: Evolution of Division of Labor and Location Pattern of Residences and Transactions Panel (e) represents a general equilibrium with a very high level of division of labor (n=M), where there is an integrated market and a single city. Big arrows denote the direction of the evolution of division of labor and the location patterns of residences and transactions caused by improvements of transaction efficiency. Note that if m1 in the symmetric model. As division of labor evolves (i.e., n increases) due to improved transaction conditions, the number of separate local communities (which is also the number of cities) decreases, the area size of each community as well as its urban or rural area increases, the land price in the urban area increases absolutely as well as relatively to that in the rural area relative

389

per capita land consumption between the urban and rural areas declines. 3 The degree of concentration of residential location increases not only because the relative population size of urban and rural residents increases, but also because the average population size of cities and the population density of the urban area increase as division of labor evolves. In summary, we have Proposition 11.2: Improvements in transaction conditions will generate the following concurrent phenomena. The ratio of urban to rural land prices increases, the network of division of labor is enlarged, the number of traded goods for each individual as well as for society as a whole increases, the number of traded goods produced in the urban area increases absolutely as well as relatively to that in the rural area, the population ratio of urban to rural residents increases, each individual’s level of specialization increases, the number of markets increases, the diversity of economic structure increases, the number of transactions for each individual, trade dependence, and interdependence among individuals of different occupations all increase, the extent of the market and the extent of endogenous comparative advantage increase, the degree of market integration and production concentration increase, and per capita real income and productivity of each good increase.

A distinguishing feature of the type II economies of agglomeration in this model is that even if which nB out of n traded goods to be produced in the rural area is indeterminate in equilibrium, a high level of division of labor will make the concentration of urban residences and all transactions in the urban area emerge from ex ante identical individuals with identical production conditions of all goods. The assumption made by Yang and Rice (1994, see example 11.2) and Fujita and Krugman (1995, see example 11.1) that land intensive agricultural production must be dispersed in the rural area is not necessary for the existence of type II economies of agglomeration. Also, a variety of manufactured goods that is not land intensive may be produced in the rural area because of the trade off between economies of agglomeration and the high land prices in the city. This has a flavor of the theory of complexity: some phenomena that do not exist for each individual element of a system emerge from a complex structure of a collection of numerous identical individual elements. This is just like different DNA structures of the same molecules generating many species of animals. In this chapter, we have shown that one of the most important functions of the invisible hand (interactions between the self-interested behaviors) is to sort out simultaneously the efficient location patterns of transactions and individuals’ residences, the related network size of division of labor, and transaction efficiency. Our models predict that the potential for increases of land price in the large cities is determined by the potential for evolution of division of labor. As a large city becomes the central marketplace for an increasingly more integrated large network of division of labor, land prices in the city can go up to a degree far beyond what the marginal analysis of demand and supply may predict.

3

The result that the number of cities decreases as division of labor evolves can be changed either by endogenizing population size or by endogenizing the number of layers of city hierarchy, as discussed in section 11.5.

390

Baumgardner (1989) finds empirical evidence for the positive relationship between urbanization and individuals’ levels of specialization. Colwell and Munneke (1997) provide empirical evidence for the negative relationship between land price and distance from the city (and per capita consumption of land). Simon and Nardinelli (1996) find empirical evidence from a data set of English cities in 1861-1961 for a positive relationship between transaction conditions and city size, which is predicted by the Yang and Rice model and by the Sun and Yang model in this chapter. They have also found empirical evidence against the positive relationship between the size of firms and city size, which is predicted by the Krugman and Fujita model in this chapter. They argue that the evidence suggests that external economies, rather than internal economies of scale, are a driving force of urbanization. Here, their notion of external economies of scale, from Marshall (1890), should be interpreted as the positive network effects of division of labor, since their data set shows a positive relationship between the evolution of occupation diversity and urbanization. Also, their data set suggests a positive relationship between urbanization and evolution of the employment share of the transaction sector. More empirical works are needed for establishing the positive relationship between the land price differential of cities vs. rural areas, the degree of commercialization (level of division of labor), urbanization, and transaction efficiency. Y. Zhang (2000) has found empirical evidence that the relationship between the degree of urbanization and average size of firms in the urban areas. This rejects a positive correlation between the two variables which is referred to as the type III scale effect. The theory of indirect pricing in chapter 8, together with the Smithian models of urbanization in this chapter, imply that increases in urbanization and in the level of division of labor concur to a decrease in the average size of firms if division of labor evolves between firms as a result of improved trading efficiency of goods relative to that of labor. If division of labor evolves within firms, a type III scale effect may occur as a phenomenon based on the comparative statics of general equilibrium.

Key Terms and Review Conditions needed for cities to emerge from division of labor Relationship between urbanization, network size of division of labor, and transaction efficiency Relationship between the difference of land intensity in producing agricultural and industrial goods, and the function of urbanization in promoting division of labor General equilibrium mechanism that simultaneously determines network size of division of labor, location pattern of transactions, and transaction efficiency General equilibrium mechanism that simultaneously determines the network size of division of labor, the location pattern of individuals’ residences, and the land price differential between urban and rural areas Type I vs. type II economies of agglomeration Relationship between the potential for rises of urban land prices and evolution of division of labor

391

Role of free migration, free choice of occupation configuration, and free pricing in enabling the market to sort out simultaneously the efficient location pattern of transactions, the location pattern of individuals’ residences, the network size of division of labor, and transaction efficiency

Further Reading Classical theory of the city: Petty (1683), Thünen (1826), Wartenberg (1966); Division of labor and cities: Scott (1988), Marshall (1890, ch. 11), Smith (1776, chs. 2, 3), Petty (1683, pp. 471-2); Models of city and economies of scale: Ben-Akiva, de Palma, and Thisse (1989), Fujita, Krugman, and Venables (1999), Krugman (1991, 1993, 1994), Fujita and Krugman (1994, 1995), Tabuchi (1998), Fujita (1988, 1989), Fujita and Mori (1997), Fujita and Thisse (1996), Quigley (1998), Page (1999), Kendrick (1978); Hierarchical structure of cities: Yang and Hogbin (1990), Yang and Ng (1993, ch. 13), Fujita and Krugman (1994); Smithian models of cities and economies of specialization: Yang (1991), Yang and Rice (1994), Yang and Ng (1993, ch. 6), Sun and Yang (1998); Neoclassical models with constant returns to scale, transaction costs, cities: Kelley and Williamson (1984), Hahn (1971), Karman (1981), Kurz (1974), Mills and Hamilton (1984), Schweizer (1986), Henderson (1996); Urban biased development: Lipton (1977, 1984), Brown (1978), Sah and Stiglitz (1984), Sen (1977, 1981), Lin and Yang (1998); Economies of agglomeration, externality of cities, and size of cities: Abdel-Rahman (1988), Arnott (1979), Fujita (1989), Henderson (1974), Mills (1967), Kanemoto (1980); Dual economy: Murphy, Shleifer, and Vishny (1989a, b), Yang and Rice (1994); Land price of cities: Colwell and Munneke (1997); Empirical evidence: Simon and Nardinelli (1996), Baumgardner (1989), Y. Zhang (2000).

Questions 1. North (1981, pp.158-162) finds historical evidence for the following fact. “An urban world is a development that has occurred during the last hundred years and is associated not so much with the industrial city as with a dramatic decline in the costs of transportation, the increase in agricultural productivity, and the agglomerative benefits of central places for economic activity.” Use the model in this chapter to explain this historical fact. 2. Consider an extended version of the model in example 11.3. In the extended model, the equilibrium number of traded goods might be as large as 49. Consider the following hierarchical structures of cities. M consumer-producers are divided among M/49 local communities. In each of them, each person sells one good to and buys one good from each of the other 48 individuals. Each local community has one large central marketplace and 6 smaller central marketplaces. Each individual trades with her 6 neighboring trade partners through a small marketplace and goes to the large central marketplace to trade with the other 42 individuals. In other words, there is a hierarchical structure of cities. The large city is the central marketplace for the local community with 49 members, as well as the trade center for 7 individuals who reside near the large city. Each of the 6 small cities is a trade center among 7 individuals, similar to the one in Fig. 11.2(b). Another location pattern of transactions is that all 49 individuals go to the center of the community to trade with each other. The third pattern is that each pair of trade partners can trade at the middle point between them. The fourth

392

3.

4.

5.

6.

7.

pattern is similar to that in Fig. 11.2(b), that is, M individuals are divided as M/7 separate local communities. Discuss under what conditions each of the four patterns occurs at general equilibrium. Analyze the difference in trade volume between the large and small cities in the first pattern. Discuss the implications of a blend between the model in question 2 and the model in example 11.4 for an hierarchical structure of land prices between cities of different ranks. Use this model to predict the potential for increases of land prices in the large cities. Braudel (1984, Vol. II, chapter 2) provides historical evidence for the role of cities as the centers of transactions. Use the evidence in connection with your casual observation of the features of the cities you have seen in the real world to discuss the relevance of the models in this chapter. Analyze the role of free migration, free choice of occupation configuration, and free trade and pricing of land in enabling the market to sort out the efficient pattern of urbanization and the efficient geographical pattern of transactions. Baumgardner (1989) finds empirical evidence for the positive relationship between urbanization and individuals’ levels of specialization. Design a method to test the concurrent evolution of division of labor and the degree of urbanization against empirical observations. Find a way to test the theories developed in examples 11.2, 11.3, and 11.4 against empirical observations. Discuss the differences between the models in example 11.1 and in examples 11.2, 11.3, and 11.4. Simon and Nardinelli (1996) find empirical evidence, from a data set of English cities in 1861-1961, for a positive relationship between transaction conditions and city size, which is predicted by the Yang and Rice model and by the Sun and Yang model in this chapter. They and Y. Zhang (2000) have also found empirical evidence against the positive relationship between the size of firms and city size, which is predicted by the Krugman and Fujita model in this chapter. Find more empirical observations that can be used to test one against the other of the two types of models. Why does the Fujita-Krugman model predict a decline in the degree of urbanization as a result of improved transaction condition of manufactured goods? Fei and Ranis (1964) claim that agricultural development and a surplus of agricultural products are essential for industrialization and urbanization. But Jacobs (1969) claims that urbanization is a driving force of agricultural development rather than vice versa. She states (pp. 6-9), “If we wait for the emergence of agricultural surplus without cities, such surplus never take place. Industrialization and urbanization are the driving force of agricultural surplus rather than the surplus being the necessary condition for industrialization and urban development.” Use the concept of general equilibrium to comment on their views.

Exercises 1. Assume that in example 11.1., the agricultural good is the sole consumption good and all manufactured goods are employed to produce the agricultural good. Use the model to explain the structural changes caused by industrialization. Compare your explanation to the conventional theory of labor surplus and structural changes (Lewis, 1955, and Fei and Renis, 1964). 2. (Monchi Lio) Extend the model in example 11.2 to the case with three industrial goods and one agricultural good. Solve for general equilibrium and its inframarginal comparative statics. Show that a dual economy, featuring an asymmetric structure of division of labor (i.e., urban residents have a higher level of specialization than rural residents), may occur during the transitional period from a low level of balanced division of labor (urban and rural residents have the same level of specialization and productivity) to a high level of balanced division of labor.

393

3. (Yang and Rice, 1994) Assume that in the model in exercise 2, the production functions are same as in chapter 4. Solve for the general equilibrium and its inframarginal comparative statics. 4. Extend the model in example 11.3 to the case with the number of traded goods n∈[1, 49]. Analyze the possible equilibrium hierarchical location pattern of transactions, in which individuals trade with neighbors through a local marketplace, similar to that in Fig 11.2(b) with n = 7, and trade with non-neighbors through a larger central marketplace, which may emerge from a large network size of division of labor with n = 49. The central marketplace looks like a large city that channels more transactions than each smaller marketplace. Discuss the possible evolution of the number of layers of the hierarchical system of cities if the level of division of labor is allowed to be [1, m]. 5. Assume that in the model in example 11.4, total land area is a fixed constant, but land areas for urban and rural areas are endogenous variables. Solve for the comparative statics of the general equilibrium. Analyze the effects of the evolution of division of labor on the relative area of cities and countryside.

394

Chapter 12: Industrialization, Structural Changes, Economic Development, and Division of Labor in Roundabout Production

12.1. The Features of Industrialization The purpose of this chapter is twofold. First, we shall use the Smithian models to predict the emergence of new producer goods and related new technology from the evolution of division of labor. Second, a Smithian model of endogenous specialization and endogenous number of links in a roundabout production chain will be developed to investigate industrialization. From as far back as Smith (1776, p. 14, p. 105), Joseph Harris (1757), Josiah Tucker (1756, 1774), and Hegel (1821, p. 129), to Marshall (1890, p. 256) and Walker (1874, pp. 36-37), many economists have recognized that the emergence of new tools and machines, and the related invention of new technologies, are dependent on the development of division of labor. This classical mainstream view of invention and technology substantially differs from the neoclassical saving and technology fundamentalism. 1 According to the neoclassical view, innovation is a matter of investment in research and development (R&D), regardless of the levels of specialization for individuals and the level of division of labor for society (see chapter 15). In contrast, according to the classical mainstream, the invention of new machines and technology is a matter of the size of the network of division of labor and the related extent of the market. If the network of division of labor is not sufficiently developed, not only can new technology not be invented, but even if it were invented, it would be commercially nonviable. That is why the invention of paper, the compass, printing technology, and metallurgical technology by the Chinese in the 12th century could not generate industrialization, whereas the commercialization of these technologies through the development in division of labor in Europe promoted other inventions that led to the Industrial Revolution in 1750-1830 (Elvin, 1973). However, all Smithian models of endogenous specialization developed so far in the previous chapters cannot predict the emergence of new producer goods from the evolution in division of labor. In order to formalize the classical ideas about the emergence of new producer goods from the evolution in division of labor, we shall extend the model of endogenous number of consumption goods and endogenous specialization in example 7.2 to endogenize the number of producer goods. If we specify the CES production function in the model of endogenous specialization in chapter 2, the classical ideas about the intimate relationship 1

The relationship between inventions, the network size of division of labor, transaction conditions, and division of labor in inventing activities during the Industrial Revolution (1750-1830) is documented by Mokyr (1993, p. 26, p. 35), Rosenberg and Birdzell (1986, pp. 163-165), and Marshall (1890, p. 256). According to them, the development of international trade prior to the Industrial Revolution provided a sufficiently great extent of the market and the related network size of division of labor necessary for the emergence of new technology.

395

between invention of new technology, the size of the network of division of labor, and the institution of the firm can be formalized. According to Mokyr (1990, 1993), Huang (1991), Rosenberg and Birdzell (1986, pp. 145-84), North (1981), Macfarlane (1988), Baechler (1976), and Sachs (1998), the driving mechanism for the Industrial Revolution worked as follows. A variety of polity and rivalry between hostile sovereignties in the same culture in Europe encouraged many different institutional experiments. As a consequence of the great variety of institutional experimentation and internal and external political pluralism, a particular set of institutions emerged in Britain prior to the Industrial Revolution. 2 This set of institutions, featuring great adaptability and social learning capacity with institutional arrangements, significantly improved transaction conditions. Prior to and during the Industrial Revolution, extensive international trade, due to improved transportation conditions, stimulated evolution of division of labor. Constitutional monarchy and parliamentary democracy provided long-run political stability. Patent laws and evolving common laws secured property rights. Secured residual rights to firms reduced transaction costs in setting up firms and encouraged specialized entrepreneurial activities, and secured rights to intellectual properties directly improved transaction conditions for technology and encouraged specialized inventions of new technology. When patent laws were not enough to protect entrepreneurial ideas and rights to inventions, the institution of the firm was used to protect intellectual property rights via residual rights of the firm and trade secrets. As the sources cited in chapters 1 and 10 suggest, a stable, non-predatory tax system and the government’s laissez-faire policy encouraged business activities and the evolution of division of labor. . Free association (i.e., where setting up private firms need no approval or license from the government) improved transaction conditions for the evolution of the institution of the firm. Hence, endogenous and exogenous transaction costs for each transaction were significantly reduced, the level of division of labor in inventing and other activities increased, and new producer goods and related new technology emerged. We will use two Smith-Young models of endogenous specialization to formalize this mechanism for economic development and technical progress. The earliest theory of industrialization was proposed by Smith (1776) and Young (1928). Smith conjectured that a decrease of the income share of the agricultural sector is because of the relative difference in the benefits of specialization, compared to the seasonal adjustment cost caused by specialization between the industrial and agricultural sectors. An 2

According to Mokyr (1990, Part III, chapters 7-10), political pluralism in Europe also encouraged a variety of experiments with different education systems. The rivalry between the different education systems was a driving force of economic development too. The British education system was quite conducive to economic development in the early stage of the Industrial Revolution, when entrepreneurship and practical experience were much more important than basic sciences, but was outperformed by some continental education systems in the second wave of the Industrial Revolution, which required formal training in engineering and sciences. Industrial standardization in the continent and in the US also outperformed the nonstandardized British industrial system. 3 According to North ( 1968, 1981, p. 166), “Productivity increase as a result of declining transaction costs had been going on since at least 1600, when the Dutch flute (a specialized merchant cargo ship) was used in the Baltic trade and subsequently adopted on other routes. The declining transaction costs – a result of reduced piracy, increases in size of ships, growing trade, and reduced turnaround time – led to substantial productivity growth beginning 150 years (at least) before the Industrial Revolution; and they, more than technological change were responsible for productivity increases.”

396

extension of the conjecture implies that a decline in the income share of the agricultural sector occurs not because of a change in tastes, in income, or in exogenous technical conditions, but because the agricultural sector has a higher coordination cost of the division of labor compared to the benefits derived from the division of labor, and it can improve productivity only by importing an increasingly larger number of industrial goods. These goods are produced by a high level of division of labor in the manufacturing sector, where transaction costs are more likely to be outweighed by economies of division of labor. Young considered industrialization as a process that involves evolution of division of labor in the roundabout production process, which enlarges the market network and increases productivity. There are at least three other types of models of industrialization. The first is the model of labor surplus and dual economy (Lewis, 1955, Fei and Ranis, 1964). In the model of labor surplus, the expansion of the industrial sector is explained by labor surplus in the agricultural sector and exogenous technical progress or capital accumulation in the industrial sector. As exogenous technical progress takes place, or as investment is used to raise the capital-labor ratio in the industrial sector, marginal productivity of labor increases, so that demand for labor increases. Because of the existence of a labor surplus, increasing demand would not raise the wage rate and the cost of the expansion of the industrial sector. Hence, the industrial sector can be developed at a zero or low cost to the agricultural sector. Labor surplus in this model is caused by an ad hoc assumption that the price of labor is higher than the equilibrium level for some unspecified institutional reason. Since there is no trade off between exploitation of exogenous comparative advantage and transaction costs in the model of labor surplus, this model cannot explain productivity progress in the absence of disequilibrium in the labor market. As shown in chapter 3, if we abandon the neoclassical dichotomy between pure consumers and firms, it is possible to specify the trade off between the exploitation of exogenous comparative advantage and transaction costs in a model with constant returns to scale technology. The trade off can be used to explain economic development by transaction efficiency in the absence of disequilibrium in the labor market. The second type of theory of industrialization is called by Krugman (1995) “high development economics,” and was developed by Rosenstein-Rodan (1943), Nurkse (1952), Fleming (1955), and Hirschman (1958). Those authors did not use general equilibrium models to formalize their vague ideas. There are two ways to interpret their ideas. According to Krugman (1995), their ideas imply that economies of scale are important factor for industrialization. Krugman argues that the theory of labor surplus was more popular than high development economics because the former was easier to formulate in the context of the model with constant returns to scale, while economists did not know the right way to formalize the latter idea using the general equilibrium model with economies of scale. Hence, the models of monopolistic competition in chapter 5 provide technical vehicles for substantiating high development economics and the theory of industrialization. However, most high development economists did not mention economies of scale. They talk about interdependencies of profitability in different industrial sectors, balanced vs. unbalanced industrialization, circular causation in the industrialization process, and pecuniary external economies of the industrial linkage network. All these notions are not difficult to formalize in a general equilibrium model. Circular causation is, of course, a

397

notion of general equilibrium. In a standard neoclassical general equilibrium model, each individual’s decision in choosing her quantities demanded and supplied is dependent on prices, while general equilibrium prices are determined by all individuals’ decisions in choosing their quantities. This circular causation implies that all interdependent endogenous variables must be simultaneously determined by a general equilibrium mechanism (or a fixed point). Comparative statics of general equilibrium is a powerful technical vehicle to substantiate the mechanism. Hence, high development economics relates to the notion of general equilibrium. When economists were unfamiliar with the technical substance of general equilibrium models, they could only use vague words to address general equilibrium phenomena, such as circular causation, interdependent decisions in different industries, pecuniary externality of industrial linkage (external economies that can be exploited via the market price system), and so on. (See questions 7-9 in chapter 5 and questions 16-17 in this chapter for more detail of high development economics.) However, there are three types of general equilibrium models. In a neoclassical general equilibrium model with constant returns to scale, circular causation is between quantities and prices and between individuals’ decisions in different sectors. In a general equilibrium model with economies of scale and endogenous number of goods in chapter 5, circular causation is among quantities, prices, productivity, per capita real income, and the number of goods, in addition to interdependencies among different markets and different individuals’ decisions. In a Smithian general equilibrium model in chapters 4, 6, and 7, there are interdependencies of the network size of division of labor, the extent of the market, productivity, trade dependence, the diversity of economics structure, the number of goods, the degree of market integration, and the degree of endogenous comparative advantage, in addition to interdependencies among quantities, prices, different individuals’ decisions, and different markets. It seems to us that high development economists’ discussion about pecuniary externality based on the industrial linkage network, circular causation, and balanced vs. unbalanced industrialization relates more closely to the positive network effect of division of labor in a long roundabout production chain than to economies of scale. The essence of Rosenstein-Rodan’s idea (1943) about big push industrialization is to advocate for state-led industrialization because of coordination failure in exploiting the network effects of division of labor in a decentralized market. Hirschman’s idea (1958) about the pecuniary externality of industrial linkages relates more or less to market-led industrialization, since the network effects of division of labor are pecuniary (which can be exploited by the price system). The term “balanced vs. unbalanced industrialization” may be misleading. Unbalanced industrialization strategy may be associated with specialization of a country in a particular sector and with the international division of labor between countries. Hence, from a view of the world market, such a strategy is a balanced industrialization strategy, although it is not balanced within a single country (Sheahan, 1958). High development economics and the related theory of industrialization have been formalized by general equilibrium models with economies of scale in chapter 5. Recently, Smith and Young’s theory of industrialization was formalized by Shi and Yang (1995) and Sun and Lio (1997). The Smith-Young model of industrialization and endogenous specialization can be used to formalize high development economics, too.

398

In this chapter, we use a Smith-Young general equilibrium model to predict a very important phenomenon of industrialization noted by Young (1928), that is, an increase in roundaboutness of production. The models of economies of scale in chapter 5 can predict concurrent increases in productivity, in the number of goods, and in the output share of the industrial sector. They cannot, however, predict concurrent evolution in individuals’ levels of specialization, in productivity, and in the number of links of a roundabout production chain. The number of links was called by Young “roundaboutness.” Industrialization is characterized by the following concurrent phenomena. Division of labor evolves and each individual’s level of specialization increases, the degrees of commercialization and trade dependence rise, new producer goods and related new technology emerge from evolution in division of labor, the degree of diversity of economic structure, the extent of endogenous comparative advantage, the degree of market integration, and the degree of production concentration all go up, and the institution of the firm and the labor market emerge and develop as division of labor evolves. 4 More importantly, the number of links in a long roundabout production chain increases and some new links of the industrial structure emerge from the evolution in division of labor. A comparison between a less developed economy and a modern developed economy illustrates the point convincingly. In an ordinary American farm, the farmer may use sophisticate tractors and other equipment to work the land and use various trucks to move things. All such machines are produced through a very long roundabout production process. However, in a Chinese peasant family with a plot of land, shoulder poles are used to move things and hoes are used to work the land. These simple tools are produced through a very short production chain. Of course, the long roundabout production chain in the US cannot be supported by a very low level of division of labor. Rather, it is supported by a large network of division of labor, which is in turn based on very high transaction efficiency provided by a good legal system that protects individuals’ property rights, good infrastracture of transportation, banking, and other transaction-related facilities, and moral code and cultural traditions related to specification and enforcement of contracts. The low degree of production roundaboutness in China is associated with a very low degree of commercialization. This degree in rural China was 0.3 before 1978, that is, a typical rural Chinese produced 70% of what she consumed (Yang, Wang, and Wills, 1992). As we have learned from the previous chapters, the low degree of commercialization corresponds to a low level of division of labor that is in turn associated with a low transaction efficiency caused by a legal system that allows the government to arbitrarily infringe upon individuals’ private properties, a deficient banking system due to government monopoly in the financial market, and underdeveloped transportation infrastructure. Hence, a general equilibrium model that describes industrialization must be able, at the minimum, to predict the following concurrent phenomena. Individuals’ levels of specialization increase, the number of links in a roundabout production chain increases, 4

Mokyr (1993, pp. 65-66) documents the evolution of division of labor during the Industrial Revolution. This evolution is sometimes referred to as “industrious revolution,” which implies that self-provided home production is replaced with commercialized production and a network of artisans, with a low level of division of labor and low degree of roundaboutness replaced with a large network of firms based on a high level of division of labor and great degree of roundaboutness.

399

the number of producer goods in each of the links increases, productivity and per capita real income increase, the market network expands, and the institution of the firm emerges and develops as transaction conditions are improved. Let us first tell the story behind the formal model in this chapter. In the story, there are many ex ante identical consumer-producers. Each of them could produce 4 types of goods: food, hoes, tractors, and machine tools. Labor is essential in producing machine tools. Labor and machine tools are essential for the production of tractors. Labor is essential for the production of hoes. Each individual can either use labor, or hoes and labor, or tractors and labor, or both hoes and tractors together with labor, to produce food. But if a tractor is used, part of the labor must be allocated to the production of machine tools. There are economies of complementarity between tractors and hoes in raising productivity of food. There are economies of specialization in producing each good. Trade will incur transaction costs. If hoes and tractors are not produced, there is only one link in production: labor is employed to produce food. If tractors are not produced, there are only two links in production: the production of hoes and the production of food. There is only one producer good in the upstream link. If tractors and hoes are produced, then machine tools, which are essential for the production of tractors, must be produced too. There are three links of roundabout production: the production of machine tools, the production of tractors and hoes, and the production of food, employing tractors and hoes. There are two producer goods in the middle link of the roundabout production process. There are three types of economies of roundaboutness. The total factor productivity of the downstream goods increases with the quantities of upstream goods employed in producing the downstream goods (type A economies of roundabout production); the total factor productivity of the downstream goods increases with the number of upstream goods (type B economies of roundabout production); the total factor productivity of the final goods increases with the number of links of the roundabout production chain (type C economies of roundabout production). Suppose that there exist all three types of economies of roundabout production in the Smithian model. Hence, the total factor productivity of food is the highest when all producer goods (hoes, tractors, and machine tools) are produced and is the lowest when none of them is produced. However, there is a trade off between economies of roundabout production and economies of specialization, since each individual’s level of specialization would be very low if she produced many goods. If she wants to keep her level of specialization and the degree of roundaboutness high at the same time, then she must trade with others, so that there are trade offs between economies of specialization, economies of roundabout production, and transaction costs. Suppose transaction efficiency is very low, then economies of specialization are outweighed by transaction costs, so that individuals have to choose autarky where the scope for trading off economies of specialization against economies of roundabout production is very narrow. Hence, only a few goods that directly relate to final consumption are produced in autarky. For instance, individuals may produce food with labor alone. As transaction efficiency is slightly improved, individuals can choose a larger network of division of labor, so that the scope for trading off economies of specialization against economies of roundabout production is enlarged. Therefore, the degree of roundaboutness and all individuals’ levels of specialization can increase side by

400

side through the division of labor between different specialists. For instance, the general equilibrium jumps from autarky with no producer goods to the division of labor between specialist manufacturers of hoes and professional farmers. As transaction efficiency is further improved, horizontal division of labor between the production of hoes and the production of tractors creates more scope for the vertical division of labor between the production of tractors and the production of machine tools, so that the number of links in roundabout production is further increased from 2 to 3. In this process, not only does a new link emerge from evolution in industrial structure, but also the number of producer goods in the existing upstream link increases. In other words, a higher transaction efficiency increases society’s capacity to acquire knowledge in different professions through increasing the size of the network of division of labor and the related extent of the market. The network effects cause new producer goods and related new technology to become commercially viable. The story of the invention of the steam engine by Boulton and Watt verifies our conjecture. Marshall (1890, p. 256) attributed this invention to a deep division of labor in inventing activities, which was induced by patent laws that improved transaction efficiency of intellectual properties. If transaction efficiency for labor is higher than that for producer goods, then the evolution in division of labor will be associated with the emergence and development of the institution of the firm. Hence, improvements in transaction efficiency will generate the concurrent phenomena that are associated with industrialization and raise the income share of the roundabout production sector (sometimes called the heavy industry sector). In sections 12.2-12.4, we first use a model of endogenous specialization and endogenous number of links of the roundabout production chain to formalize Smith and Young’s theory of industrialization. We then use a more general model to investigate the relationship between economic development, industrialization, structural changes, and the evolution of the number of producer goods in section 12.5.

Questions to Ask Yourself when Reading this Chapter What is the driving mechanism of industrialization that is characterized by the concurrent evolution of division of labor, of production roundaboutness, of the institution of the firm, of the income share of the industrial sector, and of the income share of the roundabout production sectors? What are the implications of private residual rights to the firm for the evolution of production roundaboutness? What are the implications of free pricing, free enterprise, and free choice between occupation configurations for the evolution of division of labor in roundabout production?

12.2. Industrialization and Evolution of Division of Labor in Roundabout Production Example 12.1: A Smith-Young model of industrialization. Consider an economy with a continuum of ex ante identical consumer-producers of mass M. Each consumer-producer’s ex ante utility function is

401

(12.1) u = z + kzd where z is the self-provided quantity of food, zd is the amount of food purchased, and k is transaction efficiency. The ex ante production function of food is 1 1 z p ≡ z + zs = M ax{lz − α , (y + ky d ) 3 (lz − α ), (x + kx d ) 3 (lz − α ) (12.2) 1 1 (y + ky d ) 3 (x + kx d ) 3 (lz − α )} where zp is the output level of food, zs is the amount of food sold, lz is the amount of time allocated to the production of food, y is the amount of hoes self-provided, yd is the amount of hoes purchased, x is the amount of tractors self-provided, xd is the amount of tractors purchased, k is transaction efficiency, and α is the fixed learning cost in each activity. The specification of the production function for food implies that there are four ways to produce food: using only labor, using hoes together with labor, using tractors together with labor, or using both hoes and tractors together with labor. 1 It is not difficult to see that if y + ky d > 1, then (y + ky d ) 3 (lz − α ) > lz − α , which implies that it is more productive if hoes are employed than if they are not, even if the input level of labor is the same for the two cases. This means that there are type C economies of roundabout production of food. If we compare the total factor productivities of food for the two ways of production, we can also see that for x+kxd > 1, total factor productivity is higher when hoes are employed. Similarly, it can be shown that the total factor productivity of food is higher when tractors are employed than when they are not, because 1 1 1 (y + ky d ) 3 (x + kx d ) 3 (lz − α ) > (y + ky d ) 3 (lz − α ) . This means that there are type B economies of roundabout production of food. It can also be shown that the total factor productivity of food increases with the amount of tractors or hoes employed, that is, there are type A economies of roundabout production. The ex ante production function for hoes is (12.3) y p ≡ y + y s = Max{l y − α ,0} where yp is the output level of hoes, ys is the amount sold, ly is the amount of time allocated to the production of hoes, and α is the fixed learning cost in producing hoes. The ex ante production function of tractors is 1 x p ≡ x + x s = Max{( w + kw d ) 2 (l x − α ), 0} (12.4) where xp is the output level of tractors, xs is the amount sold, lx is the amount of time allocated to the production of tractors, w is the amount of machine tools self-provided, wd is the amount of machine tools purchased, and α is the fixed learning cost in producing tractors. The ex ante production function of machine tools is (12.5) w p ≡ w + w s = Max{l w − α , 0} where wp is the output level of tractors, ws is the amount sold, lw is the amount of time allocated to the production of machine tools. The ex ante endowment of non-leisure time is (12.6) l x + l y + l z + l w = 24

li can be considered as an individual’s level of specialization in producing good i. It is not difficult to verify that the total factor productivity of food or tractors increases with an individual’s level of specialization in producing the good, and that labor productivity of hoes or machine tools increases with an individual’s level of specialization in producing the good. Hence, there are economies of specialization in producing each good. We draw

402

the distinction between emergence of a new industry and emergence of a new sector. A new industry which might comprise several sectors emerges as a new link in the roundabout production chain emerges. A new sector producing a certain type of goods emerges if the number of goods at a certain link of the roundabout production chain increases. Hence, a new industry emerges from an increase in the number of links of the roundabout production chain and a new sector emerges from an increase in the number of producer goods at a particular link of the roundabout production chain. Here, a link is defined as the input-output relationship between an upstream and a downstream industry. The number of links is defined as the degree of production roundaboutness.

12.3. Corner Equilibria and the Emergence of New Industry

You are now familiar with inframarginal analysis. Hence, we need not repeat the technical detail of the two-step approach of the inframarginal analysis, but shall just define various structures, listed in Fig. 12.1, and summarize all corner equilibria in Table 12.1. There are 12 structures that we have to consider. Four of them are autarky structures. A(z) represents an autarky structure where only labor is employed to produce food and all producer goods are not produced. A(zy) represents an autarky structure where hoes are employed to produce food. A(zxw) represents an autarky structure where machine tools are employed to produce tractors which are employed to produce food. A(zxyw) is an autarky structure where all three intermediate goods are employed to produce food. All four autarky structures except structure A(zxw) are shown in Fig. 12.1. Structure C comprises a configuration producing only food and a configuration producing only hoes. Each individual is completely specialized, but the number of producer goods in upstream industry is small and the number of links in roundabout production is 2. Tractors and machine tools are not produced. In structure D, all producer goods, hoes, tractors, and machine tools are produced. This structure comprises a configuration producing both food and hoes and a configuration producing both tractors and machine tools. Each individual produces two goods and has an intermediate level of specialization, but the degree of production roundaboutness and the variety of producer goods at the middle link of the roundabout production are great.

403

Autarky

Structure C

Structure E

A(zyxw)

Structure D

Structure F

Structure G

Figure 12.1: Various Industrial Structures

Structure E comprises three configurations. A professional farmer buys hoes and tractors and sells food. A completely specialized manufacturer of hoes sells hoes and buys food. The third configuration is not completely specialized. It produces both tractors and machine tools, sells tractors, and buys food. Structure F is symmetric with structure E. The producers of tractors and machine tools are completely specialized, but the third non-specialized configuration produces both hoes and food. Structure G is a structure with the complete division of labor, which implies not only that all individuals are completely specialized, but also that the degree of production roundaboutness and the number of producer goods at each link are greatest. There are four completely specialized configurations. Each of them sells its produce. Each of the professional manufacturers of hoes, tractors, and machine tools buys food, each professional farmer buys hoes and tractors, and each professional manufacturer of tractors also buys machine tools. All of the structures are shown in Fig. 12.1, where configurations are defined by letters in the brackets): the letter before a slash denotes the good sold, and the letter after a slash denote those goods purchased. For instance, configuration (x/z) denotes that an individual produces both tractors and machine tools, sells tractors, x, and buys food, z; (z/xy) denotes a professional farmer selling food and buying tractors and hoes.

Table 12.1: Corner Equilibria

404

Structure Relative prices A(z) A(zy) A(zxw) A(zxyw) py/pz = (1/3)22/3 C [(24-α)/k]1/3/3 px/pz = D 3[(24-2α)/k]1/3/28/3 E F G

px/pz = 22/3(24-α)1/3/3 py/pz = pw/pz = (2k)0.5(24-α)5/6/3

Number of specialists

My/Mz = [(24-α)pz/py3]3/2 Mx/Mz = [k(12-α)]0.5(3pz/2px)3/2

Per capita real income 24-α 3[(24-2α)/4]4/3 3[(24-3α)/9]4/324/3 3[(24-4α)/11]11/625/3 (24-α)4/3(2k)2/3/3 (24-2α)11/6k2/3/(31/325/3) [k(24-α)]4/3 [(24-2α)/27]0.521/3 (24-α)11/6k5/6/27/3??

Mx/Mz = 2k(pz/px)3(24-α)pw/27py My/Mz = pz3[(24-α)k/py]2/(27px) Mw/Mx = [(24-α)k/4] (px/pw)3

(24-α)11/620.5 k3/2/3

There are more structures that are not listed in Fig. 12.2. Structure H comprises a nonprofessional configuration that produces both food and tractors, sells food, and buys machine tools, and a professional configuration selling machine tools and buying food. In this structure, hoes are not produced. In structure I, which is symmetric with H, a professional farmer produces food, a non-professional manufacturer produces both tractors and machine tools, and hoes are not produced. Structure J is the same as structure G except that hoes are not produced. If trade of intermediate goods is replaced with trade of labor, there are more structures with the institution of the firm. Some of them are shown in Fig. 12.2. The corner equilibria in major structures are summarized in Table 12.1. From comparisons of per capita real incomes across structures, we can show that the set of candidates for the general equilibrium structure comprises A(z), A(zy), A(zxyw), C, D, G. Each of the other structures generates lower per capita real income than at least one of the above structures. Three methods are used to exclude these structures. If we compare per capita real income in a structure with those in two other similar structures, we can obtain two critical values of k. When the two structures to compare are appropriately chosen, the initial structure generates a higher per capita real income than both of the others only if k is between the two critical values. For instance, structure F generates a higher per capita real income than structure D if and only if k > k', and structure F generates a higher per capita real income than structure G if and only if k < k". This implies that structure F is a candidate for the general equilibrium structure only if k ∈ (k', k"). Here, the critical values k', k" can be obtained by comparing per capital real incomes in the three structures that are given in Table 19.1. They are dependent on α. But a comparison between k" and k' indicates that k' > k", that is, the interval of (k', k") is empty. This implies that structure F generates a lower per capita real income than either

405

structure D or structure G, or the per capita real income in F cannot be greater than that in structure D and G at the same time. According to the Yao theorem, this implies that the corner equilibrium in structure F cannot be a general equilibrium. The second method that we have used is to compare the critical values of k with 1. Since k cannot be larger than 1, if a critical value of k that makes a structure at least as good as another structure is greater than 1, then the former cannot be a candidate for the equilibrium structure. For instance, the per capita real income in structure G is greater than in structure C if and only if k > k"'. But it can be shown that k"' > 1 if and only if α is smaller than a constant. Hence, we can conclude that structure G cannot be a candidate for the general equilibrium structure if α is greater than that constant. The third method that we have used is to identify the condition for per capita real income in each structure to be non-positive. It is obvious from Table 19.1 that if α is greater than a certain value, per capita real income in a particular structure is non-positive. Repeatedly using the three methods, we can exclude structures A(zxw), E, F, H, I, and J from the set of candidates for the general equilibrium structure. The results, of course, relate to some of our specific assumptions. For instance, we assume that each individual has 24 units of time available for production and that the elasticity parameters of outputs with respect to input levels of intermediate goods are specific numbers. In addition, we have assumed the Cobb-Douglas production function and that the fixed learning cost and transaction efficiency are the same for all goods. If we relax these assumptions, then each of the structures that we have outlined could be a general equilibrium structure within a certain parameter subspace. Shi and Yang (1995) have examined the effects of relaxing some of the assumptions. For example, they have assumed the CES production function with an elasticity of substitution that might not be 1. They have also assumed that the elasticity of output with respect to input is a parameter rather than a number. They have shown that within a certain parameter subspace, each of the structures could be a general equilibrium structure. 12.4. General Equilibrium, Industrialization, and Structural Changes

Comparisons of per capita real incomes across structures, together with the Yao theorem, yield the general equilibrium and its inframarginal comparative statics, summarized in Table 12.2. In order to compare topological properties between different structures, we define the level of division of labor of an economy by three measures: each individual’s level of specialization, the number of links in the roundabout production chain, and the number of goods at each link of the chain in a structure. According to this definition, structure C, in which each individual is completely specialized, the number of goods is 2, and the number of links is 2, has roughly the same level of division of labor as structure D, in which each individual has a lower level of specialization than in C, but the number of goods is 4 and the number of links of the roundabout production chain is 3. We now read the results in Table 12.2 in connection with the graphs in Fig. 12.2. There are 5 patterns of evolution in division of labor. Let us look the case with α∈(0, 0.92). Within this interval of parameter values, if transaction efficiency is sufficiently low, autarky structure A(zxyw) is the general equilibrium, where each individual self-provides all four goods and productivity and per capita real income are very low. Table 12.2: Emergence of New Industry and Evolution in Division of Labor

406

α K Structure

α k Structure

∈ (0, 0.92) < k1 ∈(k1, k2) > k2 A(zxyw) D G

∈ (3.57, 7.8) < k4 ∈(k4, k2) A(z) D

where k1 ≡ 3225[(12-2α)/11(12-α)]11/4, k3 ≡ 9(24-2α)-3/42-1.5, k5 ≡ 31.5/[2(24-2α)0.5],

∈ (0.92, 3.57) < k3 ∈(k3, k2) A(zy) D

∈ (7.8, 23.5) < k5 > k5 A(z) C

> k2 G

> k2 G

(23.5, 24) < k6 > k 6 A(z) G

k2 ≡ (34/27)0.2[(24-2α)/(24-α)]11/5, k4 ≡ 22.5 3.0.5(24-α)1.5/(24-2α)11/4, k6 ≡ 32/3/[21/3(24-α)5/9].

As transaction efficiency is improved to be greater than k1, the general equilibrium jumps to structure D, where some individuals produce both food and hoes and others produce both tractors and machine tools. The number of goods produced by each individual is reduced from 4 to 2, so that each individual’s level of specialization rises. As transaction efficiency is further improved to be greater than k2, the general equilibrium jumps to the complete division of labor, where each individual is completely specialized. For this pattern of evolution in division of labor, each individual’s level of specialization evolves in the absence of evolution in the degree of production roundaboutness and in the variety of producer goods at each link. This is because the fixed learning cost α is very small, so that economies of specialization are not significant. Thus, the tension between economies of specialization and economies of roundaboutness is not sufficiently great to induce evolution in production roundaboutness. As the fixed learning cost and, accordingly, economies of specialization increase, the correspondingly greater tension between economies of specialization and economies of roundaboutness will generate concurrent evolution both in individuals’ levels of specialization and in production roundaboutness. Suppose α∈(0.92, 3.57). If transaction efficiency is sufficiently low, autarky structure A(zy) is the general equilibrium structure, where each individual self-provides food and hoes, each individual’s level of specialization is not high, only two goods are produced, the number of links of roundabout production is 2, and the number of producer goods at the upstream industry is 1. Also, productivity and per capita real income are low and no market exists in autarky. As transaction efficiency is improved, the general equilibrium jumps to structure D, where a new link and two new producer goods emerge, although each individual’s level of specialization remains unchanged. Productivity and per capita real income are higher than in A(zy), because more economies of roundabout production are exploited. As transaction efficiency is further improved, the general equilibrium jumps to structure G, where each individual’s level of specialization is increased so that productivity, per capita real income, and number of transactions are increased. This pattern of evolution in division of labor generates all concurrent phenomena that are associated with industrialization except evolution of the institution of the firm. Individuals’ levels of specialization increase, the number of links in the roundabout production chain increases, the number of producer goods in each of the links increases, productivity and per capita real income increase, the size of the market network expands, the degree of market integration and production concentration increases, and the extent of endogenous comparative advantage 407

rises. New ex post production functions and related new technology and new industries emerge from this process. This endogenous technical progress differs from the exogenous technical progress in the theory of labor surplus and dual economy. Suppose the fixed learning cost is greater, so that α∈(3.57, 7.8). Then only one good will be produced in autarky because of a greater tension between economies of specialization and economies of roundaboutness. If transaction efficiency is extremely low, then the general equilibrium is structure A(z) where no producer goods are produced. As transaction efficiency is improved, the general equilibrium jumps to structure D, where a new link and two producer goods emerge despite a decline of each individual’s level of specialization. As transaction efficiency is further improved, the general equilibrium jumps to structure G with the complete division of labor, generating evolution in each person’s level of specialization again. In this pattern of the evolution of division of labor, each individual’s level of specialization experiences non-monotonic changes. It declines first and then increases. But the degree of production roundaboutness and the level of division of labor (involving each person’s level of specialization, the degree of production roundaboutness, and variety of goods at each link) rises with the evolution of industrial structure. Suppose α∈(7.8, 23.5), the degree of production roundaboutness increases as transaction efficiency is sufficiently improved, so that the general equilibrium jumps from structure A(z) to structure C. However, structure G with the complete division of labor cannot be the general equilibrium. You may see that if the elasticity of output of tractors with respect to input of machine tools is much larger than 1/3, then the general equilibrium will jump from structure C to structure G as transaction efficiency k tends to 1. Suppose α∈(23.5, 24), each individual’s level of specialization remains unchanged. and the degree of production roundaboutness and variety of producer goods at the middle link increase concurrently as transaction efficiency is sufficiently improved, so that the general equilibrium jumps from structure A(z) to structure G with the complete division of labor. If the number of possible goods is much larger than 4, then the story about industrialization will be much richer, so that the concurrent evolution of the three aspects of the division of labor — individuals’ levels of specialization, the number of links of the roundabout production chain, and the number of goods at each link of the chain — will be easier to see. 12.4.1. Changes in the Employment Shares of the Industrial and Agricultural Sectors From Tables 12.1 and 12.2, we can see that as transaction efficiency is improved and the general equilibrium jumps from autarky to the division of labor, for example structure C or D, the number of professional farmers in the structure with division of labor is smaller than the number of individuals who self-provide food. This implies, on the one hand, that the number of individuals in the agricultural sector declines compared to the number of individuals in the industrial sector, and on the other hand, that the income share of industrial goods rises due to both the increase in the number of producer goods and the evolution in division of labor. The structural changes caused by the concurrent evolution in division of labor and in production roundaboutness can be verified by empirical data. The input and output tables of the US (Department of Commerce, 1975) indicate that the income share of the sector producing intermediate goods increases and the income share of the sector producing consumption goods declines over time.

408

Shi and Yang (1995, see Yang and Ng, 1993, chapter 12) extend the model in this section to the case with good v that is essential for the production of good y. They assume that goods y and v are intermediate goods or services (such as planting and harvesting) in the agricultural sector and that the transaction efficiency coefficients for the two goods are much smaller than that for goods x and w in the industrial sector. Then they show that as transaction efficiency is improved, division of labor will evolve only in the industrial sector, so that the income share of the industrial sector rises and the agricultural sector is increasingly dependent on importing the benefit of division of labor from the industrial sector. This substantiates Smith’s conjecture that the increase in the income share of the industrial sector is due to relatively more significant economies of specialization compared to coordination costs in the industrial sector than in the agricultural sector. This approach to explaining structural changes, which are different aspects of evolution in division of labor, substantially differs from that of Kuznets and Chenery. Kuznets (1966) explained structural changes by an increase in income and by exogenous changes in preferences or in technology. However, structural changes can take place in the Smithian model in the absence of exogenous changes in parameters of the production and utility functions. Explaining structural changes by changes in incomes is certainly not a general equilibrium view. In a general equilibrium model, per capita real income is endogenous. It should be explained either by parameters in static models (comparative statics of general equilibrium), or by a spontaneous mechanism in dynamic models. For instance, per capital real income in the model in this section is determined by the level of division of labor, which is in turn determined by transaction efficiency. Again, we can see that productivity progress in the Smithian model is generated by evolution in division of labor in the absence of changes in ex ante production functions. Hence, it can be considered as endogenous technical progress caused by institutional changes or urbanization that affect transaction efficiency. But the distinguishing feature of endogenous technical progress in the Smithian model in this chapter is that it is associated with the emergence of new industries and evolution in production roundaboutness. The model in this section formalizes Schumpeter’s idea about creative destruction. From Fig. 12.1 and Table 12.2, we can see that for α∈(0.92, 3.57) as transaction conditions are improved, the general equilibrium evolves from autarky to structure D, followed by structure G. In this process, some occupation configuration with a low level of division of labor, such as configurations (x/z) and (z/x) in structure D, disappears, replaced by new occupation configurations with higher levels of specialization, such as configurations (z/xy), (x/wz), (y/z) and (w/z) in structure G. Also, configurations producing new goods may emerge from creative destruction. Yang and Ng (1993, p. 313) have shown that this model can be extended to predict the disappearance of some goods which have low transaction efficiency and insignificant economies of specialization in production as new goods emerge from the evolution of division of labor and the roundabout production chain. This creative destruction differs from Aghion and Howitt’s (1992) model of creative destruction, which does not explore the connection between the disappearance of old goods or the emergence of new goods, and the evolution of individuals’ levels of specialization. The policy implications of the model enable us to identify fatal flaws in various industrial policies. The Smithian model shows that one of the functions of the market is to sort out the efficient industrial structure and pattern of its evolution. If the model is

409

asymmetric and has many possible goods and possible links, then it is impossible for any policy maker to figure out what is the efficient industrial structure. However, the invisible hand (interactions between self-interested decisions) can do so. Some historical examples may illustrate this point. In China prior to the 19th century, policy makers in the government and intellectuals advocated an industrial policy “promoting the agricultural sector and suppressing commerce.” This industrial policy precluded ancient China from industrialization, before Britain was industrialized under a laissez-faire regime. The Japanese government had an industrial policy in the 1950s that restricted the development of the automobile industry. In the Japanese government’s judgement, Japan had no comparative advantage in manufacturing automobiles. But under a private rights and free enterprise system, it is the owners of private firms, rather than the government, that have the ultimate right to choose the industrial pattern. Hence, the industrial policy of the Japanese government was rejected by the market. From many such cases, we can see that it is those countries that have many complicated industrial policies that promote or protect some industries and ignore or suppress others that have shown poor performance in economic development. Shi and Yang have also shown that if the production function of food is of the CES type and its parameters are not fixed numbers, then structure F may be the general equilibrium in the transitional period as the economy evolves from autarky to the complete division of labor. Structure F is a dual structure (see Fig. 12.1), in which producers of tractors and machine tools are completely specialized, while producers of food and hoes are not completely specialized. Hence, a professional producer of machine tools or a professional producer of tractors has a higher productivity and a higher level of commercializedincome than an individual self-providing hoes and selling food. This is referred to as a dual structure. The natural dual structure in a free market will generate equal per capita real income between the industrial and agricultural sectors despite unequal commercialized incomes. It emerges in the transitional period from a low level of division of labor to a high level of division of labor, and disappears as the complete division of labor has been reached. If more goods are introduced into the model, the number of corner equilibria will increase more than proportionally. Many of these cannot be solved analytically. Hence, the inframarginal comparative statics of general equilibrium can be obtained only through numerical simulation on the computer. The complexity of calculation and variety of possible patterns of evolution of industrial structure imply that it is impossible for a central planning system to simulate what is going on in the market, and that the market is much more powerful than any one decision maker in sorting out the complex task of determining the efficient industrial structure. 12.4.2. The Number of Possible Structures of Transactions Increases More Than Proportionally as Division of Labor Evolves in Roundabout Production As division of labor evolves in roundabout production, the possibilities for replacing trade in intermediate goods with trade in labor imply that the number of structures with firms increases more than proportionally. In particular, considering structures with different specialist-producers being employers of firms, this point is even easier to see.

410

Structure G1

Structure G1a

Structure G2

Firms

firms

a firm

firms

Employees Structure G3 Structure G4

self-employed

Employees Structure G5

Figure 12.2: Structures with Firms

Let us look at Fig. 12.2, where possible structures with firms based on the complete division of labor (structure G) are drawn. In each of these structures, there are four types of specialist producers of food (z), hoes (y), tractors (x), and machine tools (w). G1 represents a structure in which a specialist producer of food hires specialist producers of hoes and tractors, and buys machine tools from and sells food to independent specialist-producers of machine tools. The rectangles with thick borders denote firms, circles denote employees, and the rectangles with thin borders denote independent specialist producers (or self-employed). Structure G1a has the same structure of division of labor and transactions as structure G1, but has a different ownership structure of the firm. In structure G1a, it is the specialist producer of tractors instead of the specialist producer of food that owns the firm. There is another variant of structure G1 where the specialist producer of hoes is the owner of the firm. The other graphs in Fig. 12.2 represent other different structures of the firm based on the same structure of division of labor as in structure G. For each of them, there are more 411

variants with the same structure of transactions, but with different ownership structures of the firm. In fact, on the basis of the structure of division of labor in G, there are at least 13 different structures of transactions and ownership of the firm. It is not difficult to see that the number of possible structures of transactions and ownership of the firm increases more than proportionally as the level of division of labor evolves in the roundabout production chain. Hence, the potential for improving transaction efficiency and for promoting productivity increasingly comes from entrepreneurial activities that search for the efficient structure of transactions and ownership of the firm as division of labor evolves. Rosenberg and Birdzell (1986, pp. 145-84), and Mokyr (1990, 1993, pp. 26-110) have documented the evolution of the institution of the firm and the relationship between industrialization, the institution of the firm, and invention and innovation during 1750-1830. According to the documentation, entrepreneurial activities were much more important than scientists’ activities for the technical revolution in the Industrial Revolution. Entrepreneurial activities were encouraged by secured private property rights and patent laws in Britain. Significant improvements in transaction conditions, the emergence of world market, and development of the commercial organization created the conditions for the development of entrepreneurship. According to the documentation, for those entrepreneurial activities that could not be protected by patent laws, the institution of the firm was used to protect entrepreneurs' intellectual property via trade secrets and claims to residual rights of the firm. Also, commercial value of many important inventions was realized using the institution of the firm. Moreover, the institution of the firm was an important vehicle for providing venture capital for technical inventions and innovations, and for providing working capital. Protection of residual rights of owners of the firm, trademarks, business names, and free associations by common laws was one of the most important driving forces of the Industrial Revolution (North, 1981 and Mokyr, 1993). With these institutional conditions, British could commercialize many inventions and innovations, some of which were imported from other countries where inventions were commercially nonviable. Also, a large network of division of labor was organized within a firm to significantly reduce transaction costs caused by a high level of division of labor during this period of time. Although this section has explored how the market sorts out the efficient pattern of division of labor in a roundabout production chain through interactions between selfinterested decisions, the functioning of the market in the real world is much more sophisticated than that described in the simple model. For instance, in the simple model, we assume that the total factor productivity of the final goods monotonically increases with the number of links in the roundabout production chain. In the real world, such a monotonic relationship may not hold universally. In some industries, as the degree of production roundaboutness increases slightly, the total factor productivity of final goods may decline at first, and then rise as the roundaboutness is further increased. The first steam engine-driven locomotive was slower and much more expensive than a horse. If dynamic economies of specialized learning by doing are explicitly considered (see chapter 16), it is possible that type C economies of roundabout production can be realized only if a sufficiently high degree of roundaboutness is maintained for a sufficiently long period of time. Suppose that each of 1,000 sectors producing the final goods can have a long roundabout production chain. But only 100 of the 1,000 sectors have type C economies of roundabout production. The rest of the sectors have diseconomies of roundabout production. Also, the

412

economies of roundabout production can be realized only if the roundaboutness in several of the 100 sectors simultaneously increases. For such a model, there are myriad possible structures. If account is taken of interdependency between information about relative prices and decisions in choosing one of many corner solutions, as described in chapter 17, it may take a long time for society to search out the efficient industrial structure, despite the power of the market in performing this task. What we can observe from the Industrial Revolution is a process through which an efficient industrial structure with the right pattern of division of labor in a long roundabout production chain has been sorted out by the market under the common law system that protects private residual rights to the firm and other private rights to various properties. Before the Industrial Revolution, many other industrial structures with long roundabout production chains had been experimented with. For instance, a quite long roundabout production method in producing a special vehicle out of wood was developed in the 220s in China. That roundabout production method could not stand the test of time, since it did not use durable steel or engines that could provide much more power than human and animal power. Hence, economies of roundabout production were too small to offset transaction costs and resource costs associated with roundabout production. In the Industrial Revolution, the invention of the engine and the commercial use of steel and all kinds of machines made out of steel and driven by engines, together with the evolution in division of labor in inventing activities and in roundabout production activities related to those inventions, brought about an efficient industrial structure that generated significant economies of roundaboutness. According to the model in this chapter, a high transaction efficiency provided by patent laws, a fair and adaptive common law system, and a laissez-faire regime were essential for the development of a large network of division of labor in roundabout production, which was in turn essential for the Industrial Revolution.

12.5. Evolution in the Number of Producer Goods and Economic Development

For the model in example 12.1, the maximum number of producer goods is 3. In this section, we use a model with m∈(1, ∝) producer goods to study the relationship between industrialization, the evolution of division of labor, and the evolution of number of producer goods. Example 12.2. A simplified version of the Sun-Lio model of industrialization (1997). Consider an economy with a continuum of ex ante identical consumer-producers of mass M. There are one consumer good, y, and m types of intermediate goods, i = 1, 2, …, m. For an individual, the self-provided quantities of the consumer good y and producer good i are y and xi, respectively. The quantities sold of the consumer good y and producer goods i are ys and xis, respectively. The quantities purchased of the goods are yd and xid, respectively. An individual uses both labor and m intermediate goods to produce the consumer good y. The consumer good is produced by a Cobb-Douglas production function with inputs ly and V, given by y p ≡ y + y s = e − cmV β l yα ,

413

m

V = [ ∑ ( x i + kxid ) ρ ]1 ρ ,

α + β = 1,

i =1

α , β , ρ ,k ∈ (0,1)

where yp is the output level of y. ly is the individual’s amount of labor allocated to the production of y. V can be considered as a composite intermediate good, which is a CES function of inputs of m producer goods. The total factor productivity of y is an increasing function of the number of intermediate goods m, although the Cobb-Douglas function displays constant returns. It is assumed that α+β>1 in the original Sun-Lio model. Since that assumption makes the algebra cumbersome, we will consider that assumption later on. A producer of the consumer good can either self-provide or buy the intermediate goods used in the production process. The transaction efficiency coefficient is k. e-cm is the management cost of m producer goods in terms of loss of the output of the final goods. This management cost increases with the number of producer goods employed in producing the final goods, since the number of the first order conditions of the optimum decision increases with m. The management cost can be interpreted as the calculation cost of the optimum decision, which generates the trade off between economies of variety of producer goods and calculation costs. The production function of intermediate good i exhibits economies of specialization, given by i = 1,2,..., m xip ≡ xi + xis = lib , b > 1 , p where xi is the output level of good i. li is an individual’s level of specialization in producing good i. Parameter b represents the degree of economies of specialization in producing the intermediate good. The endowment constraint for each individual is: m

l y + ∑ li = 1,

l y , li ∈[0, 1] .

i =1

Each individual’s utility function is u = y + ky d , where k is the transaction efficiency coefficient. The budget constraint for an individual is given by m

m

y + ∑ pi x = y + ∑ pi xis d

d i

s

i =1

i =1

where pi is the price of good i in terms of the consumer good. (a) Autarky: m=2, n−1=0

(b) Partial Division of Labor: m=3, n=2

A y

y

x2 x1

y

x1

(c) Complete Division of Labor: m=n=4 y x4

x1 414

x3/y

y/x2x3

x2/y

x2

x3 y

x1/y

x4/y

y/x1x2x3x4 y

x3

x2

y

y

x2/y

y

x3/y

Figure 12.3: Industrialization and Evolution of Division of Labor in the Sun-Lio Model

There are three types of structures. In autarky structure A, each individual selfprovides m producer goods and the final consumption good, as shown in Fig. 12.3(a). In structure P, with partial division of labor, shown in Fig. 12.3(b), the population is divided between occupation configurations (y/xi) and (xi/y). A person choosing (y/xi) selfprovides m-n producer goods, buys n producer goods, and sells the final good. A person choosing (xi/y) sells producer good i and buys the consumption good. In structure, C, with complete division of labor, shown in Fig. 12.3(c), the population is divided between occupation configurations (y/xm) and (xi/y). A person choosing (y/xm) in C buys m producer goods and sells the final good. Configuration (xi/y) in C is the same as in P. Inserting ys = yd = xis = xid = 0 into an individual’s decision problem, we can solve for the optimum decision and per capita real income in autarky as follows. (12.7) u A = e − β (1−bρ ) ρ α α (bβ ) bβ (α + bβ ) − (α +bβ ) [ β (1 − bρ ) (cρ )] β (1−bρ ) ρ , l y = α (α + bβ ) , m A = β (1 − bρ ) (cρ ) where uA is the per capita real income and mA is the equilibrium number of intermediate goods in autarky. Since the solution of mA in (12.7) is negative for b > 1/ρ but mA cannot be non-positive, (12.7) implies that the corner equilibrium in autarky does not exist for b > 1/ρ. Differentiation of (12.7) yields dmA/dβ > 0, dmA/dρ < 0, dmA/dc < 0, and dmA/db < 0. The decision problem for a person choosing configuration (y/xi) in structure P can be obtained by assuming that y, ys, ly, lj, xj, xrd > 0 and yd, lr, xjs, xjd, xrs, xr = 0, where r = 1, 2, …, n denotes producer goods purchased, and j = n+1, n+2, …, m, denotes producer goods self-provided. This decision problem is given as follows. (12.8) Max: u y = e − cm [ ∑ x ρj + ∑ (kx rd ) ρ ] β ρ l αy − y s j∈J

s.t. l y + ∑ l j = 1 , j ∈J

r ∈R

y s = ∑ pr x rd r ∈R

where uy is the utility for configuration (y/x), R is the set of n purchased intermediate goods, and J is the set of m − n self-provided intermediate goods. We can use the symmetry which implies that ∑xjρ= (m-n)xjρ, ∑(kxjd)ρ= n(kxjd)ρ, ∑lj = (m-n)lj, ∑prxj= nprxj, to further simplify the decision problem in (12.8). Using y, ys, ly, lj, xj, xrd = 0 and yd, lr, yd, xrs, > 0, we have the decision problem for an individual choosing configuration (x/y): (12.9) Max: u x = k y y d = k y p r s.t. lr = x rs = 1 ,

y d = pr x rs = pr .

415

where ux is the utility for configuration (x/y), The solutions of the decision problems (12.8) and (12.9), together with utility equalization and the market clearing conditions, determine the corner equilibrium in structure P. The corner equilibrium is summarized as follows. (12.10) pi = p = e − cmD kx{1+[(cbρs)/(1-β)(1-bρ)]}(1-β)(b-1) [(1-β)/(cbρ)]}(1-β)b(1-bρ)(1-β)(b-1/ρ)(1-ρ)(1-ρ)/ρ(cρ)1-β/ρββ/ρ l y = 1 {1 + (cbρs) [α (1 − bρ )]} ,

x d = k[(1 − β ) (cρ ) + s (1 − bρ )] −1 (1 − ρ ) −1 , m = [ β (1 − bρ ) (cρ )] + [ ρ (b − 1) (1 − ρ )]n = [ β (1 − ρ ) (cρ )] − [ ρ (b − 1) (1 − bρ )]s n = m-s, My = M/(1+nxd), Mx = xdMy, where the corner equilibrium value of s is given by (12.11) f ( s) ≡ [(1 − β ) (cρ ) + s (1 − bρ )]{cbρ [(1 − β )(1 − bρ ) + cbsρ ]}b (1 − ρ )[(1 − bρ ) (1 − ρ )]1 ρ − k 2 = 0 . where m is the corner equilibrium number of intermediate goods in structure P, n is the corner equilibrium number of traded intermediate goods and represents the level of division of labor in equilibrium, and s is the corner equilibrium number of self-provided intermediate goods and represents the level of self-sufficiency. Mx is the number of producers of a traded intermediate good and My is the number of sellers of the final good. (12.10) indicates that the corner equilibrium value of price pi is negative if ly is positive and if b > 1/ρ. This implies that the corner equilibrium in structure P does not exist for b > 1/ρ. A comparison between m in (12.10) and mA in (12.7) indicates that the number of producer goods in structure P is always larger than in autarky. Differentiating (12.11) and then using the implicit function theorem, it can be shown (12.12)

ds/dk = -(∂f/∂k)/(∂f/∂s) < 0

where ∂f/∂k, ∂f/∂s < 0 if α+β=1, ρ ∈(0, 1), and b∈(1, 1/ρ). If structure P is a general equilibrium structure, p in (12.10) must be positive, which means that b < 1/ρ. Hence, (12.12) must hold if structure P occurs in equilibrium. Manipulating (12.10)-(12.12) yields the comparative statics of the corner equilibrium in structure P: (12.13a) dm/dk > 0, dn/dk > 0, (12.13b) d(m-n)/dk < 0, dly/dk > 0, dxd/dk > 0. Using the envelope theorem, it can be shown that per capita real income in structure P increases as k increases. Since the per capita real income in autarky is independent of transaction efficiency k, the per capita real income in structure P is more likely to be greater than in autarky as k increases. This, together with the Yao theorem in chapter 4, implies that the general equilibrium will jump from autarky to structure P as transaction efficiency is improved. (12.13a) implies that the number of all available producer goods m and the number of traded intermediate goods, n, increase concurrently, as transaction efficiency is improved. (12.13) implies that as transaction efficiency is improved, the number of traded intermediate goods, n, increases faster than the number of all

416

intermediate goods, m, does. Hence, as transaction efficiency is sufficiently improved, the general equilibrium will jump from the partial division of labor to the complete division of labor (structure C). Also, (12.13b) implies that in this process, the level of specialization of each producer of the final good increases and her demand for each intermediate good increases. Since the optimum values of endogenous variables are discontinuous as n changes from a value smaller than m to m, we cannot obtain the corner equilibrium in structure C by simply letting n = m in (12.10)-(12.13). But it is not difficult to solve for the corner equilibrium in structure C by following the same procedure for solving the corner equilibrium in structure P. The corner equilibrium and its comparative statics are given as follows. (12.14) m = β (1 − ρ ) ( ρc) , x d = ρck [(1 − ρ )(1 − β )] β

p = k 2 β −1 e − β (1− ρ ) ρ β β ρ (1 − β ) 1− β [ ρc (1 − ρ )] [(1 − ρ ) ( ρc)] β

β ρ

β ρ

,

u = k 2 β e − β (1− ρ ) ρ β β ρ (1 − β ) 1− β [ ρc (1 − ρ )] [(1 − ρ ) ( ρc)] , dm dβ > 0 , dm dρ < 0 , dm dc < 0 , du dk > 0 , where m = n is the number of traded intermediate goods as well as the number of all available intermediate goods in the complete division of labor. Somehow, the corner equilibrium in structure C is analogous to the general equilibrium in the Ethier model in example 5.2 of chapter 5. From this view, the Ethier model is a special case of the SunLio model, that is, structure C in the Sun-Lio model is equivalent to the Ethier model. Fig. 12.3 provides an intuitive illustration of industrialization, structural changes, and the evolution of division of labor in the Sun-Lio model. We first consider the parameter subspace b < 1/ρ. If transaction efficiency is very low, autarky is the general equilibrium where the number of available intermediate goods is very small and there is no market. As transaction efficiency is improved, the general equilibrium jumps to the partial division of labor in panel (b), where the ex post production functions of a new intermediate good and the markets for two intermediate goods and the final good emerge from the network of division of labor. As transaction efficiency is further improved, the general equilibrium jumps to the complete division of labor in panel (c), where one more new intermediate good and two more markets for intermediate goods emerge from the evolution of the network of division of labor and related transactions. The evolution of division of labor can continue as transaction conditions are improved, since there is no limit for the evolution of the number of goods, which creates unlimited scope for the evolution of division of labor in roundabout production so long as the population size is not limited and ρ, c are very small (β(1-ρ)/cρ is very large). For the parameter subspace b > 1/ρ (economies of specialization dominate economies of complementarity), the general equilibrium is always associated with structure C. As the management cost coefficient c declines, the equilibrium number of intermediate goods increases, but all individuals are always completely specialized. In other words, gradual evolution of specialization occurs only if economies of complementarity dominate economies of specialization. Assume that the final good is the agricultural good and the intermediate goods are industrial goods (tractors, fertilizer, and other equipment) and that b < 1/ρ. Now we consider the relative population size of industrial and agricultural sectors. This ratio is R = nMx/My

417

where n is the number of different occupation configurations selling n intermediate goods, Mx is the number of manufacturers selling one type of industrial goods, and My is the number of farmers. From the budget constraints in (12.8) and (12.9), it can be shown that Mx/My = xd (see (12.10)). Then from (12.10)-(12.13), it can be shown that dxd/dk = (dxd/ds)(ds/dk) > 0, where dxd/ds < 0 from (12.10) and ds/dk < 0 from (12.12). Hence, we have dR/dk = (∂R/∂xd)(dxd/dk) + (∂R/∂n)(dn/dk) > 0 where dn/dk > 0 due to (12.13). This result implies that as improvements in transaction conditions generate industrialization, the employment share in the industrial sector increases compared to the agricultural sector, even if the industrial sector does not produce any final goods. Because of economies of specialization and economies of roundabout production in this model, productivities of all goods will increase as improvements in transaction efficiency drive division of labor to evolve in roundabout production. Also, the extent of the market, the degree of endogenous comparative advantage, the diversity of occupations and of economic structure, production concentration, and market integration all increase as division of labor evolves in roundabout production. Sun and Lio (1997) have shown that the comparative statics of the general equilibrium still hold even if α+β>1, which implies that there are economies of specialization in the agricultural sector. This distinguishes their model from the Ethier model in example 5.2, where the agricultural sector has constant returns to scale technology. Lio and Sun solve for more corner equilibria with firms of this model, using the approach developed in chapter 8. They have shown that industrialization and a declining average size of firms can concur if transaction efficiency is improved in such a way that transaction conditions for goods become better than that for labor. Hence, a possible empirical work to test the Sun-Lio model against the Ethier model can be conducted. If a negative correlation between the relative size of the industrial and agricultural sectors and the average size of firms is verified by empirical observation, then the Ethier model, which predicts a positive correlation between the two variables, is rejected and the Sun-Lio model is confirmed. The positive correlation between the two variables or between the degree of urbanization and average size of firms is referred to as a type III scale effect.

Key Terms and Review Type A, type B, and type C economies of roundabout production Conditions under which a business that creates a new link in the roundabout production chain can make money Relationships between transaction efficiency, the size of the market network, the size of the population or resource base, three types of economies of roundabout production, the equilibrium level of division of labor, and the equilibrium number of links in the roundabout production chain Mechanism that generates a decline in the income share of the agricultural sector and a rise in the income share of the industrial sector. Relationship between this phenomenon and the relative

418

degree of economies of division of labor compared with transaction costs in the agricultural vs. industrial sector Why will the scope for the development of the institution of the firm be enlarged more than proportionally as division of labor in roundabout production evolves? Significance of private residual rights to the firm for the evolution of production roundaboutness Implications of free pricing, free enterprising, and free choice between profession configurations for the evolution of division of labor in roundabout production

Further Reading Industrial Revolution: Macfarlane (1988), Baechler and Mann (1988), Jones (1981), Weber (1961), Baechler (1976), Braudel (1984), Rosenberg and Birdzell (1986), Mokyr (1990, 1993), Hartwell (1965), Hughes (1970), Hicks (1969), Reynolds (1985), Morris and Adelman (1988); Historical and empirical evidence for the theory in this chapter: Kubo (1985), Chenery (1979), Kaldor (1967), Braudel (1984), Chandler (1990), Department of Commerce, (1975), Liu and Yang (2000); Classical and new Smithian models of industrialization: Smith (1776), Yang and Y-K. Ng (1993, ch.14), Young (1928), Shi and Yang (1995, 1998), Sun and Lio (1997); High development economics and the theory of industrialization: Rosenstein-Rodan (1943), Nurkse (1952), Fleming (1955), Hirschman (1958), Krugman (1995); Structural changes: Kuznets (1966), Chenery (1979). The models of industrialization with economies of scale and endogenous number of goods: Murphy, Shleifer, and Vishny (1989a, b), Krugman and Venables (1995), Yang and Wong (1998), Kelly (1997).

Questions 1. According to Rosenberg and Birdzell (1986, p. 156), extensive use of steel, coal, and mechanical power was a feature of the Industrial Revolution. One interpretation of the use of steel in terms of the model in example 12.1 is an increase of degree of type A economies of roundabout production. The durability of steel implies that the elasticity of output with respect to intermediate input is great. Hence, as transaction efficiency is improved, division of labor is more likely to evolve in producing steel and other sectors that use it. Use the model in example 12.1 to explain why many machines made of wood could not generate an industrial revolution in Song Dynasty China. 2. According to Mokyr (1990, pp. 235-50, 1993), violation of private property rights by the government, the absence of patent laws, more effective regulations by the government and guilds, and a strong tradition of mercantilism, which advocated protectionism in the European Continent, explain why the Industrial Revolution did not take place first in the Continent. According to him, the following features of the Chinese institutions explain why the Industrial Revolution could not occur in China before the 19th century. The State monopolized important industries and inventing activities, and could arbitrarily infringe upon property rights and confiscate the properties of private firms. The State monopolized trade and ideology, and provided an incentive to the elite only for political or military careers. Also, the State carried out an active industrial policy to promote agriculture and to suppress commerce, and directly intervened in economic activities. There was no free city in China and the feudal system was replaced with a central government system after the 1st century. Compare this analysis with North, Mokyr, and others’ analysis of the conditions for the Industrial Revolution in section 12.1.

419

Choose a developing country and examine whether the conditions for the British Industrial Revolution are still essential for industrialization of this country, and if obstacles for industrialization in 18th century France and China are still obstacles for industrialization of this country. 3. Interpret the inframarginal comparative statics of general equilibrium in this chapter in connection to North’s following observation (1981, p. 167). “The Industrial Revolution, as I perceive it, was initiated by increasing size of markets, which resulted in pressures to replace medieval and crown restrictions circumscribing entrepreneurs with better specified common laws. The growing size of the market also induced changes in organization, away from vertical integration as exemplified in home and handicraft production to specialization. With specialization came the increasing transaction costs of measuring the inputs and outputs. The resultant increased supervision and central monitoring of inputs to improve quality radically lowered the cost of devising new techniques. From handcraft to the putting-out system to the factory system spans more than three centuries; the key to explaining the transformation is growth in the size of the market and problems of quality control (that is, measurement of the characteristics of the good).” 4. Marshall (1989, p. 241) described the relationship between the network of division of labor, transaction conditions, and the development of specialized machinery as follows. “The development of the organism, whether social or physical, involves an increasing subdivision of functions between its separate parts on the one hand, and on the other a more intimate connection between them. Each part gets to be less and less self-sufficient, to depend for its well-being more and more on other parts, so that any disorder in any part of a highlydeveloped organism will affect other parts also. This increased subdivision of functions, or ‘differentiation,’ as it is called, manifests itself with regard to industry in such forms as the division of labour, and the development of specialized skill, knowledge and machinery: while ‘integration,’ that is, a growing intimacy and firmness of the connections between the separate parts of the industrial organism, shows itself in such forms as the increase of security of commercial credit, and of the means and habits of communication by sea and by road, by railway and telegraph, by post and printing-press.” Use the models in this chapter to formalize this description. 5. Many new growth models explain the emergence of new producer goods by investment in the R&D sector. This kind of model cannot explain why producers in less developed economies usually do not adopt the latest machinery and technology available at low cost (Olson, 1996), and why numerous good-will attempts to introduce the newest production processes into less developed countries meet with disappointing failure, as noted by Stigler (1951). Many peasants in less developed countries do not use roundabout productive equipment and vehicles because a high level of division of labor is essential for producing the equipment at low price. But the government monopoly in the sector producing these producer goods, and in the distribution system and banking system, cause very high transaction costs, which make a high level of division of labor and sophisticated private organization nonviable. Also, the use of machines needs many very specialized services to provide cheap parts, instruments, and repair and transaction services. Due to the absence of a great variety of highly professional services, peasants prefer very primitive tools with a low degree of roundaboutness. As Stigler (1951, p. 193) had noticed, the production process in the American industrialization model is usually too specialized for less developed economies, as in them neither the vast network of auxiliary industries which producers in the United States can take for granted can be available nor the necessary narrowly specialized personnel can be supplied. Benjamin Franklin, observing manufactures in the United States, a backward economy at his time, also pointed out that: “Manufactures… are carried on by a multiplicity of hands, each of which is expert only in his own part, no one of them a master of the whole,” so all the experts in the associated network of division of labor are needed to set up a manufacture in a foreign and under-developed land.

420

6.

7.

8.

9.

But usually after “a complete set of good and skillful hands are collected and carried over, they find so much of the system imperfect, so many things wanting to carry on the trade to advantage, so many difficulties to overcome… and the projects vanishes into smoke” (cited by Stigler, 1951, p. 193). Use the models in this chapter to explain Stigler and Franklin’s observations. In response to question 5, many economists may point to purchasing power and income of peasants as the explanation for the low production roundaboutness in a developing country. But Young (1928) pointed out: “Taking a country’s economic endowment as given, however, the most important single factor in determining the effectiveness of its industry appears to be the size of the market. But just what constitutes a large market? Not area or population alone, but buying power, the capacity to absorb a large annual output of goods. This trite observation, however, at once suggests another equally trite, namely, that capacity to buy depends upon capacity to produce.” But production capacity is dependent on the level of division of labor. Hence (Young, p. 533), “in the light of this broader conception of the market, Adam Smith’s dictum amounts to the theorem that the division of labor depends in large part upon the division of labor…. Even with a stationary population and in the absence of new discoveries in pure or applied science there are no limits to the process of expansion except the limits beyond which demand is not elastic and returns do not increase.” Use the models in this chapter to formalize this idea of Young’s about the relationship between the extent of the market, division of labor, and roundabout production. See also Young’s explanation of the Industrial Revolution, which “has come to be generally regarded, not as a cataclysm brought about by certain inspired improvements in industrial technique, but as a series of changes related in an orderly way to prior changes in organization and to the enlargement of markets” (p. 536). McGuirk and Mundlak (1992) report evidence for the effect of transaction conditions on the choice of techniques of different degrees of roundaboutness. According to them, the modern crop varieties (MVs) generate more output, but require considerably more fertilizer per unit of land than do traditional varieties, which implies that MVs involve production processes using more intermediate goods and being more roundabout. Although the technique of MVs has been known, it has to compete with traditional ones for adoption. The adoption of MVs is positively and strongly influenced by the density of roads. The importance of roads therefore indicates that linking rural areas to market, or in our terminology, that the improvement in transaction conditions of these rural areas, strongly affects the adoption of more roundabout techniques as hypothesized by the Smithian model. Find more empirical evidence for the models in this chapter. North (1968) has suggested that we should recognize that differences in ability to make efficient use of available knowledge are a factor as pre-eminent as differences in the knowledge state for explaining the widely disparate experience of national economies. The development of division of labor allows us to cross the gap between what has been known and what can be realized. If there lacks a well-developed network of division of labor to support high degrees of roundaboutness, then to heavily invest in R&D seems to be a recipe for lowering the average productivity of the knowledge stock rather than for rapid economic progress. Use the models in this chapter to substantiate North’s conjecture. If all individuals would not buy roundabout productive machines because of expected high prices of the machines, then for the sector producing the machines the extent of the market would be very small and the level of division of labor very low, so that the prices of the machines would be indeed high. Also, if a sector producing final goods increases its demand for steel, the extent of the market for steel will be enlarged and its price may decline due to higher productivity generated by a higher level of division of labor within the sector producing steel. Hence, many other sectors may be able to afford the cheaper steel, so that a sequence of positive feedback may take place among many professional sectors. This implies that there are network

421

effects of division of labor between roundabout production and the final sectors. Use the models in this chapter to explain how the market coordinates the division of labor and utilizes the network effects. Discuss the implications of free choice of occupation configurations, free pricing, and free enterprising for the market to utilize the network effects. Many economists call such network effect “linkage externality” (see, for instance, Hirschman, 1958). Use the models in this chapter to analyze under what conditions the network effect may not be associated with market failure. 10. According Mokyr (1993, p. 26), the positive feedback loop between transaction efficiency, technical inventions, and network size of division of labor was an important driving force of the British Industrial Revolution during 1750-1830. Use the Chu model in exercise 14 of chapter 7, which specifies the feedback loop between transaction efficiency, the level of specialization in the transacting sector, and the extent of the market, and the models in this chapter to conduct a thought experiment to explain the historical fact. 11. As an economy develops, many families self-provide increasingly more household services, such as using a washing machine at home rather than relying on a specialized laundry shop, and mowing the lawn using a mower rather than relying on specialized gardeners. Professors may use computers to do some jobs that used to be done by a secretary and professional publishing houses. However, the decrease in the level of specialization in the downstream sector usually concurs with the increase in division of labor and specialization in the upstream sector that specialized in producing washing machines, lawn mowers, or computers. Based on the models in this chapter, develop a general equilibrium model to explain changes in the distribution of the degree of division of labor between upstream and downstream production activities. Explain why the increase in division of labor for society as a whole is an irreversible process, despite the changes that occur in the distribution of degree of division of labor. 12. Shi and Yang (1998) introduce additional goods into the model in example 12.1 to show that as transaction efficiency is improved, the level of division of labor in an increasingly longer roundabout production chain evolves, thereby creating more scope for finer division of labor between firms and within each firm. Hence, a hierarchical industrial structure between firms and a hierarchical structure within each firm may concurrently evolve. If transaction efficiency for labor and for intermediate goods is improved at different speeds, the equilibrium dividing line between the decentralized network hierarchy in the market and the centralized hierarchy within each firm may evolve too. Discuss the conditions under which the decentralized hierarchy in the market becomes increasingly less important than the centralized hierarchy within each firm, a phenomenon described by Chandler (1990). 13. Analyze why the potential to make money by playing around with the choice of structure of residual rights increases as the level of division of labor in an increasingly longer roundabout production chain evolves. 14. It has been claimed that in a modern society, all individuals are completely specialized and buy all the goods they consume from the market, so that there is not much room for a finer division of labor. Hence, models of endogenous specialization are not particularly relevant to a modern economy. Use examples, such as the emergence of the electric tooth brush and commercially viable robot used to do housework, to illustrate that the potential for further division of labor in producing consumption tools to replace existing self-provided consumption activities can never be exhausted, except for the limitations imposed by population size (the number of different professions cannot be larger than population size) and transaction costs. Then use examples, such as the finer division of labor in producing more than ten thousand parts of a robot or an automobile, and many subprocesses involved in producing each of them, to illustrate the infinite possibility for a finer division of labor in roundabout production. 15. From input-output tables of 8 countries, Kubo (1985) has found empirical evidence for concurrent increases in the output share of manufactured intermediate goods and in per capita

422

real income. According to the input-output tables of the US, the output share of the roundabout production sector steadily increased from 0.44 in 1947, to 0.54, in 1958, 0.55, in 1961, 0.57 in 1963, and 0.62 in 1967 (see Department of Commerce, 1975). Kaldor (1967) had also found empirical evidence for concurrent increases in the income share of the manufacturing sector and in per capita income. Try to find other methods to test the hypotheses generated by the models in this chapter against empirical observations. 16. Use the model in this chapter to show that the ideas in high development economics (see questions 8 and 9 in chapter 5) can be more appropriately formalized by the concepts of network effects and equilibrium network of division of labor. Use the concept of general equilibrium to analyze how interactions between self-interested decisions in the market can successfully coordinate individuals’ decisions in choosing patterns of specialization in order to utilize the network effects of division of labor. 17. Fleming (1955) argues that the “horizontal” external economies of Rosenstein-Rodan were less important than the “vertical” external economies. His notion of horizontal external economies relates to type B economies of roundabout production and the network effects of division of labor, while his concept of vertical external economies relates to type C economies of roundabout production and network effects of division of labor. Assess Fleming’s view in connection to the model in this chapter. Why did Scitovsky (1954) argue that such externality (network effects) is pecuniary?

Exercises 1. Consider the model in example 12.1. Assume the production function (12.2) is replaced with zp = Max{Min {lz -α, y+kyd}, x+kxd} and xp = Min {lx -α, w+kwd}. Solve for the inframarginal comparative statics of the general equilibrium. 2. Consider the model in example 12.1. Assume that transaction efficiency k differs from good to good. Identify the conditions under which the general equilibrium shifts from the autarky corner equilibrium producing goods x, y, z to the corner equilibrium with the complete division of labor with goods x, y, w produced. This implies that some goods may disappear as division of labor evolves. 3. Assume that in the model in this chapter, the production function of good y is yp = Min {ly -α, v+kvvd} and vp ≡ v+vs = lv -α. Suppose that transaction efficiency ki, i = x, y, z, w, v, differs from good to good, and that the endowment constraint for working time is lx + ly + lz + lw + lv = 1. v is a producer good used to produce y. Solve for the inframarginal comparative statics of the general equilibrium. Show that if kv, ky are significantly smaller than kz, kx, kw, the division of labor evolves only in the sectors producing z, x, and y and does not evolve in the sectors producing y and v. If y is interpreted as harvesting and v is interpreted as sawing, then the model can explain why the development of division of labor in the agricultural sector is not as fast as in the industrial sector by the difference in transaction costs between the two sectors. Use the model to formalize Smith’s conjecture on the rationale for the increasing income share of the industrial sector compared to the agricultural sector. 4. Assume that in the model in this chapter, good w can be used to produce goods x and y, so that the production function of y is yp = Min {ly -α, w+kwd}. Solve for the inframarginal comparative statics of the general equilibrium. Analyze the implications of the interdependencies between different production activities in the complicated input-output network for the equilibrium level of division of labor. 5. (Shi-Yang model, 1995) Assume that in example 12.1, the production function for tractors (12.2) is replaced with the CES function zp = [(x+kxd)ρ+ (y+kyd)ρ] 1/ρlz0.5. Solve the general

423

equilibrium and its inframarginal comparative statics. (Note that some corner equilibria may not be solved analytically and computer simulation is needed for solving inframarginal comparative statics of general equilibrium.) 6. Sun and Lio (1997) assume that transaction efficiency between the final goods and intermediate goods is different. Following their assumption, you may work out the comparative statics of the general equilibrium to show the effect of the relative transaction condition on industrialization. Assume α+β>1, as in the Sun-Lio original model. Solve for general equilibrium and its comparative statics (see Sun and Lio, 1996, for the answer). 7. Assume in an extended version of the Sun-Lio model that there are two final goods; one of them needs intermediate goods in the production process and the other does not. Solve for the comparative statics of the general equilibrium. Then use your results to analyze the relationship between industrialization and the evolution of division of labor. 8. (Yang and Ng, 1993, chapter 12) Consider an economy with a consumption good (car) which can be produced by employing two types of specialized machine tools and labor, or by employing one of the two types of machine tools and labor. The CES production functions of cars are ex ante identical for M consumer-producers. β

z p ≡ z + zs = [(x + tx d )ρ + (y + ty d )ρ ] ρ lzα , β∈(0,1), ρ∈(0,1) where xd and yd are the respective amounts of the two intermediate goods purchased from the market, and 1-t is their transaction cost coefficient. The respective self-provided amounts of the two goods are x and y, lz is a person's level of specialization in producing the consumer good, and z+zs is the output level of this consumer good. The production functions for the intermediate goods are x+xs = lxa and y+ys = lya s s where x+x and y+y are the respective output levels of the intermediate goods and lx and ly are a person's respective levels of specialization in producing the two intermediate goods. The endowment constraint for labor is lz +lx +ly = 1, li ∈[0,1], i = z, x, y The transaction cost coefficient for the final good is 1-k. The utility function is ex ante identical for all individuals and given by u = z+kzd Solve for general equilibrium and its inframarginal comparative statics. 9. Show that in the Sun-Lio model in example 12.2 the income share of agricultural good (final good) decreases as transaction conditions are improved. Some economists call this Engel's law and attribute it to changes in tastes and income. Why can Engel's law hold in the absence of changes of tastes and production functions (or in the absence of changes of demand and supply sides)? 10. If intermediate goods in the Sun-Lio model are interpreted as capital goods, then as transaction conditions are improved, the equilibrium degree of capital intensity will evolve. Assume that there are two countries with the same population size (or labor endowment) in the Sun-Lio model. Show that a country will export increasingly more capital-intensive goods even if the two countries have no exogenous endowment comparative advantage. Compare your results with the HO model in chapter 3 and discuss essential differences in meanings of the notion of factor intensity between a neoclassical model with constant returns to scale and the Smithian model with economies of specialization. 11. Assume that transaction efficiency is different between two countries in the Sun-Lio model in example 12.2. Use the comparative statics of general equilibrium to show that improvements in trading efficiency are more important for economic development than choice of a particular set of goods to export. Use this model to analyze development patterns and strategies. Compare this extended model with the Krugman-Venables model in example 5.2 in chapter 5.

424

425

Part V: Dynamic Mechanisms for Economic Development

Chapter 13: Neoclassical Models of Economic Growth

13.1. Exogenous vs. Endogenous Growth The Ramsey model (1928) is representative of the neoclassical growth models. In that model, saving can be used to raise per capita capital that contributes to the growth rate of per capita consumption in the future at the cost of current consumption. Ramsey used dynamic marginal analysis (calculus of variations) to solve for the efficient trade off between current and future consumption, which determines the optimum time path of saving, production, and consumption. We define endogenous growth as long run growth in per capita real income or in per capita consumption that has the following features. (i) The long-run growth can take place in the absence of any exogenous changes of parameters. (ii) The growth is based on individuals’ intertemporal optimum decisions (dynamic self-interested behavior). The Ramsey model meets the second criterion, since the optimum saving rate that maximizes total discounted utility in the Ramsey model describes self-interested behavior. If the production function in the Ramsey model is linear (a so called AK function), the Ramsey model meets the first criterion too. Hence, a specific AK version of the Ramsey model is the first endogenous growth model. We define exogenous growth as growth that does not meet the foregoing two criteria. In the 1940s and 1950s, exogenous growth models (the Harrod-Domar model and the Solow model) were developed. The Harrod-Domar model is a system of state equations: It = v (Yt+1 - Yt), St = It = sYt, where v is a coefficient of the investment requirement for each unit of increase in income, s is a fixed saving rate, St is the aggregate saving level, It is the aggregate investment level, and Yt is the aggregate income (and output) level at time t. The parameter v is assumed to be greater than 1 since one period’s output is typically less than the value of capital required to produce it. The system of equations generates an explosive time path of demand for investment, characterized by the difference equation Yt+1 = [(s+v)/v]Yt = [(s+v)/v]2Yt-1 … = [(s+v)/v]t-1Y1 = [(s+v)/v]tY0. This equation does not have a steady state and generates an explosive increase in Y at rate s/v over time. Since no production function (supply side) is specified, the equilibrium growth cannot be quarantined by the equation. If the Leontief production function Yt = Min{Kt/v, Lt/a}, where Lt is the amount of labor employed to produce Yt, is specified, 426

then the equilibrium growth is consistent with the above difference equation only if the initial labor supply is not less than sK0/v, and the labor supply increases at a rate not lower than s/v. Even if we ignore the problem of the existence of equilibrium growth, the Harrod-Domar model is an exogenous growth model in the sense that no decision-making process of individuals is specified and the saving rate s is exogenously given. The Solow model (1956) specifies a Cobb-Douglas production function, Y = AKαL1-α, in addition to the saving equation, income and investment identities, and the market clearing condition for investment I = K& , S=I S = sY, Y ≡ C + S, where Y, K, L, S, I, C are functions of time t and K& ≡ dK/dt is the change rate of capital. This system of equations yields a state equation in k ≡ K/L k& = sAkα - kn where n ≡ L& /L is an exogenously given parameter of the growth rate of population size. For simplicity, the labor force is assumed to be the same as the population size. Letting k& = 0, we obtain a steady state of k, which is a function of the parameters s, A, and n. The steady state is an analogue of static equilibrium. In the long run (as t tends to infinity), k and per capita income y ≡ Y/L will converge to the steady state and stay there forever (growth stops) if the parameters are fixed. In this sense, the Solow model is an exogenous growth model, since it cannot generate long-run growth in the absence of exogenous changes in parameters. Also, the growth in the Solow model does not meet the second criterion for endogenous growth, that is, in the Solow model the saving rate s is exogenously given rather than endogenously determined by an intertemporal optimum decision (behavior). In the 1960s, many growth models were developed. Most of them follow the Ramsey model in specifying a dynamic optimization problem. Hence, they meet the second criterion for an endogenous growth model. Some of them meet the first criterion too. The Uzawa model (1965) is representative of these. All of the growth models mentioned are macroeconomic models which do not spell out the microeconomic mechanism for economic growth in the following sense. It is assumed that investment can raise productivity in the future through increasing per capita capital. From a Smith-Young point of view, an increase in capital is an increase in division of labor in the roundabout production chain. The neoclassical growth models do not explain why and how the increased capital per person can increase productivity. A new wave of neoclassical growth models occurred in the 1980s. Judd (1985) developed a dynamic general equilibrium model, built upon the Dixit-Stiglitz (DS) model (1977). The trade off between current and future consumption is added to the trade off between economies of scale and consumption variety to tell a story about endogenous growth and spontaneous evolution in the number of goods. Romer (1990) developed a dynamic equilibrium model, built upon the Ethier model (1982), to explain economic growth by spontaneous evolution in the number of producer goods. Since then, many of this kind of neoclassical endogenous growth models have been developed. Since the reduced form of many of the models can be considered as a special version of the Ramsey model with a linear production function, referred to as the AK model, and many of the models involve endogenous research and development (R&D) decisions, the neoclassical endogenous growth models are called AK models or R&D based models.

427

The new growth models not only generate long-run endogenous growth on the basis of individuals’ intertemporal optimum decisions in the absence of exogenous changes in parameters, but also explain the growth by interactions between self-interested dynamic decisions. They are dynamic microeconomic general equilibrium models that endogenize the relative prices of different goods and factors. They are, however, still neoclassical growth models in the sense that the neoclassical dichotomy between pure consumers and firms is retained, the neoclassical notion of economies of scale is used, and neoclassical (dynamic) marginal analysis is employed as the main analytical instrument. Hence, the models cannot explain endogenous evolution in the degree of market integration and in the levels of specialization of individuals. It can however predict an aspect of endogenous evolution in the network size of division of labor: evolution in the number of available goods. Since economies of scale are the central notion used in the new endogenous growth models, the models generate scale effects. There are five types of scale effects. A type I scale effect implies that the growth rate of per capita income and per capita consumption or per capital income go up as the size or growth rate of the population increases. A type II scale effect implies that this productivity or growth performance positively correlates to average size of firms. A type III scale effect implies a positive correlation between the income share of the industrial sector and the average size of industrial firms, or a positive correlation between the degree of urbanization and the average size of firms. A type IV scale effect implies that the growth rate of per capita income goes up as the investment rate increases. A type V scale effect exists if the growth rate of per capita income goes up as the size of the research and development sector increases. The scale effects are wildly at odds with the empirical evidence. The AK model generates type I and type IV scale effects, and R&D based model generates type I and type V scale effects. Jones (1995a, b) and the empirical work reviewed in Dasgupta (1995) and National Research Council (1986) have rejected the type I, type IV, and type V scale effects. Technically, the essential instrument to manage the neoclassical endogenous growth models is dynamic marginal analysis (calculus of variations). Control theory is not necessary for managing the models, though many authors use this. Dynamic inframarginal analysis (control theory and dynamic programming) is essential for managing the Smith-Young endogenous growth model, which will be studied in the next chapter. Section 13.2 studies the Ramsey model and one of its special versions, the AK model. Section 13.3 studies the R&D based model.

Questions to Ask Yourself when Reading this Chapter What is the driving mechanism of economic growth in neoclassical growth models? What is the difference between endogenous and exogenous growth? Why do neoclassical endogenous growth models generate scale effects that are rejected by empirical evidence?

428

13.2. The Ramsey Model and the AK Model We shall first tell the story behind the Ramsey model. Each individual’s utility at each point in time displays diminishing marginal utility and she gives value to time, so that each individual prefers a fairly even distribution of consumption over time and prefers current consumption to future consumption of the same amount of goods. It is assumed that saving and investment can be used to increase per capita capital, while per capita income in the future is an increasing function of per capita capital. The microeconomic mechanism that links productivity and per capita capital is not elaborated. The tension between consumption and saving, together with the productivity implication of saving and the preference for current consumption and for a fairly even distribution of consumption over time, therefore generates a trade off between current and future consumption. The optimum intertemporal decision is to efficiently trade off current consumption against future consumption in order to maximize total discounted utility over the decision horizon. The efficient trade off will generate an optimum time path of savings, consumption, and production. The optimum saving rate is usually not a constant. Example 13.1: The Ramsey model with the Cobb-Douglas production function. Assume each individual’s utility at time t is (13.1) u = f (c) where c is her consumption level at time t. We may take a specific function, where f(c) = (cα-1)/α, α∈(0, 1). This utility function displays diminishing marginal utility. The assumption of diminishing marginal utility implies that an individual does not prefer concentrating consumption at a point in time. This rules out the optimum decision that consumes nothing in the early stage, and saves all resources to increase per capita capital and concentrates consumption at a later stage. Assume that total population size is L at time t, aggregate income at t is Y ≡ C + I, where C is aggregate consumption and I is aggregate investment at time t. Assume aggregate capital at t is K and its change rate at t is K& ≡ dK /dt . Since the change rate is caused by investment, in the absence of depreciation of capital, we have I = K& . Plugging this into the income identity yields Y = C+I = C+ K& If we divide all variables by the population L, which is assumed to be the same as the labor force for simplicity, we have y ≡ Y/L, c ≡ C/L, k ≡ K/L. Hence, the income identity in terms of per capita variables becomes y = c + K& / L Since k& = ( K& / L) − ( KL& / L2 ) , we have K& / L = k& + kn , where n ≡ L& /L is an exogenously given growth rate of population. Inserting this back into the income identity, we have

(13.2)

y = c + k& + nk or c = y − k& − nk

429

Suppose per capita output is an increasing function of per capita capital, or y = g(k) and g’(.) > 0 and g” (.) < 0. If the aggregate production function is of the Cobb-Douglas form, or Y = AKβL1-β, then (13.3a)

g (k) = Akβ.

If the production function is of the AK form, or Y = AK, then (13.3b)

g(k) = Ak.

Inserting (13.3) into (13.2), then into (13.1), we can express utility at t as a function of k and k& . We now assume that an individual’s utility over the decision horizon is a weighted average of utilities at each point in time within the horizon. The weight is a continuously compounded discount factor e-ρt, where ρ is a subjective discount rate, which reflects the value of time for the individual, and e ≈ 2.718 is the base of natural logarithm. To understand where the discount factor comes from, we need to tell a story of a banking deposit. Suppose that you deposit $A in a bank at the beginning of the year. If interest is earned at the rate ρ, the principal and interest at the end of the year is A+ρA=A(1+ρ). Now suppose you withdraw your principal and accrued interest from the bank in the middle of the year. At the interest rate for half a year, ρ/2, your total asset is A + Aρ/2 = A(1+ρ/2) at the end of June. Then you deposit the money (principal A plus interest Aρ/2 in the bank again. The value of your asset at the end of the year will be A(1+ρ/2) + A(ρ/2)(1+ρ/2) = A(1+ρ/2)2 = A(1+ρ+ρ2/4), which is greater than A(1+ρ), the value of your asset with no withdrawal and redeposit in the middle of the year. In general, if you do such withdrawals and redeposits m times each year, then the value of your asset will be A[1+(ρ/m)]m at the end of the year. Suppose you do this for t years. Then the value of your asset at the end of year t is A[1+(ρ/m)]mt = A{[1+(ρ/m)]m/ρ}ρt. The limit of the formula as m tends to infinity is a well-known constant, which is B = Aeρt . We call B the future value of a present amount $A, compounded continuously. Alternatively, we call A = Be-ρt the present value of $B in the future with continuously compounded discounting. The value of e-ρt is between 0 and 1 and is referred to as the continuously compounded discount factor. In practice, banks never pay continuously compounded interest. Instead, they pay interest at higher rates for long-term deposits than for short-term deposits. This practice uses different interest rates to approximate continuous compounding at the same rate. Assume that each individual’s objective is to maximize her total discounted utility over her decision horizon. The present value of utility at time t is F = u e-ρt. Inserting (13.2) and (13.3) into u, we can express the present value of utility as F(k, k& , t) = f[g(k)- k& - nk] e-ρt. The total present value of utility over the decision horizon T can be expressed as an integration of F(k, k& , t) from t = 0 to t = T, where the decision horizon T can be infinity. Hence, the individual’s dynamic optimum decision at t =0 is:

430

(13.4)

•

Max: U (T ) ≡ ∫ F ( k , k , t )dt = ∫ u e − ρt dt T

0

T

0

where u = f (c), c = g (k ) − k& − nk , and the decision variables are k and k& . Integration can be viewed as the approximation of summation. The boundary conditions are k = k0 for t = 0 and k = kT for t = T. This is a problem in the calculus of variations. U(T) is called the objective functional, which is a function of k , which is in turn a function of t. But U is not a function of t, U is dependent on the terminal time, T. The trade off in the problem is between current and future consumption. An increase in k will increase future consumption through g(k) and will reduce current consumption through - k& - nk in c = g(k) - k& - nk. Here, nk is capital allocated to all newly born babies and k& is current per capita savings; each of the two terms has negative effect on current consumption. The efficient trade off is given by the Euler equation, which is a dynamic marginal condition equivalent to the static marginal condition that marginal benefit equals marginal cost. We will not prove the Euler equation here. Rather, we provide some economic intuition for the first order condition for the intertemporal optimization problem. Since dynamic marginal analysis is analogous to static marginal analysis, the efficient trade off requires equal marginal benefit and marginal cost of investment. But in the dynamic marginal analysis, the marginal benefit generated by an investment lasts for a long time, since capital can be used for many years after it is formed. The marginal benefit at each point in time when investment has been made is ∂F/∂k. The total marginal benefit after an investment is made is therefore ∫(∂F/∂k)dt. The marginal cost of the investment is instant and does not last for a long time, since it reduces only current consumption through an increase in per capita saving which relates to k& . Hence, the marginal cost of investment is ∂ F /∂ k& . If the total marginal benefit is greater than the instant marginal cost of the investment, then the total benefit net of cost can be increased by increasing investment. If the total marginal benefit is smaller than the instant marginal cost of the investment, then the total benefit net of cost can be increased by reducing investment. The efficient trade off will be achieved if the total marginal benefit equals the instant marginal cost, or if ∫(∂F/∂k)dt = ∂ F /∂ k& Differentiating two sides of the equation and noting that d[∫(∂F/∂k)dt]/dt = ∫d[(∂F/∂k)dt]/dt = ∫d(∂F/∂k) = ∂F/∂k, we obtain the first order condition for the efficient trade off, which is referred to as the Euler equation: (13.5)

∂ F / ∂ k = d (∂ F / ∂ k& ) / dt

The Euler equation is usually a second order differential equation in k. For the utility 1 , the Euler function f(c) = (cα-1)/α and the production function g(k) = Akβ, where β ∈(0,) equation is c& / c = (Aβkβ-1-n-ρ)/(1-α) (13.6)

431

where c = Ak β − k& − nk and c& = ( Aβk β −1 − n)k& − k&& . This is a second order nonlinear differential equation in k. We cannot obtain an analytical solution of the equilibrium that gives the optimum time path of per capita capital, k. But we can use a phase diagram to figure out qualitatively the dynamics of the optimum time path of k. To do so, we rearrange the first order condition as a system of differential equations in k and c (13.7)

c& = ( Aβk β −1 − n − ρ )c /(1 − α ) k& = Ak β − nk − c

0 k* (Aβ/n)1/(1-β) n1/(β-1) Figure 13.1: Phase Diagram of the Ramsey Model Letting c& = 0, we obtain k = [β/(n+r)]1/(1-β), which is a vertical line in the phase diagram of k and c in Fig. 13.1, where the horizontal axis represents the value of k, the vertical axis represents the value of c, and arrows represent the direction of movement of the two variables over time. If the system is in the region on the right-hand side of the vertical line, c& < 0 or c decreases with time. This is denoted by downward arrows in regimes (2) and (3) in the phase diagram. If the system is in regions (1) and (4) in the phase diagram, c& > 0 or c increases with time. This is denoted by upward arrows in regimes (1) and (4) in the phase diagram. Letting k& = 0 , we obtain c = Akβ-nk, which is a concave curve cutting the origin, whose maximum point is at k = (Aβ/n) 1/(1-β). If the system is in regions (1) and (2) below the curve, k& > 0, or k increases with time. This is denoted by eastward arrows in regimes (1) and (2) in the phase diagram. If the system is in regions (3) and (4) in the phase diagram, k& < 0 or k decreases with time. This is denoted by westward arrows in regimes (3) and (4) in the phase diagram. You can see that the phase diagram uses a two-dimensional graph of k and c to describe a threedimensional system of k, c, and t. The time dimension t is implicitly given by directed arrows. The steady state of the dynamic optimum decision is given by setting k& = c& = 0 or by the intersection between the two curves in the phase diagram: (13.8)

k* = [Aβ/(n+ρ)]1/(1-ρ), c* = [Aβ/(n+ρ)]ρ/(1-ρ)[1-Anβ/(n+ρ)] 432

(13.8) gives the static optimum levels of per capita consumption c and per capita capital k. Assume that the total factor productivity parameter A exogenously evolves according to the rule A = A0ebt, then k* and y* evolve at rate β/(1-β). This is referred to as the steady growth rate. The steady growth rate may depend also on the growth rate of population size and the time preference parameter if population grows at a variable rate. The dynamic optimum decision given by the Euler equation describes the conditions for optimum transitional dynamics from the initial state to the static optimum. The dynamics are characterized by the stability of the static optimum or steady state. A steady state is stable if a deviation of the system from the steady state will generate movement of endogenous variables back toward the steady state. Otherwise the steady state is unstable. It can be seen from the phase diagram in Fig. 13.1 that the steady state is stable in regions (1) and (3), but is unstable in regions (2) and (4). This feature of dynamics is referred to as saddle-path stability. If the economy starts from a point near the saddle path in region (1), it will evolve from that point toward the steady state, where it will remain forever thereafter. Hence, there is no long-run growth. All growth takes place as transitional dynamics. In the transitional period from the initial state to the steady state (static optimum), the trade off is between the benefit and the cost of a faster move to the steady state. The Euler equation gives the condition for the efficient trade off in the transitional process. It can be seen that those time paths of c and k in region 2 are not optimal, since they will ultimately cut the vertical axis, generating 0 per capita capital and thereby 0 per capita consumption. Also, those time paths in region 4 are not optimal, since they generate lower per capita consumption than the saddle path from the same per capita capital at each point in time. If the phase diagram is not used, we can use the following approach to analyzing the stability of the steady state. We first expand the system of differential equations in (13.7) as a Taylor series in the neighborhood of the steady state. We take the linear terms with the first order derivatives in the series as the proxies of the original differential equations. By doing so, the original nonlinear differential equations are converted to linear differential equations. Then we can check the eigenvalues of the coefficient matrix of the system of linear differential equations. If the two eigenvalues are real and positive, then the system is unstable. If the two eigenvalues are real and negative, the system is stable. If the two eigenvalues are real with opposite signs, then the system is saddle-path stable. If the two eigenvalues are complex with negative real parts, then the system converges to the steady state in an oscillating manner. If the two eigenvalues are complex with positive real parts, the system is unstable and oscillating. If the two eigenvalues are complex with 0 real parts, the trajectories are then elliptical around the steady state. This version of the Ramsey model is sometimes referred as the neoclassical growth model, which cannot generate long-run endogenous growth in the absence of exogenous evolution in parameters. But if we assume that the parameter of total factor productivity, A, exogenously evolves over time, then this version of the Ramsey model will generate exogenous growth driven by exogenous technical progress. Such exogenous technical progress is not affected by individuals’ decisions concerning economic organization and resource allocation.

433

The neoclassical growth model predicts a negative effect of the growth rate of population n on the growth rate of per capita income and per capita consumption. From (13.6), it is clear that the optimum growth rate of per capita consumption c& /c is a decreasing function of the growth rate of population n. From the steady state, given in (13.8), it can be seen that as the growth rate of population increases, the steady state levels of per capita consumption and per capita capital decline. The intuition behind the negative effect of the growth rate of population on economic growth runs as follows. If population increases, then part of saving must be used to equip newly born babies with capital (hospitals, freeways, and other facilities), so that saving used to increase per capita capital is reduced. Since per capita output is an increasing function of per capita capital, this decrease in saving used to increase per capita capital will slow down economic growth. This intuition may not be compatible with observations of a positive correlation between economic growth and population growth in the early growth stages of the US, Australia, and New Zealand, though it shows some consistency with the negative correlation between economic growth and population growth found in some African and South Asian countries (Dasgupta, 1995). As shown by the Smith-Young models, scale effects (negative or positive) are not essential for economic growth. If transaction efficiency is very low due to deficiencies of the legal system and other institutional arrangements, a large and high density population will be divided into many separate local markets with a low growth rate of per capita income. As transaction efficiency is improved, the local markets will merge into an increasingly more integrated market with a higher growth rate of per capita income. Example 13.2: AK Model. 1 Now we consider a special version of the Ramsey model: the AK model, where the production function is Y =AK, or y =Ak. We assume the growth rate of population is 0. For the AK model, the Euler equation becomes (13.9)

c& / c = ( A − ρ ) / (1 − α ) or k&& + [ ρ − (2 − α ) A]k& / (1 − α ) + ( A − ρ ) Ak / (1 − α ) = 0

with the boundary conditions k = k0 for t = 0 and k = kT for t = T. This is a linear second order homogeneous differential equation in k. Its steady state is k = 0, which is not stable. This is a feature of long-run endogenous growth. The solution of the differential equation is: (13.10)

k * = B1 e 2 At + B2 e 2 ( A − ρ ) t /(1−α )

where the integration constants B1 and B2 are given by the system of equations

k0 = B 1 + B 2 and k T = B1 e 2 AT + B2 e 2 ( A − ρ ) T /(1−α ) (13.10) and the production function y = Ak yield the optimum time path of per capita income. The optimum growth rate of per capita consumption, given in (13.9), is a 1

Romer (1986) extends this version of the Ramsey model by specifying external economies of scale and interactions between self-interested decisions. Its reduced form is the same as the AK model.

434

constant. But the optimum growth rates of per capita income and capital per person are not constants. The differentiation of (13.10) with respect to t yields the optimum growth rate of per capita capital k& /k and the optimum per capita saving rate i = I / N = K& / N = k& , which, together with the production function, yield the optimum growth rate of per capita income y& /y = Ak& /k. From the production function Y = AK, it is obvious that Y& /Y = K& /K = (I/K)(AK/Y) = A(I/Y), that is, the growth rate of income is an increasing function of the investment rate. This type IV scale effect is rejected by empirical evidence found by Jones (1995). The growth rate of per capita consumption is always positive for A > ρ. Hence, longrun endogenous growth can take place in the absence of exogenous changes in parameters. However, a constant growth rate of per capita consumption is inconsistent with the take off phenomenon in the industrialization process, which is associated with an accelerating growth (increasing growth rate) of per capita consumption and income, documented by Romer (1986) and Chen, Lin, and Yang (1999). It is also inconsistent with a slowing down of growth in the post industrialization era, documented by Chen, Lin, and Yang (1999). A test of the explanatory power of a growth model is to see if it can predict both accelerating and decelerating growth. Many authors introduce new features into the Ramsey model to enable it to tell more stories. For instance, the UzawaLucas model in exercise 3 introduces externality and a trade off between working and education to endogenize evolution in the income share of human capital. An extensive empirical literature has been developed to test the two versions of the Ramsey model: the neoclassical version in example 13.1 and the AK version in example 13.2. It is claimed that the neoclassical version predicts conditional convergence, while the AK version would not predict this. Absolute convergence takes place when poorer areas grow faster than richer ones whatever the respective characteristics, represented by parameters of tastes, production conditions, and population size and its growth, whereas there is conditional convergence when a country or a region grows faster, the farther it is below its own steady state. The latter form of convergence is the weaker. Under certain conditions, conditional convergence even allows for rich countries to grow faster than poorer ones. Transitional dynamics in example 13.1 are determined by a system of nonlinear differential equations in (13.7). Using simulation on the computer, it can be shown that sequential decelerating-accelerating-decelerating growth pattern is possible during a transitional period. Hence, the transitional dynamics of the Ramsey model in example 13.1 do not always predict conditional convergence. If the total factor productivity parameter A in (13.8) evolves according to the moving rule A = A0ebt, the steady growth rates of k and y are β/(1-β) and they may depend on the growth rate of population, and the time preference parameter too if population grows at a variable rate. If the growth rate of population and parameters of time preference and production differ across countries and exogenous technical progress is present, the Ramsey model does not predict conditional convergence. Hence, all empirical work, such as Sala-i-Martin (1996) and Romer (1986), that confirms or rejects conditional convergence may not confirm or reject the Ramsey model. 2 Sala-i-Martin (1996) defines absolute β-convergence as the case in which poor economies tend to grow faster than rich ones and defines σ-convergence as the case in which the dispersion of real per capita GDP

2

435

The real empirical distinction between the neoclassical and AK versions of the Ramsey model relates to type I scale effect. For the former, the growth rate of per capita income decreases with the growth rate of population, whereas the growth rate of per capita income increases with population size in the latter. Unfortunately, empirical evidences reviewed in Dasgupta (1995) and the National Research Council (1986) confirm neither of the predictions. The second piece of empirical work is to find evidence for or against decreasing returns to capital. Romer (1987) has found evidence for the capital elasticity of output that is greater than one. But King and Levine (1994) find evidence for the elasticity that is smaller than one. In this literature, some interesting work rejects all of the neoclassical prediction that capital-labor ratio increases as an economy grows. Cho and Graham (1996) have found that many poor countries ran down their capital-labor ratios between 19601985. This reminds us that the neoclassical framework and concepts may not be appropriate for analyzing the real economic development process. According to SmithYoung’s theory of economic development, an increase in capital in statistical data is an indirect reflection of finer division of labor in roundabout production or evolution of division of labor between firms, and an increase in labor in statistical data reflects the evolution of division of labor within firms (see models in chapters 8 and 12). It may have nothing to do with increasing or decreasing returns to capital. A declining capital-labor ratio in economic development may be associated with faster evolution of division of labor within firms, than that between firms. Evolution of division of labor within firms will increase trade in labor and decrease trade in intermediate goods and services, while evolution of division of labor between firms have the opposite effects, resulting in faster increases in trade of labor than in trade volume of goods. This analysis indicates that it is more important to find the right analytical framework than to run regression on the basis of inappropriate concepts and analytical frameworks. Various versions of the Ramsey model share the feature that they are aggregate decision models. The relative prices of different goods, and interactions between selfinterested decisions, are not endogenized. In the next section, we shall consider dynamic microeconomic equilibrium models, which endogenize the consequence of interactions between self-interested intertemporal decisions.

13.3. R&D Based Endogenous Growth Models

R&D based endogenous growth models have the following features. They are dynamic general equilibrium rather than decision models, so that they endogenize not only selfinterested behavior, but also prices as the consequence of interactions between selfinterested decisions. To endogenize evolution in the number of goods. they use the trade off between economies of scale and economies of complementarity between goods in raising either utility or productivity. The CES function is a crucial vehicle for levels of a group of economies tends to decrease over time. His empirical works show that there was neither σ-convergence nor absolute β-convergence in the cross-country distribution of world GDP between 1960 and 1990, although the sample of OECD economies displays σ-convergence and so do the samples of regions within a country, such as the US, Japan, Germany, the UK, France, Italy, or Spain. Romer (1986) finds evidence for divergence from time series data.

436

endogenizing the number of goods in the R&D based growth models. We use Barro and Sala-i-Martin's extended version (1995) of the Romer model (1990) to illustrate these features. Example 13.3: Barro and Sala-i-Martin's version (1995) of the Romer model (1990). The pure consumer’s dynamic decision problem is T

Max : U (T ) = ∫ [(c α − 1) / α ]e 0

− ρt

dt s.t. c + s& = rs + w

where s is the saving level at time t, r is the market interest rate at time t, so that rs is the level of interest earnings at time t, and s& is the change rate of saving. We assume that each consumer is endowed with 1 unit of labor and receives the wage rate w. Later, we will see that perfect competition in the market for final goods and monopolistic competition in the markets for intermediate goods drive profit to 0. Hence, the consumer’s income comes only from interest earnings and wages. α∈(0, 1) is a parameter of elasticity of substitution between consumption at different points in time since ∫[(cα1)/α]e-ρtdt ≈ ∑s {[cα(s)-1]/α}e-ρsΔts, which is a CES function of c. ρ is a subjective discount rate. Using the budget constraint, we can express the function to be integrated as a function of s, s& , and t: F ≡ [(rs + w − s&) α − 1](1 / α )e − ρt The Euler equation ∂ F / ∂ s = d(∂ F / ∂ s&) / dt yields (13.11)

c& / c = (r − ρ) /(1 − α)

where c = rs + w − s& . This is a second order differential equation in s. The production function of the final good is (13.12)

y = AL1y−β Σ in=1 xiβ

where β∈(0, 1), y is the output level of the final good, Ly is the amount of labor allocated to the production of the final good, xi is the amount of intermediate good i employed to produce the final good, and n is the number of intermediate goods. This production function displays constant returns to scale of Ly and xi. But it is a type of CES function in xi and total factor productivity is a monotonically increasing function of the number of intermediate goods. Hence, this function has external economies associated with the number of intermediate goods, which can generate endogenous productivity progress. The profit of the representative firm producing the final good is π y = y − wL y − Σ in=1 pi xi

where the decision variables are Ly and xi. We assume the final good to be the numeraire, so its price is 1. pi is the price of intermediate good i in terms of the final good. The two first order conditions, the zero profit condition, and the market clearing condition for labor yield

437

(13.13a)

w = (1 − β) An(βA / pi ) β /(1−β )

(13.13b)

xi = L(βA / pi )

(13.13c)

y = AnL(β A / pi )

1

( 1− β )

β

( 1− β )

where the symmetry of the model is used and L is labor supply as well as population size. Next, we consider the firm producing intermediate good i. The firm spends b units of the final good to invent intermediate good i and gets a patent for it. Hence, the market for intermediate goods is monopolistically competitive. There is only one firm producing an intermediate good, so that the price of the good is the monopolist’s decision variable. But free entry will drive pure profit to 0. Hence, total gross profit just breaks even the investment to invent the good. If we assume that the production of good i employs labor, the decision problem for a firm producing good i that emerges at time t will be asymmetric to the decision problem for the firm producing another good, which emerges at time t’. This asymmetry renders the algebra intractable. Hence, we assume that only final goods are used as inputs to produce an intermediate good. Suppose 1 unit of the final good is needed to produce 1 unit of each intermediate good, so that the gross profit in producing intermediate good i is (pi − 1)xi . Inserting the demand function for intermediate good i, given in (13.13b), into the gross profit formula, the gross profit for the firm is thus (13.14)

π i = (pi − 1)L (βA / pi )

1

(1− β )

The optimum price that maximizes the gross profit is then (13.15)

pi = 1 /β > 1 .

This implies that the prices of all intermediate goods that are available from the market are the same at any point in time. This ensures the symmetry of the model. It can be verified that if labor is employed to produce the intermediate goods, the symmetry cannot be retained. Inserting the optimum price into (13.14), we can compute the total present value of gross profit from the time when the intermediate good becomes available to terminal time T. The total present value of gross profit is also the value of the firm in the market V(t). (13.16a)

V (t ) = ∫ ( pi − 1) x i e − r (τ − t ) dτ T

t

= [ L( β 2 A)

1

( 1− β )

/ β ]∫ e − r (τ − t ) dτ T

t

Free entry and arbitrage will drive pure profit to 0, that is, the total present value of gross profit equals investment in inventing the good, or (13.16b)

V (t ) = b .

438

With Barro and Sala-i-Martin's assumption of a constant r, (13.16) yields the equilibrium interest rate (13.17)

r = ( L / b)(β 2 A)

1

( 1− β )

(1 − β) / β

Inserting the equilibrium price of the final good, given in (13.15), into (13.13b) yields the equilibrium wage rate. Hence, (13.13b), (13.15), and (13.17) give all the information about the dynamic equilibrium prices of goods and factors. Plugging the equilibrium interest rate, given in (13.17), into (13.11) yields the equilibrium time path of the growth rate of per capita consumption: (13.18)

c& / c = {[( L / b)(β 2 A)

1

( 1− β )

(1 − β) / β] − ρ} /(1 − α)

This growth rate is an increasing function of population size L. That is, the Romer model has a Type I scale effect, which means a country with a larger population size grows faster than a smaller country. This empirical implication is rejected by empirical evidence in Dasgupta (1995) and from the National Research Council (1986). We can see that India did not have a high growth rate of per capita consumption until the recent reform period, despite its large population size. This is true as well for pre-reform China. Inserting the equilibrium price of the final good, given in (13.15), into the demand function for intermediate goods in (13.13b) yields the equilibrium quantity of each intermediate good (13.19)

xi = L(β 2 A)

1

( 1− β )

Plugging this back into the production function of the final good, given in (13.12), and using the market clearing condition for labor, we can express the equilibrium quantity of the final good as a function of the number of intermediate goods, n: (13.20)

y = (β 2β A)

1

( 1− β )

Ln

Taking the logarithm of the two sides of the equation and then differentiating it with respect to t, we can see that the growth rate of output of the final goods is an increasing function of the growth rate of the number of intermediate goods, n& /n and the growth rate of population L& /L. Noting that the size of the R&D sector is b n& , we can see that the growth rate of output of the final good is an increasing function of the size of the R&D sector. This is a Type V scale effect. This scale effect of the Romer model is rejected by empirical evidence in developed countries (Jones, 1995). The size of the R&D sector in the US increased by several times in the last several decades, but the growth rate of output was quite steady during the same period of time. In order to figure out the equilibrium dynamics of the model, we now consider the market clearing condition for the final good. Each consumer’s demand for the final good is c, so that L consumers’ total demand for the final good is Lc. 1 unit of the final good is needed to produce 1 unit of each of n intermediate goods that are available from the

439

market at time t. Hence, total demand for the final goods from the n sectors is nxi . The number of new goods that emerges at time t is n& . Each of them needs b units of the final good to invent. Hence, the demand for the final good from the R&D sector at time t is b n& . The market clearing condition for the final good is therefore: (13.21)

y = cL + nxi + bn&

Inserting (13.20) into (13.21), we have, together with (13.11), a system of first order linear differential equations: (13.22a) (13.22b)

c& = Dc n& = ( L / b)( En − c)

where D ≡ [(Aβ1+β)1/(1-β)(1-β)(L/b)-ρ]/(1-α) > 0 iff (13.22c)

(Aβ1+β)1/(1-β)(1-β)L > bρ.

Also, we have E ≡ (β 2β A)

1

( 1− β )

(1 − β 2 ) and n& is positive iff

(13.22d) En > c. We can thus use the phase diagram of Figure 13.2 to describe the equilibrium dynamics of the Romer model. From (13.22), we can see that the necessary condition for long-run growth is that the population size L and total factor productivity of the final good A are sufficiently large, compared to the invention cost coefficient b and the subjective discount rate ρ. If this condition (13.22c) is satisfied, then a unique steady state of the equilibrium, given by n& = c& = 0, is c = n = 0, which is of course unstable. This is a distinctive feature of longrun endogenous growth, which implies that as soon as the economy starts to deviate from the steady state, it never comes back. Suppose condition (13.22c) is met; then the condition for long-run growth that is associated with an increasing number of intermediate goods, given by (13.22d), is that the economy starts from a sufficiently large number of intermediate goods, compared to per capita consumption of the final good. This condition can be further illustrated by the phase diagram. Letting n& = 0 , we obtain a straight line in the phase diagram, given by n = c/E. Underneath the line, the dynamic equilibrium number of intermediate goods keeps decreasing, while above the line, this number keeps increasing.

440

Figure 13.2: Phase Diagram of the Romer Model

From (13.22a), we can see that c always increases for a positive c if the condition (13.22c) is met. Hence, if (13.22c) holds, there are only two regions in the phase diagram. Above the locus n& = 0 , economic growth is characterized by simultaneous increases in per capita consumption and in the number of intermediate goods, while below the locus n& = 0 , endogenous growth in per capita consumption is associated with a decline in the number of intermediate goods. If the initial number of intermediate goods is sufficiently large compared to per capita consumption, so that (13.22d) is met and the economy starts from a point above the locus n& = 0 , then endogenous economic growth features spontaneous evolution in the number of intermediate goods or the incessant emergence of new machines and related new technology. It is not difficult to verify that the coefficient matrix of the system of constant coefficient differential equations in (13.22) has two positive real eigenvalues. This can be confirmed by ∂ c& /∂ c > 0 and ∂ n& /∂ n > 0 . This implies that the steady state of the dynamic equilibrium is unstable, a feature of long-run endogenous economic growth. The intuition behind the dynamic equilibrium runs as follows. If the population size L and total factor productivity of the final good A are sufficiently large, compared to the invention cost coefficient b and the subjective discount rate ρ, and the initial number of intermediate goods is not small, then saving can be used to invent more new machines, which improve productivity and raise income. Hence, consumption and saving can increase side by side. This implies more investment in the R&D sector and more invention of new machines, which will improve productivity and raise income again. This positive feedback, or virtuous circle, will generate incessant evolution in per capita consumption and in the number of intermediate goods. The intuition of the scale effect in the Romer model is that since the invention cost of a good b can be shared by more individuals as the population size increases, the per capita invention cost of each new good declines as the population expands. Though the intuition of the scale effect seems to make sense, it might be misleading. In the Romer model, the neoclassical dichotomy between pure consumers and firms is assumed. This implies that the whole economy is always an integrated market and separate local markets never occur in dynamic equilibrium. Each consumer indirectly consumes all n intermediate goods that are available from the integrated market at a particular point in time. This implies that the neoclassical endogenous growth models 441

cannot endogenize the evolution of the degree of market integration or the network size of division of labor. The scale effect is based on this feature of the neoclassical endogenous growth models. If we abandon the neoclassical dichotomy and adopt the Smith-Young framework with endogenous specialization, then the economy may be divided into many separate local business communities that do not trade with each other when transaction efficiency is very low. Hence, a large population size is not sufficient for an integrated network of division of labor to emerge from equilibrium. In the absence of that network, each local community duplicates the invention cost or learning cost of other local communities, and a large population size cannot fully utilize the positive network effect of division of labor between a professional R&D sector and the rest of the economy. Hence, from a SmithYoung point of view, whether positive network effects of the division of labor between the professional R&D sector and the rest of the economy can be exploited is determined by the equilibrium network size of division of labor, which is determined by transaction conditions rather than by the population size. As transaction conditions are improved, or as division of labor spontaneously evolves to a sufficiently high level (as shown in the next chapter), many separate local communities will merge into an increasingly more integrated market network, thereby generating endogenous growth and related development phenomena. This can take place in the absence of population growth and other scale effects. When we talk about a large market, as in the US or China, what we really mean is that transaction conditions are good, rather than that the population size is large. We know the population size of Europe is comparable to that of the US. But different languages and cultures, different tariff and monetary systems, and fragmented stock market, TV, and distribution networks in Europe imply that transaction conditions are substantially inferior to those in the US. Hence, the same population size does not mean the same size of the market. The population size in Taiwan (22 million) is much smaller than in mainland China (1.3 billion). But international and domestic trade volume for Taiwan was greater than that for mainland China in the 1970s and 1980s. When we say the Australian market is too small, what we really mean is that transaction efficiency for trade between this continent and other continents is too low due to Australia’s isolated geographical position. This implies that a large population size does not necessarily imply a large size of the market. The extent of the market, as we have shown in the Smith-Young models, is determined by the equilibrium network size of division of labor, which is determined by transaction conditions in a static model or by endogenous evolution in division of labor in a dynamic equilibrium model. If we understand the distinction between the network effect of division of labor and economies of scale, we will see that the intuition for scale effect is misleading. This is why the scale effect is conclusively rejected by empirical evidence. In the model in example 13.3, the dynamic equilibrium is not Pareto optimal since individual decision makers do not take into account the positive effect of the number of intermediate goods on the total factor productivity of the final good. As in other R&D based growth models, the external economies and spill-over effects that are not exploited by the price system make the equilibrium growth inefficient compared to the Pareto optimum. For some endogenous growth models, such as the Romer model (1986) and

442

Lucas model (1988), no competitive equilibrium exists if external economies are internalized in individuals’ decision making. Inserting the production functions of x and y and the endowment constraint of labor into the utility function of the representative consumer, the Pareto optimum in example 13.3 can be defined as the solution to the dynamic optimization problem maximizing the total discounted utility of the representative consumer. It can be shown that the Pareto optimum growth rate of per capita consumption is [(Aββ)1/(1-β)(1-β)(L/b)-ρ]/(1-α), which is greater than the equilibrium growth rate of per capita consumption, given in (13.18), for β∈(0, 1). This implies that the external economies and spill-over effects are not the driving force behind long-run economic growth in the R&D based growth models. Rather they are an obstacle to growth. Spill-over effects are a source of endogenous transaction costs, which impede economic growth by discouraging investment in intellectual property. China’s experience before the 20th century is a good example. Then there were neither patent laws nor other laws to protect the residual rights of owners of firms in China. Hence, there were substantial spill-over effects from smart Chinese inventions. Since the inventors of the new technology and entrepreneurial ideas could not appropriate incomes from their intellectual properties, the Chinese were reluctant to invest in intellectual property and entrepreneurial activities despite the high IQ of the Chinese people. Hence, many Chinese inventions could not be commercialized and expanded to create an industrial revolution because of the spill-over effects. The real story of the economic growth process is that patent laws, laws that protected free associations (including free enterprises) and private properties, de facto laissez-faire policies that prevailed in 18th and 19th century Britain, and other related institutions significantly reduced all kinds of endogenous transaction costs, including those caused by spill-over effects, so that evolution in division of labor between the production of intellectual properties and the production of tangible goods was significantly speeded up in the 18th and 19th centuries in Britain and Western Europe (see Baechler, 1976, Macfarlane, 1988, Mokyr, 1993, North, 1981, and Rosenberg and Birdzell, 1986). The driving force of this process was not spill-over effects, but rather the emergence of institutions that internalized these effects and that reduced endogenous transaction costs caused by these effects.

Key Terms and Review Exogenous vs. endogenous growth Differences between the Harrod-Domar model, the Sollow model, the AK model, and R&D based models Euler equation and dynamic marginal analysis Type I, II, III, IV, and V scale effects; why they are rejected by empirical observations? Saving and investment fundamentalism, technology fundamentalism Dynamic general equilibrium mechanisms generating spontaneous coevolution of the number of goods and productivity Absolute vs. conditional convergence, β convergence, and σ convergence

443

Further Reading Neoclassical growth models: Barro (1991, 1997), Barro and Sala-i-Martin (1991, 1992, 1995), Rebelo (1991), Solow (1956); R&D based models and other endogenous growth models: Judd (1985), Lucas (1988, 1993), Romer (1986, 1987, 1990), Grossman and Helpman (1989, 1990, 1991), Aghion and Howitt (1992), Alwyn Young (1991), Weitzman (1998); Empirical evidences: Sala-i-Martin (1996), Jones (1995a, b), Chen, Lin, and Yang (1999), National Research Council (1986), Dasgupta (1995), Cho and Graham (1996), King and Levine (1994), Mankiw, Romer, and Weil (1992), Romer (1987), Liu and Yang (1999), Temple (1999), Aghion and Howitt (1998), Temple (1999); Historical evidence: Baechler (1976), Macfarlane (1988), Mokyr (1993), North (1981), Rosenberg and Birdzell (1986), Marshall (1890), Allyn Young, Braudel (1979), Chandler (1990), Solow (1956), and Lucas (1988), Craft (1997); Empirical research on micro development phenomena: Deaton and Paxson (1998a, b), Paxson, 1999, Deaton and Case (1998, 1999a, b).

Questions 1. What are the differences between the Ramsey model, the Harrod-Domar model, and the Solow model? 2. Romer (1986) and Lucas (1988) argue that the neoclassical growth model cannot predict observed divergence of growth rates of per capita income between different countries. Use the distinction between the concepts of conditional and absolute convergence to show that the Ramsey model in example 13.1 may predict conditional divergence of growth rates of per capita consumption. In your analysis, consider the following three cases. (i) transitional dynamics for a sufficient large difference between the initial state and steady state; (ii) steady state with exogenous evolution of A = A0e-bt; (iii) population grows at a variable rate. 3. What are the differences between the Ramsey model and the R&D based model? 4. The driving force of the AK model and R&D based models are (internal or external) economies of scale and the driving force of the Smith-Young models in the previous chapters and the Smith-Young growth models in chapters 14, 15, 16, and 18 is the network effect of division of labor. The difference between the two approaches to explaining economic development originates in the debate between Allyn Young, who rejected the notion of economies of scale as a misrepresentation of economies of division of labor, and his student Knight, who rejected the existence of any kinds of increasing returns, and Marshall, who used the notion of external economies of scale to represent economies of division of labor. Discuss the difference between the two approaches to explaining economic development. 5. In the Romer model (1986) and the Lucas model (1988), the key feature that ensures the existence of equilibrium is that economies of scale are external to firms or there exists externality of education. If the external economies are internalized by the market, what will happen to the equilibria in these two models? Suppose that a central planner solves for an optimum growth plan, which takes into account of all external economies of scale and externality. What will be the optimum growth rates of per capita consumption? 6. An economist argues that since the population size of Australia is less than 20 million and that of the US is more than 200 million, the extent of the market in Australia is much smaller than in the US. Hence, all kinds of machines are much cheaper in the US than in Australia. The new endogenous growth models recently developed by Judd and Romer generate a similar prediction: that larger economies will generate higher growth rates and levels of per capita income. Use the model in this chapter to comment on this view. In your analysis, you may use the Smith-Young

444

theorem that division of labor depends upon the extent of the market and the extent of the market is determined by the level of division of labor, to clarify the relationship between the extent of the market, population size, transaction efficiency, and the network size of division of labor. 7. The driving force of economic growth in the models in this chapter is an ad hoc “if and only if” relationship between investment and productivity. Give some counter-examples to such a relationship. According to Smith and Young, investment creates economic growth because it promotes division of labor in roundabout production. Discuss the difference between the neoclassical ad hoc relationship between investment and growth and the classical way of explaining the wealth of the nation by division of labor. (See chapter 14 for more about this.) 8. Why cannot the models in this chapter explain the evolution of individuals’ specialization, the emergence of the firm, the increase of the income share of the industrial sector and transaction costs, and many of the other interesting phenomena usually associated with economic development?

Exercises 1. Consider the Ramsey model in example 13.1. Assume the production function is Y = A K β L1− β and the change rate of capital is K& = I − γ K if the depreciation rate of capital, γ, is taken into account. Solve the optimum growth rates of per capita consumption. Use a phase graph to describe the dynamics of per capita consumption and the capital-labor ratio. 2. Assume that in the model in exercise 1 the production function takes the AK form. Solve for the dynamics of optimum growth. 3. Consider the Uzawa-Lucas model, which is an extension of the Ramsey model. Redefine labor L in the Ramsey model as uH, where u ∈ (0,1) is the fraction of total human capital that is devoted to the production of goods and 1-u is the fraction devoted to education. Hence, the production function is Y = AK β (uH )1−β , where H is total available human capital at each point in time. The growth rate H& / H is a linear increasing function of 1-u. The rest of the model is the same as in the Ramsey model. Solve for the optimum growth plan. Use the trade off between education and production and the trade off between current and future consumption to tell the story behind your solution. 4. (T. N. Srinivasan 1964) Interpret H in the Uzawa-Lucas model as population size and 1-u as the fraction of human resources used to produce offspring. Discuss the implications of a model with endogenous population growth. 5. (Romer, 1986) A representative consumer maximizes U = ∫0T ue-ρtdt, subject to u = (cb–1)/b, w+rs = (ds/dt)+c, where c is consumption, w is wage rate, s is saving level, and r is interest rate. The population size is one. The income identity is i+c=y, where i = dk/dt, y is given by the production function y = Bkαl1-α for a representative firm. This production function displays constant returns to scale for each firm. But there are external economies of scale, given by B = A(K/L)β, where K is the total amount of capital employed and L is the total amount of labor employed in production. In equilibrium, K=k and L=l=1 if the number of firms is assumed to be one. It is assumed that α+β≥1. Solve for the dynamic general equilibrium. Under what condition is the solution of this model with external economies of scale the same as that of the AK model?. Analyze the difference between this model and the AK model in connection to Pareto optimality of equilibrium. 6. Use the Ramsey model in 13.1 to show that the steady growth rates of per capita capital and per capita income are dependent on taste and production parameters α and β when total factor productivity A exogenously grows at rate b. Use your result to show that the Ramsey model

445

predicts conditional divergence, that is, the growth rates of two countries with different values of parameters α and β never converge, even if exogenous technical progress is the same for them. 7. (Aghion-Howitt, 1992) Consider an economy with a representative consumer consuming y. The representative firm producing y has the production function ys = Asxsα, where α∈(0,1), xs is the amount of intermediate good of generation s. In the market, only one generation of good is produced. When a new generation of good emerges, it replaces the old generation and As = γAs-1 where γ>1 looks like an exogenous technical progress coefficient. The probability for the emergence of a new generation of intermediate good is λn where n is the amount of labor employed for invention. The production of each unit of intermediate good needs one unit of labor. The market for intermediate goods is monopolistically competitive. This implies that the producer of the available intermediate good can manipulate the interaction between price and quantity of the good to maximize profit. But free entry will establish the following asset equation, which is analogous to a zero profit condition in static models. rVs = πs-λnsVs where r is the interest rate, Vs is the value of the firm producing a good of generation s, πs is its profit, λns is the probability that this generation of good is replaced by the next generation of good, λnsVs is the expected loss of value of the firm if this replacement occurs, and Vs is the discounted expected payoff to the sth innovation. The population size and labor force are L. In the labor market, the wage rate for a worker producing the intermediate good must be the same as that for a researcher. The expected value of n units of labor in research is λnVs, so that this arbitrage condition requires ws = λnVs/n = λVs. A steady state is defined by ωs = ωs-1, where ωs = ws/As. Show that the expected growth rate of y is λnlnγ, which implies a type V scale effect (growth rate of per capita income increases with the size of the R&D sector). Solve for the equilibrium and show that the probability of the emergence of a new generation of goods λn is an increasing function of population size L, which implies a type I scale effect (growth rate of per capita income increases with the population size). Why are the type I and type V scale effects rejected by empirical evidence? 8. (Mankiw, Romer, and Weil, 1992) Consider the neoclassical model in example 13.1 where output is given by Y = (AL)αK1-α. The technology parameter A grows at rate x, the population at rate n, and the stock of capital depreciates at rate δ. There is a constant saving rate, s. Find an expression for the rate of growth of income toward the steady state that depends on initial income. Use this model to analyze a convergence phenomenon and upon what the convergence is conditional. Assume the production function is Y = (AL)1-α-βKαHβ, where 0 0 if a ρi > ρ n . D From (14.14), aρi>ρn if nt∈(1,m). Hence, the comparative advantage of an expert over a novice increases endogenously as the division of labor evolves (even though there is no exogenous comparative advantage). The income share of transaction costs, S, is equal to the ratio of the cost of bought goods lost in transit to nominal income. Since prtxrtd is the same for all r∈R, therefore, (1Kt)(nt-1)prtxrtd is the transaction cost and (nt-1)prtxrtd=prtxrts is per capita nominal income at time t. Hence

(1 - K t )(nt - 1) prt x drt (nt - 1) prt x drt

k nt From (14.16), aρi>ρn if nt∈(1,m). Hence, the comparative advantage of an expert over a novice increases endogenously as the division of labor evolves (even though there is no exogenous comparative advantage). The income share of transaction costs, S, is equal to the ratio of the cost of bought goods lost in transit to nominal income. Since prtxrtd is the same for all r∈R, therefore, (1Kt)(nt-1)prtxrtd is the transaction cost and (nt-1)prtxrtd=prtxrts is percapita nominal income at time t. Hence ( kd nt / nt dk ) - 1 dS ∂S = > 0, (14.26a) if nt < m. dk ∂ nt nt is the income share of the transaction cost. Differentiation of (14.26a) yields

(14.25)

S ≡

= 1-

466

( kd nt / nt dk ) - 1 dS ∂S = > 0, if nt < m. dk ∂ nt nt Condition (14.26b) implies that the income share of transaction costs increases as the division of labor evolves and as transaction efficiency is improved (the latter result holds provided that the level of the division of labor is elastic with respect to transaction efficiency). Since transaction costs can be viewed as roundabout production costs, condition (14.26b) implies that the income share of the roundabout productive sector rises as the division of labor evolves. It is interesting to note that transaction efficiency Kt = k/nt decreases as division of labor spontaneously evolves (nt increases). Since K& t / K t = k& / k − n& t / nt , it is possible that transaction efficiency Kt declines as transaction condition parameter k increases. This occurs when the increase in n caused by an increase in k dominates the increase in k itself. This result is intuitive. As transaction condition is improved, the network of division of labor expands. Individuals must trade with more distant partners, so that transaction efficiency declines provided increases in division of labor are faster than increases in k. The results in this section are summarized in the following proposition. (14.26b)

Proposition 14.2: The extent of the market, trade dependence, the extent of endogenous comparative advantage of an expert relative to a novice, and the income share of transaction costs increase as the division of labor evolves over time. 14.5. Empirical Evidences and Rethinking Endogenous Growth Theory

The Smithian model in this chapter generates the following empirical implications. (1) The income share of the transaction sector increases as division of labor evolves and per capita real income increases. (2) Growth performance and speed of evolution of division of labor critically depend on transaction conditions. (3) Economic development is positively associated with evolution of the degree of commercialization. Hypothesis (1) is verified by North’s empirical work (1986) which shows that the employment share of the transaction sector increased with economic development in the US in the past century. Hypothesis (2) is verified by historical evidences documented in North (1958) and North and Weingast (1989) and by empirical evidence provided in Barro (1997), Easton and Walker (1997), Gwartney and Lawson (1996, 1997), Gallup and Sachs (1998), and Sachs and Warner (1997). North shows that the continuous fall of ocean freight rates contributed significantly to early economic development in Europe. He and Weingast show that it was the institution (constitutional monarch and parliamentary democracy) established after the Glorious Revolution (1688) that ensured a credible commitment of the British government to the constitutional order and significantly reduced endogenous transaction costs caused by rent seeking, corruption, and state opportunism. Hence, economic development could take off in the UK in the 18th and 19th century. Barro (1997), Easton and Walker (1997), Frye and Shleifer (1997), Sachs and Warner (1997) have found empirical evidence for effects of institutions that affect transaction conditions on development performance. Hypothesis 3 is verified by historical evidence in Mokyr (1993, pp. 65-66) and empirical evidence in Yang, Wang, and Wills (1992). Mokyr documents evolution of the 467

degree of commercialization during the Industrial Revolution. Yang, Wang, and Wills document the evolution of degree of commercialization in China and find positive effects of transaction conditions in specifying and enforcing property rights on the evolution and economic growth. In addition, the Smithian model can be used to address the puzzle of scale effect and the debate over convergence in the literature of endogenous growth theory. Two classes of major endogenous growth models, the AK model and R&D-based model, discussed in chapter 13, have recently been tested against empirical data (see Jones, 1995a, b). The AK model generates a Type-IV scale effect, which is a positive relationship between the growth rate in per capita GDP and the investment rate 1 . The scale effect is rejected by the data, “suggesting that the AK models do not provide a good description of the driving forces behind growth” (Jones, 1995a, pp. 508-509). The R&D-based model generates a Type-V scale effect, which is a positive relationship between the growth rate in per capita GDP and the level of resources devoted to R&D 2 . Type-V scale effect is also rejected by empirical observations (Jones, 1995a, b). Jones (1995b), Young (1998), and Segerstrom (1998) have developed some models to salvage the R&D-based model, but the modified models still have type-I scale effect, a positive relationship between the growth rate in per capita GDP and the growth rate of population, which is also wildly at odds with empirical evidence surveyed by Dasgupta (1995). As Jones (1995b) indicates, endogenous growth cannot be preserved if the scale effect in the R&D-based model is eliminated. The Smithian model in this chapter has the following attractive features that can be used to address the puzzle of the scale effect. The driving force of economic growth in the Smithian model is the positive network effect of division of labor rather than economies of scale. Economies of division of labor differ from economies of scale as discussed in Allyn Young (1928). Investment in terms of transaction costs and related loss of current consumption enlarges scope for specialized learning by doing which enhances social learning capacity and related network effects on aggregate productivity in future. This implicit investment mechanism can generate long-term endogenous growth in the absence of interpersonal loan and commercialized saving. 3 It does not necessarily generate a positive correlation between tangible saving rate (or investment rate) and growth rates of per capita real income. The endogenous evolution of the number of traded goods in the Smithian model is associated with endogenous evolution in the size of the network of division of labor. As the size of the network increases, many separate local communities merge into an increasingly more integrated market. This can take place in the absence of an increase in population size and of other scale effects. Hence, the speed at which new traded goods emerge is determined by the speed of evolution of division of labor rather than by population size or the size of the R&D sector. In other words, in the R&D-based models, there is an “if and only if” relationship between investment in R&D and the number of new goods and related technology. But in the Smithian model, there is no such relationship. Endogenous technical progress is a matter of whether the network of division of labor evolves to a sufficiently large size to create a 1

According to Jones (1995a,b) and Barro and Sala-i-Martin (1995), the Romer model (1987), the Rebelo model (1987, 1991), the Barro model (1991), and the Benhabib and Jovanovic model (1991) can be considered as the AK model since their reduced forms are the same as that of the AK model. 2 Judd (1985), Romer (1990), Grossman and Helpman (1990, 1991), and Aghion and Howitt (1992), among others, are along this line. 3 The relationship between interpersonal loan and division of labor will be investigated in chapter 16.

468

social learning capacity and to make new traded goods commercially viable. The individual-specific economies of specialized learning by doing distinguishes the Smithian model from the other models with learning by doing (Arrow, 1962, Lucas, 1988, Stokey, 1991, Young, 1993, and others). In the Smithian model, the blend of individuals’ specialized learning by doing and an increase in the size of the network of division of labor can generate network effects of social learning without a scale effect. By contrast, the learning by doing in the other models is independent of evolution of division of labor and generates a scale effect. The growth rates of level of division of labor and of per capita real income in (14.20) are independent of population size M. The population size plays a very passive role in this model. It sets up a limit for the evolution in division of labor: the number of occupations cannot be larger than population size. Let us now turn to the debate over convergence. The new theory of endogenous growth was motivated in part by the criticism of the convergence theory based on the neoclassical growth model (Lucas, 1988, Romer, 1986). The absolute convergence hypothesis - per capita incomes of countries converge to one another in the long-run independently of their initial conditions - has been rejected by empirical data (Barro, 1991). Some new endogenous growth models are developed to predict the divergence phenomenon, accommodating the empirical evidence. However, the new theoretical models are not only disturbed by the puzzle of scale effects, they are also challenged by the new evidence on convergence. Many slightly different concepts of convergence and divergence are proposed (see Sala-i-Martin, 1996, Galor, 1996). However, all of these new concepts of convergence do not alter the fact that convergence and divergence, no matter how defined, may coexist and that such coexistence has not received the attention it deserves. One of the empirical implications of the Smithian model is a sequential pattern in divergence and convergence phenomena. The Smithian model implies that three stages of growth will take place sequentially: preindustrialization growth, accelerating growth and take off, and mature growth. Growth rate first declines, then increases, and finally declines again. This is consistent with Rostow’s (1960) description of the three historical stages of economic growth. As the transaction-condition parameter k increases, the growth rate of per capita real income rises, despite the fact that changes in k are not necessary for accelerating growth and for endogenous evolution in division of labor. The result of this comparative dynamics can be used to explain cross-country growth differentials, since different tariff regimes and degrees of openness, different institutional arrangements, different legal systems and related property rights regimes, and different geographical conditions across countries all imply different values of k across countries. Hence, those countries with a larger k enter the take off stage earlier. The UK, for example, entered the take off stage earlier than other countries since it is an island country which implied a higher shipment efficiency in the UK than in hinterland countries, such as Germany and China, when automobiles and trains were not available. The UK was the first country to have Statute of Monopolies (patent laws, 1624) which significantly improved transaction efficiency in trading intellectual property (see North, 1981). Evolving common laws and de facto laissez faire policy and deregulation of the British government, that started before Smith’s advocacy for free trade significantly improved transaction conditions (Mokyr, 1993). It is because of the deficient legal system, the violation of private property rights, extreme protectionism

469

(low level of openness), and political instability, all of which generated a small k, that France and China entered the take off stage later than Britain (Landes, 1998, pp. 34-36, Fairbank, 1962, Mokyr, 1990, pp. 235-50, 1993).. In a sense our model in this chapter shares a feature with Alwyn Young’s model (1991): learning speed and the growth rate of per capita real income decline over time if each individual’s number of traded goods is fixed. As the number of traded goods increases, the network of division of labor expands, thereby creating more scope for specialized learning by producing a greater variety of traded goods in society. It is obvious that for an economy that has experienced mature growth, the time path of the structure of division of labor and per capita real income are like those in Fig 14.3(b). As t increases from its initial value towards infinity, the curve representing per capita real income is first concave, then convex, finally concave again, if short-run fluctuation is eliminated. However, economies may differ in their parameter k that represents transaction conditions. We should therefore see that different countries enter the take off stage at different points in time. Between each pair of economies that enter the take off stage at different points in time, the difference in per capita real incomes should be an inverted U curve in the coordinates of time and per capita real income. That is, when the country that enters the take off stage earlier starts accelerating growth, the latecomer is still in the decelerating growth stage. Their per capita real incomes and growth rates will diverge. As the latecomer ultimately enters the take off stage and the leader reaches the mature growth stage, the differences in their per capita real incomes and growth rate diminish, and they experience convergence. This sequential divergence and convergence is illustrated in Fig. 14.5, in which per capita real incomes between two economies (UK and Germany) diverge before t1 and converge thereafter. The convergence may be conditional and different economies may not end up with the same income level and growth rate due to differences in k between them and to possible changes in k over time. The maintained hypothesis to test is that for a pair of economies that have experienced mature growth, the time path of the per capita income differential between them should be an inverted U curve. ut

Britain

Germany

t1

t

Figure 14.5: Sequential Divergence and Convergence

470

Chen, Lin, and Yang (1997) have tested the hypothesis against the data set of fifteen OECD countries over the long period of 1870-1992, provided by Maddison (1991) and Penn World Table 5.6. These countries are chosen because they all have experienced the stages of preindustrialization decelerating growth, take off, and mature growth with declining growth rate. The UK is taken to be the benchmark country for examining the sequential divergence and convergence phenomena, as the UK was the first country to experience a take off. The data show that the differences in per capita real income between the UK and the other 15 countries are roughly inverted U curves. Overall, the data set strongly supports the maintained hypothesis: an inverted U relation exists for long-run per capita real income differentials between the UK and thirteen out of fourteen countries. It conclusively rejects the hypotheses of a monotonically increasing difference in per capita real income. Also, it rejects hypothesis of a monotonically decreasing difference in per capita real income, except for Canada. The difference in per capita real income between UK and Canada monotonically decreases over time because of missing data of divergence which occurred before 1879, the first year for which internationally comparable data are available. The result is consistent with the Barro regression in Barro (1991) and Barro and Salai-Martin (1992), which shows that within part (1960-1990) of the time periods considered by Chen, Lin, and Yang (1870-1992), there is convergence among the OECD countries. The Barro regression misses the divergence part of the story, partly because it neglects the data before 1960 and partly because the regression of average growth rates within a period on the initial income may hide information about early divergence. The Smithian endogenous growth model is supported by Sachs and Warner's (1995) empirical work which uses a Barro regression to show that for those countries with high degree of openness and high institution quality convergence occurs, but for all countries with high and low degrees of openness there is no evidence for convergence. The Smithian model in this chapter predicts that if the transaction condition parameter k is very small, a country will stay in autarky (development trap) forever, while a country with a large k will enter takeoff stage eventually. Between these two countries, convergence never takes place. Since Sachs and Warner use the Barro regression and use data after 1960, their work misses possible divergence as well. What differentiates Smith-Young development and growth models from other endogenous growth models is that they make endogenous the level of specialization of individuals and the network size of division of labor. This feature allows us to capture Young's (1928, p. 539) insight that "the securing of increasing returns depends on the progressive division of labor". It also establishes a formal basis for his extension of Smith's famous proposition: That not only does the division of labor depend on the extent of the market "but the extent of the market also depends on the division of labor". In proposition 14.2 it was shown that as the division of labor evolves, the extent of the market will increase. Although the circular causation between the extent of the market and the level of division of labor in this dynamic general equilibrium model is similar to that in a Smith-Young static general equilibrium model, comovement of the extent of the market and network size of division of labor can take place in the absence of exogenous evolution of transaction conditions and other parameters in the dynamic model. In other words, the dynamic general equilibrium model has higher degree of endogenization than the static general equilibrium model.

471

As static Ricardian and Smithian models in chapters 3 and 4 formalize Lewis’ idea on evolution of dual structure between autarchic and commercialised sectors to completely commercialised economy, the model in this chapter can generate such evolution in the absence of exogenous evolution of trading efficiency. Hence, neither "labor surplus" nor "surplus of agricultural products" are necessary for this evolution in economic structure. From our theory, the necessary condition for this transition of economic structure is the sufficient evolution of the division of labor. Therefore, the key issue for economic development and the transition of economic structure is the initiation and speeding up of the evolution of the division of labor rather than the existence of a labor surplus. Institutions that determine transaction conditions are essential determinants of the speed of evolution of division of labor. According to Kuznets (1966) and Chenery’s (1979) theory of structural changes, any transition of economic structure is based on an increase in per capita income. According to the Smithian model, however, the increase in per capita real income and all other phenomena associated with structural changes are simply different aspects of the evolution of the division of labor. It does not make sense to explain one aspect of this evolution by another. All of the interdependent endogenous variables should be explained by a dynamic general equilibrium mechanism. Allyn Young (1928) called such a mechanism “moving equilibrium.” In other words, Kuznets and Chenery miss the nature of circular causation (feedback loop) between per capita income and other endogenous variables in a general equilibrium mechanism for structural changes. There are many different ways to specify a dynamic equilibrium model that can predict evolution in division of labor. In the next chapter we will specify a model that explains the coevolution of the division of labor by a tradeoff between economies of division of labor and costs in acquiring information on the efficient pattern of division of labor. In chapter 18, we will explain the evolution of the division of labor in terms of tradeoffs between economies of specialized learning by doing, cyclical unemployment, and transaction costs. Also, Wen (1997, see exercise 4) specifies k as a public good produced from government tax revenue. She explores a dynamic equilibrium mechanism that simultaneously determines interdependent aggregate productivity, income, optimum income share of government spending on transport infrastructure, transportation efficiency, and network size of division of labor. Zhang (1997, see exercise 5) introduces government monetary and fiscal policies into the model in this chapter to explore network effects of the policies on macroeconomic variables. A common feature of all of the different methods for predicting the evolution of the division of labor is that more rapidly increasing diseconomies of division of labor than economies of division of labor, as the level of division of labor increases, are necessary to generate the gradual evolution of the division of labor. A technical difference between Smith-Young growth models and other growth models is that dynamic inframarginal analysis (bang-bang control) is essential for managing the Smith-Young growth models, while dynamic marginal analysis (calculus of variations) is enough and the control theory is not necessary for managing other growth models, though many authors use the control theory to manage their models. The limitation of the method developed in this chapter is that it is not easy to apply to reasonably realistic asymmetric models. Symmetry of the model is essential to keep tractable this kind of dynamic general equilibrium model. But symmetry cannot be

472

preserved if the CES utility or production function is introduced into this kind of model, since the decision problems for individuals producing new goods who must change occupation are asymmetric to those who do not change occupation. Hence, control theory does not work and dynamic programming is needed if the number of goods is an endogenous variable or if the parameters of tastes and of production and transaction conditions are not the same across goods in this kind of model. In Borland and Yang (1995), it is shown that the algebra is cumbersome and results are very difficult to obtain even if dynamic programming is applied to asymmetric Smith-Young growth models. In the next chapter, we will develop a new method based on the concept of Walrasian sequential equilibrium and show that it is easy to dynamize all static Smith-Young models in this textbook by applying that approach. From chapter 6, we speculate that if exogenous comparative advantages are introduced into the dynamic model, it can be shown that endogenous advantages may be used to offset exogenous disadvantages. Suppose, for instance, that person A is exogenously more productive than person B in producing good 1 at t=0 when both of them have the same labor allocation. However, if person B's level of specialization in producing good 1 is higher than person A's for a sufficiently long period of time, B's productivity of good 1 may be higher than A's. Hence, for this kind of dynamic model, in order to win in market competition it is much more important to get a person involved in a self-enforced evolutionary process than to rely on inherited genius. If a person overestimates the implications of her exogenous advantage, she may turn out to be a loser to an exogenously less capable person who can effectively get herself involved in a self-accelerated evolutionary process (via, for instance, a successful self-selling strategy or advertisement). In question 1 at the end of this chapter, you are asked to use Smith-Young models to analyze a vicious circle between unemployment and endogenous disadvantage in accumulating professional human capital through learning by doing. Appendix 14.1: The Relationship between the Control Theory and Calculus of Variations The intertemporal decision problem in (14.7) is equivalent to maximizing the following Lagrange function F = ue-rt + αi(li- L& i ) + ∑j αj(lj- L& j ) + β(1- lI - ∑j lj) where li = L& i , lj = L& j , and u can be expressed as a function of xis, xrd, n, li, lj using all constraints in (14.7), the symmetry, and equal prices of all goods. We have omitted the subscript of time for xis, xrd, n, u, αi, li, L& i , β, αj, L& j . αi and αj are the Lagrange multipliers for labor allocated to produce traded goods i and nontraded goods j, respectively. β is the Lagrange multiplier for the labor endowment constraint. Since ls (s = i, j) may discontinuously jump between the interior and corner values, F may not be differentiable with respect to L& s , so that the calculus of variations, which requires continuous L& s , may not be applicable. In order to avoid this trouble, we specify a Hamiltonian function H = u + γilI + ∑j γjlj + λ (1- lI - ∑j lj) which does not directly contain L& s , though ls = L& s . Here, λ and γs are dynamic shadow prices of labor endowment and labor allocated to the production of good s, respectively. They are called

473

costate variables in the control theory. ls n, xis, and xrd are called control variables. β = λe-rt, αs = γsert are the corresponding discounted shadow prices. Suppose that the control variables do not take on corner values. Then, the application of the Euler equation to the Lagrange function F generates a set of the first order conditions in terms of H: ∂F/∂αs= d[∂F/∂(dαs/dt)]/dt = 0, which is equivalent to (14.14a): ∂H/∂γst=dLst/dt, ∂F/∂Ls = d(∂F/∂ L& s )/dt, which is equivalent to (14.14b): ∂H/∂Ls=rγs-dγs/dt, ∂F/∂n = d[∂F/∂(dn/dt)]/dt = 0, which is equivalent to (14.14c) (i): ∂H/∂nt=0, for nt∈(1,m). If the corner solutions are considered, then (ii) and (iii) in (14.14c) will be included in a general condition for maximizing F or H with respect to n. Maximization of F with respect to ls generates the same first order condition for the maximization of H with respect to ls which is (14.14d): (i) lst=1 if γst>λt; (ii) lst∈(0,1) if γst=λt; (iii) lst=0 if γst 0 is a parameter. Solve for dynamic general equilibrium and analyze effect of fiscal policy s on evolution of division of labor and economic development. According to Zhang, many macroeconomic models can be worked out to predict effects of monetary and fiscal policies on aggregate variables which are determined by the network size of division of labor, if the effects of the policies on n via their effects on transaction conditions (K) can be appropriately specified. Try developing some Smith-Young macroeconomic models based on this idea.

477

Chapter 15: Social Experiments and Evolution of Knowledge of Economic Development 0B

15.1. How Does Organization Knowledge Acquired by Society Determine Economic Development? 1B

From what we have learned in the previous chapters, we understand that the level of division of labor determines the speed of accumulation of professional knowledge of production (human capital) and the capacity of society to acquire knowledge, while individuals’ knowledge about the efficient levels of specialization determines which level of division of labor will be chosen by society. But in the Smith-Young framework, each individual must choose one from many corner solutions, and society must choose one from many corner equilibria. Because endogenous variables are not continuous between corner solutions and between corner equilibria, the optimum corner solution can be identified and the economy can settle down in the Pareto optimum corner equilibrium only after completion of a total benefit-cost analysis of all corner solutions in addition to a marginal analysis of each. If it takes time for an individual to calculate a corner solution and for society to sort out the corner equilibrium prices in a structure, and if the calculation and pricing processes cause nontrivial costs, then we may have a very interesting interdependency between individuals’ dynamic decisions and the organization information that they have acquired. Which configuration an individual chooses is dependent on corner equilibrium prices in different structures that she knows, since she needs the information about relative prices to calculate real incomes in different structures, to compare them, and then to tell which configuration should be chosen. However, the information of corner equilibrium relative prices that is available is in turn determined by which structure and which configurations are chosen by individuals. For instance, if all individuals choose the autarky configuration, then they never know the corner equilibrium relative prices in other structures involving division of labor, so that they cannot tell whether they should engage in division of labor or which pattern of division of labor they should choose. This interdependency between decision and information is analogous to the interdependence between quantities and prices in a Walrasian general equilibrium model. Hence, our job in this chapter is to investigate the mechanism that simultaneously determines both of them. Suppose an individual decides to go to a public place (or the marketplace, as we call it) to meet somebody else, and through bargaining to sort out relative prices under which both parties agree to specialize in different occupations. If no mutually agreeable prices can be worked out, then at least the individual can come back to autarky. But if both parties can find mutually beneficial terms of division of labor, then both parties can be better off than in autarky. No matter which case occurs, the individual always has an expected information gain from the pricing process: she receives the autarky payoff (not worse off than in

478

autarky) with probability ρ, and receives a higher payoff yielded by mutually beneficial division of labor with probability 1-ρ. The pricing process, however, incurs bargaining costs between individuals or communication costs between the Walrasian auctioneer and individuals. Hence, there is a trade off between expected information gains from a social experiment with a certain structure of division of labor and the related pricing process and pricing costs (experimentation costs). The bargaining or Walrasian pricing mechanism becomes a vehicle to organize social experiments with various structures of division of labor. The principal questions that we shall address in this chapter are: how do individuals’ dynamic decisions about the price search process, or about an organization experiment, affect the evolution of the organization information that they acquire; and how does this information affect individuals’ dynamic decisions? The interactions between acquisition of organization information and dynamic decisions in choosing a structure of division of labor are complex, since they involve a process of social experimentation in searching for the efficient network of division of labor. This is much more complex than a single decision maker’s search process, as studied in Aghion, et al (1991) and Morgan and Manning (1985). You may suggest using the notion of sequential equilibrium of Kreps and Wilson (1982) to describe the interactions between dynamic decisions and the evolution of information (see example 9.8 and exercise 4 in chapter 9). But we have two problems in directly applying the notion of sequential equilibrium. The first is conceptual and the second is technical. The sequential equilibrium (or Bayes perfect equilibrium) model is based on information asymmetry. The focus of the model is on possible devolution of information asymmetry rather than increases in organization information acquired by all individuals. We must find a way to specify the trade off between information gains and related costs in connection with possible concurrent evolution in the network of division of labor and in information about the efficient network of division of labor. We need some conceptual innovation here. The unbounded sequential rationality and complete information for one player (despite incomplete information for the other player) in Kreps’ sequential equilibrium model does not work for our purpose. We need the notions of bounded rationality and adaptive behavior to describe the complex interactions between individuals’ dynamic decisions, which affect social experiments, and organization information, which is acquired by society. Hence, we will develop the concept of Walrasian sequential equilibrium in this chapter. The following two features distinguish our notion of Walrasian sequential equilibrium from Selten and Kreps’ notion of sequential equilibrium. First, in our Walrasian sequential equilibrium model, all individuals have no information at the outset, and the lack of information is symmetric between different individuals, whereas in the Kreps sequential equilibrium model, asymmetric incomplete information between individuals is assumed. Though uncertainty exists in Kreps’ sequential equilibrium model, each decision maker’s dynamic decision never changes over time for given parameter values, despite the fact that there are different dynamic decisions for different parameter subspaces. Within some of them screening equilibrium occurs and within others pooling equilibrium occurs. In our Walrasian sequential equilibrium, evolution in organization information acquired by society generates adaptive decisions, so that each individual’s dynamic programming problem in one period may be different from that in the next period. The whole decision problem, rather than merely a strategy, must be

479

adjusted in response to updated information. This makes our Walrasian sequential equilibrium model more sophisticated and more realistic than that of Kreps. The increased sophistication of our approach has its cost. It is prohibitively difficult to endogenize simultaneously direct interactions between individuals’ decisions, evolution in information, and evolution in division of labor. Only very simple sequential equilibrium models in game theory can be solved, and even completely symmetric models of endogenous evolution of division of labor are very difficult to manage. Hence, we ignore the direct interactions between individuals’ decisions in our Walrasian sequential equilibrium model. However individual decision makers interact with each other indirectly through the Walrasian pricing mechanism. Hence, our Walrasian sequential equilibrium comprises a sequence of static Walrasian corner equilibria. This enables our models to have high explanatory power while remaining reasonably tractable. The information symmetry in our Walrasian sequential equilibrium model is a setback. This assumption is made to avoid the problem of coordination and mismatch in experiments with various patterns of division of labor, thereby keeping the model tractable at the cost of realism. If information asymmetry is introduced, the coordination problem may generate interesting implications of the role of entrepreneurship in experiments with economic organization (see question 3). A technical advantage of the features of our approach is that all static Smithian models can be dynamized without much additional technical complexity. Also, this approach solves a well known recursive paradox associated with the decision problem based on bounded rationality (see Conlisk, 1996 for the notion of recursive paradox and a recent comprehensive survey of the literature of bounded rationality). This paradox implies that a decision or equilibrium model cannot be well closed in the absence of unbounded rationality. We will show that there is a way to close satisfactorily a dynamic decision problem and a dynamic general equilibrium model in the presence of bounded rationality. Our Walrasian sequential equilibrium model also echoes the criticisms of the recent endogenous growth models of Judd (1985), Romer (1990, see chapter 13), Grossman and Helpman (1989), and Yang and Borland (1991, see chapter 14) which feature, very unrealistically, an infinite decision horizon, complete information, unbounded rationality, and deterministic dynamics. As Nelson (1995) points out, the real economic growth process is an evolutionary process that features uncertainties about the direction of the evolution and with a certain trend of the evolution. The Walrasian sequential equilibrium model in this chapter is characterized by these two features. The first Walrasian sequential equilibrium model is developed by Ng and Yang (1997). Zhao (1999) extends the notion to the case with an endogenous decision horizon and many goods. He has applied the approach to endogenize the concurrent evolution of division of labor and the institution of the firm. Two examples may help to motivate our study of the Walrasian sequential equilibrium model. The founding of the McDonald’s restaurant network can be considered as an experiment with a pattern of high level of division of labor between the specialized production of management and planning, and the specialized production of direct services within the franchise, and between the specialized production of food and the specialized production of other goods. Since all variables and demand and supply functions are discontinuous from corner solution to corner solution, marginal analysis based on interior solutions could not provide the founder (Ray Kroc) of this franchise with the information necessary for the right decision. Instead, he decided to use the market to experiment with a

480

new pattern of business organization involving a higher level of division of labor within the franchise and between the franchise and the rest of the economy. Instead of adjusting prices at the margin, he tried a price of restaurant services that was much lower than the prevailing price. According to his calculation, the higher level of division of labor would generate productivity gains (for instance, a high productivity generated by a high level of division of labor between the production of standardized cooking equipment and the production of food, and between specialized management and head-office planning and specialized production of restaurant services by franchisees), on the one hand, and more transaction costs on the other. McDonald’s’ franchise arrangements adopted a form of hostage mechanism, by which great discretionary power of the franchiser and the intentionally great asset specificity of the franchisees would serve to protect the intangible intellectual property of the franchiser. It was hoped that these arrangements would reduce endogenous transaction costs to the extent that the benefit of the higher level of division of labor would outweigh its cost, so that the substantially lower price of services could stand the test of the social experiment. Though the subsequent success of the McDonald’s chain has clearly substantiated this idea, the founder might have gone into bankruptcy if the social experiment had proved the business to be inefficient compared to the prevailing pattern of organization. But such social experimentation through the price system is necessary for society to acquire information about the efficient pattern of division of labor, even if it may generate business failure because of the interdependency between decisions in choosing a pattern of organization and the available information about prices, and because of discontinuity of decision variables between different patterns of division of labor. The second example involves the business practice of large scale experimenting in the production of a new product. A successful research and development project that invents the new product may not be able to stand the test of large scale commercialized production. Its ability to do so cannot be ascertained by the production costs of other new products. In order to tell to what degree the new product can generate economies of division of labor for society as a whole, a social experiment must be conducted. Without the experiment, potential buyers do not know the benefit of the product to them in comparison to its price, and the manufacturer does not know to what degree the average cost can be reduced to support a sufficiently low price to keep a reasonable market. Without knowledge of the price of the product, potential buyers cannot make purchase decisions. But if the price is determined simply by the high average cost incurred in the R&D process, nobody will buy the product. Hence, the entrepreneur must make a guess about the possible corner equilibrium price in the new structure of division of labor between the production of the new product and the production of other goods. A promotion campaign may be initiated, and the price set at a level much lower than its current average production cost in the hope that potential buyers will give up the self-provision of substitutes for the new product and choose the new structure of division of labor. If the corner equilibrium in the new structure of division of labor is Pareto inferior to the prevailing corner equilibrium, then the entrepreneur will go bankrupt. If the new corner equilibrium is Pareto superior to the prevailing one, then she may make a fortune. The stock market can then be used to share the risk in the social experiments initiated by the entrepreneur. Also, the R&D process must involve experimentation with different structures of division of labor between different specialties in the R&D activities. The success of the invention itself is determined by these

481

organizational experiments. Hence, a business success is more dependent on social experimentation with a new structure of division of labor than on technical conditions. A striking feature of experiments with various structures of division of labor is that mistakes are not only unavoidable, but also necessary for distinguishing the efficient structure from inefficient ones. The first welfare theorem about the Pareto optimality of market equilibrium in textbooks is incompatible with the notion of experimenting. An experiment with a Pareto inefficient structure of division of labor is certainly not Pareto optimal. But without experimenting with inefficient as well efficient structures, society can never know which structure is efficient and which is not. This is because of the discontinuity of endogenous variables across structures and the interdependence between information and decisions. It follows that because of bounded rationality, the Pareto optimum is a utopia and the simple and direct method of pursuing the Pareto optimum is not efficient. A sophisticated pursuit of the Pareto optimum structure of division of labor should encourage experiments with Pareto inefficient as well as Pareto efficient structures. The simple and direct pursuit of the Pareto optimum may impede the efficient search, since such a pursuit is like asking a researcher to find the optimum design without experimenting with inefficient patterns. Casual observation suggests that countries with many organizational inventions and innovations usually have relatively higher rates of bankruptcy of firms. This view of bounded rationality helps us not to overestimate successful businesses that are successful by and large because of luck in their experiments with various structures of division of labor. It also helps us not to underestimate the value of failed businesses which might be necessary for society to acquire information about the efficient pattern of division of labor. In the model to be considered, there are many ex ante identical consumer-producers with preferences for diverse consumption and production functions displaying economies of specialization. Complicated interactions between economies of specialization and transaction costs in the market generate uncertainties about real income for different patterns of division of labor. Each person's optimal decision is a corner solution. Combinations of different corner solutions generate many corner equilibria. Individuals may experiment with each possible pattern of division of labor via a Walrasian auction or Nash bargaining mechanism at a point in time, and thereby eliminate uncertainties and acquire information about the efficient pattern of division of labor over time. However, the costs in discovering prices generate a tradeoff between information gains and experimentation costs in the information acquisition process. A decentralized market will trade off gains from information acquisition against experimentation costs to determine the equilibrium pattern of experiments with patterns of division of labor over time. In the process, individuals use Bayes' rule and dynamic programming to adjust their beliefs and behavior according to updated information. The determinants of the dynamics of the Walrasian sequential equilibrium are the transportation cost coefficient for trading one unit of goods, the degree of economies of specialization, the degree of economies of complementarity between two producer goods in producing the final good, the discount rate, and the pricing cost coefficient. Suppose the transportation cost coefficient and the degrees of economies of specialization and complementarity are fixed. If pricing costs are high, then the market will not experiment with any sophisticated pattern of division of labor. If pricing costs are sufficiently low, all possible patterns of division of labor will be experimented with. In this

482

process, simple patterns of division of labor are experimented with before the more complicated ones, so that a gradual evolution of division of labor may occur. For a fixed pricing cost coefficient, more patterns of division of labor will be experimented with as the transportation cost coefficient decreases and/or as the degree of economies of specialization increases. Section 15.2 specifies a static Smithian equilibrium model. Then in section 15.3, the time dimension and the information problem are introduced into the model.. Section 15.4 solves for the Walrasian sequential equilibrium and its inframarginal comparative dynamics.

Questions to Ask Yourself when Reading this Chapter Why are social experiments with various structures of division of labor a driving force of economic development in the presence of interdependency between organization information acquired by society and individuals’ decisions in choosing profession configurations? How does the price system coordinate social experiments with various structures of division of labor to facilitate the acquisition of organization information? What is the difference between social experiments with various structures of division of labor and a decision maker’s search process for the efficient decision? How does the trade off between the information gains of social experiments and their costs determine the pattern of evolution of division of labor? Why is an adaptive decision rule more efficient than a deterministic decision rule when individuals are short of information and have bounded rationality? How is the capacity of society to acquire information about production technology and to achieve high productivity determined by its capacity to acquire organization information?

15.2. A Static Model with Endogenous Length of the Roundabout Production Chain and Endogenous Division of Labor 2B

Example 15.1: A static Smithian model with endogenous production roundaboutness. In this section, we consider a model where each consumer-producer has the following utility and production functions and endowment constraint u = y+kyd (utility function) α α p s d 0.5 (production function of final good) y ≡ y+y = Max{ly , ly (x+kx ) } xp ≡ x+xs = lxβ (production function of intermediate good) lx + ly = L, li ∈ [0, L] (endowment constraint of working time) where y and x are respectively the amounts of the final good (called food) and the intermediate good (called hoe) that are self-provided, ys and xs are the amounts of the two goods sold, yd and xd are the amounts of the two goods purchased, yp and xp are the output levels of the two goods, k is the transaction efficiency of goods, and li is the individual’s level of specialization in producing good i. Food can be produced either from labor or from labor and hoes. Each individual is endowed with L units of working time. α is the

483

degree of economies of specialization in producing food. When only labor is employed to produce food, there exist economies of specialization in producing food if α >1; when both labor and hoes are employed in producing food, there are economies of specialization if α > 21 . The total factor input for the latter case is TF ≡ X 0.5/( 0.5+α ) l y α /( 0.5+α ) where X ≡ x + kx d . The total factor productivity is TFP ≡ yp/TF = X 0.5(α − 0.5) /(α + 0.5) l y α (α − 0.5) /(α + 0.5) , which increases as the level of specialization in producing

y, ly, rises if α > 12 . The production function of hoes displays economies of specialization if β > 1 . The system of production functions displays economies of division of labor if there are economies of specialization in producing both goods. If the production function of a good displays economies of specialization and the other displays diseconomies of specialization, the economies of division of labor exist when the economies of specialization dominate the diseconomies of specialization.

(a) Structure A

(b) Structure B

(c) Structure C

Figure 15.1: Configurations and Structures in the Static Model

Applying inframarginal analysis, we can solve for the corner equilibria in three structures. The first autarky structure A is shown in Fig. 15.1(a), where each individual self-provides food in the absence of hoes. The second autarky structure B is shown in Fig. 15.1(b), where each individual self-provides both hoes and food. Table 15.1: Three Corner Equilibria

Configuration and structure A B (x/y) (y/x)

Corner solutions and corner equilibria

lx = 0 , ly = L , y = Lα , u = Lα 0.5βL αL lx = , ly = , x = l x β , y = x 0.5 l y α , u = y 0.5β + α 0.5β + α l x = L , l y = 0 , x s = Lβ , y d = lx = 0 , ly = L , y = s

kp y L2α 4 px

484

p x Lβ kp x Lβ ,u = py py

,x = d

py y s px

,y=

kp y L2α 4 px

,u= y

C

py px

= 2 L0.5β −α , M y =

M 2

⎛ py ⎞ 1 + 0.25k ⎜ ⎟ L2α − β ⎝ px ⎠

, Mx = M − My

u = 0.5kL0.5β +α The structure with division of labor, C, is shown in Fig. 15.1(c), where some individuals choose specialization in producing hoes, or configuration (x/y), and other individuals choose specialization in producing food, or configuration (y/x). All information about corner solutions in the four configurations and the corner equilibria in the three structures is summarized in Table 15.1. Comparisons of per capita real incomes in all structures, and application of the Yao theorem, yield the general equilibrium and its inframarginal comparative statics, summarized in the following table.

Table 15.2: Static General Equilibrium and Its Inframarginal Comparative Statics

Parameter Subspace Equilibrium Structure

L < L0 k < k0 A

k > k0

L > L0 k < k1

k > k1

C

B

C

where L 0 ≡ (1 + 2α /β )(1 + β /2α )2α /β , k0 ≡ 2 L− β /α , k 1 ≡ 2α α (0.5β ) 0.5β (0.5β + α ) −0.5β –α . Since dL 0 /d (α /β ) > 0 and L < L 0 imply that the relative degree of economies of specialization of food to hoes, α /β , is sufficiently large, while L > L 0 implies that economies of specialization in producing food is not that significant in comparison to that in producing hoes ( α /β is small). The results in Table 15.2 imply that if economies of specialization in producing food are sufficiently more significant than in producing hoes, then individuals use labor alone to produce food, and hoes are not produced in autarky. As transaction efficiency is improved, the general equilibrium jumps from autarky to the division of labor and a new intermediate good emerges from the exogenous evolution in division of labor. If economies of specialization in producing hoes are significant compared to food production, then the evolution in division of labor is not associated with evolution in the length of the roundabout production chain and the emergence of new producer goods.

15.3. Interactions Between Dynamic Decisions and Evolution in Organization Information 3B

Example 15.2: A Walrasian sequential equilibrium model. We now introduce the time dimension and the information problem into the static model. But we assume that there is no real dynamic learning by doing, nor uncertainty in production and consumption. This assumption is not highly realistic, but is essential for keeping the model tractable. The time dimension and information problem affect only what individuals know about corner solutions and corner equilibrium prices in different structures. There are 4 periods, t = 0, 485

1, 2, 3. In period 0, all individuals are in structure A and each of them knows her real income uA = Lα (see Table 15.1). She does not know per capita real incomes in structures B and C. If she wants to know real income in structure B, she must spend the time necessary to calculate the optimum decision in that structure and the real income yielded by the decision. This computation process not only needs time, but also causes disutility. Suppose the fraction 1-sB of expected utility disappears due to the computation cost. Then only the fraction sB of expected utility can be received if the individual carries out the computation. If she wants to know per capita real income in structure C, she must pay two kinds of experimentation costs. First, she must bargain with another person to sort out the terms of trade required by the division of labor, or alternatively sort out the price through a Walrasian auction mechanism. Though the Nash bargaining and Walrasian mechanisms will generate the same terms of trade, either will incur a pricing cost. Second, she must compute corner solutions of the two configurations in order to make a decision in choosing a profession. This computation causes disutility. If an individual wants to try a structure, she can always propose a relative price to attract others to get involved in bargaining. But bilateral bargaining is not sufficient to sort out the corner equilibrium numbers of different specialists. The corner equilibrium numbers, which relate to the corner equilibrium relative price, can be sorted out only if all individuals participate in the experiment with structure C. We shall show that all individuals’ decisions about the experimentation pattern are consistent. Otherwise, coordination difficulty may occur. Suppose the three types of experimentation costs for structure C are summarized by the experimentation efficiency coefficient sC, which is smaller than sB due to pricing and more computation in C than in B. It is assumed that each individual’s subjective discount 1 . factor is δ ∈ (0,) We now consider each individual’s information at t = 0 and the relationship between the available information and her decision about experimenting with configurations in B and C. In period 0, each individual does not know real incomes in structures B and C, nor the probability distribution function of those real incomes. But she knows there are 6 possible ranking orders of three per capita real income levels in the three structures. Let the order of letters A, B, C represent the ranking of per capita real incomes in structures A, B, C. The 6 possible rankings are: ABC, ACB, BAC, BCA, CAB, CBA, where, for instance, ABC denotes that the per capita real income in structure A is greater than that in B, which is greater than in structure C, and BAC denotes that per capita real income in B is greater than that in A, which is greater than in C. We assume that each individual has no information about per capita real incomes in structures B and C in period 0. This implies that each of the 6 rankings occurs with probability 1/6. Also, we assume that each individual knows the difference between two consecutive levels of per capita real incomes, which is an exogenously given parameter b0 in period 0. She can update her information about b according to a Bayes updating rule and observed differences between per capita real incomes in different structures, as shown later on. It is not difficult to show that the expected per capita real income in structure B or C based on the information in period 0 is uA. That is, each individual knows only the real income in structure A, uA. We call this structure of information at period 0 lack of information, which is different from incomplete information. If an individual experiments with configuration B in period 1, then her expected utility in period 1, computed in period 0 is

486

(15.1)

E 0 [u1 ( B)] = s B [0.5u A + (1 / 3)(u A + b0 ) + (1 / 6)(u A + 2b0 )] = s B δ (u A + 2b0 / 3)

The expected utility can be worked out as follows. According to what an individual knows in period 0, the probability that uA > uB is 0.5, since ABC, ACB, CAB account for half of the 6 rankings. If any of the three rankings proves correct, the individual will return to structure A after the experiment with structure B. Hence, based on what she knows in period 0, she expects to receive real income uA with probability 0.5 after the experiment with B. Since BAC and CBA account for 1/3 of the 6 rankings and uB = uA + b0 for the two rankings, in period 0 the individual expects to receive uA + b0 with probability 1/3 after the experiment with B in period 1. Finally, ranking BCA, which implies uB = uA + 2b0, occurs with probability 1/6. The individual expects to receive uB = uA + 2b0 after the experiment with B. This, together with the consideration of the experiment efficiency coefficient sB, implies that in period 0, the individual’s expected utility for the experiment with configuration B in period 1 is (15.1). Following this procedure, we can compute the expected utility in period 0 for the experiment with structure j in period t, E0[ut(j)]. Assume that each individual’s decision horizon is of 2 periods. Then an individual’s dynamic programming problem in period 0 can be described by Fig. 15.1, where individuals are in structure A in period 0. In period 1, each individual can choose any among 4 configurations: A, B, (x/y), (y/x). Since the dynamic programming process depends only on information that a person has in period 0, the discount factor ρ, experiment efficiency si, and b0, and they are the same for every individual, all other individuals will choose either (x/y) or (y/x) if one chooses to experiment with (x/y) or (y/x) in period 1. Free choice between occupation configurations and the Walrasian pricing mechanism (or Nash bargaining) will coordinate the division of M individuals between configurations (x/y) and (y/x) as soon as one of them is chosen by somebody. This implies that structure C will be experimented with if an individual chooses to experiment with either configuration (x/y) or (y/x) in period 1. Therefore, as shown in Fig. 15.1, there are 3 nodes: A, B, C, in period 1.

Period 0

Period 1

487

Period 2

u≡uA, v≡ uA+2b/3, w≡ uA+b Figure 15.1: An Individual’s Dynamic Programming Problem in Period 0

We assume that in each period, each individual has perfect recall of the past history of the economy. This, together with the feature of path dependence of the dynamic equilibrium, implies that there are more nodes in period 2 than in period 1. Nodes A, B, C in period 2 are the same as in period 1. Node BO implies staying with the better between A and B with no new experiment in period 2 after the experiment with B in period 1. Node CO implies staying with the better between A and C with no new experiment in period 2 after the experiment with C in period 1. Each individual’s dynamic decision in period 0 about the optimum pattern of experiment sequence in periods 1 and 2 is to maximize the following expected total discounted utility over periods 1 and 2. (15.2)

Max:

Σ 2t=1δ tE 0 [ut (i)]

where nodes that can be chosen in period 1 are i(1)=A,B,C and in period 2 are i(2)=A,B,C,BO,CO. Following the method used to establish (15.1), we can prove that E 0 [ut ( A)] = u A , E 0 [u1 ( B)] = s B (u A + 2b0 / 3) , E 0 [u1 (C )] = sC (u A + 2b0 / 3) ; If A is chosen in period 1 E 0 [u2 (B )] = sB (u A + 2b0 /3), E 0 [u2 (C )] = sC (u A + 2b0 /3) ; If B is experimented with in period 1, then E 0 [u2 (C )] = sC (u A + b0 ) ; If C is experimented with in period 1, then E 0 [u2 (B )] = sB (u A + b0 ) and E 0 [u2 (B O )] = E 0 [u2 (C O )] = u A + 2b0 /3 . The essence of the dynamic programming problem is the trade off between information gains from the experiments and the experimentation costs. If each individual has an experiment with one configuration, the expected utility will increase from uA to uA + 2b0/3. If she has two experiments with 2 configurations in different structures, the expected utility uA + b0 is even higher. This is because she can always go back to the best configuration if the one experimented with is not as good as that arising from any previous experiment. The worst situation is at least as good as before. But the probability of a higher utility is nontrivial. This is the information gain from experimentation. However, there is an experimentation cost. The fraction 1-s of the expected utility, which includes information gains, disappears because of the experimentation cost. This experimentation cost is once and for all, but the associated information gains are perpetual. If an individual has experimented with configuration B in period 1, she pays the calculation cost in period 1 and enjoys the information gains forever, with no further experimentation cost after period 1. Hence, the trade off between the information gains and the experimentation cost (or investment in information) is analogous to the trade off between current consumption and future consumption that can be raised by investment in the conventional growth model. But the investment in our model is in organization information acquired by society rather than in production, information (R&D), education, or physical capital.

488

We call a pattern of structures that are experimented with over successive periods an experiment sequence, or sequence for short. From (15.2), we can see that the expected total discounted utility, in terms of the present value in period 1, generated by sequence CB is U (CB) = sC (u A + 2b0 / 3) + s B δ (u A + b0 ) . It is always smaller than the expected total discounted utility, in terms of the present value in period 1, generated by sequence BC, which is U (B C ) = sB (u A + 2b0 /3) + sC δ (u A + b0 ). To see this, we first note that if the experimentation cost is ignored, the two expected utility levels are the same due to the lack of information in period 0. However, if account is taken of the facts that the experimentation cost is higher for C than for B because of a higher pricing cost in C, and that time has value, that is, δ∈(0, 1), then it is better for individuals to try structure B with a lower experimentation cost first if they have no information about which of B and C generates the higher per capita real income. Similarly, we can show that sequence CO is not as good as BO. Hence, we can narrow down the set of candidates for the optimum sequence, which now comprises the 4 sequences AA, AB, BO, BC. Comparisons of expected total discounted utility levels in the 4 sequences yield the analytical solution of the dynamic programming problem, summarized in the following table. Table 15.3: Optimum Dynamic Decision in Period 0

Value of s Structure sequence

s B < s B0 AA

s B > s B0 , s C < s C0 BO

s C > s C0 BC

Lα − 2b0δ / 3 Lα + b0 0 , . The dynamic optimum decision and its s ≡ C Lα + 2b0 / 3 Lα + 2b0 / 3 comparative dynamics imply that if the experimentation efficiency for structure B is too low, individuals will always stay in autarky with no experimentation. If the experimentation efficiency is increased to the critical value sB0 , but the experimentation efficiency for structure C is not high, then structure B will be experimented with in period 1 and no further experiment will take place in period 2, that is, sequence BO is chosen. If the experiment efficiency for structure C is increased to have reached the critical value s C0 , the optimum sequence is BC, which experiments with B in period 1 and with C in period 2. Since the dynamic optimum decision depends only on information in period 0, on real income in structure A, uA, and on b0, s, δ, which are the same for all individuals, the dynamic optimum decision is the same for all individuals, so that there is no coordination difficulty. As shown in Ng and Yang (1997) and in Zhao (1999), the analytical solution of such a dynamic programming problem will become very complicated as the numbers of structures and decision horizons increase. Zhao (1999) has worked out the analytical solution of such a dynamic programming problem with any limited decision horizon and with 4 structures to experiment with. But to our knowledge, the analytical solution of such a dynamic programming problem with more than 4 where s B0 ≡

489

structures to experiment with and with a decision horizon of more than 4 periods is too complicated to be tractable.

15.4. Walrasian Sequential Equilibrium and Concurrent Evolution in Organization Information and Division of Labor 4B

We now consider information updating in period 1 and interactions between information and adjustment of dynamic decisions. If individuals try structure B in period 1, then their information will be changed by such experimentation after they have seen per capita real income in B. Hence, their optimum dynamic decision in period 0 is out of date. They must adjust their dynamic decisions about further experiments according to the updated information. We assume that the decision horizon for the new dynamic programming problem based on updated information in period 1 is also of two periods. In each period in which a new structure is experimented with, the new dynamic programming problem for further experiments in the next two periods is different from the one in the last period. The recursively adjusted dynamic decision according to updated information is referred to as an adaptive decision, which distinguishes our notion of Walrasian sequential equilibrium from Kreps’ concept of sequential equilibrium in game theory. Suppose sB < sB0 . Then individuals will not try structures B and C. Their updated information in period 1 is the same as in period 0. Hence, their adjusted new dynamic programming problem in period 1 is the same as that in period 0, so that the optimum decision is to stay in autarky with no further experimentation. The recursive deduction shows that the sequential Walrasian equilibrium is a sequence of structure A over all periods. Suppose sB > sB0 . Then individuals will try structure B in period 1. Two cases may take place. If L < L 0 , individuals will find in period 1 that A is better than B, as shown in Table 15.1. Hence, they will go back to A at the end of period 1. If L > L 0 , they will find in period 1 that B is better than A and choose B at the end of period 1. No matter which case takes place, the experiment changes the information that an individual knows in period 1, so that her dynamic optimum decision in period 0 is out of date. She must reformulate a new dynamic programming problem for further experiments in periods 2 and 3. Let us see what is the information that an individual knows after she has tried B in period 1. Suppose L < L0, so that A is better than B, which implies that BAC, BCA, and CBA are impossible. The set of possible rankings now comprises ABC, ACB, CAB. A is better than C with probability 2/3 and uC = uA+b1 with probability 1/3. This method of updating information according to new observations is referred to as the Bayes updating rule. Here, b1 also needs to be updated according to any observed difference between uA and uB. We assume that before individuals have observed two differences in per capita real incomes between structures, they believe that b is the same between each consecutive pair of real income levels. After they have tried B in period 1, they have seen uA- uB ≡ θ. If θ is positive, individuals know that only rankings ABC, ACB, CAB are possible. With probability 1/3, ACB or uA- uB = 2b occurs. That is, θ = 2b with probability 1/3. Also, θ = b, or either of ABC and CAB occurs, with probability 2/3. Hence, the expected value of θ

490

is Eθ = (1/3)2b1+(2/3)b1 = (4/3)b1. This implies that according to the Bayes updating rule the estimate of b1 from observed θ is b1 = 3θ/4 = 3(uA- uB)/4, where the values of uA and uB can be found from Table 15.1. If the individual chooses structure sequence AA, that is to stay in A without experiment with C in periods 2 and 3, her expected total discounted utility in periods 2 and 3 is U(AA) = uA(1+δ). According to her updated information in period 1, only ranking CAB among ABC, ACB, CAB entails a higher utility in C than in A. Hence, if she tries C in period 3, she expects to obtain uA + b1 with probability 1/3 and uA with probability 2/3. Therefore, if she chooses structure sequence AC, that is, to stay in A in period 2 and to try a configuration in C in period 3, her expected total discounted utility over the two periods is U(AC) = uA+δ sC[(uA+b1)/3+2uA/3] = uA+δ sC(uA+b1/3). Now let us consider sequence CO in periods 2 and 3, which implies trying C in period 2 and staying with the better of A and C in period 3. Remember that we are concerned with an individual’s decision in period 1 after she has tried B and knows A is better than B. Using the Bayes updating rule, we can find that the expected total discounted utility generated by sequence CO over periods 2 and 3 is U (CO) = (u A + b1 / 3)( sC + δ ) . Comparisons between U(AA), U(AC), U(CO) yield (15.3) U(AC)>U(AA) iff sC > sC3 ≡ b1u A / (u A + b1 / 3) and U(CO)>U(AC) iff sC > sC4 ≡ [u A /(1 − δ )(u A + b1 /3))]− [δ /(1 − δ )] It can be shown that sC3 > sC4 . This implies that AC is worse than AA if s < sC4 < sC3 and AC is worse than CO if s > sC4. In other words, AC, which delays experimentation with C by one period, cannot be chosen, since it is better to try C earlier if a person wants to try it due to the perpetual value of information and the value of time. Otherwise, no experiment with C is better than the delayed experiment with it. This result is dependent on the assumption about the absence of dynamic learning by doing. If the dynamic learning by doing in chapter 14 is introduced, the result may be changed. We now need to consider only sequence AA and CO. A comparison between U(AA) and U(CO) yields (15.4) U(CO)>U(AA) iff sC > sC1 ≡ [(u A + 1 − δ )/(u A + b1 /3]− δ We have now finished the analysis for the case that sB > sB1 and L < L0. For this case, individuals will try structure B in period 1 and know that A is better than B at the end of period 1. Based on the new information, her adjusted new dynamic decision tells her that she should try C in period 2 if sC > sC1. Otherwise, she should stay in autarky forever. Let us now consider the case in which sB > sB1 and L > L0. For this case, individuals try structure B and know B is better than A by the end of period 1. Following the same procedure, we can show that, based on the updated information, individuals will find out by the end of period 1 that (15.5) U(CO)>U(BB) iff sC > sC2 ≡ [(u B + 1 + δ )/(u B + b1 /3]− δ , where b1 can be estimated according to the Bayes updating rule in the same way as before. All of the dynamic optimum decisions about further experiments over periods 2 and 3, made in period 1 according to updated information, are summarized in the following table. Table 15.4: Adjusted Optimum Dynamic Decisions in Period 1

491

L < L0 s < s1B AA

s > s1B

L > L0 s < sC2

CO

BB

A is chosen at t=1

B is chosen at t=1

s > sC2 CO

where AA denotes that an individual stays in A with no experimenting over periods 2 and 3. For L < L 0 , CO denotes that an individual tries C in period 2, chooses the better of A and C at the end of period 2, and stays with it in period 3; For L > L 0 , CO denotes that an individual tries C in period 2, chooses the better of B and C at the end of period 2, and stays with it in period 3; BB denotes that an individual stays in B with no experiment over periods 2 and 3. Let us now consider dynamic general equilibrium in the marketplace, which is the consequence of interactions between all individuals’ dynamic optimum decisions and between the dynamic decisions and information that individuals know. One of the differences between the Walrasian sequential equilibrium and Kreps’ sequential equilibrium is that in the former, individuals indirectly interact with each other through the Walrasian pricing mechanism. Also, the adaptive decision rule and the initial lack of information of all individuals in the former differ from the deterministic decision rule and the asymmetric and incomplete information in the latter. Walrasian sequential equilibrium is a sequence of sets of relative prices of traded goods, a sequence of numbers of individuals choosing various configurations, an evolutionary path of information that each individual knows, and all individuals’ dynamic optimum decisions in choosing quantities of goods produced, consumed, and traded, and in choosing the experiment sequence of configurations and the configuration sequences that are chosen after experiments in each period. We call the combination of individuals’ dynamic decisions, time paths of prices, numbers of different specialists, and information a dynamic organism. The Walrasian sequential equilibrium is a dynamic organism that satisfies the following three conditions. (i) In each period, each individual’s dynamic optimum decision in choosing an experimental sequence of configurations in the future two periods maximizes her expected total discounted utility over the two periods for given information that she knows in this period. Her choice of configuration after experimenting in each period is optimal for the given updated information generated by the experiments up to this period. Her decision in allocating resources in a given structure that is realized in a period maximizes her utility in this period for given corner equilibrium relative prices of traded goods and for given numbers of individuals choosing different configurations in this period. (ii) Information is updated according to Bayes’ rule and observed prices and numbers of different specialists on the basis of perfect recall of the past. (iii) The corner equilibrium relative price of traded goods and numbers of individuals choosing different configurations in the structure that is experimented with or is ultimately chosen in a period equalize all individuals’ utility and clear the markets for traded goods in this period. Putting together information about static equilibrium in Table 15.1 and information about dynamic decisions in periods 0 and 1 in Tables 15.2 and 15.3, we can solve for the Walrasian sequential equilibrium, as summarized in Fig. 15.3.

492

Period 0

Period 1

Period 2

Period 3

Figure 15.3: Walrasian Sequential Equilibrium: Interactions Between Evolution in Division of Labor and Evolution of Organization Information

Lα − 2b0δ / 3 Lα + b0 0 , , s ≡ C Lα + 2b / 3 Lα + 2b0 / 3 u +1+ δ −δ , L0 ≡ [1+(2α/β)][1+(β/2α)]2α/β, sC2 ≡ A u A + b1 / 3 u +1+ δ 3 2 − δ , b1 ≡ u A − u B , k 0 ≡ β /α sC2 ≡ B u B + b1 / 3 4 L 0.5β α −0.5β −α α k1 ≡ 2α (0.5β ) (0.5β + α ) ,u A = L 0.5 β α 0.5β +α u B = (0.5β ) α [L /(0.5β + α )]

where b0 is a given parameter, s B0 ≡

In Fig. 15.3, the capitalized letters in brackets denote the structures that are experimented with, and the capitalized letters without brackets denote the structures that are finally chosen. Let us interpret Fig. 15.3. Start from structure A in period 0. If sB < sB0, then individuals stay in A forever. No additional information becomes available from which they can learn, so that posterior information is the same as the prior information, that is, they have no organization information at all. If sB > sB0, individuals try structure B in period 1, denoted by (B) at the lower node in period 1. This can be verified by the dynamic decision as shown in Table 15.3. After the experiment with B, if L < L0, individuals will go back to structure A, denoted by the node A in the middle, at the end of period 1 since Tables 15.1 and 15.2 indicate that utility in A is greater than in B if L < L0. If L > L0, individuals will stay with B, denoted by the lower node B, at the end of period 1. Suppose L < L0, so that individuals have chosen A at the end of period 1. From their dynamic optimum decisions made in period 1 about structure sequence over the future two periods 2 and 3 given in Table 15.4, we can see that if sC < sC1, they will stay in A forever. Individuals have learned some organization information. They know now which is the better of A and B, but do not know which is the better of A and C or of B and C. If sC > sC1, each individual will try a configuration in structure C in period 2. Since all individuals’ 493

dynamic decisions are the same, structure C will be tried out in period 2. At the end of period 2, individuals will go back to A if k < k0, since Table 15.2 indicates that A is better than C for k < k0 and L < L0. Note that the middle node A at the end of period 1 can be reached only if L < L0. If k > k0, then the static corner equilibrium in structure C, given in Table 15.1, is realized at the end of period 2. No matter which of A and C is chosen at the end of period 2, individuals have acquired all the organization information after they have tried B and C. Now we come back to the lower node B at the end of period 1, which will be reached if sB > sB0 and L > L0. Suppose sC < sC2. From Table 15.4, we can see that individuals’ dynamic decisions at the end of period 1 are to stay in B in period 2 with no further experiments forever. This implies that individuals have learned part of the relevant organization information. If sC > sC2, then individuals will try structure C in period 2 and learn all the organization information. But for k < k1, individuals will go back to structure B at the end of period 2, since Table 15.2 indicates that B is better than C for k < k1 and L > L0. Note again that the experiment with C can take place in period 2 only if L > L0. For k > k1 and L > L0, individuals will stay with C at the end of period 2 and afterward. So far, we have partitioned the parameter space into several subspaces. Within each of them, the dynamic general equilibrium is determined by a particular sequence of structures that have been experimented with, a particular sequence of structures that have been finally chosen, and a particular evolutionary path of information. The inframarginal comparative dynamics of the Walrasian sequential equilibrium are summarized in Table 15.5. For instance, for sB > sB0, sC > sC2, L > L0, and k > k1, the equilibrium sequence of structures that have been experimented with over periods 0, 1, 2 is ABC, and the equilibrium sequence of structures that have been finally chosen is also ABC. Partial organization information is acquired at the end of period 1 and all the organization information is acquired by society at the end of period 2. For sB > sB0, sC > sC1, L < L0, and k < k0, the equilibrium sequence of structures that have been experimented with over periods 0, 1, 2 is ABC, while the equilibrium sequence of structures that have been finally chosen is AAA. Partial organization information is acquired at the end of period 1 and all organization information is acquired by society at the end of period 2. For sB > sB0, sC < sC2, and L > L0, the equilibrium sequence of structures that have been experimented with is ABB, and the equilibrium sequence of structures that have been finally chosen is also ABB. Partial organization information is acquired by society. The sequential equilibrium organization information stops evolving at the end of period 2, either because the maximum available amount has already been acquired by society, or because the efficient trade off between information gains and its cost, based on updated information, signals that the information acquisition process should stop. Hence, the chosen structure in period 3 and afterward is always the same as in period 2. But if there are many goods and many structures to try, then the concurrent evolution of division of labor and organization information can occur over many periods. Table 15.5: Inframarginal Comparative Dynamics of Walrasian Sequential Equilibrium

Parameter subspace

sB < sB0

sB > sB0 L < L0

L > L0

494

sC < sC1 Structure sequence tried AAA Structure series chosen AAA

sC > sC1 k < k0

sC < sC2 k > k0

ABA

ABC

ABC

AAA

AAA

AAC

sC > sC2 k < k1

k > k1

ABB

ABC

ABC

ABB

ABB

ABC

Since a Walrasian sequential equilibrium is partly determined by a sequence of static corner equilibria, the time paths of individuals’ resource allocation decisions, equilibrium relative prices, and numbers of individuals choosing different configurations can be found by putting Table 15.1 and Fig. 15.3 together. For instance, for sB > sB0, sC > sC2, L > L0, and k > k1, the corner equilibrium in structure B is tried out and is chosen in period 1; the corner equilibrium relative prices, numbers of different specialists, and demand and supply in C, given in Table 15.1, are tried out and are chosen in period 2. For sB > sB0, sC > sC1, L < L0, and k < k0, the corner equilibrium in B is tried out in period 1, but the chosen resource allocation in period 1 is the optimum decision in A; the corner equilibrium relative price, number of different specialists, and resource allocation are tried out in period 2, but the chosen resource allocation in period 2 and afterward is the optimum decision in structure A. As we promised, the Walrasian sequential equilibrium involves some uncertainty about the evolution of the economic organism; nevertheless, that evolution displays an identifiable trend. In period 0, nobody knows where the evolution of the economy will head. All evolutionary paths in Fig. 15.3 are possible. This evolutionary uncertainty will be gradually resolved as individuals and society gradually acquire organizational knowledge. But the resulting evolution has a recognizable trend: it involves a progression from a simple organism to an increasingly complex one. Although absence of evolution is a possibility, devolution never takes place. The evolution in organization information acquired by society is irreversible too. The intuition for this feature is that since there is no general definite relationship between the complexity of organisms and their efficiency, and since the experimentation cost is lower for the simple than for the complex organisms, when society is short of organization information it always tries a simple organism before more complex ones. Interactions between individuals’ dynamic decisions and acquired organization information are similar to, though distinct from, the sequential equilibrium in game theory. Individiduals’ dynamic decisions concerning the sequence of configurations that are experimented with, and the sequence of configurations that are finally chosen, together determine the time path of organization information that they can know, while the evolution of organization information itself determines the adjustment of dynamic decisions. However, each individual does not have perfect sequential rationality. She must use an adaptive decision rule to adjust her dynamic decision as she gradually learns organization information. This is different from Kreps’ sequential equilibrium model where for each subspace of parameters, a player’s dynamic decision rule is deterministic and never changes, though the decision itself is contingent upon updated information. Hence, each player has only one dynamic programming problem that is not adjusted over time. But in our model, each individual’s dynamic programming problem in each period may be different from the one in the next period.

495

Though there is no information asymmetry in our model, the social learning process may be more sophisticated than in Kreps’ sequential equilibrium. In our model, each individual does not know others’ utility and production functions and endowment constraints and even does not know the distribution functions of states of the physical conditions that others privately know. Hence, this can be considered as absolute information asymmetry, which is a feature of the Walrasian equilibrium model. The social learning process in our model does not involve the transmission of such private information between individuals and accordingly does not reduce the absolute information asymmetry, though individuals acquire organization information through the price system in this process. All individuals simultaneously acquire organization information at the same rate. Comparing Fig. 15.1 and Fig. 15.3, we can see that if experimentation efficiency s is sufficiently high, then the organization information that is acquired by society will spontaneously evolve over time. If transaction efficiency k is sufficiently high too, the evolution of organization information is associated with evolution also in division of labor and in the length of the roundabout production chain, and with the emergence of new machines and related new technology. The essential message from the model is that organization information acquired by society determines the network size and pattern of division of labor, which determine the capacity of society to acquire technical knowledge, which in turn determines productivity and technology progress. Institutional arrangements affect the efficiency of society in using the pricing mechanism to experiment with structures of division of labor and to acquire organization information. Our model shows that free pricing and the market mechanism cannot guarantee that all individuals will obtain all organization information unless all possible structures of division of labor have been experimented with. The free pricing and market system is a vehicle for society to organize and coordinate social experiments with various structures of division of labor in order to acquire organization information. Our model can be used to show that the application of the notion of Pareto optimum to economic analysis that involves bounded rationality is much more sophisticated than in neoclassical economics. In our Walrasian sequential equilibrium model, it is a matter of luck to have Pareto optimum sequential equilibrium. Moreover, the Pareto optimum sequential equilibrium is almost meaningless to human society. From Table 15.2 and Fig. 15.3, we can see that structure A is Pareto optimal if k < k0 and L < L0, while the sequential equilibrium achieves the Pareto optimum if sB < sB0. This implies that for a sufficiently low transaction efficiency and degree of economies of roundabout production, structure A over all periods is Pareto optimal. If experimentation efficiency happens to be low too, then no experiments will take place, so that the Pareto optimum will be achieved. If sB > sB0, unnecessary experimentation cost will be incurred, despite the fact that organization information is acquired. If sB > sB0, sC > sC2, k > k1, and L > L0, then the corner equilibrium in structure C is Pareto optimal and the sequential equilibrium will eventually settle down in the corner equilibrium. However, the sequential equilibrium is not Pareto optimal, since society can learn the organization information about the Pareto optimum pattern of division of labor only if it has experimented with all corner equilibria, including Pareto inefficient ones. In this sense, the nontrivial Pareto optimum Walrasian sequential equilibrium is a utopia. The simple way of pursuing it, recommended in textbooks, is dangerous since it may discourage experiments with Pareto inefficient patterns of division of labor, which are

496

essential for acquiring information about the Pareto optimum pattern of division of labor. We may call this the dilemma of Pareto optimality. The model can provide three insights into economic development. First, it explains why those economies with laissez-faire policy regimes, such as Hong Kong in recent decades and 19th century Britain, are more successful in economic development than those with a lot of government intervention, such as 17th century China, which discouraged commerce and the industrial manufacturing sector, and the Soviet Union, which put industrial planning under the complete control of the government. If a government believes that it knows what is the efficient industrial structure, and actively pursues industrial policies to achieve this, then such a naïve idea will slow down, and perhaps destroy, the search process for the efficient industrial structure which would otherwise be initiated by spontaneous entrepreneurial activities. The failures during the 1960s and 1970s of many development and industrial policies recommended by development economists provide evidence for the implications of our model. China and India used protective tariffs, import substitution, state enterprises, various industrial policies, and central planning to pursue industrialization during the 1950s - 1970s. But their development performance during this period was very disappointing. The Hong Kong government had no interventionist industrial policy, but rather promoted quite a classical laissez-faire regime with free duty (except for cigarettes and liquor), a trivial tariff (just enough to cover the customs administration cost), and a free private enterprise system. But it was the invisible hand in Hong Kong that created the successful labor-intensive and export-oriented industrialization pattern, which the old industrialized economies had not experienced and which were later copied by Taiwan, South Korea, Singapore, Thailand, and finally by mainland China and India. Why is such a successful development pattern always created by the invisible hand rather than by a government with an interventionist policy regime? The answer can be found in our model in this chapter. A laissez-faire atmosphere will encourage entrepreneurial activities that lead to spontaneous social experiments with various structures of division of labor, including inefficient ones. This will speed up the acquisition process of organization information, thereby speeding up economic development. Government planning of industrial development and trade pattern is incompatible with the notion of experiments with various structures of division of labor, including inefficient ones, so that it will slow down the acquisition process of organization information, thereby impeding economic development. The second insight into economic development that our model can provide relates to the concept of big push industrialization. Big push industrialization, as described in chapters 5 and 14, implies that the level of division of labor and the related size of the input-output network between interdependent specialized sectors discontinuously jumps over many intermediate levels of division of labor. Many interdependent and highly specialized sectors simultaneously emerge, through comprehensive investment programs, from this process. As we discussed before, a central planning and state enterprise system may slow down the social acquisition process of organization information. However, if developed economies have already acquired a great deal of organization information through a laissez-faire regime and through institutional arrangements that protect private property and the residual rights of owners of private enterprises, a latecomer to industrialization may use the free organization information generated by those economies to mimic the efficient structure of division of labor through central planning and the state

497

enterprise system. In this way, the latecomer may attempt to jump over many intermediate levels of division of labor and achieve big push industrialization. This conjecture is verified by the quite successful big push industrialization of the Soviet Union in the 1930s and 1950s, and of mainland China in the 1950s. This explains why von Mises (1922) and Hayek (1944) failed to predict the survival of the Soviet Style economic system for half of the 20th century. They did not realize the possibility of big push industrialization through a central planning and state enterprise system that mimics a successful industrialization pattern, despite the fact that they correctly pointed out that the Soviet style economic system was incapable of searching for the efficient pattern of organization on its own. But the condition for survival of the Soviet style economic system is imitation of the successful organization patterns that have been tried out by the free market system. As the potential for further imitation is exhausted, the fatal flaw of the centrally planned system will destroy it. The Soviet style economic system mimics the successful organization patterns tried out by the free market system by precluding, or destroying, the very institutional infrastructures that created those efficient organizational patterns. That is, by killing the goose that laid the golden egg, it ensures that it cannot have its own golden eggs. This is why the new export-oriented big push industrialization pattern created by Hong Kong cannot be created by a Soviet style economic system, though the Soviet style economic system in mainland China has been able to mimic it in the 1980s and 1990s. This also explains why a transition from a Soviet style economic system to a free market system is so difficult, since human society has had no experience of the transition that can be mimicked by Russia and China. When the Chinese communist leaders abandoned the imitation strategy of Stalin and Lenin and tried to create their own institutions, such as people’s communes and public eating halls in 1959, the result was most devastating human-made economic disaster in history. More than thirty million Chinese people died from the starvation and famine caused by this centralized institutional experiment (Chang and Wen, 1992). The experience of industrialization in Hong Kong and Taiwan provides evidence that big push industrialization can be achieved much better through the invisible hand than through a central planning system. Within 50 years, per capita real incomes in those two economies increased from less than US$200 in 1950 to about US$20,000 in the end of the last century. But the early success of China’s big push industrialization based on the Soviet style economic system in the 1950s could not prevent its failure in the long-term. The country achieved two-digit growth rates of real GDP and industrial output in some periods since 1950. However, although starting in 1950 with the same economic conditions and per capita real income as Taiwan, per capita income in China was less than US$1,000 in the end of the last century. Hence, the third insight that our model can provide is that although big push industrialization based on the Soviet style economic system may yield some short run success, it cannot survive in the long–run, since it destroys the functioning of the price system in coordinating social experiments with various structures of division of labor, and accordingly restricts the capacity of society to acquire organization information. This insight is in sharp contrast with Lange’s market socialism (Lange and Taylor, 1964). As discussed in chapter 19, market socialism is rejected by empirical evidences and by many formal models.

498

However, the fatal flaw of market socialism relates to the function of the free market in coordinating social experiments with various structures of division of labor. The function of the market is not just to allocate resources. Nor it is only to find the efficient network pattern of division of labor. Its more important function is to organize social experiments to acquire organization information. The central planning and state ownership of firms in market socialism are incompatible with the notion of experimentation, which involves the trial of inefficient patterns of organization. Market socialism gives the government monopoly power in designing institutions and in experimenting with different patterns of economic organization. Hence, the experiment process is not competitive. In particular, entrepreneurs’ claims to the residual rights of firms, together with the free price system and the function of the stock market in sharing risk, are crucial for providing entrepreneurs with an incentive to take the risk involved in such social experiments. But market socialism rejects the legitimacy of residual rights to private firms and insists on the government monopoly in experimenting with structures of division of labor and residual rights. Hence, the process of acquiring organization information will be much slower under market socialism than in a free market system based on private ownership of property and firms. Our model in this chapter explores functions of the market that are much more sophisticated than in neoclassical general equilibrium models. Hence, Lange’s market socialism, based on neoclassical general equilibrium models, can be more conclusively rejected by our theory in this chapter.

Key Terms and Review 5B

Walrasian sequential equilibrium and the difference between it and Kreps and Selten’s concept of sequential equilibrium Difference between lack of information and incomplete information Information gains resulting from experiments with various structures of division of labor Major determinants of the pattern of concurrent evolution of organization information and division of labor Bayes updating rule Interdependence between organization information and decisions in choosing configuration and its implications for the concurrent evolution of organization information and division of labor Bounded rationality Adaptive behavior How can we solve analytically for a dynamic programming problem in choosing the efficient trade off between information gains and experiment cost, and how can we put the analytical solution of this problem together with solutions of static corner equilibria of a Smithian model to work out the Walrasian sequential equilibrium? What are the implications of the decision horizon in a Walrasian sequential equilibrium model?

Further Reading 6B

Sequential equilibrium model in game theory: Kreps and Wilson (1982), Kreps (1990), Maskin and Xu (1999); Walrasian sequential equilibrium models: Yang and Y-K. Ng (1997), Zhao (1999); Search theory: Aghion, Bolton and Jullien (1991), S. Grossman (1989), Morgan and Manning

499

(1985), Reingnum (1982), Stigler (1961), Weitzman (1979), Arthur (1994), Lippman and McCall (1979); Free riding in search process: King (1995), Banerjee (1992); Neoclassical theory and models of big push industrialization: Rosenstein-Rodan (1943), Murphy, Shleifer, and Vishny (1989a, b), Nurske (1953), Fleming (1955), Hirschman (1958); Soviet Union's big push industrialization: Zaleski (1980) Lenin (1939); China's big push industrialization: Riskin (1987), World Bank (1984); Taiwan's big push industrialization: Rabushka (1987); Evolutionary economics: Nelson (1995) and references there, Brian (1994); Bounded rationality: Conlisk (1996) and references there; Market socialism vs. capitalist development: Sachs (1993), von Mises (1922), Hayek (1944, 1945), Bardhan and Roemer eds. (1993), Lange and Taylor (1964); Dynamic programming: Beckman (1968).

Questions 7B

1. Why has the automobile industry developed much more successfully in the US, where the government does not have industrial policy to this sector, than in China, where the government has very comprehensive industrial policies about the priority order of development of different sectors? Use the concept of endogenous comparative advantage in chapter 4 and the Walrasian sequential equilibrium in this chapter to analyze why this happened, and what the implications are of a private enterprise system for social experiments in acquiring organization information. 2. We have heard many stories about the successful career or business activities of somebody who has advanced through “discovering herself.” But from the theory that you have learned in this chapter, you can see that “oneself” is not predetermined. One’s professional capacity is determined by her choice of profession through which specialized experience can be accumulated. Interdependence between self-confidence in one’s professional capacity and accumulation of experience in a professional sector may generate some positive feedback effect (virtual circles). Hence, we may see some cases of a not-so-smart person getting a chance to be involved in a profession and becoming more capable in it than a much smarter individual who did not have the chance to be involved in this profession. Hence, for such success stories, “designing oneself” is a better expression than “discovering oneself.” In particular, designing oneself is an experiment with possible combinations of one’s inherited talent and all kinds of structures of division of labor. Success or failure is, to a certain degree, a matter of luck. Therefore, a positive attitude toward taking reasonable risk may be better than trying something only in the absence of risk. Use the model in this chapter to explain why many successful businessmen, such as Edison who had no formal education, were once only marginal figures in society. 3. Put the theory of the firm in chapter 8, the theory about the implications of insurance for division of labor in chapter 10, and the theory in this chapter to develop a story about the role of the stock market. A possible version of the story may run as follows. Suppose there are economies of specialization in acquiring organization information. Hence, a professional entrepreneur may have more organization information than other specialist producers of tangible goods. Hence, there is information asymmetry. The entrepreneur would like to try some structure of division of labor according to her organization information, but others would not follow according to their information. Because of the information asymmetry, the entrepreneur cannot convince others to participate in the social experiment that she believes to be lucrative. She may use the institution of the firm to buy out others in order to participate in the social experiment that she suggests. However, her organization information may be incomplete despite the fact that she has more information than others. This implies that when she uses the residual rights to a firm to indirectly price her intangible information, she also

500

4.

5.

6.

7.

8.

9.

takes all the risk of the social experiment. If she is risk averse, then she would not choose to specialize in entrepreneurial activities. But if the stock market can be used to disperse the risk of social experimentation, then a higher level of division of labor between professional entrepreneurial activity and the production of tangible goods will occur in equilibrium, so that the sequential equilibrium may be associated with a faster evolution of organization information that is acquired by society. Take the case in which an entrepreneur (or a group of entrepreneurs) uses the stock market to experiment with a large shopping center as a basis for discussing the function of the stock market in sharing the risk of social experimentation, as examined in question 3. Analyze why the success of the McDonald’s restaurant network cannot be explained by using marginal analysis and why inframarginal analysis and the notion of social experiment are essential to the explanation. The essence of the model in this chapter is that knowledge of economic organization determines productivity and technical conditions. This point becomes even more evident if many goods are introduced into the model so that the number of patterns of the division of labor and the number of experimentation patterns are increased. In this case, the number of periods necessary for experimenting with all possible patterns of the division of labor will increase more than proportionally. For a completely symmetric model, the number of possible distinct patterns of the division of labor is m-1 if there are m goods. The number becomes ∑mn=0Cnm=2m if n out of m goods are traded and preference and production parameters differ across goods, where Cnm is n combination of m factors. Suppose there are 100 goods (m=100) and it takes one day for an economy to experiment with one pattern of the division of labor. It will take 2100/365 = 3.34×1027 years to have experimented with all patterns of the division of labor if there are 10 final goods and each of them can be produced by a roundabout production chain with 2, 3, …, or 10 links. Each individual can produce 1, 2, …, 100 goods. Suppose, moreover, that it takes society one day to experiment with one structure of division of labor. How long it will take society to find the efficient structure of division of labor out of all the possible patterns of roundabout production? Use this example to analyze why it took a long time for human society to find the efficient industrial pattern that was realized in the Industrial Revolution. Zhao (1999) specifies a trade off between the benefit of a long decision horizon, which enables the amortization of a fixed investment in organization information over a longer period of time, and the higher computation cost and risk of making more mistakes. Hence, the optimum decision horizon is endogenized. Discuss the implications of the endogenization of the decision horizon. Zhao (1999) shows that if countries are ex ante different in some aspects, then their optimum decisions about experiments with various structures of division of labor may be different. If differences in language and in culture can isolate the social experiments in different countries, then social experiments with different structures of division of labor can be simultaneously implemented in a short period of time. Use this idea to explain why Europe, with many independent countries, may acquire organization information faster than China, which has had a single government for a long period of time. Discuss the possible free rider problem in the model in this chapter. If all individuals wait for others to experiment with different structures of division of labor in the hope of free riding the experiments, then the Walrasian sequential equilibrium may involve slower acquisition of organization information. Discuss why in a symmetric model, like the one in this chapter, such free riding would not occur.

Exercises 8B

501

1. Use the approach in this chapter to dynamize the Smithian model with endogenous middlemen in example 7.3. Analyze the implications of the degree of economies of specialization in transacting and production activities, the subjective discount factor, and pricing efficiency for transaction efficiency, the emergence of professional middlemen, and trade pattern. 2. Use the approach developed in this chapter to dynamize the Smithian model of the institution of the firm in chapter 8. The answer can be found in Zhao (1999). 3. Use the approach in this chapter to dynamize the Smithian model of endogenous trade theory in chapter 7. You may assume that each individual considers only the current and the next period when she makes decisions about experiments with different configurations. The answer can be found in Zhao (1999). 4. Use the approach in this chapter to dynamize the trade model with endogenous-cumexogenous comparative advantages in chapter 6. Analyze the implications of interdependence between organization information and choice of configuration for the exploitation of endogenous and exogenous comparative advantage. 5. Use the approach in this chapter to dynamize the Smithian model of urbanization in chapter 11. Analyze the implications of institutions that affect the pricing cost for the development of urbanization. 6. Use the approach in this chapter to dynamize the Smithian model of property rights and insurance in chapter 10. Discuss the implications of institutions that affect the experimentation cost of the social search process for the efficient institutions. 7. Use the approach in this chapter to dynamize the Smithian model of endogenous number of producer goods in chapter 12. Analyze the implications of interdependence between organization information and choice of configuration for the available number of producer goods in the market and the evolution of production roundaboutness. 8. Use the approach in this chapter to dynamize the Smithian model of money in chapter 17. Discuss the implications of the subjective discount factor, transaction cost, degree of economies of specialization, and the pricing cost for the emergence of money from the evolution of division of labor.

502

Part V: Macroeconomics of Development

Chapter 16: Investment, Saving, and Economic Development

16.1. Smith and Young's Theory of Investment and Saving Due to the dichotomy assumed between pure consumers and pure producers, it was customary in early neoclassical analysis that the theory of consumption and saving behavior (for instance in Friedman’s permanent income model, 1957, and Modigliani’s life cycle model, 1989) was separated from the theory of investment and capital. Many early neoclassical models of saving and investment are macroeconomic models rather than microeconomic general equilibrium models. They do not have sound microeconomic foundation of saving behavior. In recent microeconomic models of saving and credit the distinction is drawn between self-saving and interpersonal loans. A sound microeconomic foundation of saving and credit is established to explain saving and interpersonal credit as generated by gains from intertemporal trade between individuals. A very good survey and references of this literature of recent microeconomic models of saving and credit can be found from Besley (1995). In this literature there are several types of gains from self-saving. Differences in incomes at different points in time and uncertainty of future income are two common sources of gains from self-saving. Here, income differences may be caused by differences in endowments or in production capacity. In section 16.2 we consider such a model of self-saving. Also, there are several types of gains from intertemporal trade which are based on general equilibrium mechanism of saving. (a) Differences in subjective discount rates or in tastes for goods at different points in time may generate intertemporal trade. (b) A significant source of gains from intertemporal trade arises from difference in the timing of endowments or production capacities between individuals. (c) Individuals may wish to lend to others who have a better technological advantage for transferring resources over time. (d) Need for purchasing durable goods with a value that is much greater than an individual's income flow at each point in time. In section 16.2, we consider two such models of interpersonal loans. Understanding productivity implications of saving is essential for explaining the phenomenon observed by Lewis (1954, p. 155) that the "central problem in the theory of economic development is to understand the process by which a community which was previously saving … 4 or 5 per cent. of its national income or less, converts itself into an economy where voluntary saving is running at about 12 to 15 per cent. of national income or more." The most popular theory of the relationship between saving and productivity is called saving fundamentalism which claims an unconditional "if and only if" relationship between current saving and future productivity. Current saving can increase future per

504

capita capital, while labor productivity is a monotonically increasing function of per capita capital. This saving and investment fundamentalism is taken as granted in the growth models of Ramsey (1928), Solow (1956), Lucas (1988), Romer (1986, 1990), and Grossman and Helpman (1989, 1990). We may however ask why productivity in the future can be increased by saving today. This positive relationship did not exist two thousand years ago. For instance, two thousand years ago, peasants invested corn seeds each year. But that investment could only maintain simple reproduction without much increase in productivity. Also, Chinese peasants invested in houses which were completely self-provided in the 1970s. Productivity based on such investment in durable houses was extremely low (Yang, Wang, and Wills, 1992). To the question Lucas and Romer will respond by pointing to human capital generated by saving and investment. However, we will again use the Chinese case to argue that investment in human capital and education does not necessarily lead to an increase in productivity. Chinese people have a special preference for saving and for investment in education. However, this had not generated significant productivity increases until the modern school and university system was introduced into China at the end of the 19th century. In traditional Chinese schools, there was no division of labor between teachers. Each teacher taught students a broad range of knowledge, from literature to philosophy. But in a modern university, there is a very high level of division of labor between different specialist teachers and between different specialized colleges. Also educated individuals are very specialized in their professions after their graduation from universities. It is the high level of division of labor that ensures high productivity in providing education, so that investment in education can contribute significantly to productivity progress. Recent empirical evidences support our observation. Printchett (1997) shows that empirical evidences from macro data reject the unconditional positive relationship between educational capital and the rate of growth of output per worker, despite the positive effects of education on earnings from micro data. To our question above, Grossman and Helpman might respond by pointing to investment in research and development. However, Marshall attributed the invention of the steam engine by Boulton and Watt to a deep division of labor in the inventing activities (Marshall, 1890, p. 256). Edison's experience is another evidence for the implication of the division of labor for successful inventions. Not only Edison did himself specialize in inventing electrical machines for most of his life, but he also organized a professional research institution with more than one hundred employees who specialized in different inventing activities (Josephson, 1959). The observation implies that investment in physical capital goods, in education, or in research would not automatically increase productivity in the future if the investment were not used to develop the right level and pattern of division of labor. Hence, the essential question around the notion of capital is not so much as to how much we invest and save, but rather as to what level and pattern of division of labor are used to invest in machines, education, and research. The recent empirical evidences that reject type-IV scale effect (a positive relationship between growth rates in per capita GDP and investment rates) support our observation (see Jones, 1995a). Hence, most classical economists like Smith, John Stuart Mill, Karl Marx, and Marshall emphasized the connection between the division of labor and capital. Mill's wage fund argument (1848, chapter 2, sec. 2, chapter 5, sec. 3) is

505

somehow inconsistent with the modern dichotomy between investment and consumption. He stated that "capital, although the result of saving, is nevertheless consumed". This proposition implies that a theory of investment should explain why a transfer of consumption goods from their producers to the producers of producer goods can improve productivity. In other words, we should use the concept of general equilibrium to explain gains from interpersonal and intertemporal trade of goods as the engine of investment and economic development rather than following saving fundamentalism. In sections 16.3-16.4, we use a Smith-Young model of endogenous specialization to formalize the classical story of capital that is used to increase division of labor in roundabout productive activities. A dynamic general equilibrium model will be used to address the following questions. What is the relationship between saving, which generates investment, and the division of labor, which determines the extent of the market, trade dependence, and productivity? What is the mechanism that simultaneously determines the investment level and the level of division of labor? And what are determinants of the equilibrium investment (saving) rate, the interest rate, the growth rate, and the equilibrium level of division of labor? Our story of capital originates with Smith (1776) and Allyn Young (1928) who explicitly spelt out the relationship between the division of labor and capital. According to them, capital and investment is a matter of the development of division of labor in roundabout productive activities. 1 This story runs as follows. There are many ex ante identical consumer-producers in an economy where food can be produced out of labor alone or out of labor and tractors. In producing each good, there are economies of specialized learning by doing. A fixed cost is incurred in the period when an individual engages in a job for the first time, or when job shifting takes place. Each individual can choose between specialization and self-sufficiency. The advantage of specialization is to exploit the economies of specialized learning by doing and to avoid job shifting cost. However, it increases productivity in the future at the expense of current consumption because of an increase in transaction cost caused by specialization. Moreover, in producing a tractor, there is a significant fixed learning cost. The production of a tractor cannot be completed until the learning cost has reached a threshold level. Hence, there are tradeoffs among economies of specialized learning by doing, economies of roundaboutness, transaction costs, and fixed learning costs. Each consumerproducer maximizes total discounted utility over the two periods with respect to the level and pattern of specialization and the quantities of goods consumed, produced, and traded in order to efficiently trade off one against others among the four conflicting forces. The interaction between these tradeoffs determines the nature of the dynamic equilibrium for the economy. If the transaction cost coefficient is sufficiently great, the economy is in autarky in all periods - depending upon the level of fixed learning cost and the degree of economies of roundaboutness this may entail each individual self-providing 1

Smith stated (1776, p. 371) "when the division of labor has once been thoroughly introduced, the produce of a man's own labor can supply but a very small part of his occasional wants. The far greater part of them are supplied by the produce of other men's labor, which he purchases with the produce, ... of his own. But this purchase cannot be made till such time as the produce of his own labor has not only been completed, but sold. A stock of goods of different kinds, therefore, must be stored up somewhere sufficient to maintain him, and to supply him with the materials and tools of his work, till such time, at least, as both these events can be brought about."

506

food, or self-providing both food and tractor, or it may entail evolution in the number of goods. If the transaction cost coefficient is sufficiently small and economies of specialized learning by doing and of roundaboutness are significant, in the dynamic equilibrium the economy will develop a market structure in which individuals specialize in the production of either tractors or food and trade occurs. For the division of labor there are two patterns of investment and saving. If the fixed learning cost in producing tractors is not large, each individual will sacrifice consumption in period 1 to pay transaction costs in order to increase the level of division of labor, so that productivity in period 2 can be increased. This is a self-saving mechanism which does not involve interpersonal lending. Also, an evolution in the level of specialization and/or in the number of goods may take place in the dynamic equilibrium if the transaction cost coefficient and the degree of economies of specialization and of roundaboutness are neither too large nor too small. If the fixed learning cost in producing tractors is so large that the production of a tractor cannot be completed within one period because of the time required for specialized learning by producing commercially viable tractors, then an explicit saving arrangement which involves a loan from a specialist producer of food to a specialist producer of tractors in period 1 is necessary for specialization in producing roundabout productive tractors. Under the assumptions of a high fixed learning cost in producing tractors, a small transaction cost coefficient, and significant economies of specialized learning by doing and roundaboutness, dynamic general equilibrium yields the following picture. A specialist producer of food produces food using her labor only and makes a loan in terms of food to a specialist producer of tractors in period 1 when the production of a tractor is yet to be completed. In period 2, a specialist producer of tractors sells tractors to a specialist farmer in excess of the value of her purchase of food in period 2. The difference is her repayment of the loan received in period 1. Per capita consumption of food in period 1 is lower than in an alternative autarky pattern of organization. But in period 2, tractors are employed to improve the productivity of food. The discounted gains will more than offset the lower level of per capita consumption in period 1 if the transaction efficiency coefficient and economies of specialized learning by doing and roundaboutness are great. Economic growth takes place not only in the sense of an increase in per capita real income between periods, but also in the sense that total discounted real income is higher than in alternative autarky patterns of organization.

Questions to Ask Yourself when Reading this Chapter What are gains from intertemporal trade and related saving and credit? What is the distinction between self-saving and interpersonal lending? What is the relationship between interpersonal loan and division of labor? What is the difference between the theory of endogenous gains from saving and the theory of exogenous gains from saving? What are the implications of the difference for the theory of investment? What is the relationship between transaction efficiency, rate of return to investment, and division of labor in roundabout production activities in the Smith-Young theory of capital?

507

Under what conditions may the rate of return to investment suddenly jump to 0? How does the market sort out the efficient levels of saving, interpersonal lending, and investment? Why is saving and investment fundamentalism (type-IV scale effect) rejected by empirical evidence?

16.2. Neoclassical General Equilibrium Models of Self-Saving and Interpersonal Loans In this section, we first consider Leland's model of self-saving (1968) which shows that self-saving level is an increasing function of the degree of uncertainty of future income. We then consider Diamond and Dybvig's general equilibrium model of interpersonal loan (1983). Finally, we consider Besley, Coate, and Loury's model of rotating savings and informal credit associations (1993). Example 16.1: Precautionary saving in autarky (Leland, 1968). An individual's decision problem is Maxs u(y1-s) + δE[u(y2+sr)], where y1 is a certain income level in period 1, y2 ∼ N(0, σ) is a random income level with normal distribution of mean 0 and variance σ in period 2, s (a decision variable) is the saving level in period 1, r is a certain return rate of saving, and sr is total return to saving. Utility function u(.) is strictly increasing and strictly concave. According to section 9.4 in chapter 9, the certain equivalent of E[u(y2+sr)] is approximately u(sr-0.5Rσ)], where R = -u"(E[y2+sr])/u'(E[y2+sr]) = -u"(sr)/u'(sr) is the degree of risk aversion. A well known result (Leland, 1968) says that the optimum saving level s* increases with the degree of uncertainty σ, if u"'(.) > 0. We use a specific form of u(x) = lnx to show this. For this specific functional form, the optimum saving s* is given by the following first order condition f(σ,δ, r, s, y1) = r(1+δ)s-[(1-δ)σ/2rs]-(δσy1/2rs2]-δry1 = 0. The differentiation of this condition and application of the implicit function theorem yield comparative statics of the optimum decision: ds/dσ = -(∂f/∂σ)/(∂f/∂s) > 0, ds/dr = -(∂f/∂r)/(∂f/∂s) > 0,

ds/dδ = -(∂f/∂δ)/(∂f/∂s) > 0, ds/dy1 = -(∂f/∂y1)/(∂f/∂s) > 0,

where ∂f/∂r < 0 for positive consumption level in period 2 or for s*r>(σ/2)0.5, ∂f/∂σ < 0, ∂f/∂s > 0, ∂f/∂δ < 0, and ∂f/∂y1 < 0. The comparative statics say that as uncertainty of future income, σ, returns rate of saving, r, current income, y1, and/or discount factor, δ, increase, the optimum saving level increases. Also, the optimum saving level is 0 if

508

s*r 1 , x A 2 = 4δ /(1 + 3δ ) < 1 xB 1 = 2 /(1 + δ ) < 1 , xB 2 = 2(1 + δ )/(1 + 3δ ) > 1

509

This implies that person A’s demand in period 1 is greater than her supply in period 1 and her demand in period 2 is smaller than her supply in period 2, while person B’s position is opposite. Hence, a loan from person B to person A is made in period 1. Its amount is x A 1 − 1 = 1 − xB 1 = (1 − δ )/(3 + δ ) The repayment of the interpersonal loan in period 2 is 1 − x A2 = x B 2 − 1 = (1 − δ ) /(1 + 3δ ) The ratio of the repayment to the loan is (3 + δ ) / (1 + 3δ ) = p1 / p2 The difference between the ratio and 1 can be considered as the equilibrium real interest rate, which is r = [(3 + δ ) / (1 + 3δ )] − 1 = 2(1 − δ ) / (1 + 3δ ) = 2 ρ / (4 + ρ ) where δ = 1 / (1 + ρ ) is used. It is not difficult to verify that the equilibrium real interest rate r is an increasing function of person A’s subjective discount rate ρ. Also, r can be considered as an endogenous (or dynamic general equilibrium) inflation rate, since 1 unit of the consumption good in period 1 can exchange for 1+r units of the same good in period 2. In this general equilibrium model commercial saving and interpersonal loan is distinguished from self-saving. If we take the same type of goods at different points in time as different goods, then the interpersonal loan and its repayment is just the trading of different goods between individuals. The gains to such trade in this model are based on the exogenous difference in the subjective discount factors of the individuals. It is easy to extend the general equilibrium model to explain the gains from such trade by exogenous differences in production conditions or in endowments between individuals and between periods of time, or by the problem caused by differences between the timing of the purchase of durable consumption goods and the timing of consumption of the services that they provide. Compared to other neoclassical models of saving, this general equilibrium model of saving not only endogenizes the interest rate and the inflation rate, but also endogenizes the gains from exchanges of goods at different points in time. The gains from saving are endogenous since we cannot see them until the decisions are made and the equilibrium is worked out. By contrast, in many neoclassical models of saving and capital the gains from saving are exogenously given by an ad hoc positive relationship between current saving and future productivity. The productivity gain of saving can be seen from a state equation before the decisions have been made. In the general equilibrium model of saving, the rationale for inflation or deflation in the absence of money is gains from trade between goods at different points in time. However, in the general equilibrium model of saving, saving has no productivity implication. Though the productivity implication of saving can be figured out by introducing intermediate goods or economies of scale in production into the model, the intimate relationship between interpersonal loans and the division of labor cannot be explored by the models with no endogenous specialization. Example 16.3: Rotating savings and informal credit association (Besley, Coate, and Loury, 1993). There are many informal financial institutions in less developed countries where exogenous and endogenous transaction costs for founding and developing formal 510

financial market are very high. Roscas are one of the institutions. It travels under many different names, including Chit Funds (India), Susu (Ghana, Gambia), Kye (Korea), Dahui (China), and Tontines (Senegal). They operate by having a group of individuals committing to putting a certain sum of money into a pot which each period is allocated to one member of the group by a system of drawing lots (a random rosca) or by bidding (a bidding rosca). Each period of the process repeats itself, with past winners excluded, until the last member has received the pot. Imagine a world in which n individuals wish to acquire a durable good that costs b. Each has additive preferences over consumption: v(c) without the durable and v(c)+a with it. Ignoring discounting and supposing that each individual has a fixed income flow of y over a life of length T, an individual can save up for the durable under autarky and solves the following problem in doing so: Maxc, t (T-t)[v(y)+a]+tv(c) subject to t(y-c) = b, where t is the acquisition date for the durable and c is consumption during the accumulation phase. The first term in the maximand refers to the period after time t when the durable has been acquired, while the second term is utility during the period of accumulation. The constraint just says that enough saving must have been done before t to buy the durable. By eliminating t in the objective function from the constraint, it is straightforward to see that the value of the autarky program can be written as T[v(y)+a]-bμ(a), where μ(a) ≡ Minc {[v(y)+a-v(c)]/(y-c)}. The interpretation of this is clear. The first term represents maximal lifetime utility were the durable a free good, i.e., an individual could own it for this whole life without having to forego any current consumption. The second represents the utility cost of saving up. A random rosca gives each member of the group of n individuals a 1/n chance of winning the pot at each of the rosca's meeting dates. Thus viewed ex ante, the rosca gives uniformly distributed acquisition dates on the set {1, 2, …, n}, Assume that the time for obtaining the durable by self-saving is still t. Suppose now that an individual who joins the rosca wins the pot at ith meeting. Therefore, she gets the durable at time (i/n)t. Note the probability for winning at the ith meeting is 1/n. E[(i/n)] = ∑i=1n[(i/n)(1/n)] = (n+1)/2n. Hence, her life-time expected utility is thus (T-t)[v(y)+a]+t[v(c)+(n+1)a/2n] = (T)[v(y)+a]- t{v(y)-v(c)+[(n-1)a/2n]}, Suppose that the rosca aims to maximize the expected utility of its representative member, it maximizes this subject to the budget constraint t(y-c) = b, which says that there are enough funds in the pot at each meeting date to buy the durable. Eliminating t in the expected utility function from the budget constraint, the maximized expected lifetime utility in a rosca can be written as: T[v(y)+a]- bμ[(n-1)a/2n],

511

where μ[(n-1)a/2n] ≡ Minc {{v(y)+ [(n-1)a/2n] -v(c)}/(y-c)}. It is easy to prove using the envelope theorem that μ'(.) > 0 and hence that, since (n-1)/2n < 1, the random rosca lowers the utility cost of saving up to acquire the durable. The reason is, of course, plain to see. Even if it maintained the same saving pattern as under autarky, the rosca gives each of its members a chance of winning the pot early by drawing lots. In fact, all but the last member of the rosca is better off holding savings fixed. The rosca will however choose a lower savings rate than under autarky.

16.3. Smith and Young's Theory of Investment and Savings

Example 16.4: A Smith-Young model of investment (Yang, 1999). 16.3.1. The Model We consider a finite horizon (two-period) economy with a continuum of ex ante identical consumer-producers of mass M. There is a single consumer good (called food) produced by labor alone or by labor and an intermediate good (called tractor) together. Individuals can self-provide any goods or alternatively, can purchase them on the market. The self-provided amounts of food and of tractors in period t are denoted respectively yt and xt. The respective amounts sold and purchased of food in period t are yst and ydt, and those of tractors are xts and xtd. The trading efficiency coefficient of x and y is k. The utility function is (16.1a)

ut = ln(yt+kytd),

where ut will be negative infinity if yt = ytd = 0. As in chapter 14, trade in this economy is mediated through contracts signed in spot and futures markets which operate in period 1. Assume that the futures market horizon and any individual's decision horizon are of two periods. The objective function for an individual's decision problem is therefore total discounted utility, given by: (16.1b) U = u1 + u2/(1+r), where U is total discounted utility, and r is a subjective discount rate. It is assumed that a fixed learning cost in terms of labor, A, is incurred in producing tractors. The fixed learning cost in producing food is B. The production functions for an individual are assumed to exhibit economies of specialized learning by doing: y tp ≡ y t + y ts = Max{( xt + kxtd ) a ( L yt − σB), ( L yt − σB)} (16.2a) (16.2b) (16.2c)

a ∈ (0, 1), B ∈ (0, l ) x ≡ x t + x ts = Max{( L xt − σA) b ,0}, b > 1, lyt + lxt = l, lit ∈[0,l]

(16.2d)

Lit = Lit −1 + lit ,

p t

A ∈ (0, l ]

Lx0 = L y0 = 0

where ≡ yt + and ≡ xt + xts are respectively the total output levels of food and s tractors in period t, yt and xts are respectively the quantities of the two goods sold at time t. xtd is the amount of tractors purchased at time t. xt + kxtd is the amount of tractors employed. lit is an individual’s level of specialization as well as the amount of her labor ytp

yts

xtp

512

allocated to the production of good i (i = x,y) in period t, and Lit is the labor accumulated in producing good i up to period t, referred to as human capital. (16.2a) implies that food can be produced either from tractors and labor, or from labor alone. In producing a good in period t, σ = 0 if an individual has engaged in producing the good in period t-1 and does not shift between different activities in periods t and t-1; σ = 1 if an individual changes jobs in period t or t-1 or engages in producing the good for the first time in period t. Each person is assumed to be endowed with l units of labor in each period. The assumption A∈(0,l] implies that it is possible that the production process of tractors cannot be completed in period t =1 if A = l, so that a story of investment, saving, and capital may be told. It is assumed that economies of specialized learning-by-doing and the fixed learning cost are specific to each individual and to each activity. There are economies of specialization in producing each good since a person's labor productivity in producing x increases with her level of specialization in producing x for b>1 and total factor productivity of y increases with her level of specialization in producing y for a > 0 when x is used as an intermediate input. If only labor is used to produce y, then the labor productivity of y increases with the person’s level of specialization in producing y, since the utilization rate of the fixed learning cost B increases with her level of specialization. Parameter b represents the degree of economies of specialization in producing tractors. The elasticity of output of food with respect to tractors is a. Therefore, the product ab can be interpreted as the degree of type A economies of roundaboutness. (16.2d) is the state equation and initial condition for human capital Lit. We assume that A+B > l - 1 to simplify the algebra. This assumption implies that selfprovision of two goods by each individual in two periods is not an optimal decision. A Walrasian regime prevails because economies of specialized learning by doing are individual-specific and the futures market nullifies the monopoly power which might occur from specialized learning by doing. 16.3.2. Configuration Sequence and Structure Sequence This subsection considers an individual's production and trade decision problem and dynamic equilibrium. The Wen theorem can be applied to the model in this chapter. Hence, each individual sells only one good and does not buy and sell or self-provide a good at the same time. A feasible market structure consists of a set of choices of configurations by individuals. A sequence of configurations over 2 periods is a decision variable for each individual. As each individual chooses a certain sequence of configurations, a sequence of market structures is determined. For each sequence of market structure, there is a dynamic corner equilibrium which satisfies the market clearing conditions and utility equalization conditions, but may not satisfy the condition for maximizing an individual's total discounted utility with respect to choice of sequences of configurations. The remainder of this subsection characterizes the dynamic corner equilibrium for each feasible sequence of market structures and then solves for the dynamic general equilibrium where each individual maximizes her total discounted utility. The Wen theorem implies that six configurations, depicted in Fig. 16.1 where the circles represent configurations and arrowheaded lines represent flows of goods, which constitute four feasible market structures, need to be considered for the optimum decision.

513

In the first type of market structure, autarky, there is no trade and each individual self-provides any good that is required. Two configurations, E and F, meet the criterion for autarky. For configuration E the quantities traded of all goods are 0, xt = 0, and yt > 0 so that each individual self-provides food without using a tractor. For configuration F, the quantities traded of all goods are 0, but xt, yt > 0; in this case each individual self-provides both tractors and food. Each of these autarky configurations constitutes a structure. The two configurations are depicted in Fig. 16.1(a). In the second type of structure, there is trade in tractors and/or food. Denote a configuration in which an individual sells tractors and buys food in a period by (x/y), a configuration in which an individual buys food and learns how to produce a tractor but is yet to complete its production by (0/y), a configuration in which an individual sells food and buys tractors by (y/x), and a configuration in which an individual sells food but buys nothing by (y/0). Given these possible configurations, there are two structures with trade: (i) the structure denoted C consists of a division of the M individuals between configurations (0/y) and (y/0), which are depicted in Fig 1b, - that is, professional farmers sell food to professional producers of tractors, retaining an amount for their own consumption; (ii) the structure denoted D consists of a division of the M individuals between configurations (x/y) and (y/x), which are depicted in Fig. 16.1(c). There are 24=16 sequences of the four structures over two periods: EE, EF, ED, EC, FF, FE, FD, FC, DD, DE, DF, DC, CC, CE, CF, CD, where the first letter denotes the structure in period 1 and the second that in period 2. For instance, CD, as shown in Fig. 16.2, denotes that structure C is chosen in period 1 and structure D is chosen in period 2. Some of them are obviously infeasible or cannot be equilibrium. For instance, CC involves a specialist producer of tractors choosing configuration (0/y) (buying food but selling nothing) over two periods and a specialist farmer choosing (y/0) (selling food but buying nothing) over two periods. The sequence cannot be equilibrium since it is incompatible with the budget constraint. If the fixed learning cost in producing tractors A = l, then sequences Di (i = E, F, D, C), FF, FE, and EF are infeasible and only EE and CD are feasible. Sequence CD involves explicit saving since a specialist producer of tractors buys food and sells nothing in period 1. This one way trade can be considered as a loan made by a specialist farmer to a specialist producer of tractor. A dynamic general equilibrium satisfies the following conditions, which are analogous to the conditions in the fixed point theorem. (i) For a given profile of the sequences of configurations chosen by individuals, a set of numbers of individuals choosing different sequences of configurations and a sequence of relative prices of traded goods at different points in time clear the market for goods and equalize the total discounted utility of all individuals; (ii) For a given set of numbers of individuals choosing different sequences of configurations and for a given set of sequences of relative prices of traded goods, individuals maximize total discounted utility with respect to the sequences of configurations and quantities of goods produced, consumed, and traded. It is possible to solve for the dynamic general equilibrium in two steps: first, solving for a dynamic corner equilibrium for each structure sequence; then identifying the Pareto optimum dynamic corner equilibrium that generates the highest total discounted per capita real income. The first step can be divided into two substeps. The first is to solve for an individual's optimum dynamic decision for each sequence of configurations; and the second is to solve for a dynamic

514

corner equilibrium for each structure sequence using the market clearing condition in each period and the condition that total discounted utility must be equalized for all individuals.

Figure 16.1: Configurations and Market Structures

Structure sequence EF

Structure sequence ED

Structure sequence FD

period 1

period 1

period 1

period 2

period 1

period 2

period 2

period 1

Structure sequence CD

period 2

period 2

Structure sequence DD

515

Figure 16.2: Investment and Evolution of Division of Labor in Roundabout Production

In the following subsections, a dynamic corner equilibrium in each of the feasible sequences of market structures is solved for, and an expression is derived for an individual's total discounted real income in each candidate for the dynamic general equilibrium. 16.3.3. Dynamic Corner Equilibria in 16 Structure Sequences 1. Sequences EE and FF A dynamic corner equilibrium for autarky over two periods is equivalent to the solution to an individual's optimum dynamic labor allocation decision for the sequence of configurations E and/or F over two periods. In configuration E, the quantities traded of all goods are 0, xt = 0 and yt > 0; inserting these values into equations (16.1) and (16.2), and substituting from (16.2) into (16.1a), then into (16.1b), gives the total discounted value of utility for sequence EE as: (16.3)

U(EE) = ln(l-B)+ln(2l)/(1+r)

where U(EE) is the total discounted utility for sequence EE. In configuration F, the quantities of all goods traded are 0, and xt, yt > 0; inserting these values into equations (16.1) and (16.2), and substituting from (16.2) into (16.1a), then into (16.1b), gives the total discounted value of utility for sequence FF. Thus, the decision problem for the sequence is: (16.4)

Max U = lny1+lny2/(1+r) = ln[x1a(ly1-B)]+ln[x2a(ly2-B)]/(1+r) lxi = ln[(lx1-A)ab(l-lx1-B)]+ln[(lx1+lx2-A)ab(l-lx1+l-lx2-B)]/(1+r) (production function) subject to yt = xta(Lyt-B), xt = (Lxt-A)b (endowment constraint) lxt + lyt = l, Li0 = 0 (state equation and initial condition) Lit =Lit-1+ lit,

The solution to the decision problem is given by: (16.5)

ly1 = (abB+l-A)/(ab+1), lx1 = [ab(l-B)+A]/(ab+1), ly2=l/(ab+1), lx2 = abl/(ab+1), U(FF) = [(2+r)/(1+r)][abln(ab)-(ab+1)ln(ab+1)]+ [(ab+1)/(1+r)][(1+r)ln(l-A-B)+ln(2l-A-B)],

where U(FF) is the maximum total discounted utility or total discounted per capita real income for sequence FF. As shown above, the autarky configuration F cannot be in equilibrium if A+B ≥ l, which implies a negative infinite utility in F. 2. Sequences EF and FE: Following the above procedure, the corner equilibria in sequences EF and FE and the corresponding total discounted per capita real incomes can be derived. Sequence EF involves an increase in the number of goods and the emergence of

516

tractors in period 2. Sequence FE involves a decrease in the number of goods and the disappearance of tractors in period 2. 3. Sequence CD: The structure C consists of configurations (0/y) and (y/0) and structure D consists of configurations (x/y) and (y/x). Hence, this structure sequence consists of the sequence of configurations (0/y) and (x/y) and the sequence of configurations (y/0) and (y/x). There are two steps in solving for the dynamic corner equilibrium in the structure sequence: first, for each sequence of configurations the optimum dynamic labor allocation decision and demands and supplies for each good in each period (and hence the indirect total discounted utility of an individual who chooses that configuration sequence) are derived; and second, given the demands, supplies, and indirect utility function of an individual in each configuration sequence, the market clearing conditions and utility equalization conditions are used to solve for the set of corner equilibrium relative prices and the number of individuals choosing different configuration sequences. 3.1 Sequence of Configurations (0/y) and (x/y): In this sequence x2s, ytd > 0, lxt = l, and x1s = xt = lyt = yt = xtd = yts = 0. This sequence will be chosen by an individual only if A = l which means that the production process of a tractor cannot be completed in period 1 due to the large fixed learning cost. If A < l, a sequence of (x/y) over two periods will be chosen since it does not make sense to choose (0/y) which delays the sale of tractors when a tractor can actually be produced in period 1. Hence, we assume A = l in this configuration sequence, so that the decision problem for sequence of (0/y) and (x/y) is: (16.5a) Max : d yt

U = ln(ky1d)+ln(ky2d)/(1+r)

s. t.: x1s = 0 and x2s = (lx1+lx2)b lx1 = lx2 = l px2x2s = y1d + py2y2d

(production function) (endowment constraint) (budget constraint)

where pit is the price of good i in period t in terms of food in period 1 which is assumed to be the numeraire, and y1d is a loan in terms of food made by a specialist farmer to the specialist producer of tractors. The specialist tractor producer's sales in period 2, px2x2s, are greater than his purchases in period 2, py2y2d. The difference is the repayment of the loan. The solution to (16.5a) is y1d = (1+r)(2l)bpx2/(2+r), y2d = (2l)bpx2/(2+r)py2, (16.5b) x2s = (2l)b, Ux = {(2+r)[lnk+bln(2l)+lnpx2-ln(2+r)]-lnpy2}/(1+r)+ln(1+r), where xts and ytd are the supply of tractors and the demand for food in period t, respectively, Ux is the indirect total discounted utility function for the sequence. 3.2 Sequence of (y/0) and (y/x): By a similar process, the optimum dynamic decision for this sequence can be found as follows. (16.6)

x2d = (2akalpy2/px2)1/(1-a), y1s = {l-B-(1+r)(1-a)[2py2l(ak/px2)a]1/(1-a)}/(2+r) y2s = {(1+a+r)[2l(py2ak/px2)a]1/(1-a)-(l-B)/py2}/(2+r), Uy = (2+r){ln[l-B+(1-a)[2py2l(ak/px2)a]1/(1-a)]-ln(2+r)}/(1+r) +ln(1+r)-lnpy2/(1+r)

517

where Uy is the indirect total discounted utility function for the sequence. Utility maximization by individuals and the assumption of free entry (when individuals make decisions at t = 1) have the implication that the total discounted utility of individuals is equalized across the two sequences of configurations. That is, (16.7)

Ux = Uy

Let Mi represent the number of individuals selling good i. Multiplying Mi by individual demands and supplies gives market demands and supplies. The market clearing conditions for the two goods over two periods are: (16.8)

Mxx2s = Myx2d,

Mxytd = Myyts,

t = 1,2,

where Mxx2s and Myx2d are market supply and demand, respectively, for tractors in period 2, and Mxytd and Myyts are market demand and supply, respectively, for food in period t. Note that due to Walras' law one of the three market clearing conditions is not independent of the others. There are three independent equations in (16.7) and (16.8), which determine three unknown variables: Mx/My, px2, py2, where pit is the price of good i in period t in terms of food in period 1 and Mi can be solved using the population size equation M = Mx + My as soon as Mx/My is determined. The corner equilibrium values of the three variables are thus given by (16.7) and (16.8) as: (16.9)

px2 = (2-a+r)(l-B)/(1+r)k(2l)b, py2 = [(2-a+r)/ak2(2l)b]a(l-B)/(1+r)(2l)1+ab, Mx/My = ka/(2-a+r), U(CD) = ln(l-B)+[(2-a+r)ln(2-a+r)-(2+r)ln(2+r) +(ab+1)ln(2l)+a(lna+2lnk)]/(1+r)

where U(CD) is the total discounted per capita real income for structure sequence CD, which is derived by inserting the corner equilibrium relative prices into the expression for indirect total discounted utility in (16.5) or (16.6). 4. Sequences ED, FD, DD, DE, DF, DC: By two-step procedure analogous to that used to solve for the dynamic corner equilibrium of sequence CD, it is possible to solve for the dynamic corner equilibria in the 8 structure sequences. The other five of all 16 sequences, CC, EC, FC, CE, and CF, are obviously infeasible because of their incompatibility with the budget constraint.

16.4. Investment, Capital, and Division of Labor in Roundabout Production

Those corner equilibria that do not generate the highest total discounted utility do not satisfy the condition that each individual maximizes her total discounted utility with respect to sequences of configurations. We call the dynamic corner equilibrium that generates the highest total discounted per capita real income the Pareto optimum dynamic corner equilibrium. Following the method used to prove the Yao theorem in chapter 4, we can show that only the Pareto optimum dynamic corner equilibrium is the dynamic general

518

equilibrium. Comparisons among the total discounted per capita real incomes for all feasible sequences of structure yield the results in Table 16.1. 16.4.1. Dynamic General Equilibrium Structure sequence FE is obviously inefficient. Individuals prefer diverse consumption in this model. They do not choose a structure with two goods, such as F, only if the forgone economies of specialized learning by doing are greater than the economies of consumption diversity. If they can afford two goods in structure F in period 1, they will certainly be more able to afford the two goods in F in period 2 because of learning by doing. Hence, FF instead of FE will be chosen. Similarly, it can be shown that DE, which involves devolution in division of labor and in production roundaboutness, is inefficient. If D is better than E in period 1, then the benefit of division of labor must outweigh transaction costs. This will be more so in period 2 because learning by doing is faster in D than in E. A comparison between U(EF) and U(FF) indicates that U(EF) > U(FF) if A+B > l-1, which is assumed. Hence, we can further rule out structure sequence FF from consideration. Table 16.1: Total Discounted Per Capital Real Incomes in 7 Structure Sequences

Structure sequence EE FF EF ED FD DD CD

Total discounted per capita real income ln(2l)/(1+r)+ln(l-B) [(2+r)/(1+r)][abln(ab)-(ab+1)ln(ab+1)]+ [(ab+1)/(1+r)][(1+r)ln(l-A-B)+ln(2l-A-B)] {abln(ab)+(ab+1)[ln(2l-A)-ln(ab+1)]}/(1+r)+ln(l-B) {a (2lnk+lna)+(1-a)ln(1-a)+ abln(l-A)+ln(2l)}/(1+r)+ln(l-B) {a(2lnk+lna)+(1-a)ln(1-a)+abln[ab(2l-A-B)+l]+ln[(ab+2)l-AB]}/(1+r)+abln(ab)+(ab+1)[ln(l-A-B)-(2+r)ln(ab+1)/(1+r)] (2+r){a(2lnk+lna)+(1-a)ln(1-a)}/(1+r)+ abln(l-A) +ln(l-B)+[(1+ab)ln(2l)/(1+r)] ln(l-B)+[(2-a+r)ln(2-a+r)-(2+r)ln(2+r) +(ab+1)ln(2l)+ a (lna+2lnk)]/(1+r)

Hence, we can compare total discounted per capital real incomes in 6 structure sequences in Table 16.1 to partition the 6-dimension parameter space of a, b, A, B, r, k into several parameter subspaces. The dividing line between those structure sequences of autarky and those with division of labor is of course determined by some critical value of transaction efficiency k, because of the trade off between economies of specialized learning by doing and transaction costs. The dividing line between CD and DD is determined by the fixed learning cost A. For A < l, we can show that DD, which has trade in tractors in period 1, is always better than CD, which does not involve trade in tractors in period 1, since it is obviously inefficient not to trade tractors that can be completed in period 1 for A < l. Hence, CD will be a candidate for dynamic general equilibrium only if A = l, which implies that it takes one period to complete the production of a tractor.

519

We now consider structure sequences ED, FD, DD, which are candidates for dynamic general equilibrium if A < l and k is sufficiently large. From Table 16.1, we see (16.6a) (16.6b) (16.6c)

U(ED)>U(FD) iff γ > γ 0 , U(DD)>U(ED) iff γ > γ 1 , U(DD)>U(FD) iff γ > γ 2 ,

where γ = abln(l-A)/(1+r) increases with the degree of economies of specialization in producing tractors, which is b, and with the degree of economies of roundaboutness, which is ab, and decreases with the discount rate r, γ0 ≡ {abln[ab(2l-A-B)+l]+ ln[(ab+2)l-A-B)](ab+1)(2+r)ln(ab+1)-ln(2l)}/(1+r)+[abln(ab)+(ab+1)ln(l-A-B)-ln(l-B)], γ1 ≡ -[β+abln(2l)/(1 +r)]/r, β ≡ a(2lnk+lna)+(1-a)ln(1-a), γ2 ≡ [γ0-β+abln(2l)/(1+r)](1+r)-1. (16.6) implies that (16.7a) (16.7b)

U(ED)>U(DD) and U(ED)>U(FD) iff γ ∈(γ 0 , γ 1 ) which holds only if γ1 >γ 0

A comparison between γ 1 and γ 0 indicates that γ 1 > γ 0 iff A+B is sufficiently smaller than k but also sufficiently large to be close to l. Hence, if A+B is sufficiently smaller than l, we can exclude ED from consideration. Then the dividing line between FD and DD is given by (16.6c). Otherwise, (16.7b) holds, so that the set of candidates for dynamic general equilibrium comprises ED, FD, and DD. The dividing lines between them are given in (16.6a, b). Suppose k is sufficiently close to 0, then all structure sequences with division of labor generate negative infinite total discounted per capita real income. The set of candidates for general equilibrium comprises EE and EF. A comparison between U(EE) and U(EF) generates the dividing line between the two structure sequences, as shown in Table 16.2. Suppose A = l. Then, it takes a tractor specialist one period to build up enough human capital to produce a commercially viable tractor. Then, only EE and CD are feasible. ED is infeasible since a tractor is not produced in E in period 1 and it cannot be completed in period 2, even by a tractor specialist (see Fig. 16.2), a situation that is incompatible with the definition of D, which requires trade in tractors. FD is infeasible since in F, a person selfprovides both tractors and food. Even if she allocates all time to the production of tractors in period 1, a tractor can be completed only in period 2, a situation that is incompatible with the definition of F, which requires that a person drives a self-provided tractor to produce food. DD is infeasible, again because D is infeasible in period 1 for A = l. A comparison between U(EE) and U(CD) yields the dividing line between EE and CD, as shown in Table 16.2. All of the results of dynamic general equilibrium and its inframarginal comparative dynamics are summarized in Table 16.2. EE, as shown in Fig. 16.2, denotes that all individuals self-provide food in the absence of tractors in both periods. EF, as shown in Fig. 16.2, denotes that all individuals choose autarky in both periods, but they self-provide only food in period 1 and self-provide both food and tractors in period 2. In other words, tractors emerge in period 2 and there is evolution in the number of goods and in production roundaboutness over time. ED, as shown in Fig. 16.2, denotes that individuals self-provide food in period 1, while in period 2 some of them specialize in producing food and others

520

specialize in producing tractors. Evolution of division of labor takes place through increases in both individual specialization and the number of goods. FD, as shown in Fig. 16.2, denotes that individuals self-provide both food and tractors in period 1 and choose specialization and trade the two goods in period 2. In other words, evolution of division of labor takes place through an increase in individual specialization in the absence of changes in production roundaboutness. DD denotes the division of labor and trade in the two goods in the two periods without its evolution, but with an implicit self-saving in period 1. CD, as shown in Fig. 16.2, denotes the division of labor in the two periods with explicit saving and an interpersonal loan. Table 16.2: Dynamic General Equilibrium and Its Inframarginal Comparative Dynamics

Aρ0 EF Autarky with tractor emerging in t = 2

k is large, equilibrium involves division of labor k < k0 in the absence of explicit saving EE A+B is close to l A, B are small

k > k0 CD,

γ < γ1

γ > γ1

γ < γ2

γ > γ2

autarky

divisio

ED, evolution in specialization, tractor emerges in t=2

DD, division of labor without evolution

FD, evolution in specialization with 2 goods produced in 2 periods

DD, division of labor without evolution

with only food produced in 2 periods

of labor with explicit saving

where ρ0 ≡[ln(2l)-ln(2l-A)+ln(ab+1)]/[ln(2l-A)-ln(ab+1)+ln(ab)], γ = abln(l-A)/(1+r) increases with the degree of economies of specialization in producing tractors, which is b, and with the degree of economies of roundaboutness, which is ab, and decreases with the discount rate r, γ0 ≡ {abln[ab(2l-A-B)+l]+ ln[(ab+2)l-A-B)]+ (ab+1)[ln(l-A-B)-(2+r)ln(ab+1)]-ln(2l)}/(1+r)+ [abln(ab)-ln(l-B)], γ1 ≡ -[β+abln(2l)/(1+r)]/r, β ≡ a(2lnk+lna)+(1-a)ln(1-a), γ2 ≡ [γ0b+abln(2l)/(1+r)](1+r)-1, and lnk0 ≡ [(2+r)ln(2+r)-(2-a+r)ln(2-a+r)-alna-abln(2l)]/2a. Here, ab>ρ0 means that the degree of economies of specialization and roundaboutness is greater than a critical value. γ > γi means that the degree of economies of specialization and roundaboutness is greater and the discount rate is smaller than some critical value. k>k0 means that the transaction efficiency parameter is larger than a critical value. Note that γ1 and γ2 decrease as k increases, so that DD is more likely to be equilibrium compared to ED or FD if transaction efficiency is higher. Also, k0 decreases with ab, so that CD is more likely to be equilibrium compared to EE if the degrees of economies of specialization and roundaboutness are greater. The dynamic general equilibrium and its inframarginal comparative dynamics are also summarized in words in the following proposition.

521

Proposition 16.1: (1) The dynamic general equilibrium is an autarky sequence if transaction efficiency, k, is low. (i) Equilibrium is EE where each individual self-provides food over two periods if the degrees of economies of specialization and roundaboutness are not great; (ii) Equilibrium is EF which involves evolution in the number of goods and emergence of tractor in period 2, but without specialization and its evolution if the degrees of economies of specialization and roundaboutness are great. (2) The general equilibrium involves division of labor and/or its evolution but does not involve explicit saving if transaction efficiency is sufficiently high and if A 0, and dV(T*, k)/dk= ∂V(T*, k)/ ∂k > 0 where ∂2V/∂k∂T>0, ∂2V/∂T2l-1. Show that under what conditions structure sequence FF will occur in equilibrium. 5. Assume B = 0 in example 16.4. Solve for dynamic equilibrium and its comparative dynamics.

528

6. Assume that the production function in example 16.4 is yip = Min{xi+kxid, α(Lyt-σB)}. Solve for dynamic equilibrium.

529

Chapter 17: Money, Division of Labor, and Economic Development

17.1. Neoclassical vs. Classical Theories of Money In the previous chapters, we have given no consideration to the relationship between economic development and money. All transactions have been on a barter basis and relative prices have been exchange ratios of goods. In those models with only final goods and with ex ante identical individuals who prefer diverse consumption, all transactions that are essential for division of labor necessarily involve a double coincidence of demand and supply. From Fig. 7.4 and Fig. 7.5, we can see that in a model with ex ante identical consumer-producers in the absence of producer goods trade between each pair of trade partners are two ways . This implies that, for each pair of trade partners, if one sells good 1 and buys good 2, then the other must buy good 1 and sell good 2, just like when a boy and a girl simultaneously fall in love with each other: what he wants from her is what she wants to give him and what she wants from him is what he wants to give her. However the double coincidence of demand and supply may not hold under at least two circumstances. We may use the Kiyotaki-Wright (KW) model (1989), which involves ex ante differences between consumer-producers, to illustrate the first case, and the Borland-Yang (BY) model (1992) to illustrate the second case. Example 17.1: The Kiyotaki-Wright (KW) model of money. Consider the KW model, as shown in Fig. 17.1(a), where person A wants good z (meat), but produces only x (rice), person B produces only z (bread), but wants y, and person C wants good x, but produces only y. In this economy with different tastes and production capacities between individuals, trade between each pair of trade partners is one-way only, and a double coincidence of demand and supply does not hold in the absence of money. However, the absence of a double coincidence of demand and supply is necessary but not sufficient for the emergence of money. If all trade partners go to a central clearing house and simultaneously deliver goods to the right buyers according to Walrasian equilibrium prices, money is still not needed. Barter is enough to coordinate all essential transactions. But if it is impossible to implement all deliveries at the same time in such a central clearing house, money will be essential for this economy. For instance, if the production of y can take place only if person C has received x, then deliveries of x and y cannot be implemented at the same time. If it is impossible to implement all transactions at the same time, then a one-way delivery of x that takes place before deliveries of y and z is a sort of credit arrangement in the expectation of eventual delivery of z. If such a credit system is not available, as is very likely when you buy a good from a stranger on the street who you may never meet again, then person A who delivers x to person C will ask for some commodity as payment for x from C in order to secure property rights. But what A wants is z which person C does not produce, that is, there is no double coincidence of demand and supply between A and C. Suppose A accepts y, which is produced by C, but is useless for direct consumption by A. Then A can use y to exchange z with B, as shown

530

in Fig. 17.1(b) where all transactions are two-way. Commodity y is here used by person A to facilitate her further transactions. Person A does not use y for her own consumption, or for her production. A commodity that satisfies this condition is called commodity money. Hence, in the structure of transactions in Fig. 17.1(b), good y becomes commodity money for person A.

(a) Absence of double coincidence of demand and supply

(b) Good y is commodity money

Figure 17.1: The Absence of Double Coincidence of Demand and Supply based on ex ante Differences between Individuals If person A delivers x to person C, and in return C gives A a note which specifies how much C owes to A, then A may give this note to B in exchange for z produced by B. Then B can use this note in exchange for y from C. In this case, the note becomes a money substitute. Travelers’ cheques and money orders are common money substitutes, which themselves have no direct value for consumption and production, but can substitute for commodity money. If the money substitute is enforced by a government legal system and is not backed by any commodity money, we call it fiat money. US dollars that we use in daily life are fiat money. The story described in Fig. 17.1 predicts that the commodity with the lowest transaction cost will play the role of medium of exchange. This story is not particularly interesting since we can predict this with no formal model. 1 It cannot predict the emergence of money, and it cannot explore the intimate relationship between money and division of labor, since in that story individuals cannot choose their levels of specialization and they cannot survive in the absence of money or a related credit system. Furthermore, the productivity implications of money cannot be explored by that story. Plato (380 BC. pp.102-6) spelled out the connection between money and division of labor more than two thousand years ago. Smith (1776, p.37) and Turgot (1766. pp.24446, 64, 70) indicated that specialization is the driving force behind the emergence of money. 2 Borland and Yang (1992, also see Yang and Ng 1993, chapter 17) develop the 1

Kiyotaki and Wright’s original model with uncertainties looks much more complicated than the simplified version. However, the probability parameter in their model can be interpreted as the transaction cost coefficient in the simplified version. 2 According to Smith, once the division of labor has been thoroughly established, an individual supplies most of his product to others in exchange for goods he wants. But the exchange “must frequently” be “very much clogged” if one does not have what others want or others do not have what one desires. “In

531

first Smithian general equilibrium model to explain emergence of money from evolution of division of labor in roundabout production. They have shown that even if all consumer-producers are ex ante identical in all aspects, money will emerge from a sufficiently high level of division of labor in a sufficiently long roundabout production chain. In their model, specialization and division of labor is necessary, but not sufficient for the emergence of money. Also, ex ante differences between individuals are not essential for the emergence of money. Example 17.2: Borland and Yang’s model of money. The story of the emergence of money from the evolution of division of labor in roundabout production can be illustrated by the graphs in Fig. 17.2. In that model there are many ex ante identical consumerproducers. Each of them can produce steel (x) from labor, then use steel, together with labor, to produce hoes (y), then use hoes, together with labor, to produce food (z) for her own consumption. This is an autarky structure as shown in panel (a), where dots denote the transformation process from intermediate inputs to outputs. For this autarky structure, trade, market, and money are absent. This verifies the statement that division of labor is essential for the emergence of money. (a) Autarky

(b) Partial division of labor

(c) Complete division of labor

(d) Good y plays role of money

Figure 17.2: Emergence of Money and Evolution of Division of Labor

order to avoid the inconveniency of such situation, every prudent man ... have at all times by him, besides the peculiar produce of his own industry, a certain quantity of some one commodity or other, such as he imagined few people would be likely to refuse in exchange for the produce of their industry” (p.37).

532

Individuals may choose a structure of partial division of labor: either between configuration (z/y) (complete specialization in producing food) and configuration (xy/z) (producing steel x and hoe y) or between configuration (x/z) (complete specialization in producing steel x) and configuration (zy/x) (producing both hoes y and food z). In this type of structure, shown in panel (b), barter transactions with double coincidence of demand and supply are enough to facilitate partial division of labor. This substantiates the statement that specialization and division of labor are not sufficient for the emergence of money. The third type of structure with the complete division of labor is shown in panel (c), where each individual completely specializes in producing one good and trade between a specialist in x and a specialist in y or between a specialist in x and a specialist in z is of a one–way nature. A specialist in steel sells steel (x) to a specialist in hoes (y), but she does not need hoes. A specialist in food sells food (z) to a specialist in steel, but she does not need steel. If there is no central clearing house where all traded goods can be simultaneously delivered, then the complete division of labor in the roundabout production chain with three links cannot be realized in the absence of money. If economies of specialization in producing each good and transaction costs are specified, then the general equilibrium will evolve from autarky to partial division of labor, followed by the complete division of labor as transaction efficiency is improved. In order to facilitate the complete division of labor in the roundabout production chain with three links, either a commodity money, or a money substitute, or a credit system will be used as a medium of exchange. Fig. 17.2(d) shows the structure of transactions with good y as commodity money, where a x specialist exchanges x for y with a y specialist, then exchanges y for z with a z specialist. Commodity y is not used by the x specialist for consumption and production. She uses y as a medium to facilitate further transactions. It is shown in Borland and Yang (1992) that if a money substitute is not available, or a credit system involves excessive transaction costs due to a war or other social turmoil, then the commodity with the smallest transaction cost coefficient will be used as money. If all commodities have the same transaction cost coefficient, then the commodity in the middle link of the roundabout production chain will be used as money. If a credit system or a money substitute with a much smaller transaction cost coefficient is available, then the credit system or the money substitute will be used as medium of exchange. Money can promote productivity progress through facilitating a high level of division of labor in a long roundabout production chain, which is infeasible in the absence of money. In the model the equilibrium price of commodity money in terms of other goods, the degree of monetization of an economy, and the circulating quantity of money are all endogenized. In the next three sections, we use a simple general equilibrium model to illustrate the technical substance of this kind of models.

Questions to Ask Yourself when Reading this Chapter Under what circumstances does the double coincidence of demand and supply not occur? What other condition, in addition to the absence of double coincidence of demand and supply, is needed for the emergence of money?

533

What is the relationship between the level of division of labor, the length of roundabout production, transaction efficiency, and the emergence of money? Under what condition can fiat money or other money substitute play the role of medium of exchange? What features of a commodity are important for it to be chosen as money? What is the relationship between the degree of commercialization, the degree of monetization of an economy, and the level of division of labor? What are important determinants of the value of money? Why can fiat money, money substitute, and a credit system promote productivity progress? How does the market sort out the efficient monetary regime and the efficient level of division of labor? What is productivity implication of money?

17.2. A Smithian Model of Endogenous Monetary Regime and Economic Development Example 17.3: A simplified version of the Cheng model of money (1999). Consider a Smithian model with a continuum of M ex ante identical consumer-producers. Each of them has the utility function u = (x + x r )(y + y r ) where x and y denote the quantity of food and clothing self-provided respectively; and xr and yr denote the quantity of food and clothing received for consumption from the market respectively. An individual incurs a fixed learning cost in terms of labor, 0.2, for each production activity in which she engages. Because of the fixed learning cost, the production system exhibits economies of specialization. Of the two consumption goods, food is produced with a single factor labor such that x p ≡ x + x s = M ax{lx − 15 ,0} . where x is the quantity of food produced for self consumption; xs is the quantity of food sold to the market; xp is the total output level of food; and lx is the proportion of labor devoted to food production. Clothing is produced with labor and an intermediate good silk (z), using the Leontief production technology, y p ≡ y + y s = Min{ z + z r Max{l y − 15 ,0} } where y is the quantity of clothing produced for self consumption; ys is the quantity of clothing sold to the market; yp is the total output level of cloth; and ly is the proportion of labor devoted to clothing production. Silk is produced with a single factor labor such that z p ≡ z + z s = Max{l z − 15 , 0} where z is the quantity of silk produced for self production of clothing; zs is the quantity of silk sold to the market; and lz is the proportion of labor devoted to silk production. li is an individual’s level of specialization in producing good i. Each individual’s endowment constraint for time is 534

lx + ly + lz = 1 If an individual trades in the market, transaction costs are incurred. The transactions cost coefficient for good i is (1-ki ). In market transactions, an individual may accept goods in exchange solely for their ability to exchange for some other goods. These accepted goods serve as media of exchange or commodity-money, denoted with a superscript m. Denoting the total quantity of food, clothing and silk demanded by an individual for consumption or production and as a medium of exchange as xd, yd, zd, respectively, the quantity that is finally received, net of transaction costs, is therefore k x x d , k y y d , k z z d , respectively. Hence, the material balance equations between what a person receives from purchase and its use are kx xd = xr + xm (17.1)

ky yd = yr + ym

kz zd = zr + zm where the left hand side of each equation is the quantity of a good that a person receives from the purchase and the right hand side is the allocation of the quantity between consumption or production and medium of exchange. xr, yr, and zr are the quantity of food, clothing and silk allocated for consumption or production, respectively, xm, ym, and zm are the quantity of food, clothing and silk allocated as a medium of exchange respectively. To make the exchange between z and y possible without including inventories in the model, we assume that production is instantaneous once the required factors of production are available. Thus a clothing producer can buy silk from a silk producer, produce clothing, and pay the silk producer with some of the clothing produced. We also assume that trade is strictly bilateral and that an individual cannot trade with two different individuals simultaneously. This rules out the possible existence of a central clearing house and makes sequential exchanges necessary. In addition, we assume a zero discount rate to avoid complications caused by the time dimension; and we make the assumption that no enforceable credit system exists, which we subsequently relax in the discussion of money substitutes.

17.3. Possible Structures and Monetary Regimes There are 7 market structures that we have to consider. The first is structure A where M individuals choose autarky configuration. Each of them self-provides three goods, as shown in Fig. 17.3. There are three structures Ba, Bb, Bc, called partial division of labor. Structure Ba comprises configuration (x/y), which self-provides and sells x and buys y, and configuration (yz/x), which self-provides y and z, sells z, and buys x. Structure Bb comprises configuration (xy/z), which self-provides and sells x, self-provides y, and buys z, and configuration (z/x) which sells z and buys x. Structure Bc comprises configuration (zx/y), which self-provides z and x, sells x, and buys y, and configuration (y/z), which self-provides and sells clothing and buys z. All of the structures are shown in Fig. 17.3. There are four structures Cy, Cz, Cx, and D, referred to as complete division of labor. Cy comprises configurations (x/y), (y/xz), and (zym/xy). Configuration (x/y) is the same

535

as in structure Ba. Configuration (y/xz) self-provides and sells y and buys x and z. Configuration (zym/xy) sells z, buys x and y for consumption, and uses part of y as money. Structure Cz comprises configurations (y/xz) selling y and buying x and z, (z/xy) selling z and buying x and y, and (xzm/y), selling x, buying y, and using z as money. Structure Cx comprises configurations (x/y) selling x and buying y, (z/xy) selling z and buying x and y, and (yxm/zx), selling y, buying z and y, and using x as money. Finally we consider structure D where the circulation of commodity money is replaced by fiat money, other money substitutes, or a credit system. If the circulation of commodity money ym in structure Cy is replaced by the circulation of a money substitute, then a structure with a money substitute that is backed by commodity money y is shown as structure D in Fig. 17.3. Suppose the circulation of the money substitute involves zero transaction cost, then it makes no difference which commodity money backs the money substitute. Hence, we ignore the distinction between structures with money substitutes that are backed by different commodity monies.

Autarky structure A

StructureBb

Structure Cz

Structure Ba

Structure Bc

Structure Cx

Structure Cy

Structure D

Figure 17.3: Market Structures and Monetary Regimes Following the inframarginal analysis that you have been familiar with in the previous chapters, it is not difficult to solve for the corner equilibria in those structures with no money. The procedure to solve for the corner equilibria in those structures with money is slightly more complicated. We show that procedure for structure Cz here and leave solutions to other corner equilibria as exercises.

536

We first consider a professional farmer choosing configuration (xzm/y). She sells food x and buys clothing y. Though she does not need silk for consumption and production, she buys silk from the weaver and sells it in exchange for part of the clothing that she consumes from the tailor. Hence, the farmer’s total budget constraint is p y yd = p x x s (17.2a) where trade in z is not explicitly included. The quantity of x that is sold by her is x s ≡ xzs + x ys , where xzs is the quantity sold to the weaver z and xys is the quantity sold to the tailor. The total budget constraint can be decomposed as two bilateral trade balance conditions. When the farmer uses y as money her trade balance with the weaver is (17.2b) pzb zd = p x xzs where zd is the quantity of silk that the farmer bought from the weaver to use as money, p zb is the buying price of silk for the farmer, xzs is the quantity of food that the farmer sells to the weaver. The trade balance condition between the farmer and the tailor is (17.2c) p y y d = pzs zm + p x x ys where zm is the quantity of silk z, resold by the farmer to the tailor, pzs is the selling price of silk z, x ys is the quantity of food sold by the farmer to the tailor. Silk z is money for the farmer. She cannot have bilateral trade with double coincidence of demand and supply if she does not use silk as money in this particular structure. But if the selling and buying prices of silk are the same for the farmer, or if pzb = pzs , she will not be willing to use money, since the reselling involves extra transaction costs. Hence, the selling price must be higher than the buying price so that the difference can cover the transaction cost. The material balance equation in (17.1) implies kz zd = zm for the farmer since zr = 0 for her. This and trade balance (17.2) can simultaneously hold iff pzb = kz pzs where kz ∈(0,) 1 . The difference between the selling and buying price can be considered as a price discount that is used by the weaver to attract the farmer to use silk as money. The discount rate is kz. We may still assume that in the equilibrium the price of silk is pz, but the farmer can get the discounted buying price p zb = kz pz from the weaver. Therefore, the decision problem for a farmer choosing configuration (xzm/y) is Max: u = xy r (utility function) s.t. x + x ys + xzs = 45 (production function)

p x xzs = kz pz zd p x xys + pz zm = p y y d

(trade balance with weaver) (trade balance with tailor)

kz zd = zm (transaction condition for z) r s s d m d where x,y ,x y ,xz ,z ,z ,y are decision variables and x ys ,xzs are respective quantities sold to the tailor and weaver. We leave the solution of this problem to you as an exercise. The decision problem of a tailor choosing configuration (y/xz) is Max: u = x r y (utility function)

537

s.t. y + yxs + yzs = M in{(zxr + zzr ),45 }

(production function)

py y = p z

(trade balance with weaver)

p y yxs = p x x d + pz zzd

(trade balance with farmer)

s z

d z z

k x xd = xr (transaction condition for x) (transaction condition for z) kz (zzd + zxd ) = zxr + zzr s s s s s where yx + yz ≡ y , yx and yz are the respective amounts of clothing y sold to the farmer and weaver, zzd + zxd ≡ zd , zzd and zxd are the respective amounts of silk bought from the weaver and farmer. zxr + zzr ≡ zr , zzr and zxr are the respective amounts of silk that are received from the purchase from the weaver and farmer. Since the tailor uses silk to produce clothing and consumes clothing and food, these commodities are not money to her. The decision variables are xr, y, yxs, yzs, zxs, zzr, xd, zxd, zzd. Again we leave the solution of this problem to you as an exercise. The decision problem of a weaver choosing configuration (z/xy) is M ax:u = x r y r (utility function) s s s.t. zx + zy = 45 (production function)

pz zys = p y y d

(trade balance with tailor)

k z pz z = p x x k x xd = xr , k y yd = yr s x

d

(trade balance with farmer) (transaction contition)

where zxs + zys = zs , zxs and zys are the respective amounts of silk sold to the farmer and tailor. Since the buying price of silk for the farmer is discounted by kz, the weaver’s selling price of silk is kz pz . The decision variables are x r ,y r ,zxs ,zys ,y d ,x d . From the three decision problems, we can solve for the demand and supply functions of x, y, z and indirect utility functions for the three configurations in structure Cz. The utility equalization and market clearing conditions in the structure then yield the corner equilibrium in this structure. Repeating this calculation for all other structures, we can obtain all information about the corner equilibria in 8 structures, which is summarized in Table 17.1. You should work out all corner equilibria and compare your answer to the results in Table 17.1. Table 17.1: Corner Equilibria in 8 Structures Struc Relative number of ture different specialists

Relative price

Per capita real income (1 − 2α )(1 − 4α ) β 4(1 + β )

A Ba

1

⎛ kx ⎞ 2 =⎜ ⎟ M x ⎜⎝ k y ⎟⎠

My

1

(1 − α )(1 + β ) ⎛ k y ⎞ 2 = ⎜ ⎟ px (1 − 2α ) β ⎝ k x ⎠

py

538

(1 − α )(1 − 2α ) β k y kx 4(1 + β ) 1

1

2

2

Bb

pz βk x k z = − 2k x px

Mx βk x k z = + Mz 2kx 1

[ β 2 k x k z + 4 k x k z (1 + β )] 2 2k x

+

1 Mz = M y βk z

pz βk z = py 1 + βk z k y

2

Bc

Cz

kz β ⎛ kx ⎞ 2 ⎜ ⎟ = M x 1 + k z β ⎜⎝ k y ⎟⎠

py

My

pz

1

px

py

= kzβ

=

1 + k y kzβ

=

Mx

Cx

2kx

2

(1 − 2α ) 2 βk z k y 4(1 + βk z k y )

kzβ

−

1 2

1 + ky kz β kz β

Per capita real income

Circulation of money

(1 − α ) 2 k z β 4 kz β × 1 + k y kz β

M (1 − α ) × 2(1 + k z β )(1 + k y k z β )

1

1

2

(1 − α ) 2 4

1 pz − = (kx ky ) 2 , px

2 k x + (1 + k z ) k y k z β p z = py 2

kzβ

2

1

1

1

3

1 + k y kz β 2

2

×

1

2

1 2

1

1

3

kx k y kz β 2

1

3

1 + k y kz β 2

2

=

1

k x kzβ

M (1 − α ) k x ×

2

k x (1 + k z ) k z β

2

1

1

4 k x 2 + (1 + k z ) k z β ( k y 2 + k x 2 ) 1

1

[2 k x + (1 + k z ) k z k y β ]2 2

2

1

2 k x + (1 + k z ) k y k z β 2

2

1 Mz = M y kzβ

pF = pC 1

1

M x 1 + k y kx kzβ = My kx kzβ 2

D

(k y kx )

[ β 2 k x 2 k z 2 + 4 k x k z (1 + β )] 2 } 2

1 2

2

1

My

2

ky + kx 1

Mz = Mx

[ β k x k z + 4 k x k z (1 + β )] 2kx 2

2

Relative price

My

Mz

1

2

Struc Relative number of ture different specialists

Cy

(1 − 2α ) 2 β − βk x k z { + 4(1 + β ) 2

2

k x kz β 1

1 + k y k x kz β 2

2

1

2

2

px = kx pz

0.5 M (1 − α )

(1 − α ) 2 4 ×

1 2

kx k y kz β 1

px

2

1 + ky kzβ

M (1 − α )

2

=

pz = py

1

kx kzβ kzβ 2

(1 − α ) 2 4

1

2(1 + k y k z β ) 1

kx kzβ

1

1 + k y kzβ 2

1

×

×

2

k x k y kz β

2

2

1

px = kx pz

2

1

2

1

py

1

1 + kx + kzβ ( kx + k y kx )

1 + k y kx kzβ

1

M x 1 + k y kzβ = My kx kzβ 1 Mz = M y kzβ

1

1

1 + k y kz β 2

1

1

1

1 + kx + kzβ ( k y + kx ) 2

2

2

2

According to the Yao theorem, the general equilibrium is the corner equilibrium with the highest per capita real income. We can then compare per capita real incomes in all possible corner equilibria. The corner equilibrium in structure D is calculated on the basis of the assumption that the transaction efficiency coefficient for the money substitute and fiat money is 1. It is not difficult to show that per capita real income in D is always higher than in other structures with complete division of labor. For simplicity we assume that kx = 0.25. Comparisons between per capita real incomes in three structures with complete

539

division of labor and commodity money suggests that structure Cx is the best if ky, kz < 0.25; Cy is the best if ky, > kz, 0.25; and structure Cz is the best if kz,> ky, 0.25. Let us now consider the three structures with partial division of labor. A comparison between per capita real incomes in structures Bb and Bc suggests that Bb is better than 1

1

Bc iff k y < k y1 ≡ ( k z2 + 30k z ) 2 / k z [8 − ( k z2 + 30k z ) 2 ] . But ky1 is always greater than 1 for any kz ∈(0, 1), while ky cannot be greater than 1. This implies that Bb is always better than Bc. We can therefore focus on structures Ba and Bb. A comparison between per capita real incomes in Ba and Bb suggests that Ba is better than Bb iff k y > k y 0 ≡ (3 / 4) 2 ( k z2 + 30k z ) . After this partitioning of the parameter space, we can see that the set of candidates for general equilibrium comprises A, Ba, and Cy if the transaction efficiency of clothing y is higher than that of other goods; A, Bb, and Cz if the transaction efficiency of silk z is higher than that of other goods; and A, Ba or Bb, and Cx if the transaction efficiency of food x is higher than that of other goods. Based on the partitioning of the parameter space into three subspaces, we can find the critical values of transaction efficiency that further partition each of the parameter subspaces. The resulting general equilibrium and its inframarginal comparative statics are summarized in Table 17.2. Table 17.2: Inframargianl Comparative Statics of General Equilibrium and Emergence of Money from Evolution in Division of Labor k y < k y0 Money substitutes are not available

k y> kz , 1 /4 kz< kz∈(.23, .23 kz0) A Bb

k z> k y , 1 /4 kz> kz< kz1 kz0 Cy Bb

kz> kz1 Cz

Money substitutes are available

1 /4 > k y , kz kz< kz∈(0.2, kz> 0.23 kz2) kz2 A Bb Cx

kz< kz∈(0.23 kz> 0.23 , kz3) kz3 A Bb D

k y > k y0 Money substitutes are not available

Money available

k y> kz , 1 /4 k z> k y , 1 /4 ky ky1 Cy

ky< 1/4 A

ky∈(0.25, ky2) Ba

1 / 4 >k y,

ky> ky2 Cz

kz

ky
ky3

D

where k y 0 ≡ (3 / 4) 2 ( k z2 + 30k z ) , k z0 is given by

f 0 ( k y , k z ) ≡ 2 7 k y 2 k z − 9( k z2 + 30k z ) 2 (1 + k y k z ) = 0 , k z1 is given by 3

f 1 (k z , k y ) ≡ 2 7 k y k z

1

3

2

− 9( k z2 + 30k z ) 2 (1 + k y 2 k z 2 ) = 0 , k z2 is given by 1

1

540

3

f2 (kz ,k y ) ≡ 18(kz2 + 30kz ) /[2 7 kz − 9 kz (kz2 + 30kz ) ], k z3 is given by 1

1

2

2

f 3 ( k z , k y ) ≡ 2 7 k y k z − 9( k z2 + 30k z ) 0.5 (1 + k y 2 k z ) = 0 . 1

k y1 ≡ 3 / 5k z , k y2 ≡ 3 / 5k z 2 , k y3 is given by f3 (kz ,k y ) = 0 . 3

In words, the inframarginal comparative statics of the general equilibrium in Table 17.2 can be summarized as follows. If transaction efficiency is very low, then the general equilibrium is autarky where the market and money are not needed. As transaction efficiency is improved, the general equilibrium evolves from autarky to partial division of labor, where the market emerges from the partial division of labor, but money is not needed, followed by complete division of labor, where money is essential for the complete division of labor. If social and institutional conditions ensure that the transaction cost coefficient of fiat money, a credit system or other money substitutes is sufficiently small, then the money substitute will be used as the medium of exchange to facilitate the complete division of labor. But if, for instance, the money substitute can be easily counterfeited, the supply of fiat money increases drastically, so that the value of fiat money declines quickly, or a war impedes the enforcement of the credit system, then the commodity money with the lowest transaction cost coefficient will be used as the medium of exchange to facilitate the complete division of labor. Cheng (1999) shows that if kx is a constant between 0 and 1 rather than fixed at 0.25, then structure Bc may be general equilibrium within a parameter subspace. The Borland and Yang model (1992, also see Yang and Ng, 1993, chapter 17) and the Cheng model show that specialization and division of labor is essential but not sufficient for the emergence of money. A sufficiently high level of division of labor that involves roundabout production is essential for the emergence of money. The Borland and Yang model also shows that a sufficiently high level of division of labor in a sufficiently long roundabout production chain is essential for the emergence of money. Because of the trade off between economies of specialization and transaction costs in the Smithian models of money, the emergence of money can promote productivity progress by facilitating a high level of division of labor in a long roundabout production chain. Money promotes productivity progress in an interesting way in the Smithian models. Transaction costs may be increased because of the emergence of money. For instance, if money and its substitute are not available, due to the institutional environment (for instance, use of money is restricted, as in a Soviet style economic system), and transaction efficiency of goods is sufficiently high, then the equilibrium is a structure with partial division of labor and the complete division of labor is infeasible. As improvements in the institutional environment reduce the transaction cost coefficient for money or its substitute, then money will emerge and the complete division of labor becomes general equilibrium. In the structure with complete division of labor both productivity and transaction costs are increased in comparison to a structure with partial division of labor, provided the productivity progress benefit outweighs the increased transaction costs. Smith conjectured that a more salable commodity is more likely to play the role of medium of exchange. There are two ways to interpret the notion of salability of a commodity. According to some economists, a commodity is more salable if more individuals accept it for their consumption and production. According to Smithian models of money, this interpretation is wrong. A commodity is more likely to be used as money

541

if its transaction cost coefficient is smaller. In the Borland and Yang model of money in which steel is used to produce hoes, which is used to produce food, all individuals accept food for consumption in a structure with complete division of labor, but only specialist producers of hoes need steel. According to the first interpretation of salability, food is more salable than steel and hoes. But according to our interpretation of salability, steel is more salable if its transaction cost coefficient is much smaller than those of hoes and food. Historically, it was some precious metal that very few individuals used for their consumption and production that was used as money. Food, with its low transaction efficiency due to its perishability or the low value of each unit of quantity, is rarely used as money despite the fact that everybody needs it. The commodities that are used as money usually have the following features: a high value of each unit of quantity, so that it cost little to carry the commodity in great value, ease of divisibility, and physical stability (not readily perishable). All of these features imply a low transaction cost coefficient, which includes storage cost and loss of value in transit or in dividing. The Smithian models of money are general equilibrium models. 3 Hence, the equilibrium quantity of commodity money in circulation is endogenized. Also, the equilibrium price of commodity money in terms of other goods, which includes its value for consumption or production as well as its value as medium of exchange, is endogenized. 4 The circulation volume and value of commodity money not only continuously change within a structure in response to marginal changes in parameters, but also discontinuously jump between structures with various monetary regimes and different network patterns of division of labor as parameter values shift between subspaces. It can be shown that as transaction efficiency is improved and division of labor evolves in an increasingly longer roundabout production chain, the circulation and value of commodity money increase and the degree of monetization of the economy increases. This is a new way to explain the drastic increase of the price of gold during the Industrial Revolution. It can also be shown that use of a money substitute and a credit system can reduce the circulation of commodity money and thereby reduce the price of commodity money in terms of other goods.

Key Terms and Review Commodity money, fiat money, money substitutes, credit system Double coincidence of demand and supply and emergence of money Relationship between the level of division of labor, the length of roundabout production chain, transaction efficiency, and emergence of money Conditions for fiat money to substitute for commodity money Properties of a commodity that is likely to be used as money

3

R. Jones (1976) first developed a model formalizing the idea that money is a natural consequence of the “unconcerted” market behaviour of individuals. His model was later extended by Oh (1989). 4 According to von Mises, “The earliest value of money links up with the commodity-value of the monetary material. But the value of money since then has been influenced not merely by the factors dependent on the ‘industrial’ uses, which determine the value of the material of which the commodity-money is made, but also by those which result from its use as money” (1924, p.106).

542

Relationship between the network size of division of labor, the degree of commercialization, and the degree of monetization of an economy Productivity implications of commodity money and fiat money Function of the market in searching for the efficient monetary regime and level of division of labor

Further Reading Cheng (1996, 1998, 1999), Jevons (1893), Borland and Yang (1992), Yang and Y-K. Ng (1993, ch. 17), Ostroy and Starr (1990), Alchian (1977), Brunner and Meltzer (1971), Clower (1967), Green (1987), Parkin (1986), R. Jones (1976), King and Plosser (1986), Kiyotaki and Wright (1993, 1989), Lucas (1980), Oh. (1989), Starrett (1973), Ostroy (1973), Smith (1776, Chapter 4), Menger (1871), von Mises (1934).

Questions 1. In a Soviet style economy, the government controls the pricing of most commodities. The official prices under government control are usually far away from their market clearing values. But those transactions facilitated by barter or commodity money between firms and between individuals can be done without compliance to official prices which are relevant only to transactions in terms of official fiat money. Hence, we can see a lot of “back door” transactions based on barter or commodity money in a Soviet style economy. Explain why such back door transactions are so prevalent in a Soviet style economy. What is the implication of this feature of a Soviet style economy for economic development? 2. After 1990, firms in Russia prefer barter or transactions in term of commodity money to transactions in terms of fiat money due to extremely high inflation rates. Use the model in this chapter to explain the phenomenon. 3. Some economists interpret Smith’s concept of salability of a commodity as the population share of those who need the commodity for consumption or production. Is this interpretation correct? Why or why not? 4. Use a Smithian model of money to illustrate that use of money may increase transaction costs. What are the implications of the increase in transaction costs that is associated with the emergence of money for economic development? 5. Discuss the mechanism to endogenize value of money in a Smithian model of money. Analyze what is the implication of monetary policy for productivity progress and evolution of division of labor. 6. How do institutional arrangements determine the degree of monetization, the level of division of labor, and productivity of an economy through affecting transaction efficiency? 7. Test the theory developed in this chapter against empirical observation. For instance test concurrent evolution of division of labor and the degree of monetization of an economy (income share of economic activities that are facilitated by money). 8. Somebody asked an economist about the quick way to make money. The economist replied: there is no general rule for making money. You have to understand economies of division of labor and the function of money in reducing transaction costs and in facilitating division of labor for a particular business situation in order to understand the general equilibrium mechanism under which money can be made. Comment on this economist's answer.

543

9. Use the Smithian model of money to explain drastic decline of price of gold in the end of the 20th century as a result of the fact that many governments no longer use gold to reserve value of financial assets.

Exercises 1. Solve for simplified the Kiyotaki-Wright model where person A’s utility function is u A = kx and her production function is z = lA where lA is a fixed endowment of person A. Person B’s utility function is u B = ty and her production function is x = lB where lB is person B’s endowment of labor. Person C’s utility is uC = sz and her production function is y = lC where lC is her endowment of labor. x, y, z are respective amounts of three goods and k,t,s are respective transaction efficiency coefficients of the three goods, which could be interpreted as probabilities for receiving the goods purchased and which relate to probabilities that different types of persons are matched in the original KW model. Trade must be sequential and the discount rate is 0. Identify the condition for a particular good to be money in equilibrium. 2. Solve for the general equilibrium and its inframarginal comparative statics of the BorlandYang model of money. Each consumer-producer’s utility function is u = z + zc , where z is the amount of food self-provided, zc is the amount of food received for consumption from purchase in the market. The production function of food is z+zs = [(y+ yc)lza].5, where a>1, zs is the amount of food sold in the market, y is the amount of hoe self-provided, yc is the amount of hoe that is received from the purchase in the market. lz is an individual’s level of specialization in producing z. The production function for hoe is y+ys = [(x+xc)lya].5, where ys is the amount of hoe sold, x is the amount of steel self-provided, xc is the amount of steel that is received from the purchase in the market, ly is an individual’s level of specialization in producing hoe. The production function of steel is x + xs = lx - A, where xs is the amount of steel sold, and lx is an individual’s level of specialization in producing x. The endowment constraint for working time is lx + ly + lz = 1. The material balance between use and production are txd = xc + xm, ryd = yc + ym, kzd = zc + zm. Superscript d denotes amount purchased, c denotes amount used for consumption or production, m denotes amount used as money. t, r, k are respective transaction efficiency coefficients for steel, hoes, and food. 3. Suppose that in the Cheng model in example 17.3, kx is a parameter which might not equal to 0.25. Solve for inframarginal comparative statics of general equilibrium. Calculate the equilibrium value of money in terms of a numeraire good. Calculate the equilibrium degree of monetarization. Use your calculation to explain drastic increases and decreases in the price of gold in the 19th and 20th centuries and to explain concurrent increases in the degree of monetarization and commercialization as two aspects of economic development. . As increasingly commodity money is replaced by fiat money as the media of exchange in the end of this century, what will happen to the price of gold relative to other goods? 4. Assume that the government issues fiat money Q in the model in example 17.3 and uses Q to buy x in period 1, then sells x for fiat money in period 2, then use fiat money to buy y and z in period 3, and finally sells y and z for fiat money again. What is the effect of change in Q on nominal prices of goods and on the equilibrium level of division of labor and productivity. If Q changes in the end of period 3, will equilibrium level of division of labor and resource allocation be affected? Use your answer to analyze implication of monetary policies.

544

Chapter 18: Endogenous Business Cycles, Cyclical Unemployment, and Endogenous, Long-run Growth

18.1. Rethinking Macroeconomic Phenomena in Economic Development Macroeconomic phenomena relate to aggregate demand and supply and their relationship with the absolute general level of prices. Aggregate demand is the sum of the values of the total market demands for all individual goods. It differs from total market demand for a particular good, which is referred to as a disaggregate variable. Aggregate demand, aggregate supply, and the general price level are referred to as aggregate variables. From the Smithian static and dynamic general equilibrium models that we have examined in previous chapters, we can see that per capita real income can be considered as the absolute price of labor, which is endogenously determined by the equilibrium level of division of labor. The endogenization of the absolute price level is associated with the endogenization of the network size of division of labor and related aggregate demand in the market place. In the Smithian framework, a corner equilibrium sorts out resource allocation (relative prices of traded goods and numbers of individuals choosing different occupation configurations), while the general equilibrium sorts out the absolute price level of labor, the network size of division of labor, and related aggregate demand. Hence, the marginal comparative statics of a corner equilibrium in the Smithian framework has the same explanatory power as comparative statics of a neoclassical general equilibrium model, while the inframarginal comparative statics of Smithian general equilibrium can explain many macroeconomic development phenomena that neoclassical models cannot predict. Hence, we call the inframarginal comparative statics (or dynamics) analysis of Smithian models Smithian macroeconomic analysis of development, and the marginal comparative statics analysis Smithian microeconomic analysis of resource allocation. From this discussion, you can see that the focus of Smithian economics is on macroeconomic phenomena which relate to the network size of division of labor. In this section, we first consider various ways to explain unemployment and aggregate demand in the Smithian framework that relate to the models that we have already studied. Then in the rest of the chapter we develop a Smithian dynamic general equilibrium model that can simultaneously endogenize efficient business cycles, efficient unemployment, and longrun economic growth. Example 18.1: The Smithian model with endogenous risk of mass unemployment. The first Smithian general equilibrium models that can endogenize mass unemployment are those of chapter 10 (see also Yang and Wills, 1990, and Lio, 1997). In these models, the efficient trade offs among economies of division of labor, transaction costs, and coordination reliability of the network of division of labor generates an equilibrium and efficient risk of coordination failure of the network of division of labor. The comparative statics of the general equilibrium suggest that as transaction efficiency is improved, the equilibrium and efficient risk of coordination failure will rise. This risk of coordination failure is indeed a risk of mass unemployment, since when the coordination failure of a

545

very developed network of division of labor takes place, as in the Great Depression, all individuals are forced to choose autarky, which implies that many individuals are excluded from the network of division of labor and related network of the market, that is, they cannot find a job to work for the market or they are unemployed. This risk of mass unemployment has the following interesting features. First, it is efficient. The market efficiently trades off the positive network effect of division of labor on aggregate productivity against transaction costs and the risk of coordination failure to determine the efficient risk of mass unemployment, just as we efficiently choose a higher risk of being killed on the freeway by driving on it more often as transportation conditions are improved. Second, this high risk of coordination failure never exists in an autarchic society. It is associated with a high level of division of labor (or a great degree of commercialization). Unemployment and business cycles are essentially phenomena that are inherent from the nature of the network of division of labor. In autarky each individual produces every thing for herself. If her taste or technology changes such that one of the goods is not needed, she will just reduce the resources allocated to the production of that good. If she cannot work in winter or under bad weather conditions, she can just be idle. We would not call this unemployment since she still produces other goods or is busy under better weather conditions. But in a society in which each individual is completely specialized, as consumers’ tastes or technical conditions change, a professional sector may be out of the market and all specialists in that sector will be unemployed. In addition to mass unemployment caused by the efficient risk of coordination failure, there are two more types of unemployment. The first of them is “natural unemployment” and the second is cyclical unemployment. We shall model cyclical unemployment in sections 18.2-18.5. In the rest of this section we consider two ways to explain natural unemployment. Example 18.2: Natural unemployment caused by the integer problem. The integer problem in Smithian models may generate natural unemployment. Suppose that in the symmetric Smithian model with two goods in chapter 4 there are three individuals (M = 3) and the set of individuals is not a continuum. Then, the utility equalization and market clearing conditions yield the numbers of individuals choosing the two occupation configurations Mx = My = 1.5. This implies that one and a half persons specialize in producing each good. This is not only an unrealistic statement, but also it contradicts the notion of specialization that half a person specializes in producing x and her other half specializes in producing y. Suppose transaction efficiency is so high that person 1 chooses (x/y) and person 2 chooses (y/x), then persons 1 and 2 may establish an "equilibrium" with Mx = My = p = 1 that generates a higher per capita real income than the real income of person 3 who is forced to choose autarky. Person 3 has an incentive to specialize in producing a good and to sell it at a slightly lower relative price than the "equilibrium" one, so that the buyer of the good will turn to her. Thus, the prescribed equilibrium between persons 1 and 2 breaks down and the buyer of the good and person 3 may establish another "equilibrium" that forces the other person to choose autarky. That person will in turn have both the incentive and the capacity to break down the new "equilibrium" again. This process continues, such that an equilibrium can never be reached.

546

It is not difficult to see that the Walrasian equilibrium does not exist in this two goods economy if the market clearing and utility equalization conditions yield noninteger numbers of different specialists. But if two individuals have much better transaction and production conditions than the other individual, then the two individuals can establish a Nash bargaining equilibrium with the division of labor and the third person is excluded from the market network. Hence, the third person appears to be in involuntary unemployment since she is willing to be involved in the division of labor. From Fig. 18.1 we can see that if M = 3 in the model in chapter 4, then the aggregate transformation curve involves three curvilinear figures. Curve A is an individual's transformation curve. If two persons specialize in producing y and the third person produces two goods, then we can move curve A up by two units to obtain curve B. If two persons specialize in producing x and the third person produces two goods, then we can move curve A to the right by two units to obtain curve D. If a person specializes in producing x, the second specializes in producing y, and the third produces two goods, then we can move curve A up by one unit and to the right by one unit to obtain curve C. Curves B, C, and D constitute the aggregate PPF for the production function in chapter 3 if M = 3.

Figure 18.1: Aggregate Transformation Curve for M=3 Hence the number of curvilinear figures that constitute the aggregate PPF increases with the population size. As the population size tends to infinity, the aggregate transformation curve converges to a straight line and the gap between the aggregate production schedule for autarky and that for the division of labor, which represents the gains from the division of labor, is enlarged. The integer problem of equilibrium disappears as the population size tends to infinity. For instance, in the model with two final goods, the natural unemployment rate is 1/3 if the population size is 3, and is 1/101 if the population size is 101.

547

If we introduce many consumer and producer goods into the model, then the integer problem will become increasingly more serious and more complicated. From casual observation, we can see that the natural unemployment rate caused by the integer problem is higher in an economy with a higher level of division of labor. But the integer problem in a model with many goods is much more complicated than this intuition suggests. First, unequal incomes may occur in a Nash bargaining equilibrium even between ex ante nearly identical individuals. Consider the Smithian model with m final goods in example 7.2 in chapter 7, where m = 100, the number of traded goods is 50 in equilibrium, and the set of individuals is finite and the population size is 101. We assume that those individuals who are marginally less productive than others will be excluded from the network of division of labor if the integer condition does not hold. But the difference in productivity is infinitesimally small, so that the symmetry of the model is retained. The market clearing and utility equalization conditions yield a noninteger number of specialists selling each good, 101/50. Hence, one individual who is marginally less productive than others will be excluded from the network of division of labor and be compelled to choose autarky, or unemployment. The other 100 individuals form two separated networks of division of labor. In each of them, each individual sells one good to and buys one good from each of the other 49 individuals. The equilibrium unemployment rate is 1/101. If transaction efficiency is improved, so that the optimum number of traded goods becomes 80. Then 80 individuals will form a symmetric network of division of labor. But there are two possible patterns of organization for the other 21 individuals who are marginally less productive. They may form a symmetric network of division of labor with 21 traded goods if doing so makes them better off then in autarky. In this smaller network of division of labor, economies of division of labor net of transaction costs are not fully exploited, so that per capita real income is lower than in the larger network of division of labor. However, as shown in Yang and Ng (1993, chapter 5), each individual’s per capita real income under equilibrium prices might be a nonmonotonic function of the number of traded goods n. This case is illustrated in Fig. 18.2 where the vertical axis represents utility under equilibrium relative prices of traded goods and the horizontal axis represents the number of traded goods.

Figure 18.2: An Individual’s Organization Utility under Equilibrium Prices

548

As shown in Fig. 18.2, an individual’s per capita real income is a nonmonotonic function of her number of traded goods. An individual’s organization utility is maximized at n = 80 for a given transaction efficiency coefficient k. When the number of traded goods is 21, utility is lower than in autarky since transaction costs outweigh economies of specialization for n = 21. In this case, 21 individuals will choose autarky in equilibrium. The unemployment rate is 21/101. This example illustrates that there is no simple monotone relationship between the level of division of labor and the natural unemployment rate caused by the integer problem. However, it is safe to say that as the equilibrium level of division of labor goes up, the average natural unemployment rate caused by the integer problem is more likely to be higher. In reality, the natural unemployment caused by the integer problem in a highly commercialized society (with a high level of division of labor) is a very common phenomenon. For instance, suppose that universities in an economy need two more economics professors, but there are three economics Ph.D. graduates of nearly the same quality. Then one of them must be unemployed until new demand emerges. You may ask why cannot the universities hire three part time professors and require each of them to work for 2/3 of the full loading time. This cannot be equilibrium because of the economies of specialization. Since the part time professors are only partially specialized they are not as productive as those full time professors who are completely specialized. From the example of the economy with two goods and three individuals, you can see that if transaction efficiency is sufficiently high, two of the three individuals will have division of labor and complete specialization and will refuse to have division of labor with the other person who is marginally less productive, even if the third person is willing to produce x and y on a part time basis and to trade with others. As shown in chapter 6, in a Smithian model with ex ante different consumerproducers even if the set of individuals is a continuum, a dual structure may occur in the transitional stage from autarky to the complete division of labor. In this dual structure ex ante identical individuals may be divided between autarky configuration and specialization configuration. Those self-sufficient individuals look like underemployed or in unemployment since they cannot find a job to work for the market. Example 18.3: Natural unemployment caused by changes in the structure of division of labor. The second reason for natural unemployment in a Smithian general equilibrium model is changes in the pattern of the network of division of labor caused by exogenous changes in parameters. We use the symmetric Smithian model with m consumer goods and n traded goods in example 7.2, where both m and n are endogenous, to illustrate this kind of natural unemployment. Suppose an oil crisis raises the cost of gas and reduces transaction efficiency k, so that the equilibrium values of m and n suddenly decline. This implies that, suddenly, the demand for some goods disappears and individuals stop consuming some nonessential goods. The specialist producers of those goods will lose their jobs. But because of fixed learning costs or job shifting costs, these individuals are not as productive as the specialist producers of the other goods which are still demanded, even if the unemployed individuals immediately shift to the professional sectors which are still in the market. Therefore, those specialist producers must be unemployed before they get a chance to acquire experience in a profession to which they are new. This kind of unemployment would not take place in an autarchic society where each individual

549

produces all goods for herself. In that case, a change in tastes or production conditions will cause an adjustment of each individual’s resource allocation between different goods in the absence of unemployment. It is easy to understand that the higher the equilibrium level of division of labor, more likely it is that such unemployment will take place in response to exogenous changes in parameters. If the dynamic effect of specialized learning by doing is considered, then any change in the structure of division of labor will force some individuals to change occupations. In the transitional period, old human capital becomes useless, and the acquisition of new professional human capital depends on a new job that creates opportunities for learning by doing. But the unemployed are not competitive with those who have jobs with opportunities for specialized learning by doing, so that unemployment itself prevents the unemployed from finding a new job. Hence, a vicious circle may drive the unemployed out of the market forever. In exercise 7, the efficiency wage model endogenizes the equilibrium unemployment rate by specifying the trade off between moral hazard and unemployment. Unemployment can play a role as a device to reduce workers' shirk. This model and the three Smithian ways discussed so far to explain unemployment and the interrelation between network size of division of labor and unemployment are not satisfactory. First, none of these models can predict long-run regular business cycles and related cyclical unemployment. The interdependence between long-run regular business cycles, cyclical unemployment, and long-run endogenous economic growth cannot be explored by these models. In particular, the implication of durable goods, compounded with a sophisticated network of division of labor, for long-run regular and endogenous business cycles and growth cannot be explored by these models. Many experienced businessmen know the intimate relationship between the stock of durable goods and business cycles. In the rest of the chapter, we will use a Smithian dynamic general equilibrium model with durable producer goods to endogenize long-run regular efficient business cycles, long-run economic growth, and efficient cyclical unemployment. We will explore the implications of efficient business cycles and efficient unemployment for long-run economic growth and evolution of the network size of division of labor. The empirical evidence for positive correlation between business cycles and productivity growth is provided by recent literature of economic growth, although the evidence is still inconclusive. Using cross sectional data on 47 countries, Kormendi and Meguire (1985) find a significant positive effect of cyclical variability (measured as the standard deviation of real output growth) on the mean annual growth rate. By constructing pooled cross-section/time series data on 113 countries, Grier and Tullock (1989) find a positive and significant effect of the standard deviation of real GDP growth on the average economic growth. Ramey and Ramey (1995) confirm this result for the OECD countries when they use standard deviation of output growth as a proxy for cyclical variability. There are a number of strands of neoclassical models on how cyclical variability may coexist with an increase in economic growth. The first strand of literature explains the positive implication of output fluctuation by assuming that the economies face a positive risk-return trade off in their choice of aggregate technology. Agents collectively would choose riskier technologies only if these technologies were expected to generate a greater return and hence greater economic growth (Black, 1979). The second strand looks at how R&D activities can be boosted when the economy goes through a recession. Typically,

550

firms may find it profitable to reallocate employees to research and reorganization activities at economic downturn because the opportunity costs in terms of the forgone production are relatively low at a recession (see Aghion and Saint-Paul, 1991). The third line of research emphasizes the precautionary savings motive at recessions. Agents are expected to behave prudently and accumulate physical and human capital as a buffer stock to protect consumption against the bad state of the economy. The precautionary accumulation of human capital is particularly relevant for economic growth. Since lowskilled employment is disproportionately affected by cyclical variability, agents may want to accumulate human capital more rapidly so as to increase job security. (see Deaton, 1991, Skinner, 1988, Dellas, 1991) The fourth line of literature is the creative destruction model largely initiated by Aghion and Howitt (1992, see exercise 7 in chapter 13). In their endogenous growth model, vertical innovations lead to the replacement of incumbent firms through a Schumpeterian process of creative destruction, and the average economic growth rate and the variance of the growth rate increase with the size of vertical innovations. The fifth line of the literature is the model of implementation cycles constructed by Shleifer (1986). If each innovator must incur a fixed cost in the period prior to innovation, large sales during booms may be necessary to enable the entrepreneur to cover her fixed costs while innovation introduced during the slumps may lose money. Thus a cyclical equilibrium may enhance innovation and productivity growth, while a stabilization policy may be harmful. The sixth line of the literature is the “cleansing effect” model initiated by Caballero and Hammour (1994), where business cycles are good for long-term economic growth because recession may cleanse the production structure by shaking out the least productive firms and allowing the entry of more efficient producers. All of the neoclassical models cannot explore the intrinsic connection between business cycles and evolution in division of labor. They cannot explore creative destruction based on evolution of division of labor which replaces old occupations of low level of specialization with highly professional new ones. In particular they cannot simultaneously predict the following concurrent phenomena: Increases in each individual's level of specialization and in the degree of commercialization (division of labor) for society as a whole; Endogenous, efficient, long-run, and regular business cycles; Endogenous, efficient, long-run, regularly cyclical unemployment; Endogenous, long-run, and cyclical economic growth; More volatile fluctuation of output level of durable goods than that of non-durable goods. The Smithian dynamic equilibrium model presented in the rest of the chapter can simultaneously predict all of the phenomena.

Questions to Ask Yourself when Reading this Chapter What is the relationship between marginal comparative statics and microeconomic phenomena and between inframarginal comparative statics and macroeconomic phenomena in Smithian economics? What is the relationship between endogenization of the network size of division of labor and endogenization of aggregate demand?

551

What are differences between unemployment caused by the integer problem, that caused by risk of coordination failure of the network of division of labor, that caused by changes in the structure of division of labor, and that caused by long-run endogenous regular and efficient business cycles? What is the difference between exogenous and endogenous business cycles? What is the relationship between long-run endogenous business cycles and long-run endogenous economic growth? What is the relationship between the division of labor in producing roundabout productive durable goods and long-run regular endogenous business cycles? What is the relationship between business cycles, transaction efficiency, economies of specialized learning by doing, job shifting costs, and durability of goods? What is the trade off in determining the efficient pattern of business cycles and economic growth in the market place? Why can the equilibrium pattern of business cycles be Pareto efficient? How does the market sort out the efficient pattern of business cycles, economic growth, and unemployment? What is the likely consequence of the government’s manipulation of the pattern of business cycles and unemployment?

18.2. Long-run Regular Efficient Business Cycles, Cyclical Unemployment, Longrun Economic Growth, and Division of Labor in Producing Durable Goods In this section, we first tell the story behind the model before you become mired in the algebra and lose your mind for economic thinking. From daily life experience, we can see that many cyclical physical processes can generate much more power than noncyclical processes. The laser is an example. The laser can generate cyclical light that has much more power than noncyclical light. The human’s sex life is cyclical. If it were not cyclical, we may not be able to have children. Engineers can give you more examples of cyclical physical processes that generate more power than noncyclical processes. The examples remind us that business cycles may have positive productivity implications. Many economists, from Karl Marx to John Maynard Keynes and Joseph Stiglitz, attribute business cycles to market failure. Many efforts have been made by governments and business communities to rectify this "market failure" by eliminating business cycles. But none of those efforts can change the basic features of the regularities of the business cycle. Moreover, the business cycle is not a significant and persistently regular phenomenon in an autarky economy with low productivity, while it is unavoidable in an economy with high levels of specialization, division of labor, and productivity. The concurrence of business cycles, a high level of division of labor, and a high productivity remind us that the persistent business cycles may have productivity implications and that there is an intricate relationship between the division of labor and the business cycle. Economic dynamics with business cycles may be more efficient than non-cyclical economic dynamics. Consider an economy with many ex ante identical consumer-producers. Each individual can produce a non-durable consumer good called food and a durable producer good called tractors. A tractor is indivisible and each driver can drive one and only one

552

tractor to produce food at any point in time. There are economies of specialized learning by doing in producing any good and two types of costs will be incurred if an individual shifts between productive activities. An individual will forget her experience built up in an activity if she shifts from that activity to another. Also there is an entry cost, such as a threshold learning cost, into any activity. Assume, further, that a tractor can be used for two years. Each consumer derives utility from food and maximizes her total discounted utility. For this simple economy, there are at least three possible organizational structures of production and consumption. The first is autarky structure A, shown in Fig. 18.4, where each person self-provides each good herself. She spends some time producing a tractor and the rest of the time driving the tractor to produce food in the first year, and produces only food using the tractor in the second year. Therefore, neither business cycle nor unemployment exists for this structure. In the second structure C (complete division of labor), shown in Fig. 18.4, the population is divided between the production of tractors and the production of food. Professional farmers drive tractors to produce food in each of the two years. Professional producers of tractors produce tractors in the first year and are unemployed in the second year. The aggregate output level is higher in the first year than in the second. This is a business cycle of two years with unemployment in the second year. The second cycle occurs over the third and fourth years, and so forth. The third structure P (partial division of labor), shown in Fig. 18.4, is the same as the second except that the producers of tractors shift to the production of food in the second year. In other words, farmers are completely specialized, but producers of tractors, who produce food as well in every other year, are not completely specialized. Autarky involves job-shifting costs but no division of labor and business cycles. Also, structure A involves no transaction costs and cannot exploit productivity gains from specialized learning by doing. Structure C with complete division of labor can speed up the accumulation of human capital through specialized learning by doing. It does not incur job shifting costs, but it generates transaction costs as well as cyclical unemployment of physical labor. Structure P with partial division of labor involves job-shifting costs for producers of tractors but does not generate business cycles. Economies of specialized learning by doing can be more fully exploited by farmers than by producers of tractors. The level of transaction costs in structure P is in between that in structure A and that in structure C. Hence, there are many trade offs among economies of specialized learning by doing, transaction costs, job shifting costs, faster accumulation of human capital, and cyclical unemployment of physical labor. If job-shifting costs, transaction efficiency, and economies of specialized learning by doing are sufficiently great, then complete division of labor with business cycles and unemployment is Pareto superior to autarky and partial division of labor without business cycles and unemployment, since the benefit from faster accumulation of human capital through specialized learning by doing and from a lower job shifting cost in structure C outweigh the transaction costs in this structure, compared to structures A and P. Hence, the market mechanism (the invisible hand) will choose the efficient structure with business cycles and unemployment. In structure C, specialist producers of tractors sell tractors and buy food in years 1, 3, 5, … The value of tractors that are sold is in excess of the value of food that is purchased. The difference is the saving that the tractor specialists will use to buy food in years 2, 4, 6, … when they are unemployed, as shown in Fig. 18.4. Since trade is one-way in years 2, 4,

553

6, … and commodity money does not work for this kind of saving of purchase power, fiat money or a credit system is essential for realization of structure C. Because of free choice of profession configurations, total discounted real income must be the same between tractor specialists and professional farmers. In other words, income in the sector producing durable goods must be sufficiently higher than in the sector producing nondurable goods during the boom period, so that the difference is enough to compensate for unemployment in the sector producing durable goods during recession. This implies that the invisible hand (price mechanism) can coordinate self-interested behavior to sort out the efficient trade offs among the conflicting forces: economies of specialized learning by doing, transaction costs, and job shifting costs. (a) Case with high transaction efficiency and job shifting costs and significant economies of specialized learning by doing

(b) Case with low transaction efficiency and job shifting costs and insignificant economies of specialized learning by doing Figure 18.3: Growth Patterns with and without Business Cycles and Unemployment The different time paths of per capita real incomes in the three structures within different subspaces of parameter values are shown in Fig. 18.3. Panel (a) shows the time paths of per capita real incomes in the three structures when transaction efficiency and job shifting cost are high and economies of specialized learning by doing are significant. In the early stage, structure A generates higher per capita real income than structures P and C

554

because of the transaction costs in the two latter structures and the fact that it takes time for economies of specialized learning by doing to speed up accumulation of human capital. As time goes by, per capita real income in structure P first exceeds that in structure A, then per capita real income in structure C overtakes that in structure A and P despite business cycles in structure C. Panel (b) shows the time paths of per capita real incomes in the three structures when transaction efficiency and job shifting cost are low and economies of specialized learning by doing are insignificant. Structure A always generates a higher per capita real income than structures P and C. Even if the per capita real income in C catches up to that in A and P later on because of a faster accumulation of human capital in C, C may be still Pareto inferior to A and P because of a lower total discounted per capita real income in C than in A and P. Three features distinguish our Smithian theory of business cycles from the existing business cycle models. First, in our model the network size of division of labor and related levels of specialization for each individual are endogenized in a micro-dynamic equilibrium model. Second, the Smithian model generates the following three macroeconomic phenomena simultaneously: Persistent, regular, endogenous, and efficient business cycles; endogenous cyclical and efficient unemployment; long-run endogenous economic growth that might be speeded up by business cycles and cyclical unemployment. Our model is characterized by economies of specialized learning by doing, shifting costs between jobs, and indivisibility and durability of producer goods. These characteristics are necessary for a dynamic equilibrium with the business cycles to be Pareto superior to non-cyclical dynamics. Our model explores the implications of business cycles and cyclical unemployment for long-run endogenous economic growth. It predicts that output of durables fluctuates more than output of non-durables, a macroeconomic phenomenon confirmed by a lot of empirical evidence and considered by many economists as one of the important phenomena that need to be explained by macroeconomic theory (see, for instance, Barro, 1997). Third, our model can be used to explore the roles of fiat money and saving in enabling the market to use business cycles and cyclical unemployment to speed up accumulation of human capital, thereby speeding up endogenous long-run economic growth. In our model, saving is used to finance purchases by specialist producers of durable goods who are unemployed during recession, such that the market can use business cycles to avoid job shifting costs and speed up human capital accumulation. Hence, the gains from saving are not based on trade between goods at different points in time. Therefore, commodity money cannot be used to facilitate such saving. Money substitutes, fiat money, or a credit system is essential for such saving to facilitate efficient business cycles and efficient cyclical unemployment. Compared with shock-dependent business cycle models, such as the Samuelson model (1939) and the Hicks model (1950), our model is an endogenous business cycle model which can generate persistent business cycles in the absence of any exogenous shocks. Our model can generate productivity implications of business cycles and unemployment which cannot be generated by other endogenous business cycle models, such as those of Vogt (1969) and Goodwin (1951). In contrast to labor shift models (see Lilien, 1982, and Black, 1987), in the model presented in this chapter business cycles and unemployment occur when individuals do not shift between professional sectors, whereas unemployment is caused by such shifts in the labor shift models. Hence, the incompatibility between empirical

555

observations, which indicate much more job shifting during the booming period than that during recession, and labor shift models (see Abraham and Katz, 1986, and Murphy and Topel, 1987) may be avoided by our theory. Recently developed real business cycle models (see Kydland and Prescott, 1982, Long, Jr. and Plosser, 1983, and King and Plosser, 1984) need an exogenous stochastic process to generate some "business cycle phenomena" which are not business cycles, according to Prescott (1986). However, our model can generate persistent business cycles in the absence of any exogenous stochastic process. All forenamed business cycle models are macroeconomic models, whereas our model in this chapter is a micro-dynamic equilibrium model. Weitzman's micro-equilibrium model with increasing returns to scale (1982) has endogenized unemployment. However, he considers unemployment as a consequence of coordination failure in the market and his model cannot generate persistent business cycles. The models of monopolistic competition and sticky prices (see, for example, Mankiw, 1985, Ball, Mankiw, and D. Romer, 1988) and the models of efficiency wage (see, for example, Yellen, 1984, Stiglitz, 1986, and exercise 7) attribute unemployment to a market failure in equilibrating demand and supply. They cannot generate endogenously persistent business cycles. Stiglitz has developed a model (1992) to explain business fluctuations again by the failure of the capital market caused by incomplete information. The business cycles in Ng's (1986, 1992) mesoeconomic model is based also on coordination failure to maintain an efficient equilibrium in an imperfectly competitive economy with a continuum of real equilibria. In contrast, the model in this chapter attributes business cycles and unemployment to market success.

18.3. A Smithian Dynamic Equilibrium Model of Business Cycles, Unemployment, and Economic Development Example 18.4: The Yang model (1993) of endogenous and efficient business cycles. We consider a model with a continuum of M ex ante identical consumer-producers. There is a non-durable consumer good called food and a durable producer good called tractors. At any point in time an individual can drive one and only one tractor to produce food and a tractor can be used for two years. The amount of food which an individual self-provides in year t is denoted by yt . The amount of food sold in year t is yst . The amount of food purchased in year t is ydt . The transaction efficiency coefficient for food is k, so that kydt is the amount available for consumption from the purchase of food. The quantity of food consumed in year t is yt +kydt . For the moment we assume that each individual's decision horizon is of two years and her subjective discount factor is δ∈(0,1). An individual’s objective function is her total discounted utility which is a function of the quantity of food consumed: (18.1)

U = ln(y1 +kyd1 ) + δln(y2 +kyd2 ).

In producing food, the output level is determined by tractor input, current labor input, and production experience which depends on the total accumulated labor in producing food. It is assumed that an individual will forget all her experience in producing a good and therefore previous labor has no effect on the current output level of the same good if she shifts between activities. Also, an entry cost into an activity will be incurred in year t if an

556

individual shifts into this activity in year t. Hence, the production function of food is specified as follows. (18.2a) (18.2b) (18.2c) (18.2d) (18.2e)

a>1 and α>0 yt +yst =Xtα (Lyt -cyt )a , Xt =Min{Σtτ=1 (xτ +xdτ ), 1}, Σtτ=1 (xτ +xdτ )≥1 xτ and xdτ are non-negative integers, Lyt =Σtτ=s lyτ where s is the latest time when a person enters into the production of good y; the initial condition is: Ly0 =0. cyt = c if a person enters into sector y in year t, and cyt = 0 if a person has stayed in sector y since she previously entered into this sector.

where yt +yst is a person's output level of food. Xt is the effective input level of tractors used to produce food. xτ is the self-provided quantity of tractors in year τ, and xdτ is the quantity of tractors bought in year τ. The two variables must be integers because of the indivisibility of a tractor. The output level of food in year 2 depends not only on the input level of tractors in year 2, but also on that in year 1, since the tractor is a durable good that can be used for two years. (18.2b) implies that a person can drive one and only one tractor at any point in time, so that extra tractors have no effect on an individual's output level of food. Lyt is a person's level of human capital in producing food in year t. This level equals a person's accumulated labor in producing food if no shift between jobs occurs and equals the current labor input level, lyt , if any shift between jobs occurs in year t or t-1. The entry cost coefficient c is a given positive constant. Expressions (18.2b)-(18.2e) are crucial for the model to generate the productivity implications of business cycles and unemployment. Letting xst denote the quantity sold of tractors in year t; a consumer-producer's production function of tractors is: (18.3a) (18.3b) (18.3c)

xt +xst =(Lxt -cxt)b , b>1 Lxt =Σtτ=s lxτ where s is the latest time when a person enters into the production of x; the initial condition is: Lx0 = 0. cxt = c if a person enters into sector x in year t cxt =0 if a person has stayed in sector x since she previously entered into this sector

where xt +xst is an individual's output level of tractors, which may not be an integer if we assume that several producers of tractors can produce an integer number of tractors together; Lxt is a person's level of human capital in producing tractors; liτ is a person's level of labor input into the production of good i as well as her level of specialization in producing good i in year τ. It is assumed that each consumer-producer is endowed with 2 units of labor and that economies of specialized learning by doing are individual-specific and activity-specific. Hence, there is an endowment constraint in year t for each consumer-producer. (18.4)

lxt + lyt ≤ 2

∀t

557

The system of production (18.2)-(18.4) displays economies of specialized learning by doing which implies that a person's labor productivity of any good is higher if she specializes producing that good over all time than if she shifts between jobs and produces all goods. This system formalizes a tradeoff between economies of specialized learning by doing and unemployment which can be avoided by increasing job shifting costs when durable producer goods are indivisible. In order to fully exploit economies of specialized learning by doing, the population should be divided between professional farming and professional tractor manufacturing. But the division of labor will generate unemployment of professional producers of tractors in year 2, since tractors are indivisible durable producer goods. In order to avoid unemployment and associated business cycles, producers of tractors should shift to producing food in year 2. But this will generate shifting costs between jobs and prevent full exploitation of economies of specialized learning by doing. If the decision horizon is much longer than two years, this tradeoff will be more obvious. Also, we have a tradeoff between economies of specialization and transaction costs (related to the coefficient 1-k). If transaction efficiency k is sufficiently low, then economies of specialization are outweighed by transaction costs. Hence autarky that does not involve any business cycles and unemployment is more efficient than the complete division of labor which may generate business cycles and unemployment. If transaction efficiency is sufficiently high, then the dynamic equilibrium in a decentralized market may be the complete division of labor that generates efficient unemployment in year 2 and business cycles. This story is worked out in the next section.

18.4.

Cyclical vs. non-cyclical Corner Equilibria

18.4.1

Regime Specification, Configurations and Market Structures

As in chapter 14, all trade is entirely determined in a futures market which operates at t = 0 and through two year contracts. This ensures a Walrasian regime with price-taking behavior at t = 0. Following the approach to dynamic equilibrium models based on corner solutions, developed in chapter 16, it can be shown that each consumer-producer's optimal decision in this model is a corner solution and that an individual does not buy and sell the same goods; she sells at most one good at any point in time. Because of the indivisibility and durability of tractors, it is trivial to show that a professional farmer buys one tractor in year 1 and does not buy tractors in year 2. Having taken this into account, there are five possible corner solutions for each consumer-producer. The combinations of the five corner solutions generate three possible market structures. In the first configuration, autarky, denoted by A and depicted in Fig. 18.4, there is no trade and each individual self-provides all goods. That is, autarky implies a configuration with xts = xtd = yts = ytd = 0. For configuration A, yt, x1 >0 so that each individual self-provides a tractor which is an input along with labor in producing food. M individuals choosing configuration A constitute structure A. The second market structure is referred to as complete division of labor, or simply C. Let (x/y) denote a configuration in which an individual sells tractors in year 1 and buys food in two years, and (y/x) denote a configuration in which an individual sells food in two years and buys a tractor in year 1. Market structure C consists of the division of the M individuals

558

between configurations (x/y) and (y/x), that is, professional farmers exchange food for tractors in year 1 with professional producers of tractors. The latter save some money in year 1 in order to buy food in year 2 when they are unemployed. Market structure C is depicted Fig. 18.4.

Structure A

Structure C (complete division of labor with business cycles

Structure P (partial division of labor without business cycle

Figure 18.4: Structures with and without Business Cycles 18.4.2

The Dynamic corner equilibrium in Autarky

The third market structure is referred to as partial division of labor, or simply P. Denote by (xy/y) a configuration in which an individual specializes in producing tractors in year 1, retains a tractor for himself, sells the rest of the tractors in year 1, buys food in both years, and drives the tractor to self-provide part of the food required in year 2. Market structure P consists of the division of the M individuals between configurations (xy/y) and (y/x). In this case, professional farmers are the same as in market structure C, but individuals choosing configuration (xy/y) produce tractors in year 1 and shift to the production of food in year 2. Compared to market structure C, this market structure involves no business cycles and unemployment, but job shifting costs are incurred and economies of specialized learning by doing cannot be fully exploited in configuration (xy/y). Market structure P is depicted in Fig. 18.4. A dynamic corner equilibrium in the two years when autarky prevails is defined by the solution to an individual's total discounted utility-maximizing labor decision for that configuration. In configuration A, the quantities traded of all goods are 0 and yt >0, x1 =1, x2 =0. Inserting these values into equations (18.1)-(18.4), and substituting from (18.2)-(18.4) into (18.1), gives the decision problem for configuration A as: (18.5a)

Max : U = lny1 +δlny2

lit , xt , y t

559

s.t.

y1 =x1α (Ly1 -c)a , x1 =(Lx1 -c)b =1, x2 =0 y2 =x1α (Ly2 -c)a Ly1 = ly1 , Lx1 = lx1 , Ly2 =ly1 +ly2 lx1 +ly1 =2, ly2 =2

(production function of y at t=1) (production function of x at t=1) (production function of y at t=2) (definition of human capital) (endowment constraints)

The solution of (18.5a) is lx1 =1+c, ly1 =1-c, y1=(1-c)a, y2=(3-2c)a , so that: (18.5b)

U(A) = ln(1-c)a +δln(3-2c)a

where U(A) is the per capita total discounted real income when an individual chooses configuration A. Note that due to the absence of trade, no transaction costs are incurred in this configuration, but experience cannot be effectively accumulated because of job-shifting costs. Hence, U(A) tends to 0 if c is sufficiently large to be close to 1. There is no business cycle and unemployment in this market structure, but accumulation of human capital is very slow since each individual must change jobs in each year. The per capita consumption of food in year 2, y2=(3-2c)a , is higher than that in year 1, y1=(1-c)a . In particular, as the decision horizon T increases from 2 to a very large number, accumulation of human capital cannot exceed the experience of two years since each individual must change jobs between producing tractors and food every other year. The total discounted per capita real income for T year in autarky is

U T ( A ) = 2[ln(1 − c) + δ ln(3 − 2c)]S where S ≡ 1 + δ 2 + δ 4 +L+δ T = (1 − δ T + 2 ) / (1 − δ 2 ) . The limit of S as T tends to infinity is1 / (1 − δ 2 ) . From the formula, we can see that UT(A) converges to a constant as T tends to infinity. In other words, there is no long-run continuous accumulation of professional human capital because of frequent shifts between jobs in autarky. Later we will see that structure C can speed up accumulation of human capital through continuous accumulation of professional human capital, so that total discounted per capita real income tends to infinity as T goes to infinity. 18.4.3

Market Structure C

Structure C consists of configurations (x/y) and (y/x). There are two steps in solving for the dynamic corner equilibrium of a market structure with trade: first, for each type of configuration in the market structure the utility-maximizing labor allocation decision and demands and supplies for each good (and hence the total discounted indirect utility of an individual who chooses that configuration) are derived; and second, given the demands and supplies of an individual in each configuration, the market clearing conditions and utility equalization conditions are used to solve for the set of dynamic corner equilibrium relative prices and numbers of individuals choosing each configuration. Configuration (y/x): In this configuration yt, yts>0, x1d =1, lyt =2, and xt = xts = lxt = x2d =0. Hence the decision problem for this configuration is:

560

(18.6a)

Max : s yt , yt

s.t.

Uy = lny1 +δlny2

y1+ys1 =(xd1 )α (Ly1 -c)a , xd1 =1, y2 +ys2 = (xd1 )αLy2a Ly1 = ly1 = 2, ly2 = 2, Ly2 = Ly1 +ly2 = 4 py1ys1 +py2ys2 = px1xd1

(production function of y at t=1) (integer condition for tractor) (production function of y at t=2) (endowment constraints) (budget constraint)

where pit is the price of good i in year t. We assume that food in year 2 is the numeraire, that is, py2 =1. The solution to (18.6a) is (18.6b)

Uy =(1+δ)ln[py1 (2-c)a +4a -px1 ]-lnpy1 -(1+δ)ln(1+δ)+δlnr ys2 = [4a -δpy1 (2-c)a +δpx1 ]/(1+δ), y2 =4a -ys2 y1 =(2-c)a -ys1 xd1 = 1, ys1 =(px1 -ys2 )/py1 ,

where Uy is the total discounted indirect utility function, xd1 and yst are the demand and supply functions for configuration (y/x). Note that a professional farmer's decision involves borrowing money (the income in year 1 py1 ys1 must be smaller than the expenditure in year 1 px1xd1 in order to satisfy the budget constraint). Configuration (x/y): By a similar process, for configuration (x/y) (18.7)

Ux = (1+δ)[lnk+ln(2-c)b +lnpx1 -ln(1+δ)]-lnpy1 +δlnδ yd2 = δpx1 (2-c)b/(1+δ), xs1 = (2-c)b , yd1 = (px1 xs1 -yd2 )/py1

where Ux is the total discounted indirect utility function, xs1 and ydt are the supply and demand functions for configuration (x/y). Note that a tractor specialist's decision involves savings. The income in year 1 px1 xs1 must be larger than the expenditure in year 1 py1 yd1 in order to satisfy the budget constraint. It is interesting to see that this market structure cannot operate in the absence of fiat money or a credit system, since professional farmers choosing configuration (y/x) sell and do not buy, and professional producers of tractors buy and do not sell in year 2, while tractors cannot be saved and used to pay for food in year 2 by professional producers of tractors. That is, commodity money cannot facilitate trade across years in this structure. Utility maximization by individuals and the assumption of free choice of profession configuration have the implication that the total discounted utility of individuals is equalized across configurations. That is, (18.8)

Uy = Ux

where Ui is a function of relative prices of goods in different years. Let Mi represent the number (measure) of individuals selling good i. Multiplying Mi by individual demands and supplies gives total market demands and supplies. The market clearing condition for food and tractors in two years are (18.9)

Mx xs1 = My xd1 , Mx yd1 = My ys1 , Mx yd2 = My ys2

561

where Mx xs1 is the total market supply of and My xd1 is the total market demand for tractors in year 1, Mx ydt is the market demand for and My yst is the market supply of food in year t. Note that due to Walras' law one of the three market clearing conditions in (18.9) is not independent of the others. The equilibrium relative number of individuals choosing each configuration Mxy ≡ Mx/My and the equilibrium relative prices px1 and py1 are determined by three independent equations in (18.8) and (18.9). Hence, the dynamic corner equilibrium in market structure C is given by (18.10a)

px1 = 4a (1+δ)/δ[1+k(2-c)b ], py1 =4a /δ(2-c)a , Mxy =(2-c)-b U(C)=aδln4+[b(1+δ)+a]ln(2-c)-ln[1+k(2-c)b ]+(1+δ)lnk

where U(C) is the total discounted per capita real income for the dynamic corner equilibrium in market structure C. If the decision horizon is T > 2 years, then there are T/2 business cycles in market structure C. Each cycle is a duplication of the dynamic corner equilibrium given in (18.10a), except that the initial condition Li0 = 0 is replaced with a level of human capital accumulated in producing good i at the end of the last cycle. Since no job shift occurs in this market structure, the dynamic corner equilibrium in year T is (18.10b)

px1 = (2T)a (1+δ)/δ [1+kTb ], py1 = (2T)a /δTa , Mxy =T-b UT (C) = aδln(2T)+[b(1+δ)+a]ln(T-c)-ln[1+k(T-c)b ]+(1+δ)lnk

It is easy to see that the per capita real income in year T does not involve any job-shifting cost c and that UT (C) increases with T. But the per capita total discounted real income in autarky will not increase with T since learning by doing is interrupted by job shifting in each year for autarky. A comparison between U(C) in (18.10) and U(A) given in (18.5b) indicates that U(A)>U(C) if k is sufficiently close to 0 and if c is sufficiently small, since U(C) tends to negative infinity as k converges to 0 but U(A) is independent of k. Also, U(C)>U(A) if c is smaller than 1 but sufficiently close to 1 and k is sufficiently large, since U(A) tends to negative infinity but U(C) is positive as c tends to 1 when k is sufficiently large. This deduction yields Lemma 18.1: The total discounted utility is greater in market structure C than in autarky if c and k are sufficiently close to 1; the total discounted utility is greater in autarky than in market structure C if k and c are sufficiently close to 0; and the total discounted utility increases with the decision horizon T for market structure C and converges to a constant in autarky.

This result is intuitive. Autarky is more efficient if transaction efficiency is too low and if job shifting costs are not too large because autarky does not involve transaction costs but involves job shifting costs, while the division of labor in market structure C involves transaction costs but not job shifting costs.

562

18.4.4

Market Structure P

By a two-step procedure analogous to that used to solve for the dynamic corner equilibrium in market structure C, it is possible to solve for the dynamic corner equilibrium in market structure P. Structure P consists of the division of M individuals between configurations (y/x) and (xy/y). The corner solution for configuration (y/x) is the same as in market structure C. The corner solution for configuration (xy/y) is: (18.11)

Ux = (1+δ)ln{(2-c)a -ln(1+δ)+kpx1[(2-c)b -1]}-lnpy1 +δlnδ x1 =1, xs1 = (2-c)b -1, yd2 ={δkpx1 [(2-c)b -1]-(2-c)a }/k(1+δ), yd1 = (px1 xs1 -yd2 )/py1

where px1 and py1 are the respective prices of tractors and food in year 1 in terms of the price of food in year 2. The utility equalization condition Ux = Uy and the two independent market clearing conditions yield the dynamic corner equilibrium relative prices px1 and py1 and the relative number of individuals choosing the two configurations. Although the algebraic form of the dynamic corner equilibrium solution for relative prices, relative number of individuals choosing different configurations, and total discounted utility is very complicated, it is easy to see the effects of the transaction efficiency coefficient k, the jobshifting cost coefficient c, and the number of cycles T/2, on per capita real income. Since producers of tractors must shift jobs every other year, they will forget their experience and have to pay entry costs each year. Thus, (18.11) will be the same for each cycle of production and consumption of tractors irrespective of how long is the decision horizon. This implies that the advantage of structure C over structure P is increasingly more significant as the decision horizon increases. The indirect utility function for a professional farmer in structure P is the same as in structure C, given in (18.6b). The utility equalization condition implies that the total discounted utility must be 0 for all configurations if it is 0 for any one configuration. Hence, the total discounted utility in structure P must become negative as c tends to 2 because Ux in (18.11) tends to negative infinity as c converges to 2 for any positive and finite relative prices of traded goods. The market clearing condition will adjust relative prices such that the utility equalization condition is established. Hence, if c is sufficiently large to be close to 2, the decision horizon is sufficiently long, and the discount factor is sufficiently close to 1, then the total discounted utility in structure C will be higher than in structure P because the former tends to be very large and the latter tends to 0 under these conditions. However, if c is sufficiently smaller than 2 and the decision horizon is not long or the discount factor is sufficiently small, then Ux in (18.11) may be positive but U(C) may be 0 if k is sufficiently close to 0. It is not difficult to see that Uy in (18.6b) is independent of k and Ux in (18.11) may be positive even if k = 0, but U(C) in (18.10) tends to negative infinity as k converges to 0. Moreover, U(A) in (18.5b) tends to negative infinity but Ux in (18.11) and Uy in (18.6b) may be positive as c converges to 1 when c∈(0,1). This deduction leads us to Lemma 18.2: Total discounted utility is greater in structure P than in structures A and C if c is sufficiently close to 1 and k is sufficiently close to 0; total discounted utility is greater in structure C than in structure P if k is sufficiently close to 1, the decision horizon is sufficiently long, the discount rate is sufficiently small, and c is sufficiently close to 2.

563

Structure P, like structure C, cannot operate in the absence of money substitute or a credit system because in year 2 professional farmers sell and do not buy and individuals choosing (xy/y) buy and do not sell. Following the procedure used to prove the Yao theorem in chapter 4, we can establish that theorem for the dynamic general equilibrium model in this chapter. Hence, only the Pareto optimum dynamic corner equilibrium that generates the highest total discounted utility is the dynamic general equilibrium. Therefore, we can identify the dynamic general equilibrium by comparing the total discounted utility levels between different market structures. The comparison, together with lemmas 18.1 and 18.2, yields Proposition 18.1: If transaction efficiency is sufficiently low and job-shifting costs are not too high, autarky is the dynamic general equilibrium, and therefore productivity is low, and trade, business cycles, and unemployment do not occur; if transaction efficiency and jobshifting costs are sufficiently high, the decision horizon is sufficiently long, and the discount rate is sufficiently small, then the complete division of labor with business cycles and unemployment is the dynamic general equilibrium; if transaction efficiency and job-shifting costs are at some intermediate levels, the decision horizon is not long or the discount rate is large, then the dynamic general equilibrium is the partial division of labor without business cycles and unemployment.

Before examining the implications of proposition 18.1, some discussion is required on the question of the existence of equilibrium. From (18.10)-(18.13), we can see that no dynamic corner equilibrium exists for structure C if k is sufficiently close to 0; no dynamic corner equilibrium exists for autarky if c is sufficiently close to 1; and no dynamic corner equilibrium exists for structure P if c is sufficiently close to 2 even if the decision horizon is very long. With these qualifications in mind, the following discussion of the implications of proposition 18.1 is pertinent only if the conditions for the existence of the relevant dynamic corner equilibrium are met. Suppose the discount rate is sufficiently small, the decision horizon is sufficiently long, and job-shifting costs are not too low. Then according to proposition 18.1, as transaction efficiency is improved the dynamic general equilibrium will evolve from autarky, which involves no business cycle or unemployment, to structure C which involves business cycles and unemployment. This implies that our model has endogenized not only the business cycle and unemployment, but also the emergence of the business cycle and unemployment from the evolution of division of labor. This proposition is consistent with the casual observation that business cycles and unemployment occur only in an economy with high levels of division of labor, specialization, productivity, and trade dependence. Contrary to the market failure argument, proposition 18.1 implies that the greater the foresight of individuals, the more likely is the occurrence of efficient business cycles with unemployment in a decentralized market. It seems to us that the productivity benefits of business cycles and unemployment are the reasons for the prevalence of persistent business cycles that involve unemployment. It is easy to see that autarky and structure P fully employ physical labor but underemploy human capital, while structure C fully exploits human capital but generates cyclical unemployment of physical labor. This difference between the market structure with

564

business cycles and unemployment and those involving no business cycles and unemployment highlights the intuition behind proposition 18.1. Intuitively, if the human capital that is exploited by structure C but not exploited by structures A and P is greater than the physical labor that is employed by structures A and P but not fully employed by structure C, then C is more efficient than other structures and will be the dynamic general equilibrium. 18.4.5. Welfare and Policy Implications of the Model Following the approach used to prove the first welfare theorem in chapter 3, it is not difficult to prove that the dynamic general equilibrium in the Walrasian regime is Pareto optimal. Hence, Pareto improving government policies do not exist. At best, a successful government policy that transfers income from individuals employed to individuals unemployed can play a role equivalent to that of savings in structure C if C is the dynamic general equilibrium in a free market. But such government intervention will certainly generate distortions associated with bureaucracy. Also, such government intervention will paralyze the market mechanism that facilitates the full exploitation of economies of specialized learning by doing through savings. If individuals expect that the government will save for them via income transfers and unemployment welfare, they may have no incentive to save themselves. However, if individuals are myopic and their decision horizon is one year instead of two, then it is trivial to show that a Pareto improving government income transfer scheme may exist. Indeed, if job-shifting costs are sufficiently high, for instance, it is infeasible for a farmer to self-provide a tractor due to prohibitively high shifting costs between farming and tractor manufacturing, then autarky is infeasible. Suppose that individuals' decision horizon is of one year instead of two years, then professional tractor manufacturers will not save any money earned in year 1 for their living in year 2, so that either their total discounted utility over two years tends to negative infinity due to zero consumption in year 2, or they have to change jobs in year 2 and thereby economies of specialized learning by doing cannot be fully exploited. For this case, a Pareto improving income transfer policy exists if the government is less myopic than private businessmen (which is very unlikely). But such an income transfer scheme may institutionalize myopic behavior such that a mature credit market never emerges. Hence, even if short run benefits may be generated by a government income transfer scheme, its long-run costs are likely to outweigh the benefits.1 Casual observation of a capitalist economy indicates the prevalence of structure C, while casual observation of a Soviet style socialist economy indicates the prevalence of 1

It is difficult to draw the distinction between voluntary and involuntary unemployment in our model. In a sense, unemployment in this model can be viewed as voluntary since dynamics with unemployment and business cycles are the outcome of all individuals’ optimal decisions. However, such unemployment can also be viewed as involuntary since individuals who are unemployed are willing to work if it is possible. They cannot work during recession time because of a tradeoff between full exploitation of human capital and full employment of physical labor. Maybe, “involuntary” is the wrong word for this general equilibrium phenomenon. In general equilibrium, each individual is unhappy with the consequence of interactions between self-interested decisions since she always wants more (nonsatiated preferences), but must accept the equilibrium as it is. It is not easy to tell if she accepts the equilibrium voluntarily or involuntarily if the nonsatiated desires are considered.

565

structure P which does not involve business cycles and unemployment but may be less effective in accumulating human capital than structure C. Hence, a conjecture is that if a socialist government can control the relative number of different specialists and is tempted to rectify the "market failure" that generates business cycles and unemployment, a noncyclical pattern of division of labor without unemployment is more likely to be chosen despite the low productivity of such a pattern of economic organization. In this sense, the prevalence of non-cyclical dynamics and associated low productivity in socialist economies is evidence of government failure.

18.5.

General Price Level, Business Cycles, and Unemployment Rate

Suppose that transaction efficiency, job-shifting costs, the decision horizon, and the discount factor are sufficiently large, then structure C is the general equilibrium. Since the price of tractors in year 2 px2 is irrelevant (tractors are not traded in year 2), the price levels in different years can be compared through the comparison of price levels of food across years. From expression (18.10), it can be seen that the price of food in year t+1 relative to that in year t is (18.14)

pyt+1 /pyt = δ[2T/4T)a = δ/2a 1 py2 /py1 = δ[(2-c)/4]a 0, then dKi/dIi > 0 for I1 = I2 = ... = IN. From this comparison, what insight can one get for the role of allocative distortion?

626

Part II: The Institution of the Firm, Endogenous Transaction Costs, and Economic Development

Chapter 8: Economic Development, the Institution of the Firm, and Entrepreneurship 8.1. What is the Institution of the Firm? In the Smithian models of chapters 4, 6, 7, there is no labor trade, and there are no firms. You may wonder if this kind of model can only describe economic development before the Industrial Revolution. But it is one of the advantages of the Smithian framework over the neoclassical that only the ex ante players are consumer-producers, and there are no firms before individuals have made their decisions. The institution of the firm is a particular way of organizing transactions that are required by the division of labor. It may emerge from the division of labor only as a consequence of individuals’ decisions in choosing their levels of specialization and manner of organizing transactions. If the transaction cost coefficient for labor is smaller than that for goods, then the institution of the firm will be chosen to organize the division of labor and to promote economic development as trade and pricing of goods are replaced by the corresponding trade and pricing of labor. An example of the replacement of goods trade with labor trade is trade between a professor and his housekeeper. Outputs of services provided by housekeepers are prohibitively expensive to price because of such a great variety of services, generating an extremely high cost in measuring quality and quantities of the services item by item. Hence, trade in labor that involves pricing of labor inputs of the housekeeper will substitute for trade in her outputs. The professor pays the housekeeper according to her working hours, rather than according to quantities and qualities of each and every service items she provides. However, we do not take trade between the professor and the housekeeper to be associated with the institution of the firm. The division of labor between the professor and the housekeeper and the replacement of trade in outputs of the housekeeper with trade in her labor, are two necessary but not sufficient conditions for the emergence of the firm from the division of labor. Before we study the sufficient conditions for the existence of the firm, a rigorous definition for institution of the firm is needed. The institution of the firm is a structure of transactions based on the division of labor that satisfy the following three conditions. (i) There are two types of trade partners who are associated with a firm: the employer (she) and the employee (he). There is an asymmetric distribution of control rights or authority. The employer has control rights to

242

use the employee’s labor. He must do what he is told to do, if she so demands. That is, the ultimate rights to use the employee’s labor are owned by the employer, subject to the employee’s freedom to quit the job and to other terms of the labor contract. (ii) The contract that is associated with the asymmetric relationship between the employer and the employee never specifies how much the employer receives from the relationship. It only specifies how much the employee receives from the relationship. The employer claims the residual returns, defined as the revenue of the firm net of the wage bill and other expenses. The employer is referred to as the owner of the firm. One of the most important components of the ownership of a modern firm is the entitlement to the business name of the firm. The exclusive rights to the business name are enforced through a business name search process when the firm is registered with the government and through recognition of the name in legal cases in the judicial process. The exclusive rights are also enforced through the laws of brand. (iii) A firm must involve a process that transforms labor of the employee into something that is sold in the market by the owner of the firm. In the process, what is produced by the employee is owned by the employer (residual returns). The relationship between the professor and the housekeeper does not involve the institution of the firm, since it does not involve such a resale process. The professor directly consumes what the housekeeper produces and never resells it to the market. If an individual hires a broker to conduct stock transactions, the relationship involves asymmetric authority and rights to residual returns. But the relationship does not involve the firm since it does not satisfy condition (iii). Suppose that in the model in chapter 4, with only consumption goods, a specialist producer of x buys the labor of a specialist producer of y, directs that employee to specialize in producing y within the firm, and then sells y to the specialist producer of y in the market for y. Such roundabout transactions involve unnecessary transactions in labor. If the producer of y must buy his own produce from the market, why would he not directly sell y to the specialist producer of x in exchange for good x? The latter structure of transactions is exactly the same as the former, except that the former involves more trade in labor and therefore creates unnecessary transaction costs. This implies that the institution of the firm will not be chosen if there is no producer good or service. In this chapter, we shall show that the institution of the firm may be used to save on transaction costs if there is division of labor between the production of the final goods and the production of the intermediate goods. The rationale behind our story of the firm may not seem very plausible. Human society has been disturbed by the question of the fairness of asymmetric relationships between employer and employee. In a free enterprise system, employees have the freedom to become employers by using the free capital market and the legal system that protects free association. They also have the freedom to quit their jobs. Hence, an asymmetric relationship between the employer and the employee in a free market system differs from the relationship between a master and his slave or the feudal relationship between a lord and his servant. Notwithstanding this, many people (from Karl Marx to modern trade union activists) are still concerned with the following questions. Why must the employee do what he is told to do rather than what he likes to do? Why should not the employee have rights to the residual returns that may make a fortune for the employer? Such questions were at least partly responsible for the Russian Revolution in 1917 and

243

the Chinese Revolution in 1949 that changed the lives of a billion people over the course of more than half of the 20th century and generated very serious consequence for economic development in many current and ex-socialist economies. 1 Russia and East Europe have already abandoned the disastrous social experiments that were inspired by such questions, and China shows every prospect of doing so in the near future. However, we need a well developed theory to explain why the communist government’s infringement of residual rights of private firms is harmful for economic development, and to address the following questions. What is the role of multinational firms and foreign direct investment in economic development? What are the effects of the legal system that protect residual rights of owners of private firms on the development of entrepreneurship, which is crucial for economic development? This chapter will address such questions. In section 8.2, we outline the story behind the model. In section 8.3, a general equilibrium model of endogenous specialization and endogenous emergence of the firm is specified. Individuals’ decisions, corner equilibria in various structures, general equilibrium, and its inframarginal comparative statics are then solved. Sections 8.4 and 8.5 explore the development implications of the institution of the firm. Question to Ask Yourself when Reading this Chapter What is the institution of the firm? What are the necessary and sufficient conditions for the emergence of the firm? What is the function of the institution of the firm and what are implications of the internal organization of the firm for the equilibrium level of division of labor and productivity? What is the relationship between the legal system that protects residual rights of owners of private firms, entrepreneurship, and economic development?

8.2. Why are Claims to Residual Rights of the Firm Essential for Nurturing Entrepreneurship? -The Story behind the Model We will outline the intuition behind the formal model by telling a story about the role of the institution of the firm in economic development before you become mired in the algebra of the model and lose your capacity for economic thinking. Our story of the firm runs as follows. Each individual as a consumer must consume a final good, called cloth, the production of which requires an intermediate good, called management service, as an input. There is a tradeoff between economies of specialization and transaction costs. If transaction efficiency is high, then division of labor will occur at equilibrium. Otherwise, autarky will be chosen as the equilibrium. There are three different structures of residual rights, which can be used to organize transactions required by the division of labor. Structure D, shown in Fig. 8.1 (b), comprises markets for cloth and management services. Specialist producers of cloth 1

According a conservative estimate in Forbes (March 23, 1998, p. 80), the cost of the social experiment with the communist economic system in Cuba was $31.5 billion in 1995. In other words, without this communist system, Cuba’s GDP in 1995 would be $31.5 billion more than its realized value.

244

exchange that product for the specialist services of management. For this market structure, residual rights to returns and authority are symmetrically distributed between the trade partners, and no firms or labor market exist. Structure E, shown in Fig. 8.1(c), comprises the market for cloth and the market for labor hired to produce the management service within a firm. The producer of cloth is the owner of the firm and specialist producers of management services are employees. Control rights over employees' labor and rights to the firm's residual returns are asymmetrically distributed between the employer and her employees. The employer claims the difference between revenue and the wage bill, has control rights over her employees' labor, and sells goods that are produced from employees' labor. Structure F, shown in Fig. 8.1(d), comprises the market for cloth and the market for labor hired to produce cloth within a firm. The professional manager is the owner of the firm and specialist producers of cloth are employees. For the final two structures of residual rights, the firm emerges from the division of labor. Compared with structure D, these involve a labor market but not a market for management services. As Cheung (1983) argues, the firm replaces the market for intermediate goods with the market for labor. Although both structures E and F involve a firm and an asymmetric structure of residual rights, they entail different firm ownership structures.

Figure 8.1: Emergence of the Firm from the Division of Labor Suppose that transaction efficiency is much lower for management service than for labor. This is very likely to be the case in the real world, since the quality and quantity of the intangible entrepreneurial ideas are prohibitively expensive to measure. Potential buyers of the intellectual property in entrepreneurial ideas may refuse to pay by claiming that these are worthless as soon as they are acquired from their specialist-producer. Under this circumstance, the institution of the firm can be used to organize the division of labor more efficiently because it avoids trade in intangible intellectual property. Suppose further that transaction efficiency for labor hired to produce management services is much lower than for labor hired to produce cloth because it is prohibitively expensive to measure the efforts exerted in producing intangible management services. (Can you tell if a manager sitting in the office is pondering business management or his girl friend?) Then the division of labor can be more efficiently organized in structure F than in structure E. This is because structure F involves trade in cloth and in labor hired to produce

245

cloth, but not trade in management services nor in labor hired to produce management services, while structure E involves trade in cloth and in labor hired to produce management services. Hence, structure F will occur at equilibrium if the transaction efficiencies for labor hired to produce cloth and for cloth are sufficiently high. The claim to the residual return of the firm by the manager is the indirect price of management services. Therefore, the function of the asymmetric structure of residual rights is to get the activity with the lowest transaction efficiency involved in the division of labor while avoiding direct pricing and marketing of the output and input of that activity, thus promoting the division of labor and productivity. In a sense, the function of the asymmetric structure of residual rights is similar to that of a patent law that enforces rights to intangible intellectual property, thereby promoting the division of labor and productivity in producing the intangible. However, the asymmetric structure of residual rights to returns and control can indirectly price those intangible intellectual properties which are prohibitively expensive to price even through a patent law. Intuitively, there are two ways to do business if an individual has an idea for making money. The first is to sell the entrepreneurial idea in the market. This is very likely to create a situation in which everybody can steal the idea and refuse to pay for its use. The second way of proceeding is for the entrepreneur to hire workers to realize the idea, while keeping the idea to herself as a business secret. Then she can claim as her reward the residual returns to the firm, which represent the difference between revenue and the wage bill. If the idea is a good one, then the entrepreneur will make a fortune. If the idea is a bad one, she will become bankrupt. The residual return is the precise price of the idea and the entrepreneur gets what she deserves, so that stealing and over-or underpricing of intellectual property is avoided. To understand this, you may image that Bill Gates did not set up a company to hire others to realize his entrepreneurial ideas about how to make money from computer software. Instead, he sold his ideas as consultant services. Would anybody pay a billion dollars (which is the real market value of the ideas indicated by Bill Gates residual returns) to buy the ideas? This theory is referred to as the theory of indirect pricing, which is formalized by the Yang-Ng model (1995). It also formalizes the Cheung-Coase theory of the firm (Coase, 1937 and Cheung, 1983), that the institution of the firm can save on transaction costs by replacing trade in intermediate goods with trade in labor if the former involves higher transaction costs than the latter. The model does not endogenize transaction costs if these are defined as a departure from the Pareto optimum. However, if endogenous transaction costs are defined as those transaction costs whose value is endogenously determined by individuals' decisions and the equilibrium process, then the Yang-Ng model has endogenized transaction costs. This is because the number of transactions for individuals and for the economy as a whole is endogenized in this model due to the tradeoff between economies of specialization and transaction costs. With this theory, it is not difficult to understand the role that the institution of the firm plays in economic development. If the legal system in a country does not protect residual rights of the owners of private firms, then we will see a shortage of entrepreneurial activities. This is because entrepreneurial knowledge is very intangible, and can be indirectly priced only through claims to the residual rights of private firms. In the former Soviet Union, the government could arbitrarily infringe upon the residual rights of private firms, and monopolized rights to found firms. The Constitution of the Peoples’ Republic of

246

China regards the earning from residual rights of private firms as the source of exploitation. According to Barro (1997), Easton and Walker (1997), and Frye and Shleifer (1997), such infringement of residual rights of owners of private firms is very harmful for nurturing entrepreneurship and for economic development. Also, using the theory of indirect pricing, we can explain why large companies in the developed economies use the institution of the multinational firm to export intangible management know-how rather than directly exporting it to less development countries. Again, management know-how is very intangible. It is very easy to be under- or overpriced in direct trading. Hence, the multinational company is an effective way to indirectly price the intangibles. This will encourage division of labor and trade between professional producers of intangibles and tangibles, thereby promoting economic development. This theory has an interesting empirical implication. It predicts that the equilibrium size of the firm may decrease as division of labor evolves if the transaction conditions are improved faster for goods than for labor (see exercise 11). Empirical evidence to support the hypothesis can be found in Liu and Yang (2000), who show that productivity, level of division of labor, and per capita real income increase and the average size of firms declines concurrently as improvements in transaction conditions for goods outpace that for labor. 8.3 The Emergence of the Firm from the Evolution of Division of Labor In subsection 8.3.1, the model is specified and the concept of economies of roundabout production is defined. In subsection 8.3.2, the corner equilibria in all structures of organization and transactions are solved for. Finally, the general equilibrium and its comparative statics are solved in subsection 8.3.3. 8.3.1. Economies of Roundabout Production Example 8.1: A Smithian-Coasian model of the institution of the firm. As discussed in section 8.1, the existence of intermediate goods is essential for explaining the emergence of the firm from the division of labor. People produce intermediate goods because they may be used to improve the productivity of the final goods. There are economies of roundabout production if the productivity of a good can be improved by employing intermediate goods. There are three types of economies of roundabout production. Type A relates to the quantity of an intermediate good that is employed to produce the final goods. Type B relates to the number of intermediate goods at a link of the roundabout production chain. Type C relates to the number of links in the roundabout production chain. In this chapter we study type A of economies of roundabout production. Type B is studied in chapter 6, and will be studied again in chapter 12. Type C will be investigated in chapters 12. The development of division of labor since the Industrial Revolution has been taking place mainly in the roundabout production of these three types. In the model in this chapter, each consumer-producer has the following system of the production involving economies of roundabout production. (8.1a)

y + y s = ( x + tx d ) c l y a ,

(8.1b)

x + x s = lx b

247

(8.1c)

lx + ly = 1

y ,y s ,x,x d ,x s ,lx ,ly ≥ 0

where li is an individual’s level of specialization as well as her amount of labor allocated to the production of good i. x and y are respective quantities of the intermediate and consumption goods self-provided, xs and ys are respective quantities of the two goods that are sold, xd is the quantity of the intermediate goods that is bought, t is the transaction efficiency coefficient for the intermediate goods, and a and b are parameters of production conditions. x + t xd is the quantity of the intermediate good that is employed to produce the final good. The exponentially weighted average of this quantity and the amount of labor employed, (x + t xd )c/(c+a) lya/(c+a), is called the total factor input in producing good y. The ratio of output y + ys to total factor input is called total factor productivity (TFP), given by TFP = [(x + t xd )c lya ](a+c-1)/(a+c). The TFP increases with an individual’s level of specialization in producing y if a+c > 1. A production function of a good with two inputs displays economies of specialization if the total factor productivity increases with an individual’s level of specialization in producing the good. A production function of a good displays type A of economies of roundabout production if the total factor productivity of the good increases with the quantity of the intermediate good employed. In this chapter, the parameter c(a+c-1)/(a+c) can be considered as the degree of economies of roundabout production of type A, and parameter a(a+c-1)/(a+c) can be considered as the degree of economies of specialization in producing the final good. We assume that a = c for simplicity in the rest of the chapter, so that TFP increases with the quantity of the intermediate good employed and with the level of specialization in producing good y if a > 0.5. Hence, a can be considered as the degree of economies of roundaboutness, as well as the degree of economies of specialization in producing y. Suppose that the transaction efficiency coefficient for the final good y is k, and that all ex ante identical consumer-producers have the following utility function. (8.2)

u = y + ky d .

8.3.2. The Corner Equilibria in Four Structures The Wen theorem can be reestablished and refined for the model with intermediate goods. Hence, an individual sells at most one good and does not buy and self-provide the same good. She self-provides the consumer good if she sells it. Since intermediate good does not directly contribute to utility, she does not self-provide the intermediate good unless she produces the final good. Structure A (autarky), where each individual chooses a configuration with x = y s = x d = y d = 0 , as shown in Fig. 8.1(a). The decision problem for each individual in this structure is: Max: u = y = x a ly a = lx ab (1 − lx )a s

and its solution is: lx = b (1 + b) ,

ly = 1 (1 + b),

x = [b (1 + b)]b

248

u A = y = [b b (1 + b)1+b ]a where per capita real income in structure A, uA is per capita output of the consumption good as well. Structure D, comprising configurations (x/y) and (y/x), as shown in Fig. 8.1(b). There is no asymmetric distribution of residual rights in this structure. Individuals exchange goods for goods in the absence of the institution of the firm and a related labor market. Configuration (x/y) is defined by x = y = y s = ly = 0 and x s ,lx ,y d > 0 . Inserting the values of the variables and the budget constraint into the utility function yields the decision for this configuration. Indeed, there is no scope for adjusting the values of the decision variables, which are fixed by the definition of the configuration and the budget constraint. Here, the specialist-producer of good x does not self-provide x, which is not a consumption good. Configuration (y/x) is defined by x = x s = y d = lx = 0 and x d , y , y s , l y > 0 . Marginal analysis of the configuration yields the corner solution. The corner solutions for the two configurations are summarized as follows. x s = 1 , y d = p x / p y , u x = kp x / p y (x/y): 1 1−

1 1−

x d = (ata p y / p x ) a ,

(y/x):

y s = (ata p y /p x ) a p x / p y

a

u y = (atp y / p x ) a (1 − a ) 1−

where ui is the indirect utility function of an individual selling good i. Having considered the market clearing and utility equalization conditions and the population size equation Mx + My = M in structure D, we can solve for the corner equilibrium in that structure as follows. p y / p x = [k /(1 − a )]1− a /(at)a , u D = a a (1 − a )1− a (tk )a

(1 − a )M 1 − a + ak where Mi is the number of individuals selling good i, and uD is the per capita real income in structure D. Per capita real income is per capita consumption of the final good, and its reciprocal is the absolute price of labor, which includes labor allocated to the production of both final and intermediate goods. Structure E, comprising configurations (lx/y) and (y/lx), as shown in Fig. 8.1(c). (y/lx) denotes a specialist producer of y who hires workers and directs them to specialize in producing x within the firm. (lx / y) denotes a worker who is hired to produce the intermediate good and who buys the final good. The decision problem of the employer choosing (y/lx) is: Max: uy = y

M

x

=

akM , 1 − a + ak

s.t. y + y s = (x d ly )a ,

M

ly = 1 ,

y

=

(production conditions for specialist of y)

x = ( sl x ) , lx = 1 , (production conditions for specialist of x) d s x = Nx (equality between quantities of x produced and employed) s p y y = wNl x = wN (budget constraint) s

b

where N is the number of workers hired by the employer, w is the wage rate, and 1-s is the transaction cost coefficient for each unit of labor hired. The quantity of labor employed in production is thus slx. Nlx is the employer’s demand for labor. Each worker

249

in the firm produces xs = (slx )b = sb when he is directed to specialize in producing x (lx = 1). Hence, the employer receives intermediate good xd = Nxs. Superscripts s and d denote supply and demand for inputs and outputs within the firm. Note that lx is an employee’s quantity of labor, but is the employer’s decision variable. This is what we mean by residual control rights or asymmetric distribution of authority. However, the employee always has the right to quit the job and to find another employer. More important than this, he can use the free markets for capital, labor and goods to choose to become an employer himself and to found his own enterprise. This distinguishes the asymmetric relationship between employer and employee in a capitalist firm from the asymmetric relationship between a master and his slave and from the feudal relationship between a lord and his servant. The employer’s rights to residual returns relate to the difference between the output level of y within the firm and the quantity of y that is sold by the firm. Note that the production function of good x is still specified for each worker. It displays economies of specialization for each worker rather than economies of the scale of labor in the firm. All individual workers, production functions, and the employer’s production function are aggregated as the production function for the firm, which is y+ys = (xdly)a = (Nsbly)a. This production function for the firm displays local economies of scale to xd and ly for ly ≤ 1 and a∈(0.5, 1). But, there also are economies of specialization in producing y for the employer and in producing x for each worker. Hence, the local economies of scale for the firm are associated with economies of division of labor within the firm, which cannot be obtained by simply pooling labor together in the absence of specialization and division of labor. Note that the total factor is (xd)0.5ly0.5. This formalizes the distinction between economies of scale generated by pooling labor together within a firm and economies of specialization, drawn by Young (1928). If a > 1, the production of the firm displays global economies of scale to employed labor, N , that is, total factor productivity increases as the employer hires more workers. For a>1, the Kuhn-Tucker condition for the interior optimum number of workers is not satisfied, so that the optimum value of N is as large as possible. Hence, there does not exist a corner equilibrium with firms. With a ∈(0.5, 1), the solution of the decision problem for configuration (y/lx) is N = ( s ab ap y / w) 1

(1− a )

1

, y s = ( s ab a ) 1− a ( p y / w) a /(1− a )

u y = y = (1 − a )( s b ap y / w) a /(1− a )

where uy is the employer’s indirect utility function. Note that the interior solution of N is relevant only for a < 1. Each worker’s decision is simple. He sells all his labor, so that the budget constraint is p y y d = w lx s where lx s = 1 is supply of labor. The worker’s utility is thus

u x = ky d = kw / p y Let the number of individuals choosing (y/lx) be My; then the market supply of good y is Myys and the market demand for labor is MyN. Let the number of individuals choosing (lx/y) be Mx ; then the market demand for good y is Mx yd and the market supply of labor is Mx. The market clearing conditions for good y and for labor are equivalent to each other due to Walras’ law. Hence, we consider only one of them. Together with the utility equalization condition and two corner solutions, we have

250

M x y s = M y y d , y s = ( s ab a )

1 1− a

( p y / w) a /(1− a ) , y d = w / p y

u x = u y or kw / p y = (1 − a )( s b ap y w)

a /(1− a )

This yields the corner equilibrium in structure E as follows. ak N = Mx / My = w / p y = [(1 − a ) / k ]1− a ( s b a ) a 1− a u E = ( s b ka ) a (1 − a ) 1− a where uE is the per capita real income in structure E. Its reciprocal is also the absolute labor price of the final good. Structure F, comprising configurations (ly/x) and (x/ly), as shown in Fig. 8.1(d). (x/ly), denotes a specialist producer of x who hires workers and directs them to specialize in producing y using her produce x within the firm. (ly/x) denotes a worker who is hired to produce the final good, using the intermediate good, and who buys the final good. The decision problem of the employer choosing (x/ly) is: Max: u x = Y

Y + Y s ≡ N ys y s = (x d rly )a ,

(total output of y for a firm) ly = 1 (production condition for each employee)

xd = x s / N x s = l x b , lx = 1 p yY s = w ly N = w N

(quantity of x employed by each employee) (production condition of employer) (budget constraint)

where the upper-case letters represent output levels for the firm, and the lower-case letters represent quantities of goods for each individual. Y + Ys is the total output of the final good for the firm, Y is the residual return to the employer, Ys is the total amount sold by the firm, ys is the output level of the final good produced by each employee, xd is the amount of the intermediate good used by each employee to produce y, and r is the transaction efficiency coefficient for the labor of employees. Because of the transaction cost of labor, the employer receives rly when she buys ly. N is the number of workers hired by each employer and xs is the amount of the intermediate good produced by the employer. The superscripts d and s for the lower-case letters represent internal demand for inputs and supply of outputs within the firm, while the superscripts d and s for the upper-case letters represent demand and supply in the market place. The solution of the decision problem is: 1

1 a

N = r[(1 − a )p y /w ]a , Y s = ( p y / w) (1− a ) / a r (1 − a ) , u x = Y = ar[(1 − a )p y /w ](1− a )/a where ux is the employer’s indirect utility function. The decision problem of a specialist worker producing y is simple. He sells all of his labor to exchange for good y. Hence, from the utility function u y = ky d and the budget constraint p y y d = wl y = w , we obtain his indirect utility function: u y = kw / p y The market clearing and utility equalization conditions yield the corner equilibrium in structure F:

251

w / p y = (ar / k ) a (1 − a ) 1− a ,

N =M

y

/M

x

=

k (1 − a ) a

u F = (ar)a [k (1 − a )]1−a where uF is the per capita real income in this structure. Let us put all information relating to the four corner equilibria together in Table 8.1. Table 8.1: Corner Equilibria in Four Structures

Structure A

D

Relative Price

py

Numbers of specialists

Mx =

⎛ k ⎞ =⎜ ⎟ px ⎝ 1 − a ⎠

(at )

−a

akM 1 − a + ak (1 − a ) M My = 1 − a + ak

Demand Function

⎛ bb ⎞ ⎜ ⎟ ⎝ (1 + b)1+ b ⎠

a

(as )

w ⎛ ar ⎞ = ⎜ ⎟ (1 − a )1− a py ⎝ k ⎠

aM (1 − a ) k + a k (1 − a ) M My = (1 − a ) k + a Mx =

1

1

p y ⎞ 1− a ⎛ p y (1 − a ) ⎞ a ⎛ ⎟ N d = r⎜ N d = ⎜ s ab a ⎟ w ⎝ ⎠ w⎠ ⎝ d d y = w / py y = w / py a

ys = a

a

b −a

akM 1 − a + ak (1 − a ) M My = 1 − a + ak

1

1 1− a

w ⎛1− a⎞ =⎜ ⎟ py ⎝ k ⎠

F 1− a

Mx =

p y ⎞ 1− a ⎛ ⎟ x d = ⎜ at a px ⎠ ⎝ yd = px / py

Supply Function

Real income

E 1− a

a

1 1 ⎛ b s p y ⎞ 1− a s ⎛ py ⎞ ⎛ p y ⎞ 1− a s s a 1− a ⎜ l ⎟ Y = (1 − a ) x ⎜ ⎟ y = a ⎜t ⎟ ⎝ w⎠ ⎝ w ⎠ ⎝ px ⎠ s ly = 1 =1

xs = 1 (tka ) a (1 − a ) 1− a

( s b ka ) a (1 − a ) 1− a

1− a a

r

(ar ) a [ k (1 − a )]1− a

8.3.3. General Equilibrium Structure of Transactions and Residual Rights Per capita real incomes in the four structures are dependent on the transaction efficiency parameters t, s, k, the degree of economies of specialization b, and the degree of economies of roundabout production a. According to the Yao theorem, all we have to do in solving for the general equilibrium in a model with ex ante identical individuals is to identify the Pareto optimum corner equilibrium from the four corner equilibria. Letting per capita real incomes in each pair of structures be equal, we will obtain several equations that partition the parameter space of five dimensions into several subspaces. Our job is then to identify which structure is the general equilibrium structure within each of the subspaces. Essentially, this is to solve for a system of simultaneous inequalities. There is no standard procedure for solving a system of simultaneous inequalities. Experience and skill in ruling out Pareto inefficient structures as far as possible through identifying incompatibility and contradictions between inequalities are crucial for finding the solution. From working with many of the models in this text, you will gain skills in manipulating such systems of inequalities. For the current model, let us solve for the

252

system of simultaneous inequalities in two steps. First, we compare per capita real incomes in structures D, E, and F. We have: (8.4a) u E > u D iff t < s b (8.4b) u E > u F iff k > k 8 ≡ (r / s b ) a /( 2 a −1) (8.4c) u D > u F iff k > k7 ≡ (r /t)a /(2 a −1) A comparison between k7 and k8 indicates (8.4d) k8 > k7 iff t > s b . (8.4d) can be used to partition the parameter space into two subspaces first. For t < sa or k8 < k7, information in (8.4) can be summarized in Fig. 8.2.

Figure 8.2: Case with t < sb or k8 < k7

This figure implies that for t < sb or k8 < k7, among the three structures with the division of labor, Structure E generates the greatest per capita real income if k > k8; Structure F generates the greatest per capita real income if k < k8; Structure D cannot be general equilibrium since uD< uE for any k For the case with t > sb or k8 > k7, the information in (8.4) can be summarized as in the following figure.

Figure 8.3: Case with t > sb or k8 > k7

This figure implies that for t > sb or k8 > k7, among the three structures with the division of labor, Structure D generates the greatest per capita real income if k > k7; Structure F generates the greatest per capita real income if k < k7; Structure E cannot be general equilibrium since uE< uD for any k Putting the information together and considering per capita real income in autarky yields: Table 8.2: Candidates for Equilibrium Structure

253

t < sb k < k8 F, A

t > sb k < k7 F, A

k > k8 E, A

k > k7 D, A

Comparisons between per capita real incomes in each pair of structures for the parameter subspace in Table 8.2 yield the following results of the general equilibrium and its inframarginal comparative statics. Table 8.3: General Equilibrium and Its Inframarginal Comparative Statics

Values of t and s Value of k Relative to r,t,s,a Equilibrium structure Where

t < sb

k < k8 < k11 A

> k11 F

t > sb

k > k8 < k10 A

> k10 E

k < k7 < k11 A

> k11 F

k > k7 < k9 A

k > k9 D

k7 ≡ (r /t)a /(2 a −1) is given by uD = uE, k 8 ≡ (r / s b ) a /( 2 a −1) is given by uE = uF, k9 ≡ (1 − a )(a −1)/a b b /ta (1 + b)1+b is given by uA = uD, k 10 ≡ (1 − a ) ( a −1)/ a b b / as b (1 + b) 1+b is given by uA = uE, k11 ≡ [b b /ar(1 + b)1+b ]a /(1− a ) /(1 − a ) is given by uA = uF.

If you use the constraints that all critical values ki are between 0 and 1, you can partition the parameter space further. We leave this as an exercise to you. In terms of intuition, Table 8.3 tells the following story. (I) The structure with division of labor and the producer of y as the employer (structure E) cannot be general equilibrium if the transaction efficiency for labor employed to produce the intermediate good ( s ) is low compared to that for the intermediate good ( t ), or if t > sa, since structure E must trade labor employed to produce the intermediate good. (I.a) Under this circumstance, if the transaction efficiencies for the final and intermediate goods (k and t) are sufficiently high, compared to the transaction efficiency for labor employed to produce the final good ( r ), or if k > k7, the structure with the division of labor and the producer of x as the employer (structure F) cannot be general equilibrium either, since F must trade labor employed to produce the final good. Note the relationship between this statement and the formula for k7. Hence, only structures A and D are candidates for the equilibrium structure. If the transaction efficiencies for the final and intermediate goods are high, D is the equilibrium; otherwise, A is the equilibrium. (I.b) If the transaction efficiency for the intermediate good (t) is low compared to the transaction efficiency for labor employed to produce the final good ( r ), or if k < k7, the structure with the division of labor and with no firms (structure D) cannot be general equilibrium, since D must trade the intermediate good. Hence, only structures A and F are candidates for the equilibrium structure. If the transaction efficiencies for the final

254

good and the labor hired to produce the final good are high, F is the equilibrium; otherwise, A is the equilibrium. (II) Structure D cannot be equilibrium if t is small compared to s, or if t < sa, since structure D must trade the intermediate good that involves a small t. (II.a) If k and s are sufficiently large compared to r, or if k > k8, structure F cannot be equilibrium since F is associated with r. Hence, only structures A and E are candidates for the equilibrium structure. If k and s are sufficiently large (or k > k10), E is the equilibrium; otherwise, A is the equilibrium. (II.b) If s is small compared to r, or if k < k8, structure E cannot be equilibrium since E is associated with s. If k and r are sufficiently large, F is the equilibrium; otherwise, A is the equilibrium. The inframarginal comparative statics of general equilibrium are summarized in the following proposition. Proposition 8.1: The general equilibrium is autarky if transaction efficiency is low, and it is the division of labor if transaction efficiency is high. The division of labor is coordinated through the institution of the firm and the labor market if the transaction efficiency for labor is higher than that for intermediate goods. Otherwise, it is organized through the markets for the intermediate and final goods. When the general equilibrium is associated with the firm, the specialist-producer of the final good is the owner of the firm if the transaction efficiency for labor employed to produce the intermediate good is higher than that for labor employed to produce the final good. Otherwise, the specialistproducer of the intermediate good is the owner of the firm. The institution of the firm can get the activity with the lowest transaction efficiency involved in the division of labor while avoiding the direct pricing and marketing of the outputs and inputs of that activity. The residual returns claimed by the employer are the indirect price of her efforts.

The essence of the theory of indirect pricing can be summarized as follows. If individuals engage in division of labor in producing two goods x and y, trade in two of the four elements comprising outputs x, y, and inputs lx, ly can be used to organize the division of labor. Hence, there are six possible structures of transactions (2 combinations of 4 elements) that can be used to organize the division of labor: x and y (structure D), y and lx (structure E), y and ly (structure F), x and lx (not feasible, since a specialist of x who must consume y cannot buy y), x and ly (also not feasible), ly and lx (a structure that may be seen in some collective organization with a direct exchange of labor, but is rarely seen in the real world). Hence, individuals can at least consider three of the structures and choose one of them to avoid trade that involves the lowest transaction efficiency. Later, we shall show that as the number of traded goods and the level of division of labor increase, the number of possible structures of transactions increases more than proportionally. This implies that the choice of transactions structure is increasingly more important than the choice of production structure and resource allocation for a given structure of production for economic development as division of labor develops. This is why, in a highly commercialized society (with a high level of division of labor), there are more opportunities for entrepreneurs to make fortunes from manipulating structures of transactions.

255

8.4. The Distinction Between ex ante and ex post Production Functions and the Role of the Institution of the Firm in Economic Development

For inframarginal analysis, the equilibrium system of production functions discontinuously jumps across structures as parameters shift between the subspaces that demarcate structures. This feature of the Smithian system of production generates important implications for endogenous productivity progress. Hence, it is important to draw the distinction between the ex ante production function, which is the production function that is specified before individuals have made their decisions, and the ex post production function, which can be seen only after individuals have chosen configurations and the economy is settled down in a structure. The ex ante production functions are specified in (8.1). Since all decision variables are allowed to take on zero and positive values, there are multiple production configurations for different profiles of zero and positive values of decision variables. As individuals choose different configurations and the economy settles down in different structures, each individual’s system of production differs from configuration to configuration and the system of production for society differs from structure to structure. If an individual chooses autarky (x, y, lx, ly > 0, xs, ys, xd, yd = 0), then her ex post production function of y is y = x a ly a = lx ab (1 − lx )a = (1 − ly )ab ly a where the endowment constraint is used. The marginal productivity of y and the derivative of the marginal productivity are dy = ay (bl x −1 − l y −1 ) dl y d2y dy =0 2 < 0 when dl y dl y

This implies diminishing marginal labor productivity of y within the neighborhood of the corner solution in configuration A. But if structure E is chosen, then the ex post production function of a firm in producing y is given in (8.7). It is y + y s = (x d ly )a = (N sb )a As discussed in the previous subsection, this ex post production function for the firm displays economies of specialization in producing y if a > 0.5 and exhibits global increasing returns to scale of labor, N, if a > 1 and local economies of scale if a∈(0.5, 1). Hence, the ex post production function for the firm may emerge from the division of labor as the general equilibrium shifts from autarky to structure E. The ex post production function in E is not only different from the ex post production function in autarky, but also different from the ex ante production functions in (8.1), which do not involve the firm and economies of scale of the firm. Rosen (1977) was the first economist to spell out the distinction between ex ante and ex post production functions. George Stigler (1953) noted the discontinuous jumps of cost functions, which are based on the production function, as a result of changes in the level of specialization for the firm. In the Smithian framework, the production function 256

for the firm may emerge from individuals’ decisions in choosing a certain structure of transactions required by the division of labor. In particular, the production function for a firm is a combination of many individuals’ production functions. An owner of the firm combines her system of production with all employees’ systems of production to get a system of production for the firm. This implies that in the Smithian framework, the firm is no longer a black box represented by an ad hoc production function for the firm. The theory of the firm in this chapter has spelled out how the production function for the firm emerges, and what are the development implications of the internal organization of the firm.

8.5. Coase Theorem and Other Theories of the Firm

From the discussion in the previous subsections, we can see that division of labor are necessary but not sufficient for the existence of economies of the firm. This proposition was first proposed by Coase (1937). As Cheung (1983) argues, the other necessary condition for the existence of the firm is that the transaction efficiency for intermediate goods must be lower than that for labor employed to produce the intermediate goods. Cheung’s theory refines Coase’s idea about the firm. Coase (1937) argues that the institution of the firm is used to replace the market with administration within the firm. According to Cheung, the institution of the firm replaces the market for intermediate goods with the market for labor, instead of replacing the market with a non-market institution. Coase (1960) claims that the structure of ownership makes no difference to the efficiency of the market if the transaction cost is zero, and that the market will choose a structure of ownership to maximize the benefit of division of labor, net of transaction costs (the Coase theorem). Our model substantiates the Coase theorem. From Table 8.1, it is obvious that structures D, E, F generate the same per capita real income if t = k = s = r = 1 (no transaction costs). The structure of ownership of the firm makes a difference only if transaction costs are not zero. Also, proposition 8.1 implies the second statement of the Coase theorem, that the market will choose the most efficient structure of ownership and property rights. We have refined Coase’s ideas about transaction costs. He claims that the institution of the firm can be used to reduce transaction costs. But our proposition 8.1 implies that as transaction efficiency is improved, total transaction costs will be increased as the general equilibrium shifts from autarky to structure E or F. Hence, the institution of the firm may increase transaction costs when it promotes division of labor, as long as increased economies of division of labor outweigh the increased transaction costs. From Table 8.2, we can see that for t < sa and k9 > k > k8, k10, the institution of the firm in structure E generates the highest per capita real income and productivity, while the division of labor in structure D generates a lower per capita real income than in autarky. Hence, if the institution of the firm is not allowed, the division of labor will not be chosen and autarky with low productivity will be chosen. If the institution of the firm is allowed, then individuals will choose the division of labor and associated high productivity in structure E. Hence, the institution of the firm can promote the division of labor and economic development by reducing transaction costs compared to D and by

257

increasing transaction costs compared to autarky. Hence, a good legal system that protects residual rights of owners of private firms is a very important driving force of economic development. Recent literature on the theory of the firm comprises three sub-fields. One of them is represented by the Hart-Grossman-Moore model of incomplete contract and two-sided moral hazard (see chapter 9 and Hart 1995). As pointed out by Holmstrom and Roberts (1998, pp. 79-82), the model of incomplete contract simultaneously addresses the benefits and the costs of ownership. Markets are identified with the right to bargain and, when necessary, to exit with the assets owned. This greatly clarifies that market’s institutional role, as well as its value in providing entrepreneurial incentives. On the other hand, firms are poorly defined in the model of incomplete contract. Also, it cannot explain the difference between contractual arrangements between Japanese companies and US companies. It cannot explain the complex network of contracts in the new high-tech sector that does not always use integration to avoid the temptation to exploit partners using their lock-in investment that is relationship-specific. Recently, the model of incomplete contract is criticized by Maskin and Tirol (1999a, b), who show that unforeseeable contingencies (which are often invoked in order to justify contractual incompleteness) and sequential rationality (parties must foresee the payoff consequences of contracts and investments) are incompatible. They show that even ex ante undescribability is often irrelevant, since sophisticated mechanisms can be used to implement the same payoff outcomes as if contingencies were describable. Our model in this chapter shows that a theoretical foundation for investigating emergence and evolution of the institution of the firm and related structure of residual rights can be established in the absence of undescribability. However, labor contract in the model in this chapter can be interpreted as incomplete contract in the sense that it requires the employee to do whatever he is told to do rather than specifying exactly what he is supposed to do. The second research line in this literature is represented by Holmstrom and Milgrom (1994). Related to this research line, many models of multiple layers of principal-agent relationships are developed (see Gibbons, 1998 and Bolton and Scharfstein, 1998 for recent reviews). Holmstrom and Milgrom argue that the function of firms cannot be properly understood without considering additional incentive instruments that can serve as substitutes for outright ownership. Employees, for instance, typically own no assets, yet they often do work quite effectively. In these theories, asset ownership gives access to many incentive instruments and the role of the firm is to coordinate the use of them all. That may also explain why non-investing parties, including the firm itself, own assets. They use BskyB, a satellite broadcasting system in Rupert Murdoch’s media empire, as an example to motivate their model (see Holmstrom and Roberts, p. 85). This company is an example of a highly successful organization that has created its wealth, not by owning physical assets, but by crafting ingenious contracts that have given it influence over an effective network of media players. Satellite broadcasting requires a variety of highly complementary activities, including acquisition and development of programming, provision of the distribution system (satellites, transmitters, and home receivers) and development of encryption devices (to limit reception to those who pay), all of which must be carried out before the service can be offered.

258

An example of how agency issue can affect the boundaries of an organization is whether a firm employs its sales force directly or uses outside sales agents. The bestknown example here involves electronic parts companies, some of which hire their own sales agents while others sell through separate supply companies (see Holmstrom and Roberts, 1998, p. 86). Originally, is was expected that the observed variation in this choice would relate to the degree of asset specificity; for example, the extent to which investment by sales people with knowledge about products was specific to a particular company. Instead, measurement costs and agency concerns turned out to be central. An employee sales force is used when individual performance is difficult to measure and when non-selling activities (like giving customer support or gathering information about customers’ needs) are important to the firm; otherwise, outside companies are used. Holmstrom and Milgrom (1991, 1994) rationalize this pattern with a model of a multi-task agency, in which salespeople carry out three tasks: making current sales, cultivating long-term customer satisfaction, and gathering and relaying information on customer needs. If the latter two activities are important and if the three activities compete for the agent’s time, then the marginal rewards to improved performance on each must be comparable in strength; otherwise, the ill-paid activities will be slighted. Because performance in non-selling activities is arguably hard to measure, it may be best to provide balanced, necessarily lower-powered incentives for all three activities. Offering weak incentives to an outside sales agent can be problematic, however, because the agent may then divert all effort to selling other firms’ products that come with stronger rewards for sales. With an employee, this problem can be handled with a salary and a low commission rate, because the employee’s outside activities are more easily constrained and promotion and other broader incentives can be used within the firm to influence the agent’s behavior. One of the Holmstrom and Milgrom models is presented in example 9.3. A synthesis of the theory in this chapter and Hart’s theory of incomplete contract, and Maskin, Tirole, Milgrom, and Holmstrom’s criticisms can be found from exercise 17 in chapter 9. The model in this chapter complements the Holmstrom and Milgrom model with the trade off between stronger incentive and greater measurement costs. Our model explains why residual rights of the entrepreneur who designs contractual arrangements that efficiently trade off incentive provision against measurement costs, are essential for her to have the right incentive to sort out the efficient trade off. Her entrepreneurial services are intangible intellectual properties that can be indirectly priced only via residual rights, the institution of the firm, and the related labor market. The case of the franchise network in question 31 of chapter 1 shows that when transaction efficiency of intangible intellectual properties can be effectively priced via a hostage mechanism, the division of labor between the production of intellectual properties and the production of tangible services can be organized by market relationships between the franchiser and franchisees. The third subfield in this literature focuses on the pyramidal structure of hierarchy. A recent survey of this subfield can be found from Borland and Eichberger (1998). The pyramidal structure of hierarchy investigated in this literature may not necessarily be related to asymmetric residual rights to returns and control, which are essential for the existence of the institution of the firm. The relationship between the theory of the firm in this chapter and hierarchical structure of transactions, division of labor, and residual rights can be found from Shi and Yang (1998) and Yang (2000, chapter 20).

259

Finally, a literature on the reliability of an economic system has been developed to address the problems that relate to the theory of the firm. This literature is more relevant to the problems of economic development that are addressed in chapter 10, and we will discuss it in that chapter. Recent reviews of this literature can be found from Sah (1991), Kremer (1993), Blanchard and Kremer (1997), and Lio (1998). Key Terms and Review Institution of the firm Economies of specialization in producing a good requiring more than one input factor Relationship between economies of specialization in producing a good, economies of division of labor, and economies of the institution of the firm Distinction between ex ante and ex post production functions Necessary and sufficient conditions for the emergence of the firm from division of labor Function of the institution of the firm and implications of the internal organization within the firm for the equilibrium level of division of labor and productivity Relationship between individuals’ production functions and the production function of a firm Difference between rights to residual returns and rights to residual control and the relationship between those residual rights and the function of the institution of the firm Role of freedom of choice of profession configuration and freedom of enterprise in enabling the institution of the firm to play its function Significance of a legal system that protects the residual rights of the owners of the firm in enabling the institution of the firm to play its function

Further Reading Theory of the firm: Cheung (1983), Coase (1937, 1991), Alchian and Demsetz (1972), Jensen and Meckling (1976), Knight (1925), Stigler (1951); Theory of incomplete contract: Hart (1995), Grossman and Hart (1986), Hart and Moore (1990, 1999), Maskin and Tirole (1999a, b), Tirole (1999), Segal (1999); Theory of the firm and endogenous specialization: Bolton and Dewatripont (1994), Carter (1995), Shi and Yang (1998), Yang and Y-K. Ng (1993, ch. 9), Yang and Y-K. Ng (1995), Borland and Yang (1995), Yang (1988); Models with the trade off between incentive provision and measurement costs: Bolton and Scharfstein (1998), Holmstrom and Milgrom (1991, 1994), Holmstrom and Roberts (1998); Theory of the firm and endogenous transaction costs: Milgrom and Roberts (1990, 1992), Kreps (1990), Lewis and Sappington (1991), Aghion and Tirole (1997), and Gibbons (1998); Theory of the firm and commitment game: Dewatripont and Maskin (1995), Dewatripont and Roland (1995), Roland (2000), Dewatripont (1988), Qian (1994b); Hierarchy: O. Williamson (1967), Tirole (1986), Bolton and Dewatripont (1994), Borland and Eichberger (1998), Yang and Ng (1993, ch.14), Yang (2000, ch. 20), Van Zandt (1995), Bac (1996), Bag (1997), Calvo and Wellisz (1978, 1979), Keren and Levhari (1982), MacLeod and Malcomson (1988), Qian (1994a), Radner (1992, 1993); Empirical evidence against the type II scale effect: Aiginger and Tichy (1991), Loveman and Sengenberger (1991), Liu and Yang (2000), Murakami, Liu, and Otsuka (1996), Y. Zhang (1999), Berger and Ofek (1995), Bhagat, Shleifer, and Vishny (1990), Comment and Jarrell (1995), Fauver, Houston, and Naranjo (1998), Kaplan, and Weisbach (1992), Lang and Stulz (1994), Servaes (1996).

260

Questions 1. Alchian and Demsetz (1972) indicate that the claim of the owner of the firm to its residual returns is the distinguishing feature of the capitalist firm. If the marginal productivities of the members of the production team are interdependent, then each member does not count the effect of her effort on others’ productivity if her pay is determined by her marginal productivity in the market, thereby resulting in distortions. Hence, a monitor is essential to measure the efforts of the members and pay them according to their effects on the productivity of the entire team. But by what mechanism can the effort level of the monitor be efficiently determined? According to Alchian and Demsetz, the residual returns to the ownermonitor of the firm are the efficient institution for achieving this. Without a claim on the residual returns, nobody will have an incentive to ensure the efficient management of the firm. Hence, so called X inefficiency, which means that productivity potential cannot be exploited even if it is technically easy to achieve, will emerge from the absence of claimants to the residual returns of the firm. This is why all state-owned firms, which have no individual residual rights claimants, are associated with significant X inefficiencies. Two criticisms of Alchian and Demsetz’ theory may arise. One is proposed by Grossman and Hart (see chapter 9), who argue that the capitalist firm is distinguished not only by the asymmetric distribution of residual returns, but also by the asymmetric distribution of residual control, which imply that the owner of the firm has rights to dispose of the assets and labor of the firm. In chapter 9, the rationale for the asymmetric distribution of residual control rights will be investigated. The second criticism is that if the pricing of the effort level of the monitor is highly efficient, the production team can pay the monitor according to her performance. Interdependence of the marginal productivities of members in a production team does not necessarily imply that residual returns are the only way to resolve the problem. It is because the pricing efficiency of the monitor’s effort is even lower than the pricing efficiency of the efforts of the team members that the claim to residual returns emerges as an institution to indirectly price the effort level of the monitor. Comment on these criticisms of the Alchian-Demsetz argument. 2. Rosenberg and Birdzell (1986, pp. 145-183) have documented the history of the emergence and evolution of the firm. Use the model in this chapter, in connection to the model in chapter 11, to analyze the historical fact. “(p. 145) Starting about 1750, the factory system of production gradually became dominant in most of Western industry. It changed relationships in the workplace and, probably with more drastic social effect, changed the location of the workplace from the household to the factory. The shift to the factory was practically complete by 1880, but most commercial and industrial enterprises continued to be organized as individual proprietorship, with the exception of banks and railways. Between 1750 and 1880, the respect of the Western governments for the autonomy of the economic sphere became virtually an ideology. Apart from such sporadic intrusions as the British Factory Acts and Bismarck’s system of social insurance, governments were content to assist only when asked. Peacetime taxes were small and currencies comparatively stable (p.145).” “(p. 159) The textile industry led factory development during the first decades of the Industrial Revolution, not only in England but also in the United States. Richard Arkwright, inventor of a spinning machine, came to be known as the ‘father of the English factory system,’ owing to the numerous cotton spinning mills he promoted. The early textile mills were also a principal object of the public agitation that led to the first English factory legislation. Arkwright’s patent for a spinning machine supplies an approximate date, 1769, for the beginning of the conversion. In the British textile industry, firms tended to specialize in a single step in the process of producing cotton cloth. Instead of building fully integrated plants of the type used in the iron and steel industry and in ceramics, the British textile makers located highly specialized plants close to each other. The development of these regional textile complexes was facilitated by the substitution of steam for water power (p.159).” “(p. 167) The pioneer of

261

factory production was Josiah Wedgwood. At his works at Etruria, he divided his factory into departments by type of product and, within each department, workers were classified according to numerous specialties. N. L. Clow describes the division of labor at Etruria as follows. ‘The gradual multiplication of the processes nearby ceramic products could be produced led, as in other industries, to a marked division of labour in Josiah Wedgwood’s Etruria, where the principle of specialization was first introduced, was divided into departments according to the type of ware produced: useful, ornamental, jasper, basalt, and so on. In 1790 some 160 employees were engaged in the ‘useful’ branch, in the following categories: slip-house, clay-beaters, throwers and their attendant boys, plate makers, dish makers, hollow-ware pressers, turners of flat-ware, turners of hollow-ware, handlers, biscuitoven firemen, dippers, brushers, placers and firemen I the glost over, girl colourgrinders, painters, enamellers and gilders, and, in addition, coal getters, modellers, would makers, saggar makers, and a cooper.’ The ceramic industry was typical of later industries in its elimination of any easily visible connection between what a worker does and the marketable product of the worker’s efforts (p.167).” “Recently, Marglin, in comparing factory work to work under the putting-out system, principally as practiced in the British textile industry, has specified the following advantages of the factory to its owners: (1) stealing of materials and work in process by workers could be reduced; (2) unskilled women and children were capable of doing the narrowly specialized factory jobs and accepted lower wages for equivalent output than the more highly skilled adult male labor used in the putting-out system; (3) factory hands could be induced, by the threat of dismissal for absenteeism, to work regularly for a full week instead of working the partial and uncertain week common among cottage workers (p.179).” “By 1880, the change to market relations was substantially complete. By then, terms of employment were determined by employer offers of terms and employee acceptances, and, as in any other market, both offers and acceptances were influenced by the state of the supply of, and the demand for, labor (p.183).” 3. John bought from James a copying shop at $110,000, which did not include the rental of the real estate and copy machines. Each year, John can make up to $40,000 as profit net of all rents for real estate, copy machines, other equipment, and the wage bill for the machine keepers and for himself. James told John that the good will of the business, embodied in the client base that he had cultivated over the years, as well as his planning in putting together his client base, the location of the shop, the machines, and other factors in the right way were worth more than $110,000. This was verified by the fact that by his fourth year in the business, John had repaid his investment of $110,000 and interest, and started to make a net profit. Use this case to analyze why the shop could make a net profit and why the intellectual property of James could not be appropriately priced in the absence of the institution of the firm. 4. Use the model in this chapter to analyze increases in labor and capital shown in statistical data. According to neoclassical economics, observed increases in labor and capital inputs are simply increases in production factors employed in production. But according to the theory in this chapter, an increase in trade of labor is the result of the development of the institution of the firm, while an increase in trade of capital goods is the result of the development of division of labor in roundabout production between firms and individuals. The two phenomena can take place in the absence of increases in the total amounts of primary factors employed in production for society as a whole. Discuss the implications of the difference between these two interpretations of the data. 5. In the 19th century, France, Germany, and other major European countries followed Britain in enacting laws guaranteeing the right of free association. Analyze the implications of these laws, in conjunction with patent laws, automatic registration of company, and laws that protect private property rights, for economic development and the evolution of division of labor. In Japan and China, such laws did not exist until the end of the 19th century. Emperors

262

6.

7.

8.

9.

10.

11.

12.

were extremely sensitive to unofficial free associations and tended to infringe arbitrarily upon the residual rights of the owners of firms. Use that institutional feature, in relation to the theory in this chapter, to explain the following historical fact documented by Elvin (1973). Song China (960-1270 A.D.) possessed both the scientific knowledge and the mechanical ability to have experienced a full-fledged industrial revolution some four centuries before it occurred in Europe. The Chinese developed very elaborate contracts and sophisticated commercial organizations, but failed to have an industrial revolution at that time. Under a regime of free association, any individual can set up a firm by registering his firm with the local government. But in many less developed countries, a resident needs to apply for approval from the government to set up a firm. Many times, such as in the case for setting up a company engaging in foreign trade, a government license is essential. Also, the government agency which has such approval power has vested interests in the business in which the applicant wants to engage. For instance, in each Chinese city, there is a government committee with the approval power for setting up wholesale and retail firms. This committee is also the owner of the government monopolist wholesale and retail network in the city. Analyze the development implications of such an approval system in connection to the theory of the firm in this chapter. Apply the theory of the firm in this chapter to analyze the role of multinational firms and foreign direct investment (FDI) in economic development. Under what conditions can multinational firms more efficiently protect the rights to intellectual properties (know-how) than direct trade of the intellectual properties? In many developing countries, the governments require that foreign ownership share of firms cannot exceed a certain percentage. What are the effects of such regulation on economic development? In many joint-venture businesses between foreign companies and Chinese government, the government has control rights and owns more than 50% of the businesses. But joint-venture between a government agency and foreign private firms is very unusual in a free market economy. Analyze the implication of the institutional difference for economic development in connection to the theory in this chapter. In all Soviet-style economies, there are no laws that protect residual rights to firms. Due to Marx's ideology, in a Soviet-style socialist country such residual rights are considered to be the source of exploitation. Also, a Soviet-style government prohibits unofficial free association (including free enterprise) for political reasons. Apply the theory of the firm to analyze the implications for economic development of these institutional features of the Soviet-style economy. Many development economists argue that entrepreneurship is essential for economic development (see, for instance, Bauer and Yamey, 1957, and Kindleberger, 1958). Use the theory in this chapter to analyze the conditions for the nurture of entrepreneurship. Apply the theory of indirect pricing in this chapter to analyze why it is the shareholders rather than the managers of a company who are the owners when the division of labor between portfolio management and production management emerges. In the Soviet-style economic system, land cannot be privately owned or traded. Only pricing according to working effort is legitimate. Making income from the ownership of assets, including land and shares of the firm, is regarded as exploitation. Analyze why, under these institutional arrangements, intangible services in managing real estate will be under-priced and be short of supply. Many economists claim that the function of the institution of the firm is to internalize externalities. Coase also claims that the institution of the firm replaces market transactions with non-market arrangements with centralized planning within the firm. Apply the theory of indirect pricing to comment on this view. You may relate your discussion to Cheung’s view that the institution of the firm replaces the market for intermediate goods with the labor market. Apply the model in this chapter to substantiate Cheung, Coase, Stigler, and Young’s argument that the firm size is irrelevant to the realization of returns from the division of labor.

263

The widely cited thesis of Coase (1937) states that the firm and the market are substitutes for each other in organizing the division of labor. Cheung (1983) further suggests that the firm should be viewed as one type of contract under which a factor owner surrenders a delimited set of rights to use his or her factor in exchange for income. Therefore, a clear distinction is drawn between the firm size and the scale of division of labor. On the one hand, an increase in the firm size simply indicates that the number of one type of contract increases. As this can be achieved by decreasing the number of other types of contracts, there exists the possibility that the firm size increases but the level of division of labor remains the same or even decreases. On the other hand, since factory owners can choose different types of contracts to coordinate division of labor, economies of division of labor do not always lead to large firms. As Cheung (pp. 5-6) clearly puts it “Could it be that specialization, coordination, and economy of scale achieved by pooling input resources from many owners will yield higher income for all, so that each chooses to joint a firm… the answer is no… benefits arising from specialization and coordination can be realized without the “factor market”—the right to decide and use one’s input need not be delegated to some agent or entrepreneur, because in a product market the input owner will receive a payment for every contribution.” 13. There are many reports from the media in the 1980s and 1990s (see, for instance, “Enterprise: How Entrepreneurs are Reshaping the Economy and What Big Companies Can Learn,” Business Week, October 22, 1993, Special Issue, “Management Focus,” The Economist, March 5, 1994, p. 79, and “Manufacturers Use Supplies to Help Them Develop New Products,” Wall Street Journal, 19 December, 1994, p. 1) about de-integration, focusing on core competence, increasing specialization, contracting out or outsourcing, which feature recent changes of company structure. Use the theory in this chapter to explain the phenomena. 14. Use the theory of the firm in this chapter to analyze the implications of minimum wage laws. Then compare your results to the neoclassical analysis of the effects of such laws. 15. Holmstrom and Roberts (1998, p. 78) indicate that according to the Hart-Grossman-Moore model, as investment by the buyer B becomes more important relative to investments by the seller S, B should be given more assets. If an asset has no influence on B’s investment, it should be owned by S. For this reason, no outsider should ever own an asset that would waste bargaining chips that are precious for incentive provision. For the same reason, joint ownership, meaning that both parties have the right to veto the use of the asset, is never optimal. As a consequence, assets that are worthless unless used together should never be separately owned. Extend the model in this chapter to predict that outside shareholders should own a firm if the division of labor between portfolio management and production management occurs, and if the transaction efficiency for input and output of portfolio management is lower than that for other activities. Specialization in producing x and specialization in producing y are complementary. Each of occupations (x/y) and (y/x) has no value if it is not matched up by the other. But in the model in this chapter, separate ownership of x and y may occur in equilibrium. Use this to discuss the difference between the model in this chapter and the Hart-Grossman model in chapter 9.

Exercises 1. Assume that there is no transaction cost in the model in this chapter. But the government imposes a value tax rate t on goods sold and then returns to the sellers of goods the tax revenue collected from them. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the impact of the tax rate on the equilibrium level of division of labor and productivity and the equilibrium structure of residual rights.

264

2. Assume that in the model in exercise 1, a fraction of tax revenue 1-s is used to maintain the government bureaucratic apparatus, so that only the fraction s of the tax revenue goes back to the sellers of goods. Solve for the general equilibrium and its inframarginal comparative statics again. Analyze the impact of the bureaucracy efficiency coefficient s on the equilibrium level of division of labor and productivity. 3. Now suppose that in the model in exercise 1, the government imposes a value tax on the sale of labor instead of on the sale of goods. Then it returns all tax revenue to the sellers of labor. Solve for the general equilibrium and its inframarginal comparative statics. Analyze the impact of the tax on the equilibrium level of division of labor and productivity. Compare your answer here to that in exercise 1. Then analyze the impacts of different tax regimes on the equilibrium structure of transactions, residual rights, and ownership of the firm. 4. Assume that in the model in exercise 3, a fraction of tax revenue 1-θ is used to maintain the government bureaucratic apparatus, so that only the fraction θ of the tax revenue goes back to the sellers of labor. Solve for the general equilibrium and its inframarginal comparative statics again. Analyze the impact of the bureaucracy efficiency coefficient θ on the equilibrium level of division of labor and productivity. Compare your answer here to that in exercise 2. Then analyze the impacts of bureaucracy efficiency θ and different tax regimes on the equilibrium structure of transactions, residual rights, and ownership of the firm. 5. Analyze the impact of various tax regimes in exercises 1 and 3 on trade volume of labor and intermediate goods, which can be observed from statistical data. Explain why, within the Smithian framework, an increase in labor trade implies the development of division of labor within the firm or the replacement of the market for intermediate goods with the institution of the firm as a vehicle to organize the division of labor, while an increase in capital trade may be associated with the development of division of labor in a roundabout production chain. Both phenomena can occur in the absence of changes of total endowments for society as a whole. 6. Suppose that transaction cost is 0 in the model in this chapter, but the government enforces a minimum wage law which requires the wage rate to be higher than a constant θ. Analyze the general equilibrium implications of the minimum wage. 7. Assume that the production function in (8.1b) is replaced with x + x s = lx − b . Solve again for the general equilibrium and its inframarginal comparative statics. 8. (Yang, 1988) Add one more consumption good to the model in this chapter, so that the utility function becomes u=(y+kyd)(z+kzd), where z is the new consumption good. Solve for the general equilibrium and inframarginal comparative statics. Note that in this model, lemma 8.1 may not hold. 9. Assume that the production function (8.1a) is replaced with y + y s = Min{ x + tx d , l y }. Solve for the general equilibrium and inframarginal comparative statics. Add a fixed learning cost to the production function, so that y + y s = Min{ x + tx d ,ly − a }. How will your answer change? 10. (Yang and Ng, 1995) Assume that in the model in this chapter the transaction cost of labor is specified as a loss of goods produced by the employee in transit from the employee to the employer. The algebra can be significantly simplified. Solve for the general equilibrium and inframarginal comparative statics. 11. Consider the Liu and Yang model (2000) where each of M ex ante identical consumerproducers has the utility function u = z+kzd, where good z is food. Her system of production is Li ∈ [0, 1], i=z,x,y. x is the z+zs=(x+rxd)1/2Lz, x+xs = (y+tyd)1/2Lx, y+ys = Ly2 , Lz+Lx+Ly = 1, hoe used to produce food and y is the steel used to produce the hoe. If we ignore differences in the ownership structure of the firm, then there are 9 structures. Structure A is autarky. Structure with partial division of labor P(y) consists of configurations (zx/y), selling z, self-providing x,

265

and buying y, and (y/z), selling y and buying z. Structure with partial division of labor P(x) consists of configurations (xy/z), selling x, self-providing y, and buying z, and (z/x), selling z and buying x. Structure with partial division of labor and the firm FP(y) consists of configurations (zx/Ly), selling z, self-providing x, and buying labor Ly, and (Ly/z), selling labor Ly and buying z. Structure with partial division of labor and the firm FP(x) consists of configurations (Lx/z), selling labor Lx and buying z, and (z/Lx), selling z and buying labor Lx. Structure with the complete division of labor C consists of configurations (z/x), (y/z), and (x/yz). Structure with the complete division of labor and the firm FC(y) consists of configurations (Lx/z), (y/z) and (z/Lxy) selling z and buying y and Lx. Another structure with the complete division of labor and the firm FCL consists of configurations (Lx/z), (Ly/z), and (z/LxLy), selling z and buying Lx and Ly. Solve for the general equilibrium and its inframarginal comparative statics. Show that a complete division of labor structure, with the producer of x hiring labor to produce y within the firm and buying z from an independent specialist of z, cannot be a general equilibrium structure if t1 if an individual chooses a configuration of employer, E = ρ < 1 if she chooses a configuration of employee, and E = 1 if she chooses a configuration involving no asymmetric relationship between an employer and an employee. Solve for the general equilibrium and its inframarginal comparative statics. The solution is the same as in example 8.1 if β=0. Analyze the implications of the parameter of pursuit of relative position β≥1 for the equilibrium level of division of labor and the equilibrium structure of residual rights. Use this model to explain the effect of a strong labor union and regulations on the welfare of workers on the equilibrium level of division of labor, the relative number of employers and employees, and economic development.

266

Chapter 9: Endogenous Transaction Costs, Contract, and Economic Development

9.1 Endogenous Transaction Costs and Economic Development From the previous chapters, we can appreciate the importance of transaction costs for the evolution of division of labor and economic development. However, Barzel (1985) has raised the question: “Is transaction cost just cost?” This question draws the difference between endogenous and exogenous transaction costs to our attention. O. Williamson (1985) clearly draws the distinction between endogenous transaction costs caused by opportunistic behavior (holding up, cheating, and not-credible commitment) and tangible exogenous transaction costs. North and Thomas (1970) also note the distinction between endogenous transaction costs caused by moral hazard, adverse selection, and other types of opportunism and exogenous transaction costs. Exogenous transaction costs are those costs incurred directly or indirectly in the transacting process, and not caused by distortions as a result of conflicts of interests of decision makers. In the preceding chapter, the cost coefficient for each unit of goods purchased is an exogenous transaction cost, since it can be seen before individuals have made their decisions and it is not associated with any distortions generated by interest conflicts between self-interested decisions. Resources used in the transportation of goods are direct exogenous transaction costs. Resources used to produce transportation, communication, and transacting facilities (computers, automobiles, plastic banking cards) used in the transacting process are indirect exogenous transaction costs. Endogenous transaction costs comprise two subcategories: general and specific. General endogenous transaction costs are defined as costs incurred in transactions that can be identified only after all players have made their decisions. In other words, endogenous transaction costs are the consequence of interactions between individuals’ self-interested decisions. Total transaction costs for each individual, and for society as a whole in the preceding chapters, are endogenous, since they are determined by the number of transactions, which is endogenous in the models of endogenous specialization and endogenous number of goods. Since the definition of indirect exogenous transaction cost, such as expenses on automobiles, overlaps the definition of general endogenous transaction costs, we use a narrower definition of endogenous transaction costs in this text. Specific endogenous transaction costs are defined as those endogenous transaction costs that are associated with a departure of equilibrium from the Pareto optimum. In this text, we use the term endogenous transaction costs to represent specific endogenous transaction costs unless indicated otherwise. Endogenous transaction costs are caused by a particular human behavior. There are three types of human behavior. The first, called non-strategic self-interested behavior, has the feature that decision makers do not react directly to others’ decisions, but rather react only to prices. Behavior examined in chapters 3, 4, 7, and 8 is non-strategic behavior. The consumer’s price taking behavior in chapters 5 and 6 is non-strategic, too. The second type of behavior, called strategic behavior, has the feature that decision makers directly react to others’ decisions. This type of behavior can be classified into two subcategories: 271

non-opportunistic behavior and opportunistic behavior. Non-opportunistic strategic behavior is distinguished by the characteristic that a player’s interests are not pursued at the cost of other players’ interests. The self-interested behavior in the Nash bargaining game in this chapter is non-opportunistic strategic behavior. Opportunistic behavior is that form of strategic behavior in which a player’s interests are pursued at the cost of other players’ interests. Endogenous transaction costs are caused by opportunistic behavior in competing for a greater share of the gains from the division of labor between players. The implications of endogenous transaction costs for the equilibrium network size of division of labor and economic development are more important than those of exogenous transaction costs, since endogenous transaction costs are determined by individuals’ decisions and their choice of institutional and contractual arrangements. For example, the Industrial Revolution, which featured rapid evolution of division of labor, took place in Britain partly because the Statute of Monopolies (1624) made it the first country to have patent laws, significantly reducing theft (a type of opportunistic behavior) of intellectual property that incurs endogenous transaction costs. As shown by North and Weingast (1989), the most important driving force for the successful industrialization of Britain was the evolution of that country’s institutions in the 17th century that entailed the government’s credible commitment to constitutions. This significantly reduced state opportunism and therefore greatly reduced rent seeking in society and related endogenous transaction costs. According to Olson (1996), a typical Haitian immigrant’s productivity and real income under the institution of the US. was about five times higher than her productivity and real income under the institution in her home country in 1980. He compared per capita income between a new German immigrant and a new Haitian immigrant and attributed the difference to the difference in human capital and culture between the two groups of immigrants. After the deduction of the effects of this difference, he showed that the major part of the remaining difference in per capita real income between a local Haitian and a Haitian new immigrant cannot be explained by the differences in physical capital, resource endowment, human capital, access to technology, population density, and cultural background between Haiti and the US. This difference was mainly due to the endogenous transaction costs caused by the Haitian government's opportunistic behavior under a deficient institution. As shown in the 1997 World Development Report of the World Bank, the major obstacle of economic development is endogenous transaction costs caused by the government’s opportunistic behavior. State opportunism includes the following government behavior. In some less developed countries, government behavior is predatory and expropriate. Government officers use the coercive power of governmental apparatus and taxing power to steal citizens’ property. A typical example is the Duvalier government’s behavior in Haiti during the 1950s and 1960s. According to the World Bank (1997, p. 149), the economic pillars of Haiti’s predatory state were expropriation, extortion, the inflation tax, and corruption. Significant resources were devoted to protecting Duvalier himself, totaling 30 percent of total government expenditures during the first half of the 1960s. Agriculture, particularly coffee, was heavily taxed. Some sources estimate that Duvalier transferred more than $7 million a year out of Haiti for personal purposes. Large-scale

272

bribes also took place, through deals with foreign investors on projects that often never materialized. Extortion under the veil of “voluntary” donations was institutionalized under some political movement. According to Summers (1992), in some Sub-Saharan African countries the government pursued a patronage recruitment policy of government employment and favoritism in issuing trade licenses. Then it purposely distorted exchange rates and prices in favor of the relatives’ trade businesses. In China during the 1960s and 1970s, the government used its monopoly in the banking sector, the distribution network, in the urban real estate sector, and other important sectors to pursue tangible and intangible rents. The approval system for setting up private firms, the strict licensing system for setting up firms of foreign trade, and the monopolized job assignment system were used by the government to discriminate against the private businesses. The government used a procurement system that compelled peasants to sell under-priced agricultural goods to government agents, and the residential registration system that restricted rural residents’ mobility, to pursue the interest of urban residents, including the government elite, at the cost of rural residents. (See Yang, Wang, and Wills 1992). In this process, industrialization and economic development became hostages of state opportunism. Sen (1977), Chang and Wen (1998), and Lin and D. Yang (1998) show that the government’s opportunistic behavior that pursued the interest of urban residents at the expense of rural residents was the main cause of the most devastating famines, involving the loss of up to 30 million lives in China. State opportunism not only causes direct endogenous transaction costs, but it also indirectly encourages citizens’ opportunistic behavior. In the worst case, it causes political instability and wars. According to the empirical evidence in chapter 2, geographical conditions (i.e., bad transportation conditions and tropic ecological conditions) are important factors not only because they directly affect economic performance, but they also created historical conditions for evolution of government behavior. In a relatively well-developed market economy, information asymmetry may result in opportunistic behavior that causes socalled adverse selection and associated endogenous transaction costs. Measuring and monitoring the cost of working effort may result in so-called moral hazard and related endogenous transaction costs. There are several ways to investigate endogenous transaction costs. According to our definition of endogenous transaction costs, the distortion caused by a value tax, monopoly power, externality, and public goods is endogenous transaction cost. In many neoclassical models, monopoly power, information asymmetry, public goods, and externality are all exogenously given. A more realistic approach is to endogenize the degree of monopoly power and externality by specifying some trade offs. The degree of monopoly can be determined in the market as a consequence of interactions between conflicting self-interested decisions. The Dixit-Stiglitz model (example 5.1) is such an example. In the DS model, the efficient trade off between global economies of scale and distortions caused by monopoly power determines the equilibrium degree of monopoly and competition. In chapter 10, the trade offs between economies of division of labor, reliability of the related network of the market, and transaction costs are specified in order to endogenize the degrees of competition and externality.

273

The second way to study endogenous transaction costs is to specify unobservable or unverifiable effort that affects the risk of a bad outcome (hidden actions), or to specify information asymmetry (hidden information), then to investigate endogenous transaction costs caused by moral hazard and information asymmetry. We shall study this approach in sections 9.2 and 9.5, respectively. The third way to study endogenous transaction costs is to use game models to investigate direct interactions between strategic behaviors. The Ricardian model with tariff game in chapter 3 is used to investigate endogenous transaction costs caused by government strategic behavior. In section 9.3, we will use various game models to study opportunistic behavior and endogenous transaction costs. Some dynamic game model with information asymmetry is used to show that endogenous transaction costs may not be as great as predicted by static models with information asymmetry if interactions between strategies and information are considered. In section 9.5, we shall show that dynamic game models can be used to investigate opportunistic behavior and related endogenous transaction costs in the absence of moral hazard and information asymmetry. Our examples illustrate that game theory is a powerful instrument in analyzing complicated strategic interactions that cause endogenous transaction costs. In this chapter, we emphasize that general equilibrium models of endogenous transaction costs are much more appropriate than partial equilibrium models of endogenous transaction costs for studies of interdependence between network size of division of labor, related productivity, and endogenous transaction costs. It is important for appreciating the development implication of endogenous transaction costs to investigate the interdependence. Also, the models of endogenous specialization are essential for the studies. In section 9.2, we study moral hazard and the role of contracts in reducing endogenous transaction costs caused by moral hazard. The Stiglitz model of sharecropping is used as an example of application of the moral hazard model to development economics. In addition, the Holmstrom and Milgrom model is used to investigate the trade off between moral hazard and monitoring costs, that endogenously determines the degree of externality of the efficient contract. In section 9.3, we introduce basic concepts in game theory and major game models, and use the tool to analyze endogenous transaction costs. In particular, a dynamic game model with interactions between strategies and information (sequential equilibrium model) is used to study endogenous transaction costs in the credit market with information asymmetry. In section 9.4, we study endogenous transaction costs caused by adverse selection and holding-up behavior, and the role of reputation in reducing endogenous transaction costs. In section 9.5, we use the Grossman-Hart-Moore model to study the endogenous transaction costs caused by opportunism and incomplete contract. Finally, we use the Dewatripont and Maskin model (1995) to investigate commitment problem and soft-budget constraint that might cause endogenous transaction costs.

Questions to Ask Yourself When Reading This Chapter What are the differences between endogenous and exogenous transaction costs? What is moral hazard and how does it cause endogenous transaction costs?

274

How does the trade off between incentive provision, risk sharing, and monitoring cost determine the efficient degree of externality? What are the functions of the contract in reducing endogenous transaction costs caused by moral hazard? What are the effects of endogenous transaction costs caused by opportunistic behavior on economic development? Why will information asymmetry generate endogenous transaction costs? What is the function of Nash bargaining in avoiding trade conflict and in promoting economic development? What are the effects on economic development of endogenous transaction costs caused by competition to get a greater share of the gains from the division of labor? What is the role of reputation in reducing endogenous transaction costs? How do interactions between dynamic strategies and information asymmetry generate endogenous transaction costs in the credit market? How do non-credible commitment and soft budget constraint generate endogenous transaction costs?

9.2. Endogenous Transaction Costs Caused by Moral Hazard Moral hazard is the departure of equilibrium from the Pareto optimum caused by a special type of information asymmetry. In a model with moral hazard, the effort of one of two trade partners affects the risk of a bad outcome for the business, but the other partner cannot observe the effort level. This implies, for example, that a labor contract to pay a player according to her effort level is impossible; in other words, such a labor contract involves a prohibitively high exogenous transaction cost in measuring working effort. It is assumed that the direct effect of effort on the utility of the player choosing that effort is negative, so that if a pure or noncontingent single price is paid for the good or service that is provided, or if there is no contract, then the lowest effort level will be chosen. Hence, contingent contracted prices of goods or services become essential for reducing such endogenous transaction costs caused by moral hazard. Usually, there are three periods in a model of moral hazard. In period 1, the outcome of the business is yet to be realized, but probabilities for bad and good outcomes, and the relationships between those probabilities and one party’s effort levels, are common knowledge to all players. Two parties sign a contract in period 1 that determines terms of the deal after the realization of an outcome. In period 2, players choose effort levels for the given contractual terms. In period 3, Nature chooses an outcome according to the probabilities and players’ effort levels. Then contractual terms are implemented and gains from the business are divided. Here, the assumption that the effort level is unobservable and must be chosen before the realization of an outcome is essential to the story. This implies that the player who chooses her effort level has an incentive to cheat. Even though her real effort level may be low, and a bad outcome may be partly attributable to this, she may claim that her effort level is high, and that the bad outcome is just a result of bad luck that is out of her control. The driving force of the story of moral hazard is a trade off between efficient incentive provision and efficient risk sharing. The two players should somehow share the

275

risk of a bad outcome. But if one player cannot see the other player’s effort levels, which affect the risk, then the effect of the low effort level on the risk cannot be distinguished from bad luck. Hence, there is a conflict between incentive provision and risk sharing. If a bad outcome occurs, the player who chooses the effort level should be penalized as far as incentive provision is concerned. But she should not be penalized too severely as far as risk sharing is concerned. Hence, a contract is used to minimize endogenous transaction cost by efficiently trading off risk sharing against incentive provision. In working out the contractual terms, each player should prepare for the worst that could result from the players’ opportunistic behavior. This will ensure that both behave decently ex post. If a player behaves like a decent gentleman ex ante, without taking account of possible opportunistic behavior on each sides, then he will behave very opportunistically ex post, so that a bad outcome is more likely to occur. Since effort level is not an uncertain variable for the player who chooses the effort, information asymmetry in a model of moral hazard is different from that which we will study in sections 9.3 and 9.4. Hence, information asymmetry is referred to as hidden action in a model of moral hazard, and as hidden information in a model of adverse selection studied in sections 9.3 and 9.4. Distortions caused by hidden information are referred to as endogenous transaction costs caused by adverse selection. In this section we first study three neoclassical principal-agent models. We then study a principal-agent model with endogenous specialization and moral hazard. We shall explore the role of contingent contract in reducing endogenous transaction costs and in raising productivity. Before specifying the models, we need to learn some important concepts: expected utility function, risk aversion, and certainty equivalent. Consider a random variable x ∼ N( x , σx), where x = E(x) = ∑s∈S p(s)x(s) is the expected value of x and σx = Var(x) = E[(x- x )2] = ∑s∈S p(s)(x(s)- x )2 is the variance of x. The theory of expected utility establishes conditions under which a decision maker will rank risky prospects according to their associated expected utilities. Let u be a function that assigns to each monetary outcome x a utility u(x). Then, representing prospects by random variables, the expected utility of prospect x is E[u(x)]. For simplicity of presentation, suppose that there are only two contingent states of an event, x1 and x2. An individual’s utility function f(x) is strictly concave, so that: f (αx1 + (1 − α ) x 2 ) > αf ( x1 ) + (1 − α ) f ( x 2 ) (9.1) where α∈(0, 1) and x1 and x2 are two different consumption bundles (vectors). If we interpret α as the probability for state x1 and 1-α as the probability for state x2, then the weighted average x = αx1+(1-α)x2 is equivalent to an event with no uncertainty, or a consumption bundle that can be received through an insurance program which, by pooling risk, guarantees that the insured can receive the weighted average. Hence, (9.1) implies that a person prefers the weighted average of the two contingent states, which does not involve risk, over the contingent event. Hence, we say that the person is risk averse. This implies that a person is risk averse iff her utility function is strictly concave in contingent variables. The person is risk loving if the inequality in (9.1) is reversed. The person is risk neutral if the inequality in (9.1) is made an equality. (9.1) is referred to as Jesen inequality, which is illustrated by Fig. 9.1.

276

Figure 9.1: Risk Aversion and Strictly Concave Utility Function A twice continuously differentiable function with two independent variables is strictly concave if and only if ∂2f /∂xi2 < 0 and (∂2f /∂x12) (∂2f /∂x22)-(∂2f /∂x1∂x2) > 0. The concept of certain equivalent wealth is often used in the theory of contract. We now define this concept. Let us compare the expected utility of prospect x, E[u(x)], with a certain prospect, that is, one that yields the payment xˆ with probability 1. The certain prospect will be indifferent for the decision maker from the risky prospect x if u( xˆ ) = E[u(x)]. xˆ is then called the certain equivalent of the prospect x. Suppose that u is three times continuously differentiable and that u'(.)> 0. Then, approximately, the certain equivalent is (9.2)

xˆ ≈ x -0.5r( x )Var(x)

where r( x ) = -u"( x )/u'( x ), which is called the degree of risk aversion, at x . We can use Taylor's theorem to prove this. Var(x) is the variance of x. According to this theorem, for any z, u(z) = u( x )+(z- x )u'( x )+0.5(z- x )2u"( x )+R(z), where R(z) = u"'( zˆ )(z- x )2/6 for some zˆ ∈[ x , z] which is negligible. Hence, u(z) ≈ u( x )+(z- x )u'( x )+0.5(z- x )2u"( x ). Substituting x for z in this equation and computing the expectation, we find E[u(x)] ≈ u( x )+E[x- x ]u'( x )+0.5E[(x- x )2]u"( x ), where E[x- x ] = 0. Therefore, we have:

E[u(x)] ≈ u( x )+0.5E[(x- x )2]u"( x ) Applying Taylor's theorem again to u( xˆ ), where xˆ is close to x , yields u( xˆ ) = u( x )+( xˆ x )u'( x )+Q( xˆ ), where Q( xˆ ) = 0.5[( xˆ - x )2]u"( zˆ ), which is negligible for some zˆ ∈[ x , xˆ ]. Hence, we have: u( xˆ ) = u( x )+( xˆ - x )u'( x ) For a certain equivalent, we have u( xˆ ) = E[u(x)]. So, combining the above two equations, we have: ( xˆ - x )u'( x ) ≈ 0.5E[(x- x )2]u"( x )

277

Rearrangement of this equation yields (9.2). On the basis of our definitions of expected utility, risk aversion, and certainty equivalent, we can now study models of moral hazard. Example 9.1: A neoclassical principal-agent model (Diamond, 1983). There are two players in the model: principal and agent. The principal (he) cannot take care of his own business and must hire the agent to do the job. The agent (she) cannot have her own business and must work for others. The agent is risk averse and her utility function is ua = M − e , where M is the payment she receives from the job. Her effort level can be e = 1 or e = 0. If e = 1, the revenue of the project is: ⎧16 with probability 3 4 R =⎨ ⎩4 with probability 1 4 If e = 0, then: ⎧16 with probability 1 4 R =⎨ ⎩4 with probability 3 4 The principal’s utility is u p = R − M , which is linear in the contingent variable R. Hence, the principal is risk neutral. Suppose the principal can observe the agent’s effort level. He can calculate his expected utility for different levels of effort. Assume that the agent can get utility 1 if she works elsewhere. Then the principal can see that if he pays her M=4, she will be willing to choose e = 1 and to work for him because ua = M − e = 1 if M=4 and e=1. If e = 1 and he pays her M = 4, his expected utility is: Eu p = 34 (16 − M ) + 14 (4 − M ) = 34 (16 − 4) + 14 (4 − 4) = 9 If e = 0, the principal can pay the agent M = 1 to get her working for him, since her utility is ua = M − e = 1 if e = 0 and M = 1. Then, the principal’s expected utility for e = 0 and M = 1 is: E u p = 13 (16 − 1) + 43 (4 − 1) = 6

Certainly, the principal’s expected utility is higher for e = 1 and M = 4 than that for e = 0 and M = 1 (9>6). Hence, the principal will pay M = 4 and get the agent to work for him with effort level e = 1. But suppose the principal cannot observe the agent’s effort level, or cannot verify this in court if litigation should arise from a dispute about her effort level and corresponding pay. Then the principal must choose a contingent contract to facilitate an efficient trade off between risk sharing and incentive provision. If pay is not contingent on outcome, then it is easy to see that the agent will always choose effort e = 0, since her utility √M-e is always larger for e = 0 than for e = 1 for a noncontingent M. Suppose the principal pays MH if the outcome is good or if R = 16 and pays ML if the outcome is bad or if R = 4, where MH > ML. Then the contingent contract will get the agent working for the principal with effort level e = 1 if the following two conditions hold. The first condition is to ensure that the agent is not worse off than working elsewhere, that is, her expected utility when she chooses effort level e = 1 should not be lower than her reservation pay 1:

278

( M H − 1) + 41 ( M L − 1) ≥ 1 This is referred to as the participation constraint. The second condition is to ensure that the agent is not worse off when she chooses e = 1 than when she chooses e = 0, that is, her expected utility with effort e = 1 and MH should not be lower than her expected utility with effort e = 0 and ML. That is, 3 4

( M H − 1) + 14 ( M L − 1) ≥ 14 ( M H − 0) + 34 ( M L − 0) This condition is referred to as the incentive compatibility condition. Since the principal’s purpose is to maximize his expected utility, which is a decreasing function of M, he will choose MH and ML from the equalities in the two conditions. The two equations with two unknowns yield the efficient contingent contractual terms: M H = 6.25, M L = 0.25 It is easy to compute that the principal’s expected utility under the second best contingent contract is: Eu p = 43 (16 − 6.25) + 41 (4 − 0.25) = 8.25 3 4

which is smaller than what can be obtained from the first best labor contract when he can observe the agent’s effort level, which is 9. The difference is endogenous transaction cost caused by moral hazard. In the first best labor contract (pay M = 4 for effort e = 1 and pay M = 1 for effort e = 0), the principal takes all the risk and the agent receives her wage without risk. This contract yields efficient risk sharing in the sense that the risk-neutral principal takes all the risk and the risk-averse agent takes none. You may also interpret this as a trade contract in risk, through which the agent sells all risk to the principal, or the agent is completely insured by the principal. The first best labor contract also provides the right incentive for the agent to choose the right level of effort. This implies that if the principal can see the agent’s effort level, there is no trade off between efficient risk sharing and efficient incentive provision. But when the principal cannot observe the agent’s effort level, there is a trade off between risk sharing and incentive provision. If the principal takes all the risk and pays a noncontingent M, which is equivalent to providing the agent with complete insurance, then the agent would not choose the right effort level. But if the principal rewards or penalizes the agent exactly according to the contingent outcome, they would not have efficient risk sharing. The pay to the agent will be greater or the principal’s profit lower, because the risk is too high for the agent to take the job if the pay is not that high. Hence, the second best contingent contract efficiently trades off risk sharing against incentive provision to achieve a compromise. Though the efficient trade off has not achieved the first best, and therefore is not Pareto optimal, it nonetheless maximizes the gains from trade net of the unavoidable endogenous transaction costs caused by moral hazard. When moral hazard exists, the first best is an unachievable utopia. The second best is a realistically efficient contract. Hence, we call the contingent contract the efficient contract despite its Pareto inefficiency. It is important to note, as Hart (1995) points out, that the contingent contract in the principal-agent model is not a labor contract. The contingent contract prices output rather than effort input, because the exact rationale for the contingent contract is that a labor contract for effort input is infeasible. Hence, it is misleading to call the principal-agent model a model of the firm. The principal-agent model cannot explain why and how firms emerge, or why we need asymmetric residual returns and residual control. The

279

asymmetric relationship between employers and employees is not endogenized in the principal-agent model. Although the principal looks like an employer, we can show that he does not claim all residual returns, the agent claiming part of these through contingent pricing of outcome. For instance, if outcome R = 16 is realized, the agent gets √6.25-1>1 where the prevailing market reservation pay is 1. Furthermore, in the principal-agent model, the principal has no residual control rights over the agent’s effort level. What the agent can do (which level of effort she chooses) is completely up to her. But as shown in chapter 8, in a labor contract, what the employee does is up to the employer: the employee must do whatever she is told to do. The two main features of the institution of the firm and the related labor contract, namely, the asymmetric distribution of residual returns and residual control rights, are absent in the principal-agent model. The model of moral hazard can be applied to analyze many development problems. The sharecropping model is one of these applications. Example 9.2 (Stiglitz, 1974): Trade off between incentive provision and insurance provision in sharecropping. Sharecropping was considered inefficient by economists, since it gave the tenant only part of his marginal product and thereby did not provide full incentive. But as economists have recognized the possible endogenous transaction costs caused by moral hazard, the function of sharecropping in trading off risk sharing against incentive provision can be appreciated. 1 We consider a simple sharecropping model where the landlord is the principal and the tenant is the agent. The production function is y = θALa where L is the tenant’s input of labor in the production, y is output level, θ is a random variable and its value is θL with probability ρ and θH with probability 1-ρ, where θH>θL, and a∈(0, 1) is the elasticity parameter of output with respect to labor input. We assume that the amount of land used in the production is fixed, so that it is included in parameter A. The tenant receives the share α of realized output and his expected utility is u = αEy + C –bL, where C is a side payment from the landlord to the tenant and b is a disutility coefficient of working. The tenant’s reservation utility is u0. The landlord cannot observe or verify the labor input level of the tenant, so that pure wage will generate an unacceptable moral hazard. Hence, the landlord’s optimum contract with the tenant is given by his following decision problem. Max: (1-α)Ey – C with respect to α and C subject to the tenant’s participation constraint: u = αEy + C –bL ≥ u0 and the first order condition for the tenant’s utility maximization decision: du/dL = 0. where C can be interpreted as land rental if α = 0. The maximization of the landlord’s payoff implies that the equality in the tenant’s participation constraint holds. This, together with the tenant’s first order condition, can be used to express the optimum share α as a function of the optimum side-payment C. (9.3)

1

α = (u0 - C )/(1-ab)]1-aaa-1/A[θH(1-ρ) +θLρ].

See Singh (1989) for a survey of theories of sharecropping and formal models.

280

where ρ can be considered as the degree of risk of low output level. Inserting this into the landlord’s objective function, the first order condition for maximizing it with respect to C yields the optimum side-payment (9.4)

C* = u0 – {aa-1-1/(1-a)(1-a)/(1-ab)[θH(1-ρ) +θLρ]}1/a.

It is straightforward that the optimum side-payment is 0 if u0 is too small or if the degree of risk ρ is too great and that dC*/du0 > 0 and dC*/dρ < 0. This, together with the differentiation of (9.3), yields that dα*/dρ = (∂α/∂ρ)+ (∂α/∂C)(dC*/dρ) > 0, where ∂α/∂C < 0. If C is 0, the contract is called a pure sharecropping contract; if α = 0, then the contract is called a pure land rental contract with the rental rate as C. Hence, this model predicts that if the risk in production is sufficiently great, then the optimum contract is pure sharecropping; if the risk is sufficiently small, the optimum contract is land renting. If the risk is neither too great nor too trivial, the optimum contract is sharecropping with side payment. The model of sharecropping shows that if moral hazard is considered, a sharecropping contract may be an efficient compromise between an incentive provision and risk sharing. But this result is based on the assumption that no insurance market is available. If the markets for insurance, labor, and capital are well developed, sharecropping may not be the most efficient institution. We now use the Holmstrom and Milgrom model (1994) to show the function of the contract in achieving the efficient trade off between endogenous transaction costs caused by moral hazard and monitoring cost in reducing moral hazard. Example 9.3: Holmstrom-Milgrom model (1994). The principal pays the agent a linear compensation w = α+β(z+γy), where z = e+x is the observed outcome of the agent's effort e, x ∼ N( x , σx) is a random variable representing the firm specific uncertainty, y ∼ N( y , σy) is a random variable representing industrywide or nation-wide uncertainty, the covariance between x and y is σxy = cov(x, y) = E[(xx )(y- y )] = ∑s∈S p(s)[x(s)- x ][y(s)- y ], e is the agent's effort level that affects profit of the principal's business but cannot be observed or verified by the principal, α is a fixed wage, and β is the intensity coefficient of the contingent incentive payment. N( x , σx) is a normal probability distribution. σy = var(y) = E[(y- y )2] = ∑s∈S p(s)[y(s)- y ]2. For simplicity, we assume that x = y = 0. The agent's certain equivalent wealth (CEW, see (9.2)) is CEWe = α+βe-C(e)-0.5rβ2V, where C(e) is disutility of effort and C'(e)>0 and C"(e)>0, r is the degree of absolute risk aversion, and V ≡ Var(x+γy) = σx + γ2σy+2γσxy. The agent maximizes this with her effort level e. The first order condition yields β = C'(e).

281

This is the incentive constraint. The principal is risk-neutral, and her payoff and its certain equivalent is CEWr = P(e)-(α+βe), where P(e) is gross profit and α+βe is the expected wage payment. Assume that wealth distribution has no effect on productivity (a very strong assumption that abstracts the analysis from effects of transaction costs on productivity, which has been the focus in all Smithian models in this text). Then the efficient contract is determined by maximizing the total certain equivalent wealth of the principal and agent, which is CEW = P(e)- C(e)-0.5rβ2V. Maximizing this with respect to e, β, and γ, subject to the incentive constraint, yields the first order condition for the efficient contingent incentive contract: P'(e) = C'(e)[1+rVC"(e)],

β = C'(e),

γ = -σxy/σy

Suppose that P(e) = ae, C(e) = ce2. Then P'(e) = a, C'(e) = 2ce, and C"(e) = 2c. For these specific functional forms, the efficient contract is γ = -σxy/σy,

e = a/2c(2crV+1),

β = 2ce = a/(2crV+1).

The comparative statics of the efficient contract are de/da > 0,

de/dc < 0,

dβ/da > 0,

dβ/dc < 0.

This result indicates that as the benefit coefficient of effort a increases or as the disutility coefficient of effort c decreases, the efficient incentive intensity β increases so that the efficient contract induces a higher level of effort, e. If the unobservable x and observable y are positively correlated, (σxy > 0), the efficient γ is negative, since a good outcome is more likely due to nationwide contingence rather than firm-specific contingence. But if σxy < 0, the efficient γ is positive. This story shows that the trade off between risk sharing and incentive provision implies that too great an incentive intensity may not be efficient. If we introduce the trade off between monitoring cost and incentive provision into the model, this point becomes more obvious. Suppose Var(x+γy) = V is a decision variable. Assume that the monitoring cost M(V) is an increasing function of V, or M'(V) > 0. Also, we assume that M"(V) > 0. The new total certain equivalent is now CEW = P(e)- C(e)-0.5rβ2V+M(V). The optimum contract is given by maximizing this CEW with respect to e, V, and β, subject to the incentive constraint. The degree of measurement inaccuracy (V) can be

282

considered positively relating to the degree of externality. This model formalizes the ideas of Barzel (1985) and Cheung (1970, 1983) on the endogenous degree of externality. In exercise 5 of chapter 10, Holmstrom and Milgrom introduce the trade off between balanced incentives for two activities that the employee undertakes and strong incentive for each activity into the model in this section. They have shown that the institution of the firm can more efficiently balance the trade off by imposing some job restrictions and by providing weaker and more balanced incentives than in the market without firms. This kind of model shows that a realistic analysis of an efficient contract involves many trade offs, which are much more complicated than the simple trade off between incentive provision and risk sharing in example 9.1. Most of this kind of model are decision or partial equilibrium models that cannot be used to figure out the mechanisms that simultaneously determine the network size of division of labor, the extent of the market, the number of transactions, total endogenous and exogenous transaction costs, and productivity. The above three neoclassical principal-agent models are not general equilibrium models. The principal-agent relationship is not endogenized, and reservation pay is exogenously given. The principal cannot take care of his own business and must ask the agent to do the job, while the agent cannot have her own business and must work for others. Hence, the relationship between the emergence and development of principalagent relationships, productivity progress, and the evolution in division of labor cannot be investigated. Hence, we next consider a Smithian principal-agent model which enables us to explore these issues. We first outline the story behind the model. The Smithian model of the endogenous principal-agent relationship with two consumer goods is similar to the model in chapter 4, except that there is a risk of low transaction efficiency in exchanging goods x and y, which is affected by an x specialist’s effort in avoiding the transaction risk. The effort is not observable, so that moral hazard may arise. There are several trade offs among economies of division of labor, exogenous transaction costs, endogenous transaction costs caused by moral hazard, benefit of a high effort level in avoiding transaction risk, and cost of that high effort level. If an exogenous transaction cost coefficient is large, then autarky is equilibrium where no principal-agent relationship and market exists. If the exogenous transaction cost coefficient is small, then reciprocal principal-agent relationships emerge from the division of labor. For an equilibrium with division of labor, if the cost of a high effort level in avoiding risk is significant compared to the resulting gain from a lower transaction risk, then in a general equilibrium environment, an x specialist will be better off by choosing the low effort level, so that a single price contract is enough for coordinating the division of labor. Contingent contracts are not needed. If the cost of effort level is not significant, the avoidance of moral hazard becomes worthwhile. Hence, contingent contracts become essential for reducing moral hazard. In a general equilibrium environment with endogenous specialization and an endogenous relative price of all goods, contingent contracts may eliminate endogenous transaction costs caused by moral hazard. Yang and Yeh (1996, see exercise 16) show in a model with endogenous specialization and moral hazard for a pair of players who cannot choose between potential partners that within a certain parameter space a man works harder for others in the presence of moral hazard than working for himself in the absence of moral

283

hazard. Also, as transport conditions are improved, endogenous transaction costs and productivity may increase side by side. This is of course due to the trade off between economies of division of labor and endogenous and exogenous transaction costs. A sufficient improvement of transport condition may enlarge the scope for trading off one against the others between the conflicting forces and thereby it is more likely positive network effects of a larger network of division of labor outweigh increasing endogenous and exogenous transaction costs. Hence, welfare and endogenous transaction costs increase side by side. Example 9.4: A principal-agent model of endogenous specialization. Consider a model with a continuun of ex ante identical consumer-producers of mass M, and with two consumption goods x and y. Each person’s utility function is specified as follows. (9.5a)

u = ln[(x+kxxd)(y+kyyd)]

where x and y are the respective quantities of the two goods self-provided, and xd and yd are the respective quantities of the two goods purchased from the market. The transaction efficiency coefficient ky is a parameter, but kx is a random variable, given by the following condition. ⎧k with probability ρ (9.5b) if s ≥ β, then kx = ⎨ ⎩t with probability 1 - ρ if s < β, then kx = t where s is the effort level of a producer of x in avoiding the transaction risk and β is a parameter between 0 and 1. It is assumed that ρ∈(0, 1) and 1 > k > t and that ky = k. kxxd and kyyd are the respective quantities of the two goods that are received from the purchases of the two goods. This strictly concave utility function represents a preference with risk aversion. Each person is equipped with the same production functions for the two goods. (9.6) x+xs = Lx-a y+ys = Ly-a s where y and xs are respective quantities of the two goods sold, and Li is an individual’s level of specialization in producing good i. The production function displays economies of specialization. Each individual is endowed with one unit of time that can be allocated between production and avoiding transaction risk, so that the endowment constraint for each person is (9.7) Lx+Ly+s = 1, where s is the time allocated for avoiding transaction risk. Finally, we assume Li∈[0, 1], s, x, xs, xd, y, ys, yd ≥ 0. Each individual’s self-interested behavior is represented by a non-linear programming problem that maximizes her expected utility with respect to Li, s, x, xs, xd, y, ys, yd, subject to the production functions, endowment constraint, and nonnegative constraint. Applying the Wen theorem to the model, we can show that a person never simultaneously buys and sells the same good, never simultaneously buys and selfprovides the same good, and never sells more than one good. Taking account of the

284

possibilities for pure and contingent pricing for goods, we can identify 10 configurations and 6 structures that need to be considered. We assume a Walrasian regime, where a representative pair of consumer-producers sort out their terms of trade and sign a contract in period 1. Then they decide on their quantities of goods to consume, to produce, and to trade, and Nature chooses a realization of kx according to the players’ decisions and prior probabilities in period 2. Trade and consumption take place and the contract is implemented in period 3. In this regime, each person can observe kx, but not the effort level s, of the other. We first identify all structures that need to be considered. Then all corner equilibria in the structures will be solved. (1) There is an autarky configuration, A, where there is no market or principal-agent relationship, and each individual self-provides all goods consumed. Structure A consists of M individuals choosing configuration A, which implies a profile of decision variables with Lx, Ly, x, y>0; s = xs = xd = ys = yd = 0. The decision problem for a person choosing configuration A is Max: U ≡ Eu = E(lnx+lny) (utility function) (production functions) s.t. x = Lx-a, y = Ly-a Lx+Ly = 1 (endowment constraint) where E denotes expectation, and Li, x, y are decision variables. The optimum solution for this problem and the maximum expected utility for this configuration are listed in Table 9.1. Note that there is no transaction and related transaction risk in autarky. (2) There are two market structures with the division of labor and unique relative price of the two goods. Structure DL is a division of population between configurations (x/y)DL and (y/x)DL. Configuration (x/y)DL implies that x, xs, yd >0, s = Ly = xd = y = ys = 0, and an individual choosing this configuration specializes in producing x, chooses a low level of effort in avoiding transaction risk, and accepts only a single relative price of the two goods. Configuration (y/x)DL implies that Ly, y, ys, xd >0, s = Lx = yd = x = xs = 0, and an individual choosing this configuration specializes in producing y, and accepts only a single relative price of the two goods. Structure DH is a division of population between configurations (x/y)DH and (y/x)DH. Configuration (x/y)DH is the same as configuration (x/y)DL, except that an individual choosing this configuration chooses a high level of effort in avoiding transaction risk. Configuration (y/x)DH is the same as configuration (y/x)DL, except that her transaction efficiency coefficient k is determined by a high effort level of the specialist producer of x. Let us first consider individuals’ decision problems in structure DL. In this structure, the decision problem for a person choosing configuration (x/y)DL is Max: Ux ≡ Eux = E[ln(kyd)+lnx] (budget constraint) s.t. yd = pxs s x + x = Lx-a, (production function) Lx = 1 (endowment constraint) where Lx, xs, yd are decision variables and p≡px/py is the price of good x in terms of good y. Note that s = 0 for this configuration. The optimum decision for this configuration and the expected indirect utility function are listed in Table 9.1. The decision problem for configuration (y/x)DL is Max: Uy ≡ Euy = E[lny+ln(kxxd)] (budget constraint) s.t. ys= pxd

285

kx = t (transaction condition) s y+y = Ly-a (production function) Ly = 1 (endowment constraint) where Ly, xd, ys are decision variables. The optimum decision for this configuration and the expected indirect utility function are listed in Table 9.1. The terms of trade in period 1 will be determined by the expected utility equalization condition: Ux = Uy since individuals would keep changing their occupation in period 1 if this condition were not satisfied. The market clearing condition My ys = Mx yd or Mx xs = Myxd , together with the population equation Mx + My = M, then determines the numbers of individuals choosing the two configurations. Plugging the corner equilibrium relative price into the utility function yields the corner equilibrium expected real income in structure DL. All of the information on this corner equilibrium is in Table 9.2. Assume that a single equilibrium relative price prevails. From Table 9.1, it is clear that when pH =pL =p, an x specialist’s expected utility is ln(pk)+2[ln(1-a)-ln2] if she chooses a low effort level, and is 2[ln(1-a-β)-ln2]+ln(kp) if she chooses a high effort level. A comparison between the two indirect utility functions implies that for a single relative price, an x specialist always chooses the low level of effort in avoiding transaction risk. Hence, structure DH never occurs in equilibrium. (3) Market structure C is associated with the division of labor and with two contingent relative prices. This structure comprises a division of M individuals between configurations (x/y)C and (y/x)C. Configuration (x/y)C is the same as (x/y)DH, except that an individual choosing this configuration accepts the relative price pH when k is kH, and the relative price pL if k is kL. Configuration (y/x)C is the same as (y/x)DH, except that an individual choosing this configuration accepts the relative price pH when kx is k, and the relative price pL if kx is t. Table 9.1: Corner Solutions in 7 Configurations Configuration A (x/y)DH (y/x)DH (x/y)DL (y/x)DL (x/y)C (y/x)C

Self-provided quantities x=y=0.5-a s=β, x = (1-a-β)/2 y = (1-a)/2 s=0 x = (1-a)/2 y = (1-a)/2 s=β, x = (1-a-β)/2 y = (1-a)/2

Demand and Expected indirect utility supply 2ln(0.5-a) s x = (1-a-β)/2 ln(pk)+2[ln(1-a-β)-ln2] yd = pxs xd= ys/p ρlnk+(1-ρ)lnt-ln p ys= (1-a)/2 +2[ln(1-a)-ln2] ln(pk)+2[ln(1-a)-ln2] xs = (1-a)/2 yd = pxs ln(t/p)+2[ln(1-a)-ln2] xd = ys/p s y = (1-a)/2 xs = (1-a-β)/2 Lnk+ρlnpH+(1-ρ)lnpL+ yd = pxs 2[ln(1-a-β)-ln2] d s x =x ρln(k/pH)+(1-ρ)ln(t/pL) ys=p +2[ln(1-a)-ln2]

The procedure for solving for this corner equilibrium is the same as that for structure DL, except that the incentive compatibility condition is used, together with the utility equalization condition, to determine the two corner equilibrium relative prices. Assume 286

that in structure C, the relative price is pH when kx is k and that it is pL when kx is t. Assume that p in configuration (x/y)LD is pL. Letting the expected utility of the specialist choosing (x/y)C, given in Table 9.1, equal the expected utility for (x/y)DL, the incentive compatibility condition for C can be derived as follows. (9.8)

ln(pH/pL) > 2[ln(1-a)-ln(1-a-β)]/ρ

This condition, together with the expected utility equalization condition between configurations (x/y)C and (y/x)C, yields the corner equilibrium dual contingent relative prices in structure C. Plugging the corner equilibrium prices back into the indirect utility function of either (x/y)C or (y/x)C then yields expected per capita real income (corner equilibrium utility) in structure C. All information on the four corner equilibria is summarized in Table 2. Table 9.2: Corner Equilibria in Four Structures

Structure Corner equilibrium relative price A DL p = (t/k)0.5 DH p = [(1-a)/(1-a-β)](t/k)0.5(1-ρ) C

pL = (t/k)0.5(1-ρ) [(1-a-β)/(1-a)], pH = pL[(1-a)/(1-a-β)]2/ρ

Expected real income 2[ln(1-2a)-ln2] 2[ln(1-a)-ln2]+0.5(lnt+lnk) 0.5[(1+ρ)lnk+(1-ρ)lnt]+ln(1-a)+ln(1a-β)-2ln2 0.5[(1+ρ)lnk+(1-ρ)lnt]+ln(1-a)+ln(1a-β)-2ln2

Note that although per capita real incomes in structures DH and C are the same, individuals will not choose single non-contingent relative price in DH if (9.8) is not satisfied because of moral hazard. Hence, (9.8) sets up a dividing line between structures DH and C in addition to the dividing line between structures DH and DL. General equilibrium satisfies the following conditions. (i) Each individual maximizes her expected utility with respect to configurations and quantities of each good produced, consumed, and traded for a given set of relative prices of traded goods; (ii) The set of relative prices of traded goods and numbers of individuals choosing different configurations clears the markets for those goods subject to the incentive compatibility constraint. Since all individuals are ex ante identical, the relative prices will equalize the expected utility for all individuals selling different goods. Following inframarginal analysis in chapters 3, 4, and 6, we can solve a corner equilibrium for each structure. We can identify the conditions under which each individual has no incentive to deviate from her configuration under the corner equilibrium prices in this structure. Alternatively, we can follow the procedure to prove the Yao theorem in chapter 4 to show that the general equilibrium is the corner equilibrium with the greatest expected per capita real income subject to the incentive compatibility condition. Hence, solving for the general equilibrium becomes a matter of identifying the corner equilibrium with the highest expected real income, subject to the incentive compatibility condition (9.8). A comparison between per capita real incomes in structures A, DL, and C yields the inframarginal comparative statics of general equilibrium, summarized in Table 9.3.

287

Table 9.3: General Equilibrium and Its Inframarginal Comparative Statics

k/t < [(1-a)/(1-a-β)]a/ρ kt < [(1-2a)/(1-a)]4 kt > [(1-2a)/(1-a)]4 A DL

k/t > [(1-a)/(1-a-β)]a/ρ k1+ρt1-ρ>B k1+ρt1-ρ< B A C

where B ≡ [(1-2a)2/(1-a)(1-a-β)]2. The bottom line in this table gives the equilibrium structure for each particular parameter subspace. Table 9.3 illustrates that as transaction efficiency is improved, the general equilibrium discontinuously jumps from autarky, where there is neither market nor principal-agent relationship, to a structure with the division of labor, where the reciprocal principal-agent relationships emerge from the division of labor and market. It can be seen that the emergence of the principal-agent relationship will involve two contingent relative prices if the benefits k/t of effort in reducing transaction risk are great compared to its cost in terms of reduced production time, that is, β. Otherwise, the emergence of the principalagent relationship will involve a unique relative price of the two goods (DL). Since the production condition in this model can be represented by the graph in Fig. 7.1, a comparison between the comparative statics of general equilibrium in Table 9.3 and Fig. 7.1 suggests that as transaction conditions are improved, the equilibrium production schedule will discontinuously jump from the low line DI to the aggregate production possibility frontier MCAKBJL in Fig. 7.1. This explains why contingent contracts can be used to promote economic development. Although this model can predict the function of contingent contracts in avoiding moral hazard, the general equilibrium is always Pareto optimal. Hence, in this Smithian general equilibrium model complete contingent contract can eliminate endogenous transaction cost. The example in exercise 16 illustrates how endogenous transaction costs are caused by moral hazard when each of the two players cannot choose trade partner. The implications of moral hazard for the equilibrium network size of division of labor and economic development will be more significant if the number of goods is more than 2. The numbers of configurations and corner equilibria will increase more than proportionally as the numbers of goods in the model increase.

9.3. Game Models and Endogenous Transaction Costs

9.3.1. Game Models The Walrasian equilibrium model belongs to a special class of game models. In this class of models, it is a game rule that all players are price takers, that is, they do not directly pay attention to what other players are doing since they believe that all information about this is reflected in prices. Hence, each player chooses the optimum quantities of goods and factors that are produced and used for given prices. The interactions between individuals’ self-interested decisions therefore take place indirectly, through prices, rather

288

than directly. In this process, any player’s attempt to manipulate prices is nullified by free entry and the ability of many other players to do the same. Therefore, there are no direct strategic interactions between self-interested decisions. But for many economic games, the game rules are more general or more complicated than the price taking rule. In this section, we study game models with more general game rules. A game is defined by game rules, players, their strategies, outcomes, and players’ payoff functions on outcomes. The game rules specify who moves when, what they know when they move, what they can do, and when the game ends. The players are all the decision makers who are involved in the game, and Nature, who randomly chooses whatever the other players cannot choose when there are uncertainties in the game. A player’s strategies are the actions she can take when it is her turn to move. A profile of each and every players’ chosen strategies generates an outcome of the game that affects players’ well-being. Players’ objective functions defined on outcomes of the game are called payoff functions. In the next subsection, we use an example to illustrate all of these concepts. 9.3.2. Nash Equilibrium An example of Nash equilibrium can be found from example 3.2 in chapter 3. In that example, the government in each country maximizes a home resident’s utility with respect to the home tariff rate, given the other country’s tariff rate. If Nash bargaining is not allowed, the Nash equilibrium in that model entails a positive tariff if exogenous transaction conditions are not bad (autarky does not occur in equilibrium). The positive tariff makes an equilibrium departure from the Pareto optimum, thereby generating endogenous transaction costs. If exogenous transaction conditions are neither very good nor very bad, then the coexistence of unilateral protection tariff and unilateral laissez faire generates endogenous transaction costs that cannot be avoided even if tariff negotiation is allowed. If exogenous transaction conditions are sufficiently good, the endogenous transaction costs caused by bilateral protection tariff in structure C will offset all mutually beneficial gains from trade compared to structure Ba or Bb. Such endogenous transaction costs are incurred by competition for a greater share of the gains from division of labor. Let us use the strategic form to describe that Nash tariff game. Example 9.5: Strategic form of the Nash tariff game in the Ricardo model. We first consider structure Ba, in which country 1 produces two goods and exchanges good x for good y with country 2 (see Fig. 3.2 and Table 3.3 in chapter 3). Country i's strategy is tariff rate ti. The following strategic form of the Nash tariff game in structure Ba summarizes strategies, payoffs, and outcomes of this game. Table 9.4a: Strategic Form of the Nash Tariff Game in Structure Ba

Country 1

t1 = 0 t1=t1*

Country 2 t2 = 0 t2 > 0 U1(L), U2(H) U1(L), U2(M) U1(H), U2(M) U1(L), U2(L)

289

where the first term in each entry is the utility of an individual in country 1 and the second is that of an individual in country 2. Ui(H)>Ui(M)>Ui(L) can be found from Table 3.3. The outcome t1 = t2 = 0 is the result of bilateral laissez faire, which allocates all gains from trade to country 2. The outcome t1 = t1*, t2 = 0 implies that country 1 imposes tariff rate t1* such that an individual’s utility in country 2 is the same as in autarky. Hence, country 1 obtains most of gains from trade. The outcome t1 = 0, t2 > 0 implies that country 1 carries out a laissez faire policy while country 2 imposes a protection tariff. The outcome t1 = t1*, t2 > 0 implies that both countries impose protection tariff. We first prove that the outcome t1 = t2 = 0 (bilateral laissez faire) is not a Nash equilibrium. For t2 = 0, country 1’s utility can be increased from U1(L) to U2(H) by a shift from t1 = 0 to t1 = t1*. Hence, country 1 has an incentive to unilaterally deviate from the outcome t1 = t2 = 0. Similarly, country 2 has an incentive to unilaterally deviate away from the outcome t1 = 0, t2 > 0 or the outcome t1 = t1*, t2 > 0. For the outcome t1 = t1*, t2 = 0, any unilateral deviation reduces the deviator’s utility. Hence, it is the Nash equilibrium in structure Ba. The Nash equilibrium in structure Bb is symmetric to this. Next we consider structure C, in which each country completely specializes. Table 9.4b: Strategic Form of the Nash Tariff Game in Structure C

Country 2 Country 1

t1 = 0 t1=t1*

t2 = 0 U1(M), U2(M) U1(H), U2(L)

t2 = t2 * U1(L), U2(H) U1(L), U2(L)

where Ui(H)>Ui(M)>Ui(L) can be found from Table 3.3. As shown in example 3.2 in chapter 3, each country imposes ti* as high as possible, provided individuals in the other country stay in structure C. Following the same reasoning for the strategic form in Table 9.2a, we can show that the outcome t1 = t1*, t2 = t2* is the unique Nash equilibrium where all gains from the complete division of labor are offset by the endogenous transaction costs caused by the tariff war. A mutual laissez faire regime cannot be a Nash equilibrium, despite the fact that it is mutually beneficial. This is called coordination failure due to all players’ rational decisions. This type of game is sometimes called the prisoners’ dilemma, indicating a situation in which, while two players can be better off by cooperation, their rational behavior prevents them from choosing cooperation. More generally, a strategy profile s = (s1, s2, …, sN) of N players constitutes a Nash equilibrium if for every i = 1, .., N, ui(si, s-i) ≥ ui(si’, s-i) for all si’ that player i can choose. where ui(.) is player i's utility function and s-i is a strategy vector of all players except player i. In many Nash games, there are multiple Nash equilibria. The Murphy-ShleiferVishny model (1989) in example 5.3 is an example wherein there are Pareto rankable multiple Nash equilibria. In order to enhance the predictive power of the theory, we may use various ways to narrow down the set of candidates for the game solution by refining the concept of equilibrium. One way is to allow players to choose a pure strategy with a probability. That is, players can choose mixed strategies. We will examine this kind of

290

mixed strategy games in exercise 1 and in example 9.13. In the next subsection, we introduce the concept of subgame perfect equilibrium to refine the concept of Nash equilibrium. 9.3.3. Subgame Perfect Equilibrium A shortcoming of the Nash game model is that it does not involve the time dimension. Time dimension is important for strategic interactions. In particular, if we want to investigate endogenous transaction costs caused by an alternating offer bargaining process, we need a dynamic game model. We use the following example to illustrate the technical substance of a type of dynamic game model called a subgame perfect equilibrium model. Example 9.6: Rubinstein alternating offer bargaining model. The game is to divide a pie between two players. Nature randomly chooses a player as the first mover (he) who makes an offer in period 1. Player 2 (she) can accept the offer in period 1. This terminates the game, and the pie is divided according to his offer. But she may also reject his offer in period 1 and make a counteroffer in period 2. He can then choose between acceptance and rejection of her counteroffer in the next round of bargaining. The game can go on to an infinite horizon. But the value of time provides players with incentives to conclude the deal as soon as possible. The value of time also creates the possibility of exploiting the opponent’s impatience. This possibility ensures that a definite outcome emerges as the equilibrium. Assume that the value of time for a player can be represented by a subjective discount rate ρ∈[0, 1]. This may also be taken to be the interest rate. Since $1 principal at t = 0 can generate principal plus interest of $(1+ρ) at t = 1, $1 at t = 1 is worth only $1/(1+ρ) at t = 0. In other words, the future value of A dollars at t = 0 is B = (1+ρ)A, or the present value of B dollars at t = 1, is A = B/(1+ρ). δ ≡ 1/(1+ρ) is called the discount factor, which is between 0 and 1. The value of time, or a player’s degree of impatience, increases as the discount factor δ tends to 0 or as the discount rate ρ tends to infinity. We now use the extensive form to describe the dynamic bargaining game. At the root of the inverse tree graph, player 1 makes an offer. He can ask for a large share of the pie, denoted by x1H, or a small share x1L, or any share in between. x1 represents the share that player 1 asks for at period 1. At the nodes of the second layer, player 2 can choose A (acceptance) for any offer that player 1 made in period 1. This terminates the game according to the terms of player 1. If she does not choose A, then she rejects the offer that player 1 made in period 1. She must then make a counteroffer, x2H, x2L, or anything in between, where x2 represents the share that player 2 offers to player 1 in period 2. The dashed circles denote that each player has perfect information about the node at which he is located when it is his turn to move. That is, this is a sequential move game. For each node, there is a branch of the tree, called a span, which represents a subgame below that node. If all players’ dynamic strategies are Nash optimal, then in each subgame at any node, the players’ strategies constitute a Nash equilibrium. That is, each player’s sequence of moves must be dynamically optimal for a given opponent’s dynamic optimal strategy.

291

Figure 9.1: Extensive Form of Alternating Offer Bargaining Game

We now consider player 1’s optimum dynamic decision. Suppose he asks for x1∈[0, 1] in period 1. His principle for choosing x1 is: (i) x1 must be acceptable to player 2, since delay makes no sense in the model with no information asymmetry and with a discount factor between 0 and 1; (ii) x1 should be as large as possible, provided player 2 accepts it. Condition (i) can be achieved only if player 2’s discounted payoff from rejecting the offer is not more than her payoff from the offer. She receives 1- x1 if she takes the offer right away. If she rejects x1, then she can make a counteroffer x2 in period 2, which yields a discounted value to her δ(1- x2). Hence, (i) requires 1 − x1 ≥ δ (1 − x2 ) . Condition (ii) requires that x1 be as large as possible or the left hand side of the semi-inequality be as small as possible, that is, 1 − x1 = δ (1 − x2 ) . For the same reason, player 2 will choose x2 such that x2 = δx3 where x3 is player 1’s counter-counter offer in period 3. Considering the symmetry between bargaining situations in different rounds, we can see that in a steady equilibrium, x1 = x3 = x5 … and x2 = x4 = x6 … Hence, the two players’ optimum decisions in the first round summarize the information in all rounds of bargains. Player 1 knows that player 2’s optimum decision in period 2 is dependent on his optimum decision in period 1 because of x2 = δx1 if x1 = x3. He will put himself in her shoes to calculate her optimum decision in period 2 according to the equation, then plug this equation back into the equation 1 − x1 = δ (1 − x2 ) that gives his optimum decision in period 1, given her optimum decision in period 2. This backward deduction based on sequential rationality, which is called dynamic programming, thus yields the subgame perfect equilibrium. In other words, the following system of equations gives the solution. (9.9a)

1 − x1 = δ (1 − x2 ) ,

x2 = δx1 .

The solution is (9.9b)

x1* = 1/(1+δ),

x2* = δ/(1+δ).

292

Player 1 offers x1* and player 2 accepts this in period 1; player 2’s threatening counteroffer is x2* if player 1’s offer is not as good as x1*. The counteroffer threat is essential to restrain player 1’s greed. You can easily verify that x1* > 1-x1*, which means that the first mover has an advantage since he can hold up his opponent until period 2 to squeeze her, using her impatience. The first mover’s advantage increases as the discount factor is reduced, or as a player’s degree of impatience increases. Exercise 11 shows that if the discount factor differs from player to player, then a more patient player has an advantage, too. The first mover advantage may be offset by his greater degree of impatience than the second mover, if the advantage of the second mover’s patience outweighs the first mover advantage. 9.3.4. Bayes Equilibrium We now consider information asymmetry in a static simultaneous move Nash game. Again, we do not intend comprehensive coverage of this field of game theory. Instead, we use an example to illustrate the main concepts and this analytical approach to game models as one tool from our tool kit. Example 9.7. A Bayes equilibrium model. Consider the Nash game in a Cournot oligopoly model. The inverse demand function for a good is p = a-bx, where x = x1 + x2, and xi is the amount of the good produced by firm i which has the cost function Ci = cixi. We assume that firm 1’s marginal cost c1 is known to both firms, but firm 2’s marginal cost c2 has two possible states: a large value θh with probability ρ and a small value θl with probability 1-ρ. This two point distribution function of potential values of c2 is common knowledge for the two firms. The actual, or realized, value of c2 is chosen by the third player, Nature. After Nature has chosen a state of c2 according to the distribution function, player 2 is informed of the choice, but player 1 is not. Firm 2, then, has complete information about the realized value of c2 and firm 1 has incomplete information about c2. This is referred to as information asymmetry about the realized value of c2 between the two firms. A Bayes equilibrium is a Nash equilibrium in a simultaneous move game with information asymmetry, where the player with incomplete information maximizes his expected payoff function for given uncertainties of types of his opponent. Here, types of the informed player are associated with states of marginal cost about which the other player does not have complete information. Firm 2 has two reaction functions for two different states of c2. (9.10a)

x2(θh) = (a-θh -bx1)/2b if c2 = θh and x2(θl) = (a-θl -bx1)/2b if c2 = θl.

Firm 1’s decision problem is Max : Eπ1 = ρ{a- c1 -b[x1 + x2(θh)]}x1 +(1-ρ){a- c1 -b[x1 + x2(θl)]}x1 x1

293

where E denotes expectation. The expected profit is a weighed average of two profit levels. The weights are the respective probabilities of the two profit levels. The reaction function of firm 1 is given by the first order condition for the decision problem as follows. (9.10b)

x1 = [a- c1 -ρbx2(θh)-(1-ρ)bx2(θl)]/2b.

(9.10) yields the Bayes equilibrium: x1* = [a- 2c1 +ρθh+(1-ρ)θl]/3b, x2*(θh) = [2(a+c1)-(3+ρ)θh-(1-ρ)θl]/6b, x2*(θl) = [2(a+c1)-ρθh-(4-ρ)θl]/6b. This game model with information asymmetry involves interesting interactions between strategies and information. 9.3.5. Sequential Equilibrium Example 9.8. A sequential equilibrium model of the credit market. If we introduce information asymmetry into a dynamic game or introduce a time dimension into a Bayes game with information asymmetry, we will have an interesting type of game – a dynamic game with information asymmetry – which can generate significantly higher explaining power than the Walrasian equilibrium model. The solution of this kind of game is referred to as sequential equilibrium or perfect Bayes equilibrium. For most dynamic game models with information asymmetry, perfect Bayes equilibrium, which is an extension of Bayes equilibrium to dynamic games, is equivalent to sequential equilibrium, which is an extension of the notion of subgame perfect equilibrium to games with information asymmetry. We use an example to illustrate the concept of sequential equilibrium in a dynamic game with information asymmetry, and its implication for the analysis of credit market. This is a game between many entrepreneurs and an investor in a credit market. There are two types of entrepreneurs: capable and incapable ones, denoted by subscripts c and n, respectively. For a type c entrepreneur, the profit she can make, the net of repayment of the investment, when the investor makes an investment in her business is 20, which will be equally divided between her and the investor. The capable entrepreneur’s utility function is uc = (3×0.5θcαi-pi)αi when she receives a half of the profit θc = 20 that she makes, and consumes a car with quality αi at price pi. Here, subscript i denotes the brand i of car. There are three brands of cars. Brand 1 is BMW, with quality α1 = 4 and price p1 = 70. Brand 2 is Volvo, with quality α2 = 3 and price p2 = 11. Brand 3 is Toyota, with quality α3 = 2 and price p3 = 6. For a type n entrepreneur, the profit he can make when an investor invests in his business is 8, which will be equally divided between him and this investor. His utility function is un = (0.5θn αi-pi)αi when he receives a half of the profit θn = 8 that he makes, and consumes a car with quality αi at price pi. For simplicity, we assume that a car can be used for two periods and the discount factor is 1 (or the discount rate is 0). It is assumed that utility must be positive, or the subsistence level of utility is positive.

294

The investor has incomplete prior information about the type of entrepreneur she meets. She knows in period 1 that, on average, type c occurs with probability ρ and type n occurs with probability 1-ρ, where ρ∈(0, 1) is the ratio of the capable entrepreneurs to the total population of entrepreneurs. The investor’s utility function is v = (θi /2)-5, where θi is the profit made by the type i entrepreneur who gets the funding, of which the investor gets half. θc = 20 when the capable entrepreneur gets the funding and θn = 8 when the incapable entrepreneur gets the funding. For simplicity, we assume that an investor’s utility is 0 in period 1. In period 1, the two types of entrepreneurs choose the brands of cars that they drive, then in period 2 the investor infers the entrepreneurs’ types from the brands of cars that they drive and decides with whom to deal. This story is interesting because of the complicated interactions between information and dynamic strategies. The investor can infer that a capable entrepreneur will drive a Volvo, since uc(α2, p2) > uc(α1, p1), uc(α3, p3) and an incapable entrepreneur will drive a Toyota, since un(α3, p3) > un (α2, p2) and un (α1, p1) = 0. In other words, an incapable entrepreneur will drive a cheaper car and a capable entrepreneur will drive a more expensive Volvo car. Then from the brands of cars the entrepreneurs drive, the investor can get complete information about their types, so that she would invest in the business of the entrepreneur who drives a Volvo and refuse to do business with an entrepreneur driving a Toyota. But a rational entrepreneur will drive a Volvo even if he is incapable (check that un(α2, p2) > 0, that is, incapable entrepreneurs can afford a Volvo, despite the fact that this is not a myopic utility maximizing choice), since if he drove a Toyota, he would get no business, so that his income would be 0 and he could not afford even a Toyota. But if all entrepreneurs drive Volvo cars, the investor cannot tell their competence from their cars. They will not believe any entrepreneur claiming to be capable. Accordingly, if a capable entrepreneur wants to distinguish herself from an incapable one, she can drive a BMW, which an incapable entrepreneur cannot afford (check un(α1, p1) < 0). In other words, what the investor knows about an entrepreneur’s type is dependent on which strategy the entrepreneur chooses. But the strategy that the entrepreneur sees as optimal is, in turn, dependent on the information known to the investor, which affects the investor’s strategies. In a manner analogous to the interdependencies and feedback loops between quantities and prices in a Walrasian equilibrium model, there are infinite interactions and feedback loops between the investor’s information and her dynamic strategies, and between different players’ dynamic strategies. A sequential equilibrium is the outcome of all of the interactions between information and all players’ dynamic strategies. Denoting the brand of car that an entrepreneur chooses in period 1 by s, then in period 2, from observing s, the investor’s posterior probability for an entrepreneur to be type c is μ(s). This updated information may be different from the prior probability, ρ. Hence, a sequential equilibrium is defined by the following two conditions. (i) All players use dynamic programming (backward deduction) to solve for their optimum dynamic strategies for given information that they know; (ii) Each player’s information in each period is updated according to the observed strategies of other players on the basis of the Bayes updating rule. The Bayes updating rule is illustrated in the following solution of the sequential equilibrium. Let us now consider the investor’s decision problem. Her utility is 0 in period 1. In period 2, she has seen the brand s of cars driven by entrepreneurs and has the updated

295

information μ(s). Hence, she can compute her expected utility as Ev = μ(s)[(20/2)-5]+[1μ(s)][(8/2)-5] = 6μ(s)-1, which is greater than 0 iff μ(s) > 1/6. Based on this solution, we can work out a pooling equilibrium by assuming μ(s) = ρ > 1/6. A pooling equilibrium takes place when the investor’s prior and posterior information is the same or when μ(s) = ρ. In the pooling equilibrium, all entrepreneurs drive Volvo cars in period 1 and the investor cannot tell the capable entrepreneurs from the incapable ones, and she therefore does business with any entrepreneur in period 2. We first check if the investor’s decision to do business with any entrepreneur is optimal for her updated information. Since in a pooling equilibrium μ(s) = ρ, and we have assumed that ρ > 1/6, her expected utility is greater than 0. Therefore, her decision to do business with any entrepreneur is optimal. Though she has an incentive to have more information, we can show that, provided the investor chooses to do business with any entrepreneur, a capable entrepreneur has no incentive to distinguish herself from an incapable entrepreneur, and that an incapable entrepreneur has an incentive to pretend to be a capable entrepreneur by driving a Volvo car. You can verify that a type n entrepreneur can afford a Volvo, that his utility maximizing choice is a Toyota car, and that he will lose business if he drives a Toyota car. A c type entrepreneur’s total utility in the two periods is -p2α2 + 3×0.5θc α22 = (3×0.5θc α2-p2)α2 = 231, which is greater than that for driving a BMW, which can distinguish her from an incapable entrepreneur. Note that in period 1, the entrepreneur receives no income and pays for a Volvo car, and in period 2, she receives a half share of profit and uses the car without further payment. An n type entrepreneur’s total utility in the two periods is -p2α2 + 0.5θlα22 = (0.5θl α2-p2)α2 = 3, which is greater than the zero that occurs when there is no business. Hence, all dynamic strategies are optimal for the updated information, and the information that is updated according to observed strategies is consistent with all players’ dynamic strategies. This verifies that for ρ > 1/6, the pooling sequential equilibrium takes place. That is, if the likelihood for an entrepreneur to be capable is high (or capable entrepreneurs sufficiently outnumber the incapable ones), the investor will do business with any entrepreneur even if she cannot tell the capable from the incapable ones. Hence, the capable one has no incentive to distinguish herself from the incapable one, so that the incapable can cheat by pretending to be capable. The confused investor cannot get more information when the capable does not choose to distinguish herself from the incapable. Suppose ρ ≤ 1/6. We can show that there exists a screening or separating sequential equilibrium, in which all capable entrepreneurs drive BMWs and all incapable entrepreneurs cannot get any business. For this case, the investor’s expected utility is nonpositive if she cannot tell the capable from the incapable, so that she will not do any business unless she is convinced that an entrepreneur is capable. Hence, a capable entrepreneur has an incentive to distinguish herself from the incapable by driving a BMW, which an incapable entrepreneur cannot afford. Therefore the investor can tell the capable from the incapable, so that she invests only in the business of an entrepreneur who drives BMWs. Her posterior information is μ(s) = 1 when she has seen an entrepreneur driving a BMW and is μ(s) = 0 if she has seen an entrepreneur who not driving a BMW. In other words, if incapable entrepreneurs sufficiently outnumber capable ones, the investor expects a non-positive utility from doing business with any entrepreneur when she cannot tell which is which. Hence, she will not do any business unless she can establish who is who. This gives the capable entrepreneurs an incentive to convince the investor by 296

driving BMWs, which the incapable entrepreneurs cannot afford. Therefore, screening equilibrium results from complicated interactions between information and all players’ dynamic strategies. Let us now consider the endogenous transaction costs caused by information asymmetry in the credit market. There are two types of endogenous transaction costs in the sequential equilibrium model. Type A endogenous transaction cost is associated with the information distortion in the pooling equilibrium, where the incapable entrepreneur successfully cheats the investor by pretending to be capable. Type B endogenous transaction cost is a “convincing cost,” incurred in the screening equilibrium in a situation in which the investor may not believe the capable entrepreneur even if she tells the truth. The capable entrepreneur must sacrifice utility by driving BMWs in order to convince the investor. The convincing cost would not be necessary if the incapable entrepreneur did not cheat, that is, if information asymmetry were absent. The concepts of perfect Bayes equilibrium and sequential equilibrium are useful vehicles for the analysis of endogenous transaction costs because information asymmetry creates the scope for cheating and other opportunistic behaviors that cause endogenous transaction costs. This model can be interpreted in various ways to suit specific applications. For instance, brands of cars can be interpreted as different levels of expenditure on advertising that can be used by a producer to signal private information about his financial and production capacity, while the investor can be interpreted as a potential buyer of his products. Hence, this model can be used to explain why advertising expenditure is much higher than the level adequate to transmit information about goods to potential buyers. According to the model, if advertising expenditure is not high enough, then capable and incapable producers all can afford to advertise. Then the potential buyers cannot tell the capable from the incapable by observing the advertisement. Again, the high advertising expenditure is a convincing cost. Similar to the sharecropping model, this model of the credit market shows that the function of the market is much more sophisticated than conventional textbooks predict. This model predicts that if interactions between strategies and information are considered, a shortage of capable entrepreneurs may make cheating less likely to occur in equilibrium. Hence, the shortage of capable entrepreneurs, which is common in less developed countries, is not a serious problem for economic development. But government monopoly in the capital market, the stiff licensing system for private banking business, restrictions on the trade of land and free migration between urban and rural areas, the government's infringement of private ownership of land are detrimental for economic development. According to North (1981, pp. 158-68), medieval regulations, including usury laws and restrictions on the mobility of capital and labor, were detrimental to economic development in Britain. Their removal was essential for the Industrial Revolution.

297

9.4. The Role of Nash Bargaining Game in Reducing Endogenous Transaction Costs caused by Trade Conflict Individual specific prices, and pricing through bargaining existed long before the emergence of developed markets with impersonal common market prices and related pricing mechanisms. In less developed economies, including those in Soviet-style economies, pricing is typically determined by bargains between trade partners. In order to understand how impersonal common market prices emerge from prices that are different from player to player, and under what conditions trade negotiation is essential for reducing endogenous transaction costs, we must study bargaining. The concept of game is particularly useful in studying the bargaining process, since bargaining is characterized by direct interactions between players’ self-interested decisions. In this section, we first present a Nash bargaining model with endogenous specialization, then compare the Nash bargaining solution to the Walrasian equilibrium. We shall then consider the function of Nash bargaining in reducing endogenous transaction costs caused by a small number of players in the Walrasian model of endogenous specialization. Example 9.9: A Nash bargaining game with endogenous specialization. Consider a Nash bargaining game with two players who have complete information about their opponents’ production and utility functions, transportation conditions, endowment constraint, and threat point at which they will refuse to participate in the division of labor. Assume that the production and utility functions, endowment constraint, and transportation conditions for two ex ante identical consumer-producers are the same as in chapter 4. But the players try to sort out terms of trade through bargaining. Each player knows that choosing specialization in producing x generates utility ux = (1-xs)kyd, choosing specialization in producing y generates utility uy = (1-ys)kxd, and choosing autarky generates utility uA = 2-2a. There are two threat points or disagreement points at which each player refuses to participate in trade. The first is the bottom line given by real income in autarky uA. A player will refuse to participate in the division of labor if trade generates a lower utility than autarky. Second, a player may use the utility for the occupation configuration in producing y as the threat point when choosing the occupation configuration of x, since she can always change occupation if one occupation generates more utility than the other. Because of the budget constraint, the terms of trade are py/px = xs/yd = xd/ys, where the first equality is given by the budget constraint for the specialist of x, pxxs = pyyd and the second by the budget constraint for the specialist of y, pxxd = pyys. Since market clearing is a constraint for the deal, we have xs = xd and ys = yd. For simplicity of notation, we use X and Y to represent equal quantities demanded and supplied for the two goods. The net gain that an x specialist can receive from the division of labor is Vx = (1X)kY - uA and that for a specialist of y is Vy = (1-Y)kX - uA. The x specialist wants the relative price py/px = X/Y to be as high as possible. But he has a trade off. If Y/X is large, his net gain Vx is great, but his opponent’s net gain Vy is small, so that his opponent has little incentive to get involved in the division of labor. Accordingly, the probability of realizing the large value of Vx is small if the bargaining process is subject to any stochastic disturbance. The disturbance could be caused, for example, by a quarrel that

299

the opponent had with her husband at home before coming to the bargaining meeting. In her resulting bad mood, the smallness of her net gain from the deal may cause her to refuse to participate in the division of labor. If we consider Vy as the probability that the x specialist can realize V x , then the x specialist’s expected net payoff from the division of labor is V = V xV y + 0 × (1 − V y ) = V xV y

where 1- Vy is the probability that the net payoff cannot be realized, or that the net payoff is 0. Nash has proved that in a non-cooperative bargaining game with marginal stochastic disturbance, the Nash product V will be maximized by self-interested strategies. Hence, the Nash bargaining equilibrium is given by the following maximization problem. (9.11)

Max : X, Y

V = V xV y = [(1 − X )kY − u A ][(1 − Y )kX − u A ]

In a symmetric model with ex ante identical consumer-producers and symmetric tastes and production and transaction conditions, the Nash bargaining equilibrium defined in (9.11) is equivalent to the one defined by (9.12). If utility in an alternative occupation configuration is considered as a threat point, while utility in autarky is just a bottom line, the Nash product becomes (9.12)

V = (ux - uy) (uy - ux) = -(ux - uy)2

where ux is the utility for specialization in x and uy is the utility for specialization in y. In a Nash bargaining game, the x specialist threatens to choose specialization in producing y, while the specialist of y threatens to choose specialization in producing x if the terms of trade are unfair. Maximization of the Nash product, of course, implies the minimization of (ux - uy)2, which requires ux = uy. Hence, Nash bargaining will establish the utility equalization condition. The maximization of V with respect to X and Y subject to utility equalization generates the Nash bargaining equilibrium. The first order condition for the constrained maximization problem yields the equilibrium terms of trade k 1 X = Y = , ux = u y = , 2 4 which coincides with the Walrasian equilibrium with endogenous numbers of different specialists. The first order conditions for the problem in (9.11) ∂V/∂X = ∂V/∂Y = 0 or Y = 1-X and (1-2X)[X(1-X)k- uA] = 0 generate the same solution. However, if the consumption, production, and transportation conditions are asymmetric between the two goods, the solution for the maximization problem (9.11) differs from that for maximizing (9.12). For the case of asymmetric tastes and production and transaction conditions, but ex ante identical consumer-producers, the Nash bargaining equilibrium may be different from the Walrasian equilibrium, although both types of Nash bargaining equilibrium, as well as the Walrasian equilibrium, are Pareto optimal. Example 9.10: The function of Nash bargaining in reducing endogenous transaction costs caused by the Walrasian equilibrium in a Smithian model with a finite set of consumer-producers.

300

Consider the model in example 9.9. There are only two players (the set of players is not a continuum), but the utility function is u = (x+kxd)1/3(y+kyd)2/3. Hence, per capita real income in autarky is (22/3/3)a and the utility functions for configurations (x/y) and (y/x) are ux = (1-xs)1/3(kyd)2/3 and uy = (kxd)1/3(1-ys)2/3, respectively. Walrasian supply and demand functions for the two occupations are xs = 2/3, yd = 2p/3, ys = 1/3, xd = 1/3p, where p is the price of x in terms of y. The indirect utility functions for the two occupations are ux = (2kp)2/3/3 and uy = 22/3(k/p)1/3/3, respectively. The market clearing condition for x or y yields p = 1/2. But this relative price cannot be the equilibrium one, since the two players will choose configuration (y/x) and nobody chooses (x/y) under this relative price. This implies that the market cannot clear (there is supply for y, but no demand for y). Hence, the Walrasain corner equilibrium for the division of labor does not exist, or the Walrasian general equilibrium is always autarky for any k ∈ [0, 1] and a>1. But it is easy to show that the Nash bargaining equilibrium is the division of labor and generates higher per capita real income than in autarky for sufficiently large values of k and a. For instance, suppose k = 1. Then the Nash bargaining corner equilibrium for the division of labor is given by the following maximization problem: Max : [(1-X)1/3Y2/3-uA] [(1-Y)2/3X1/3-uA] X, Y

where X = xs = xd and Y = ys = yd are quantities demanded as well as supplied, and uA = (22/3/3)a is per capita real income in autarky. The solution of the bargaining equilibrium is Y = X = 1/2. This Nash bargaining corner equilibrium generates per capita real income ½, which is greater than in autarky iff a > ln2/(ln3-2ln2/3) ≈ 1.09. Hence, for a large value of a and k = 1, a coordination failure occurs in the Walrasian regime and the Nash bargaining can successfully coordinate the division of labor. Since maximization of the Nash product is equivalent to the maximization of a social welfare function, it is straightforward that the Nash bargaining equilibrium is always Pareto optimal. This implies that the Nash bargaining equilibrium will not cause endogenous transaction costs. In the model with endogenous specialization, the Nash bargaining outcome not only achieves the Pareto efficient resource allocation for a given level of division of labor, but also ensures the Pareto optimum level of division of labor. Our example shows that for a small number of consumer-producers in an asymmetric Smithian model, the Walrasian equilibrium generates endogenous transaction costs that caused by a coordination failure of division of labor. In our example, asymmetric tastes for goods x and y imply that specialization in y receives more utility than specialization in x under the Walrasian regime, so that nobody is willing to specialize in x. In other words, the unfair distribution of gains from the division of labor between occupations might cause a coordination failure of division of labor in the Walrasian regime with a finite number of consumer-producers. In example 3.2 of chapter 3, we have shown that even if the set of ex ante different players is a continuum, the Walrasian equilibrium may generate a very unequal distribution of gains from the division of labor. This will generate incentives for those players who receive few gains to take collective actions for rent seeking. For instance, the government in the less developed country may have an incentive to impose an import tariff to manipulate terms of trade if all gains from the division of labor go to the developed country.

301

It is interesting to note that there might be a trade off between the reduction of endogenous transaction costs through Nash bargaining and exogenous transaction costs caused by that bargaining. The Pareto optimality of the Nash bargaining solution is based on the assumption that all players know their opponents’ utility and production functions and endowments, which is essential for each player to figure out the Nash bargaining solution. But the Walrasian equilibrium can be reached even if each player has no information about other players’ utility and production functions and endowments. If the collection of all the information is very expensive, then there is a trade off between endogenous transaction costs caused by trade conflict in the Walrasian regime with a finite set of consumer-producers and exogenous cost in collecting information in the Nash bargaining game. As will be shown in example 9.10, if players do not have complete information about their opponents’ utility and production functions, endowment, and transaction conditions, Nash bargaining may generate endogenous transaction costs too. Therefore, there is a trade off between endogenous transaction costs, caused by unfair distribution of the gains from the division of labor in the Walrasian regime with a finite number of consumer-producers, and endogenous transaction costs related to the information problem in the Nash bargaining game. The Nash bargaining game model in this section is a well closed general equilibrium game model where Walras’ law holds. This feature can be used to endogenize the level of division of labor and to explore the effects of bargaining on the equilibrium size of the network of division of labor and economic development. It can be shown that the Nash bargaining equilibrium is the division of labor iff the Pareto optimum is the division of labor. Also, if the exogenous transaction cost coefficient 1-k is sufficiently large, the equilibrium is autarky; otherwise, it is the division of labor. The shortcoming of the Nash bargaining model is that it does not spell out uncertainties and a time dimension. In the next two sections, the implications of information asymmetry and the time dimension will be examined. 9.5. Endogenous Transaction Costs caused by Information Asymmetry and Holding Up

If there is information asymmetry in a bargaining game, it will create a scope for cheating (a form of opportunistic behavior). Because of possible cheating, players do not trust each other even if they tell the truth. This causes endogenous transaction costs that prevent the realization of a mutually beneficial division of labor. For the division of labor, a specialist producer of a good certainly knows more about the production of that good than does the buyer, who is specialized in producing other goods. This information asymmetry is a driving force of economies of specialization, as well as a source of endogenous transaction costs. In subsection 9.5.1, we use a Nash bargaining model with information asymmetry to illustrate endogenous transaction cost caused by adverse selection. Then we introduce alternating offer bargaining into a model of endogenous specialization in subsection 9.5.2. The subgame perfect equilibrium model is then extended to investigate endogenous transaction costs caused by holding up behavior in the absence of moral hazard and adverse selection in subsection 9.5.3. Finally, we shall address the question of how a mechanism of reputation can eliminate endogenous

302

transaction costs and promote economic development using a repeated game model in subsection 9.5.4. 9.5.1. Economic Development and Endogenous Transaction Cost caused by Adverse Selection Example 9.11: A Nash bargaining game with information asymmetry. Assume that in the bargaining model in example 9.9, y is a simple house-cleaning service which involves no information asymmetry between seller and buyer, so that a specialist producer does not know much more than a buyer about the production of y. Therefore, a y specialist’s output level y + ys = 1 is common knowledge to everybody. But suppose that good x is a sophisticated manufactured good whose production involves significant economies of specialized information, so that a specialist producer of x has more information about its production conditions than a novice buyer. Suppose that an x specialist’s output level θ is 1.5 at probability 0.5, and is 0.5 with probability 0.5. Nature randomly chooses a value of θ and informs the x specialist about the realized value of θ. The y specialist has only common knowledge about the distribution function of θ. Assume that a change of profession involves a prohibitively high cost, so that it is not a choice when specialized information is generated by the division of labor. This implies that utility for the alternative profession is not a threat point. Inserting the data into the model in example 9.9, we have the Nash product V = V xV y = [(θ − X ) kY − u A ][(1 − Y ) kX − u A ] , where utility in autarky uA=2-2a is the threat point. Suppose the specialist of x (he) tells the specialist of y (she) the realized value of θ, and that she trusts what he says. The Nash bargaining equilibrium for the complete information case is (9.13)

X = θ/2, Y = 0.5, px/py = Y/X = 1/θ, ux = (θ-X)kY = θk/4, uy = (1-Y)kX = θk/4.

This implies that the price of x in terms of y decreases as the output level θ increases. Suppose that the realized value of θ is 1.5, but the specialist of x claims that θ = 0.5 and the specialist of y trusts him. Then the equilibrium terms of trade are X = θ/2 = 1/4, Y = 0.5, px/py = Y/X = 1/θ = 2. But the realized utility of the specialist of x is ux = (θ-X)kY = (1.5-0.25)k×0.5 = 5k/8, which is greater than his realized utility when he tells the truth, θk/4 = 1.5k/4 = 3k/8. Therefore, the x specialist has an incentive to understate his output level if the y specialist has incomplete information about it. Since she is aware of the possibility of cheating, she will not trust him when he says θ = 0.5 even if he is telling the truth. If the y specialist asks for the price that maximizes the expected Nash product based on her incomplete information, then the following problem generates a Nash bargaining solution.

303

Max : X, Y

EV = 21 [(23 − X )kY − u A ][(1 − Y )kX − u A ]

+ 21 [(21 − X )kY − u A ][(1 − Y )kX − u A ]

The solution is X = Y = 0.5, ux = (θ-0.5)k×0.5, uy = k/4. But for θ = 0.5, the x specialist’s utility is nonpositive at the terms of trade. Hence, the deal can be done only if θ = 1.5. The two players’ perfect rationality implies that the Nash bargaining equilibrium terms of trade is given by (9.13), and the division of labor is chosen for θ = 1.5 and ux = uy = θk/4 = 3k/8 > uA = 2-2a. The Nash bargaining equilibrium is autarky if θ = 0.5 for any value of k. Hence, for θ = 0.5 and k > 23-2a, the Nash bargaining equilibrium in the game with information asymmetry generates the Pareto inefficient level of division of labor. Inserting θ = 0.5 into (9.13) yields the Nash bargaining equilibrium for the game with no information asymmetry, which is X = ¼, Y = 0.5 and ux = uy = θk/4 = 3k/8 > uA = 2-2a for k > 23-2a. That is, the division of labor is chosen for θ = 0.5 and k > 23-2a, if all players have complete information. But with information asymmetry, possible cheating makes players distrust each other, so that autarky is chosen for θ = 0.5 and k > 23-2a . In other words, opportunistic behavior (cheating) causes endogenous transaction costs that prevent the realization of mutually beneficial division of labor. In textbooks, this kind of endogenous transaction costs caused by information asymmetry is referred to as adverse selection. The early model of adverse selection was developed by Akerlof (1970). This is also referred to as the model of the lemon. His story is similar to the one in this section. When buyers of second-hand cars do not have complete information about the quality of the cars, they can only accept the average price based on average quality. But the seller of high quality cars will ask for a price higher than the average. Hence, it is the high quality second hand cars that cannot be sold. This generates adverse selection in the sense that only low quality cars are sold in the market. Example 9.7 shows that reality is much more sophisticated than predicted by the model of adverse selection if individuals take into account interactions between information and strategies. Adverse selection is caused not only by information asymmetry, but also by the assumption that players are so naïve that they do not infer opponents’ private information from observed strategies. Hence, if this model is extended to a sequential equilibrium model with explicit interactions between strategies and information, then it can be shown that adverse selection would not take place if players are not so naïve. The algebra of such a model is cumbersome and can be found from Yang and Zhao (1998). 9.5.2. Alternating Bargaining Game in a Model of Endogenous Specialization Example 9.11 (Yang and Zhao, 1998): An alternating offer bargaining model of endogenous specialization. Let us now introduce alternating offer bargaining into the model in example 4.1 to study the implication of sequential bargaining for the size of the network of division of labor and economic development. Each consumer-producer can choose between specialization in x or y and autarky, so that utility in autarky is a threat point. Because of symmetry, there are two subgame perfect equilibria: one with the x specialist as the first mover and the other with the y specialist as the first mover. The two

304

equilibria in which the first mover has the advantage are symmetric. Without loss of generality, we assume that the x specialist is the first mover (referred to as player 1 or he) and the y specialist is the second mover (referred to as player 2 or she). The two players have the same discount factor δ. We use subscripts to denote the period. Suppose that player 1 offers X1 in exchange for Y1 in period 1. This implies that he offers the terms of trade px/py = Y1/X1 because of the market clearing conditions xs = xd = X and ys = yd = Y, and the budget constraint px/py = Y/X. Player 1’s decision rule is the same as in example 9.5. First, he must ensure that she will take the offer. Second, he maximizes his utility subject to the acceptance constraint. Hence, his offer is given by the following problem. (9.15a)

Max : u1x = (1 − X 1 ) kY1 , s.t. u1 y ≡ (1 − Y1 ) kX 1 = δ (1 − Y2 ) kX 2 ≡ δu2 y X 1 ,Y1

where u1x is the x specialist’s utility under the terms of trade in period 1, u1y is the y specialist’s utility under the terms of trade in period 1, and u2y is the y specialist’s utility generated by her counteroffer in period 2. Similarly, the y specialist’s counteroffer in period 2 is given by Max : u2 y = kX 2 (1 − Y2 ) s.t. (1 − X 2 ) kY2 = δ (1 − X 1 ) kY1 (9.15b) X 2 ,Y2

where we have used the fact that in a steady equilibrium X1 = X3 = X5 …, Y1 = Y3 = Y5 …, X2 = X4 = X6 …, and Y2 = Y4 = Y6 … Player 1 can then use backward deduction to solve for the problem (9.15b) first, and then plug the solution back into the problem (9.15a). In other words, his sequential rationality implies that he knows that player 2’s optimum decision in period 2 is dependent on his decision in period 1, which is in turn dependent on her decision in period 2. He will fully use this interdependence to pursue his selfinterest. (9.15b) yields X 2 = 1 − Y2 , Y2 = δ (1 − X 1 )Y1 . (9.16a) Inserting this into (10.15a) and then maximizing u1x with respect to X1 and Y1, we obtain the subgame perfect equilibrium terms of trade X 1 = δ /(1 + δ ), Y1 = 1 − X 1 = 1 /(1 + δ ) (9.16b) Player 1 offers this term and player 2 accepts in period 1. Plugging this back into (9.16a) yields player 2’s threatening counteroffer in period 2: X 2 = 1 /(1 + δ ), Y2 = δ /(1 + δ ) (9.16c) In this deduction, each player maximizes her utility for a given utility level of the opponent. Hence, the first order conditions for the subgame perfect equilibrium are the same as those for a benevolent dictator’s constrained maximization problem for the Pareto optimum. Hence, dynamic bargaining with complete information will not generate endogenous transaction costs. However, it does generate an unequal distribution of gains to trade. Inserting (9.16b) into the two players’ utility functions yields the equilibrium real incomes (9.17a)

(

ux = k 1 + δ

)

2

(

> u y = δk 1 + δ

)

2

for δ ∈ ( 0,1)

u x = u y for δ = 1 (9.17b)

p x p y = Y X = 1 δ if δ ∈ ( 0,1) ; p x p y = 1 if δ = 1 .

305

The equilibrium real incomes and relative price indicate that the first mover’s advantage is greater as the discount factor falls (or as the degree of impatience increases). As the discount factor tends to 1 or as the time lag between offer and counteroffer declines, the two players’ real incomes converge to the same level and the equilibrium terms of trade converge to the level of the impersonal market. But the above deduction is relevant only if the gains from the division of labor, net of transaction costs, are great, since the threat to choose autarky is not credible in this case.

(

Suppose δ ∈ ( 0,1) . If k ≤ k1 ≡ 2 −2 a 1 + δ

)

2

δ , then u y ≤ u A in the equilibrium given by

(9.16). Player 2’s threat to choose autarky is therefore credible. But so long as k1 > k > k0 ≡ 2 2 (1− a ) , the division of labor is still mutually beneficial. For this interval of parameter values, the subgame perfect equilibrium can be solved as follows. We first solve for X2 and Y2 as functions of X1 and Y1 from (9.15b), then insert the solution into (9.15a) and replace the constraint in (9.15a) with u1 y = (1 − Y1 ) kX 1 = u A = 2 −2 a . We can thus solve for the equilibrium values of X1 and Y1 from (9.15a). The equilibrium values of X2 and Y2 can be solved using the equilibrium values of X1 and Y1. The subgame perfect equilibrium for k ≤ k 1 is summarized as follows. (9.18)

X 1 = 1 2 a k , Y1 = 1 − (1 /2 a δ ) , X 2 = 1 2 a k Y2 = 1 − (1 /2 a k ), u x = k[1 − (1 /2 a k )]2 , u y = 2 −2 a

If k < k0 ≡ 2 2(1− a ) , the solution in (10.18) implies u x < u A = 2 −2 a . Hence, the subgame perfect equilibrium is autarky for k < k0. It is given by (9.18) for k ∈ (k0, k1) and is given by (9.15) for k ∈ (k1, 1). It is straightforward that the subgame perfect equilibrium is the division of labor iff the Nash bargaining equilibrium is the division of labor. That is, the alternating offer bargaining generates not only the efficient resource allocation, but also the efficient level of division of labor. The shortcoming of the dynamic bargaining model is that it cannot explain who is the first mover. All players know that the first mover has the advantage, so that they will compete for the first mover’s position. This competition implies that the solution we have just obtained cannot be an equilibrium. In the next section, we shall show that such competition for a greater share of gains from the division of labor will generate endogenous transaction costs.

9.5.3. Economic Development and Endogenous Transaction Costs Caused by Holdin Up Example 9.13: An alternating offer bargaining model with endogenous transaction costs. We now allow players to compete for the first mover position. We add period 0 to the dynamic game in example 9.12. After period 0, the structure of the new game is the same as in example 9.12. Hence, the game in example 9.12 is a subgame within the new game. In period 0, the two players sort out who is the first mover. Consider the case k ∈ (k1, 1), which implies that the Nash bargaining equilibrium is the division of labor. Because of backward deduction, the subgame equilibrium from period 1 on is still given by (9.16) and (9.17). Assume that each player has two strategies: tough (T) and soft (S) in period 0. The tough strategy implies that a player insists on being the first mover, and will not

306

accept any terms that give a lower utility than what the first mover receives. The soft strategy implies that a player accepts the second mover’s position if the opponent is tough, and agrees to fair terms, as given by the Nash bargaining solution, if the opponent is soft too. The game in period 0 for given subgame equilibrium in period 1 is described in Table 9.5. Table 9.5: Strategic Form of the Game to Compete for First Mover Advantage Player 2 T S Player 1 T uA , uA uH , u L u L , uH uD , uD S The first term in an entry represents player 1’s payoff (utility) and the second represents that for player 2. uA = 2-2a is the real income (utility) in autarky, uD = k/4 is the real income for the division of labor given by a Nash bargaining solution. uH = k/(1+√δ)2 is the first mover’s real income in the subgame equilibrium in period 1, and uL = δk/(1+√δ)2 is the second mover’s real income in the subgame equilibrium. It is easy to see that uH > uD > uL > uA for k > k1 > k0 and δ ∈ ( 0,1) . From Table 9.5, we can see that the two players receive real income in autarky if both of them choose a tough strategy, which means that no agreement can be achieved for the terms of trade. They receive real income for the division of labor outcome given by the Nash bargaining solution, and the gains from the division of labor are equally divided between them if both of them are soft. If one player is tough and the other is soft, then the tough one gets the greater gains; nevertheless, mutually beneficial gains from the division of labor are realized, despite the unequal distribution of income. The game in period 0, for given subgame perfect equilibrium in period 1, is a typical Nash game with two pure strategy Nash equilibria. We first prove that outcomes T-T and S-S are not pure strategy Nash equilibria. We argue by negation. Suppose T-T is a Nash equilibrium, so that we consider the upper-left entry in Table 9.5. Assume that player 1’s tough strategy is given. It is then clear that player 2 can increase her utility by deviating from T, which gives her uA, to S, which shifts the outcome from T-T to T-S and brings uL (> uA) to her. This implies that she has an incentive to deviate unilaterally from outcome T-T. This implies, by the definition of a Nash equilibrium, that T-T cannot be a Nash equilibrium. Using similar reasoning, we can show that S-S is not a Nash equilibrium either. It can be seen that no player has an incentive to deviate unilaterally from an asymmetric equilibrium S-T or T-S. For the Nash pure strategy game, the theory cannot predict which of the two Nash equilibria will take place. But if each player is allowed to choose a probability distribution for each and every strategy, we will have a unique mixed strategy Nash equilibrium. The probability distribution of pure strategies is called a mixed strategy. Mixed strategy is a way to make sure that the game is fair and that all players still participate even if any pure strategy outcome must be unfair to some player. When family members have a disagreement about which TV channel should be on, a fair solution is to flip a coin and let the stochastic process sort out the conflict of interests. Suppose player i chooses the soft strategy with probability qi and chooses the tough strategy with probability 1- qi. Since the purpose of a player’s mixed strategy is to confuse his opponent, player 1 will choose q1 such that player 2 feels indifferent between 307

her choices of T and S. For a given q1, player 2’s expected utility for her choice of T is (1 − q1 )u A + q1u H and that for strategy S is (1 − q1 )u L +q 1 u D . The two utility levels are indifferent iff (9.19a) q = (uL - uA )/(uH - uD + uL - uA) where (9.19b) uA = 2-2a, uD = k/4, uL = δk/(1+√δ)2, and uH = k/(1+√δ)2. Using the symmetry of the model, we can show that the mixed strategy of player 2, q2 that makes player 1 feel indifferent between his choices of T and S is the same as (9.19a). It can be shown that (9.20) q → 1/2 as δ → 1; q → 0 as δ → 0; and ∂q/∂δ > 0. where 1-δ can be considered as the exogenous bargaining cost, which is 0 for δ = 1, and takes on its maximum value for δ = 0. The fair Nash bargaining solution takes place with probability q2 and the probability that the mutually beneficial gains from the division of labor cannot be realized is (1-q)2. Hence, (1-q)2 represents endogenous transaction costs. (9.20) indicates that in the competition for a greater share of the gains from the division of labor, endogenous transaction costs are not 0 even if exogenous transaction cost tends to 0, though the endogenous transaction cost falls as the exogenous transaction decreases. We now consider the interval k ∈ ( k0 ,k1 ) . For this case, since player 2 receives utility in autarky uA, and so her threat to opt for autarky becomes credible, we must replace uL in Table 9.5 with uA. Also, uH in Table 9.5 is now given by (9.18) instead by (9.16). Using this information, we can find player 1’s expected utility q1q 2 u D + (1 − q1 )q 2 u H + (1 − q 2 )q1u A + (1 − q1 )(1 − q 2 )u A = q1 q 2 u D + (1 − q1 )q 2 u H + (1 − q 2 )u A , which monotonically decreases with q1 for a given q2. Hence, the optimum value of q1 is 0. Because of the symmetry, the optimum value of q2 is also 0. This implies that for k
k0 ≡ 2 2 (1− a ) , the subgame

perfect equilibrium in the game to compete a greater share of gains from the division of labor is autarky, while the Nash bargaining equilibrium, which is Pareto optimal, is the division of labor for k ∈ ( k0 ,k1 ) . In addition, the subgame perfect equilibrium is autarky with probability (1-q)2 for k > k1, while the Nash bargaining equilibrium is the division of labor for certain. Therefore, the competition for a greater share of the gains from the division of labor generates endogenous transaction costs that preclude the realization of mutually beneficial division of labor. Compared to neoclassical game models that generate endogenous transaction costs, in the bargaining model of endogenous specialization the endogenous transaction costs cause not only inefficient resource allocation, but also an inefficient level of division of labor and inefficient productivity. If you compare the result in this example to Fig. 4.1, the development implication of endogenous transaction cost will be clear. For k>k0, production takes place on the PPF in the absence of endogenous transaction cost; it takes place under PPF if the endogenous transaction cost is present. 9.5.4. How Can Endogenous Transaction Costs be Eliminated by Consideration of Reputation?

308

Example 9.14: A model of endogenous specialization and repeated game. If the pure strategy game in Table 9.5 can be repeatedly played, then endogenous transaction costs may be eliminated due to the consideration of reputation. Assume there are infinite periods t = 1, 2, … There is a stage game in each period, which is the same as the pure strategy game in Table 9.5. Then in all periods, there is a super game. In the super game, each player chooses a series of pure strategies to maximize her total discounted utility. It can be shown that in the repeated game, there is at least a Nash equilibrium that makes a cooperative outcome emerge from noncooperative behavior, or that eliminates endogenous transaction costs. We first consider a profile of two players’ series of strategies. Player 1 announces that he always chooses a soft strategy as long as player 2 does so, but he will choose a tough strategy forever if player 2 chooses a tough strategy in the previous period. Player 2 can find that for this strategy of player 1 her total discounted utility for a soft strategy series is 1 − δ T +1 u D S = u D 1 + δ + δ 2 +....+δ T = uD (9.21a) 1− δ where S can be solved from S − δS = (1 − δ ) S = 1 − δ T +1 . This total discounted utility converges to u D (1 − δ ) as T tends to infinity. If player 2 chooses a tough strategy in a

(

)

(

period, her immediate utility is u H = δk 1 + δ

)

2

> k 4 . But her utility afterwards is

always uA, because player 1 will refuse to cooperate. Hence, the total discounted utility for player 2 is (9.21b) u H + δ 1 + δ + δ 2 +L+δ t−1 u A = u H + δu A (1 − δ ) .

(

)

It is easy to see that (10.21a) is greater than (10.21b) iff (9.22) u D > (1 − δ )u H + δu A where uD = k/4 > uA = 2-2a for k > k0. Also uH = k/(1+√δ)2 > uD. It can be shown that if δ > 0.5, or if the discount rate is smaller than 100%, (10.22) becomes k 4 2 + 2 > k0 3 + 2 2

(

)

(

)

which holds for k > k0 because 4 2 + 2 > 3 + 2 2 . We may thus conclude that, provided players are not very impatient, the consideration of reputation can eliminate endogenous transaction costs, thereby making cooperation emerge from noncooperative strategic behavior. Here, long-run punishment for deviation from cooperation is the key to the result. The Folk theorem in game theory shows that there are many other Nash equilibria in the super game that can generate the same results, but with limited time for punishment of deviation. For instance, when a player chooses a tough strategy in the previous period, her opponent chooses a tough strategy for three periods and then comes back to a soft strategy afterwards. There are many institutional conditions that are essential for the reputation mechanism to work in eliminating endogenous transaction costs. Society must have a consensus about the moral code, and the legal regime must provide the appropriate enforcement for punishment of deviant behavior. For instance, if in an ancient tribe the “taking” of another’s possession was not considered punishable as stealing (or if Iraq’s

309

invasion of Kuwait was not considered punishable), then the punishment for stealing (or invasion) could not be enforced. In a Soviet-style economic system, private rights to residual returns and control of firms are not protected by law, so nobody will care about reputation, which generates residual returns. Again, if laws protecting business names, copyrights, and brands cannot be reasonably enforced, the reputation mechanism will not work either. Our model of repeated games shows that the consideration of reputation can reduce endogenous transaction costs caused by competition for a larger share of gains from division of labor, thereby increasing the equilibrium network size of division of labor and promoting economic development.

9.6. The Grossman-Hart-Moore Model of Incomplete Contract

Example 9.15: The GHM model of endogenous transaction costs caused by incomplete contract and two-sided moral hazard. Consider a business venture between two players whose sales revenue may be high, R=40, or low, R=10, and whose operating costs may be high, C=30, or low, C=10. Player 1’s effort level x determines the probability of realizing the high level of sale revenue. Assume for simplicity that x∈[0,1], and that the probability equals x. The probability of the low level of revenue, R = 10, is then 1-x. Player 2’s effort level y determines the probability of the business achieving the low level of operating costs, where y∈[0,1], and we assume that this probability equals y. The probability of the high level of costs, C = 30, is then 1-y. Player 1 may be considered the salesman and player 2 the producer of goods, so that the profit of their business is jointly determined by the two players’ effort levels. There are four potential outcomes for the business. Their probabilities are presented in Table 9.4. Table 9.4: Probabilities for Four Contingent States R 40 40 20 20

C 10 30 10 30

V 30 10 10 -10

Joint probability xy x (1- y) (1-x) y (1-x)(1-y)

Suppose, for simplicity, that the state of low revenue and high costs causes bankruptcy that yields zero profit. Then the expected profit of this joint venture is V = y (40-10)+x(1-y)(40-30)+(1-x)y(20-10)+(1-x)(1-y)0 = 10 ( x y + x + y ) In order to illuminate the incentive problem and the related moral hazard, we assume that player 1’s utility is V1-αx2, where V1 is the part of the profit that he receives. Player 2’s utility is V2-5x2, where V2 is the part of the profit that she receives. In this model, there are three periods. In period 1, two players sign a contract. In period 2, players choose their effort levels. In period 3, Nature chooses a state of outcome according to the prior 310

distribution function of the states and the players' effort levels. Then realized profit is divided according to the contractual terms. If each player can see the other’s effort level so that there is no moral hazard, then they can work out their optimum effort levels from the following maximization problem and specify a contract that requires such effort levels in period 1. Max: W = V − αx 2 − 5 y 2 = 10( xy + x + y ) − αx 2 − 5 y 2 s.t. x,y ∈[0,] 1 where W is the two players’ total expected utility. Since ∂W / ∂y = 10(1 + x − y ) > 0 for all x , y ∈(0,1) , the optimum value of y is 1 according to the Kuhn-Tucker condition. The Kuhn-Tucker condition for maximizing W with respect to x then yields the optimum contractual terms, which are Pareto optimal, in the absence of moral hazard. ⎧ 1 for α ≤ 10 y* = 1, x* = ⎨ ⎩ 10 α for α > 10 , Then, the Pareto optimum total utility generated by the business can be computed as follows. ⎧25 − α if α ≤ 10 ⎪ * W = ⎨100 ⎪⎩ α + 5 if α > 10 For this case, the structure of ownership and residual rights makes no difference. Player 1 can claim all profit and then pay player 2 according to her effort level; or player 2 can claim all profit and then pay player 1 according to his effort level; or they can jointly claim the profit and then divide this according to their effort levels. All three structures of ownership of profit will generate the same outcome in the absence of moral hazard. We assume now that each player cannot see the other’s effort level, or cannot verify this in court when a dispute occurs. Hence, a two-sided moral hazard exists. In addition, complete contingent pricing of the four outcome states is prohibitively expensive, so that an incomplete contract is used to get the business going. An incomplete contract specifies ownership structure of the business and it opens the scope for renegotiation, in which a difference in structure of ownership generates a difference in disagreement point, which affects ex post bargaining power of players. We first consider a symmetric structure of ownership, D. In this structure, the two players are partners. They sort out the contractual terms through ex post Nash bargaining in period 3. The contractual terms between them provide for splitting the profit. For the given terms, each player maximizes her expected utility (which is her share of profit net of the disutility of her effort) in period 1, with respect to her effort level for a given effort level of the other party. Player 1’s expected utility is Eu1 = (V / 2) − αx 2 = 5( xy + x + y ) − αx 2 and his optimum effort level, for the given effort level of player 2, is x = 5( y + 1) / 2α . Player 2’s decision problem in period 2 in anticipating the terms determined in ex post bargaining is Max: Eu 2 = (V / 2) − 5 y 2 = 5( xy + x + y ) − 5 y 2

311

and her optimum effort level for the given effort level of player 1 is y = (x + 1)/2 . The equilibrium is determined by the two optimum decisions. Considering possible corner solutions, the equilibrium is x = 0 , y = 0 if α ∈ (0, 5 /4) x = y = 1 if α ∈ (5 /4 ,5) x = 15 / (4α − 5) , y = (2α + 5) / (4α − 5) if α > 5 The total expected utility of the two players in structure D is WD = V − αx 2 − 5 y 2 = 0 for α ∈(0, 5 /4) WD = 25 − α for α ∈(5 /4 ,5) W D = 10( xy + x + y ) − αx 2 − 5 y 2 for α > 5 which is lower than the Pareto optimum level of total expected utility W * if α ∈(0, 5 /4) or α > 5 , and is the same as the Pareto optimum if α ∈(5 /4 ,5) . The difference represents the endogenous transaction costs caused by moral hazard and an incomplete contract. There are two asymmetric structures of ownership and residual rights. In structure A, player 1 is the owner of the business and claims its residual returns via his ex post bargaining power. Player 2 receives a reservation pay, which is exogenously given in the partial equilibrium model. For simplicity, we assume that the reservation pay is 0, so that player 2 will choose y = 0. The owner’s decision problem is Eu1 = V − αx 2 = 10 x − αx 2 Max: The solution is x * = 5 / α . The total utility of the two players is WA = 25 / α which is smaller than in the Pareto optimum. Since only player 1 is accountable for the effect of his effort on outcome, residual control rights are considered as asymmetric in this structure. Similarly, we can solve for the corner equilibrium in the asymmetric structure B, where player 1 receives the reservation pay and player 2 is the owner of the business. The solution is x = 0, y = 1, and WB = 5. which again is smaller than in the Pareto optimum. Hence, each of the three structures of ownership and residual rights generates endogenous transaction costs. In structure D, the two players partly free-ride on their opponents’ efforts, so that a two-sided moral hazard causes endogenous transaction costs. These endogenous transaction costs are attributable to the moral hazard of player 2 in structure A, and of player 1 in structure B. Considering all possible outcomes, two players can always use some side payment to choose the corner equilibrium with the highest total utility in period 1. An inframarginal analysis shows that for α ∈ (0, 5 /4), WA > WB > WD ; for α ∈(5 /4 ,5) , WD > WA > WB ; for α ∈ (5 , 43.2) , WD > WB , WA ; and for α > 431 ., WB > WD > WA . Hence, the equilibrium and its inframarginal comparative statics can be summarized in the following table. Table 9.5: Equilibrium Structure of Ownership and Inframarginal Comparative Statics

312

Equilibrium Structure

α ∈(0 ,5 4 )

α ∈( 5 4 , 43.2)

α > 43.2

A

D

B

Since player 2’s disutility coefficient of effort is fixed at 5, the disutility parameter of player 1’s effort α represents the relative disutility of effort of the two players. Hence, Table 9.5 implies that the relative disutility of effort between the two players determines which structure of ownership is the equilibrium. If player 1’s disutility of effort is relatively small, then he will be the owner of the business (structure A) in the equilibrium. If player 1’s disutility of effort is relatively large, then player 2 will be the owner of the business (structure B). If the disutilities of two players’ efforts are close, then they will choose a symmetric relationship between partners (structure D). If the revenue and cost coefficients are parameterized too, it can be shown that the player whose effort has the more significant effects on profit and who has the relatively lower disutility will be the owner of the business. If the effects of the two players’ efforts on profit and disutility are close, then a symmetric structure of ownership and residual rights will occur in the equilibrium. Hence, this model verifies the second part of the Coase theorem, that contracts in the market will maximize the gains from trade net of endogenous transaction costs if those costs are unavoidable.

9.7. Non-Credible Commitment and Soft Budget Constraint

In this section, we consider the simplest version of the Dewatripont and Maskin model (1995) of the commitment game and the soft budget constraint. Example 9.16: Dewatripont and Maskin model (1995). Consider a game with two regimes. In one of them, there is only a banker who is endowed with two units of capital. She considers making a loan to a project proposed by an entrepreneur. We call this the case of centralized case. In the other regime, there are two bankers, each with one unit of capital. We call this the case of a decentralized case. There is uncertainty about the project. The project could be good or bad. In addition, information is asymmetric: only the entrepreneur knows if his project is good or bad. A banker knows this only after the investment is made. There are two periods. If the project is good one, it is completed within one period and the banker receives a gross payoff R > 1 or a net payoff R-1>0 when she invests one unit of capital in period 1. If the project is a bad one, it cannot be completed within one period and the banker must consider whether she should refinance this project. If refinancing takes place, the banker's gross payoff is r with probability p, and 0 with 1-p, where p is a function of the banker's cost for monitoring the entrepreneur: C = bp2, where C is the total monitoring cost in period 1 and b is a coefficient. We assume

(9.23)

b∈(r2/8, r2/4)

313

The entrepreneur always receives payoff A if the project is completed; he receives payoff E if the project is not completed, regardless of whether the project is good or bad. It is assumed that A > 0 > E which implies that the entrepreneur always has an incentive to get loan and complete the project. We first consider the case of good project which is completed in period 1 and generates net payoff R-1 to the banker and A to the entrepreneur regardless of the regime. For a bad project, we can see that under a centralized system, the banker has an incentive to refinance this bad project if (9.23) holds. If she does not refinance in period 1 after one unit of the loan has been made, her net payoff is -1. If she refinances this project in period 2, she can maximize the expected net payoff pr - C -2 with respect to p subject to C = bp2. The optimum expected net payoff is thus (r2/4b) - 2, which is greater than -1 if (9.23) holds. But if (9.23) holds, the bad project generates a negative profit, or (r2/4b) - 2 < 0. It is inefficient to undertake this project at all. This illustrates that due to information asymmetry and a centralized system, the commitment not to refinance the bad project is not credible, so that the soft budget constraint (refinance) associated with this noncredible commitment generates endogenous transaction cost caused by refinancing the bad project. Now we consider the case of two bankers, each with one unit of capital. Suppose that the project is bad, so that the first banker cannot refinance the project in period 2. In period 1, the first banker maximizes αpr - C -1 with respect to p subject to C = bp2. Here, α∈(0, 1) is the fraction of gross payoff generated by the completion of the project that the first banker receives, or 1-α is the fraction of gross payoff received by the second banker, who refinances this project. The optimum p is p* = αr/2b. Here, we assume that the second banker cannot observe the first banker's monitoring intensity. The second banker will not refinance this project if her expected net payoff (1-α)pr - C -1 < 0, where p = αr/2b, or if (2-3α)αr22/3, refinancing will not take place. The entrepreneur who has the bad project will anticipate this, with his sequential rationality. Therefore, he will not ask for a loan from the outset. In other words, in a decentralized system, the commitment not to refinance the bad project is credible, and thereby the budget constraint is hard. Hence, the bad project will not occur in equilibrium for α>2/3. The literature of endogenous transaction costs is one of the most rapidly developed fields of economics. It includes the studies of moral hazard, incomplete information, various game models with endogenous transaction costs (the sequential equilibrium model, models of commitment game, and so on), mechanism design, and models of incomplete contracts and residual rights. In addition to formal models, this literature includes many insights, such as North’s ideas on development implications of the institution and transaction costs, Barzel’s economics of state (Barzel, 1997), Hayek's thoughts on spontaneous order (Hayek, 1944), and Buchanan’s constitutional economics (Buchanan, 1991), that are yet to be formalized. We speculate that the formalization of the ideas requires game models that can predict the evolution of game rules (institutions). But so far, evolutionary game models can only predict the evolution of strategies and outcomes (see, for instance, Mailath, 1998 and Weibull, 1995). For instance, so far we do not understand how the institution that penalizes theft, which is essential for economic development, emerged. Hence, much more formal analysis is needed for understanding

314

the development implications of institutions and endogenous transaction costs caused by state opportunism and deficient institutions.

Key Terms and Review Endogenous vs. exogenous transaction costs Moral hazard and related endogenous transaction costs Difference between moral hazard and adverse selection Risk aversion, risk loving, and risk neutral preferences Jesen inequality Certainty equivalence Incentive compatibility and participation constraint Functions of the contract, ownership, and residual rights Game, game rules, players, strategies, outcomes, payoff functions Strategic form and extensive form of a game Nash equilibrium, subgame perfect equilibrium, Bayes equilibrium, and sequential equilibrium Super game and stage games Effects of endogenous transaction costs on economic development Under what conditions can reputation be used to reduce endogenous transaction costs? Residual returns, residual controls, two sided moral hazard, and incomplete contract How can incredible commitment and soft budget constraint cause endogenous transaction costs?

Further Reading Surveys on principal-agent models: Arrow (1985), Hart and Holmstrom (1987), Prendergast (forthcoming), Holmstrom and Roberts (1998), Bolton and Scharfstein (1998), Gibbons (1998), and references there; The model of sharecropping: Singh (1989) and Stiglitz (1974); Model on incomplete contract and ownership structure: Hart (1995), Hart and Moore (1990, 1999), Grossman and Hart (1986), Holmstrom and Roberts (1998), Maskin and Tirole (1999), Tirole (1999), Segal (1999), Yang (2000b); Models of endogenous specialization and moral hazard: Yang and Yeh (1996), Lio and Yang (1997), Yang (2000); Models of moral hazard and adverse selection: MasColell, Whinston, and Green (1995, chs. 6, 13, 14), Varian (1993, ch. 8); Literature of transaction costs economics and economics of property rights without formal models: Williamson (1975, 1985), Barzel (1982, 1985, 1989), Furubotn and Pejovich (1974), Cheung (1970, 1983), North (1990); New political economy models with endogenous stealing: Marcouiller and Young (1995), Skaperdas (1992); General equilibrium models of moral hazard: Helpman and Laffont (1975), Legros and Newman (1996), Kihlstrom and Laffont (1979); Two-sided moral hazard: Bhattacharyya and Lafontaine (1995), Cooper and Ross (1985), Eswaran and Kotwal (1985), Romano (1994); Models with endogenous specialization and endogenous transaction costs caused by information asymmetry: Laffont and Tirole (1986), Lewis and Sappington (1991); Coase theorem: Coase (1960), Cooter (1989); Implications of endogenous transaction costs and institutions for economic development: North and Weingast (1989), North (1970, 1981), Macfarlane (1988), Mokyr (1990, 1993), Sachs (1997), Rosenberg and Birdzell (1986), World

315

Bank (1997); A good text and references on formal models of endogenous transaction costs: Milgrom and Roberts (1992). A good introduction to game theory: Dixit and Nalebuff (1991, pp. 7-84). Nash game and Nash equilibrium: Kreps (1990, p. 328), Fudenberg and Tirole (1991, p. 14). Nash equilibrium with mixed strategies: Fudenberg and Tirole (1991, pp. 18-19). Kreps (1990, Ch. 11), Fudenberg and Tirole (1991, Ch. 2), Tirole (1989, Ch. 11). Nash's axiomatic game model: Osborne and Rubinstein (1990). Bayesian game: Dixit and Nalebuff (1991, Ch. 2); intermediate texts can be found in Tirole (1989, Ch. 11) and Kreps (1990, Ch. 13), Fudenberg and Tirole (1991, Ch. 6). Subgame-perfect equilibrium, or perfect equilibrium: Dixit and Nalebuff (1991, Chs. 6 and 11), Tirole (1989, Ch. 11) and Kreps (1990, Sec. 12.7 and 15.3), Fudenberg and Tirole (1991, Ch. 4). Test: Duplicate the algebra in Kreps (1990, p. 556) or Tirole (1989, pp. 430-431), Fudenberg and Tirole (1991, Ch. 2); Nash bargaining game: Nash (1950), Osborne and Rubinstein (1994), Gibbons, R. (1992), Fudenberg and Tirole (1991), Kreps (1990), Tirole (1989), Dixit and Nalebuff (1991); Alternating offer bargaining game: Rubinstein (1982, 1985), Kreps (1990), Fudenberg and Tirole (1983, 1991), Osborne and Rubinstein [1990], Binmore, Osborne, and Rubinstein (1990), Stahl (1972); Function of price: Gale (1986), North (1987), Hayek (1945), S. Grossman (1989); Information efficiency of Walrasian equilibrium: Hurwitz (1973); Endogenous transaction costs caused by trade conflict: Cheng, Sachs, and Yang (forthcoming); Super game (repeated game): Fudenberg and Tirole (1991, sec. 4.3), Tirole (1989, sec. 6.3, pp. 247-251) and Kreps (1990, sec. 14.2, pp. 509-512); Sequential equilibrium and perfect Bayes equilibrium: Laffont and Tirole (1986), Lewis and Sappington (1991), Qian (1994), Kreps and Wilson (1982), Tirole (1989, pp. 436-44), Kreps (1990, secs. 12.7 and 13.2), Fudenberg and Tirole (1991, ch. 8), Farrell and Maskin (1989), Fudenberg and Tirole (1983); Commitment game and soft budget constraint: Dewatripont and Maskin (1995), Maskin (forthcoming), Qian (1994), Maskin and Xu (1999), Roland (2000).

Questions

1. According to the economics of property rights, the most important thing for economic development is not to win a game, but rather to choose game rules that determine who is the winner. If you try to design a dynamic game with information asymmetry to predict the evolution of game rules, what results (dynamics and comparative dynamics) will you expect from this kind of model? 2. According to North (1981), Macfarlane (1988), Sachs (1997, lecture notes), Huang (1991), and Mokyr (1990, 1993), the following conditions were essential for Industrial Revolution in Britain in 1750-1830. The transportation condition was good enough for the development of division of labor. A particular geographical condition ensured that Britain could avoid war with other countries at low defense expenses and they had a transportation advantage for trade. Constitutional monarchy and parliamentary democracy provided long-run political stability. The pursuit of riches was legitimated under the prevailing ideology, so that telnets were diverted from military, religious, and bureaucratic careers to business activities. Political variety among countries in Europe and decentralized political power in Britain encouraged experiments with new ideas, a variety of institutions, and new technology. Secured property rights, including the rights to intellectual properties, encouraged invention and innovation. A stable and non-predatory tax system and the government’s laissez-faire policy encouraged business activities. The liberation of civil society with respect to the state and the separation of the Crown’s coffer from the Bank of England enriched the creativity of society and restrained rent seeking. Equity Law made Common Laws very adaptive to

316

changing economic and social conditions in the presence of justice. Free association (i.e., setting up private firms needs no approval and license from the government) provided a favorable environment for free enterprise. Analyze which of the conditions are essential for economic development of a developing country in the 20th century. Use a specific country case to illustrate your point, and analyze which of the conditions are yet to emerge in this country and what can be done. 3. Why can rational behavior generate coordination failure? Why may a coordination failure between two players in a Nash game be a coordination success for society as a whole? Why may the Nash equilibrium in a non-cooperative game converge to a Walrasian equilibrium if the number of players tends to infinity and free entry is allowed? 4. According to Baechler (1976), a variety of polity and rivalry between hostile sovereigns in Europe was the critical condition for industrialization to take place first in Europe. But as observed by Baechler, all power tends toward the absolute. Use the model of the prisoner dilemma to analyze why the Princes in Europe could not coordinate with each other to establish a political monopoly. Baechler believes that the well developed feudal system, the Church, and geopolitical diversity provided checks and balances on state powers and were responsible for the political fragmentation of Europe. Can you use a game model to formalize his conjecture? According to Mokyr (1990, 1993), the Chinese Emperor’s political monopoly and cultural monopoly of Confucianism in East Asia prior to the 19th century was detrimental for the economic development of East Asia. Analyze why such monopoly could prevail during that period of time. 5. Cheung (1969) argued that sharecropping is a way to efficiently share risk if there are transaction costs in measuring work effort. Cheung has even found empirical evidence that land reforms are detrimental for economic development. Show that in example 9.2, if there is no moral hazard, risk sharing itself does not necessitate sharecropping. In example 9.2, we implicitly assume that the market for insurance is not available. If the well developed market for insurance, labor, and capital is available, is sharecropping still the second best? 6. What is the trade off between the generality of game rules and the generality of other aspects of a model in specifying an equilibrium model? Why do economists sometimes specify ad hoc demand functions and use misleading partial equilibrium analysis in game models? 7. Why can the Bayes equilibrium model and sequential equilibrium generate significantly higher explaining power than the Walrasian equilibrium model? 8. What are the differences and connections between interactions of quantities and prices in a Walrasian equilibrium model, and interactions of information and dynamic strategies in a sequential equilibrium model? 9. Consider the ownership structure in the equipment rental market. TV sets, video cameras, diggers, buckets, and other machines and equipment can be owned by their users or rented from owners. Apply the theory of optimum ownership structure based on the GHM model to analyze the endogenous and exogenous transaction costs associated with the two structures of ownership. Identify the conditions under which each of the two structures is the general equilibrium. Use the example to illustrate why the theory of optimum ownership may have nothing to do with the institution of the firm. 10. Holmstrom and Roberts (1998) indicate that in the model of incomplete contract in example 9.15, the institution of the firm is not well defined. They (p. 85) use BskyB, a satellite broadcasting system in Rupert Murdoch’s media empire, as an example to illustrate the shortcomings of the GHM model. BskyB is a highly successful organization that has created its wealth not by owning physical assets, but by crafting ingenious contracts that have given it influence over an effective network of media players. Satellite broadcasting requires a variety of highly complementary activities, including acquisition and development of programming, provision of the distribution system (satellites, transmitters and home receivers) and

317

development of encryption devices (to limit reception to those who pay), all of which must be carried out before the service can be offered. Other similarly complex and innovative systems of complements, like electric lighting systems or early computer systems, were largely developed within a single firm. BskyB instead relies on alliances with other firms. Topsy Tail is even more of a “virtual company.” It employs three people, but has sales of personal appearance accessories (combs, hair clips and such) approaching $100 million. Topsy Tail conceives of new products, but essentially everything involved in developing, manufacturing and distributing them is handled through an extensive contractual network. Benetton and Nike, to take some bigger and more conventional firms, also extensively rely on outsourcing and a small asset base. The critical asset in these cases is of course control of the brand name, which gives them enormous power to dictate how relationships among the various players are to be organized. Use these cases to discuss the difference between the theory of the firm in chapter 8 and the theory of incomplete contract in example 9.15. 11. Why, for the sake of her own self-interest, must an individual ensure that her opponent receive a sufficiently large share of the gains from the division of labor? 12. Some economists claim that the Nash bargaining game is a cooperative game that does not capture the noncooperative nature of the bargaining process. Comment on this claim in relation to Nash’s view about the connection between the nature of a Nash bargaining game and marginal disturbance. 13. Hurwitz (1973) shows that the Walrasian regime involves the lowest exogenous cost in collecting and transmitting information. But as we have shown in example 9.11, the Walrasian regime in the new classical framework with a finite set of consumer-producers may generate trade conflict that results in endogenous transaction costs. Use the trade off between endogenous transaction costs caused by trade conflict in the Walrasian equilibrium and endogenous and exogenous information costs in a Nash bargaining game to explain the phenomenon that impersonal pricing in the Walrasian regime becomes increasingly more important than individual specific pricing in bargaining as the network size of division of labor becomes increasingly larger. Relate your discussion to North's point that impersonal pricing is essential for reducing transaction costs and promoting division of labor. 14. Why does the Walrasian equilibrium model involve more information asymmetry than the sequential equilibrium model? Analyze the function of the invisible hand in promoting information asymmetry that generates economies of division of labor and in restricting endogenous transaction costs caused by information asymmetry in a Walrasian equilibrium model with endogenous specialization. 15. Friedman uses the story of the manufacturing of pencils to illustrate how the price system transmits information in such a way as to keep individuals away from what they need not know. When the price of timber increases, the manufacturer of pencils need not to know if the rise of prices is caused by a devastating forest fire, by a change of consumers’ tastes for furniture, or by some technical change in the other sector. If the level of division of labor is very high, exogenous transaction costs in collecting information about utility and production functions of trade partners, which is essential for bargaining, as described in examples 9.8 and 9.9, will be enormous. But impersonal pricing in the Walrasian regime can avoid all of these exogenous transaction costs. Use the example to illustrate how the invisible hand promotes information asymmetry and the related economies of division of labor while restraining the costs of information transmission. 16. Draw the distinction between fair pricing in the Nash bargaining game and equal income distribution, and discuss the implications of the distinction for the debate about “trade off between efficiency and equity.”

318

17. Analyze the significance of a legal system that protects residual rights of the owners of the firm, and of laws protecting brand, copyrights, and business names, in enabling the mechanism of reputation to play its role in reducing endogenous transaction costs. 18. Why does Hart claim that the model of principal-agent is not part of the formal theory of the institution of the firm? 19. John is considering establishing a business with his Russian partner to publish a Directory of American Businesses in Russian. He hopes the business will make money from advertisements of American companies in the book and from sales revenue net of printing costs in Russia. Suppose John approaches you to seek advice about which of the following three structures of ownership he should choose: (a) He hires the Russian partner to do the job in Russia and he himself takes care of the job in the US. (b) He enters a joint venture with the partner. (c) He asks for a salary from his Russian partner to pay for the job that he takes care of, which must be done in the US. Outline your advice, which is of course dependent on specific business conditions about which you may make assumptions. For instance, if the legal framework and enforcement of laws are not good, then the Russian partner’s special personal connections to government officials and his related effort may be important for reducing the risk, so that a joint adventure is more likely to be a better choice than the arrangement wherein John hires the Russian partner. 20. According to Weber (1961, pp. 251-52) and North (1981, pp. 158-67), a variety of institutions and business formats from medieval times, such as the annuity bond, the stock certificate, the bill of exchange, the private commercial company, the private bank, the mortgage, and the security of registration with the deed of trust, was essential for the industrialization of Europe in the 19th century. Use the models in this chapter to explain why the institutions were essential for economic development. 21. According to Mokyr (1993, p.41), the gentrification of the commercial and industrial class in Britain in the 18th and 19th centuries had a positive effect on early economic development, but was blamed for the decline of Britain’s leadership in the Victorian age. Also, industrial standardization, developed in European continent and the US, helped take over Britain in the second wave of industrialization. This implies that rivalry between Britain and other European countries was a competition between different game rules which provide the elite with incentives to contribute to the influence and power of their home country in international arena. This influence and power are based on economic development performance. Design a game model to explore the implications of this kind of game for economic development in Europe and the North Atlantic in the 19th century. 22. Many institutions reduce endogenous transaction costs of one type while increasing endogenous transaction costs of the other type, as shown in Milgrom and Roberts’ model of entry deterrence (see exercise 4), where an increase in endogenous transaction costs caused by information asymmetry is associated with a decrease in endogenous transaction costs caused by monopoly. Also, patent laws reduce transaction costs in specifying and enforcing rights to intellectual property, while increasing endogenous transaction costs caused by monopoly. The institution of the firm, together with business secrecy, can protect entrepreneurial ideas in the absence of patent laws. But the protection is not as effective as that which patent laws can provide (Mokyr, 1993). Analyze the trade offs between different transaction costs associated with different institutions. You may use documentation of historical evidence about benefits and costs of patent laws and the institution of the firm provided by North (1981, p. 165), Rosenberg and Birdzell (1986, pp. 144-64), and Mokyr (1990, pp. 248-54, 1993, pp. 40-46, 58-70) for your analysis. 23. North (1958, 1986) has found empirical evidence of a negative correlation between freight rates and economic development, and of concurrent evolution of the income share of the transaction sector and per capita real income. However, this empirical evidence is relevant

319

only to exogenous transaction costs. Endogenous transaction costs are much more difficult to measure. Can you find a way to test the theories of endogenous transaction costs developed in this chapter against empirical observations?

Exercises

1. The battle of the sexes. The two players wish to go to an event together, but disagree about whether to go to a football game or the ballet. Each player gets a utility of 2 if both go to his or her preferred event, a utility of 1 if both go to the other’s preferred event, and 0 if the two are unable to agree and stay home or go out individually. Suppose the two players agree to randomize their choices to make sure it is fair for both players to participate in the game. So he chooses the football game with probability p1 such that her expected utility is indifferent between the choices of football game and ballet, and she chooses the ballet with probability p2, such that his expected utility is indifferent between the two choices. Show that there are two pure strategy Nash equilibria and solve for the mixed strategy Nash equilibrium. Nash uses a fixed point argument to prove that for any mixed strategy Nash game, there exists a Nash equilibrium. 2. Suppose in the Nash (Cournot) equilibrium model of oligopoly in example 9.6, the inverse demand function p = a-bx involves uncertainties. With probability ρ, a = θh and with probability 1-ρ, a = θl. Firm 2 has private information about the realized value of a after Nature has chosen this. But firm 1 has only common knowledge about a. Solve for the Bayes equilibrium. If it is b instead of a that involves uncertainty, what is your answer? 3. Consider the Bayes game model in example 9.6 again. Assume that information asymmetry is symmetric between the two firms: ci involve uncertainties for i = 1, 2 and firm i has complete information about ci but has incomplete information about cj. The distribution function for c1 and c2 is the same as specified in example 9.6. Use the symmetry of information asymmetry to solve for the Bayes equilibrium. 4. (The entry deterrence game, Milgrom and Roberts, 1982). In a dynamic game with information asymmetry, there are two players. Player 1 is an incumbent firm producing a good, called the insider. Player 2 is a potential entrant into the business, called the outsider. The inverse demand function of the good is p = 9-x. The insider’s cost function is θx+2.25, where θ=3 with probability ρ and θ=1 with probability 1-ρ. The insider knows the realization of θ, but the outsider does not. The outsider’s cost function 3x+2.25 is common knowledge to all players. In period 1, the insider chooses an output level that will give the outsider some signal about the type of the insider, which will in turn affect the outsider’s decision concerning entry in period 2. The outsider maximizes her expected profit in period 2 with respect to the quantity to produce, and decides whether to enter the sector for given information updated from the observation of the insider’s output in period 1. The insider maximizes total profit over the two periods with respect to his output levels in the two periods. He is the monopolist in period 1, and again in period 2 if the outsider does not get into the business then. The two firms have a Cournot equilibrium in period 2 if the outsider gets into the business in period 2. Find the two firms’ output levels in the two periods, the posterior probability μ(p1) for θ=3 when the outsider has seen the market price in period 1, p1, the market prices over the two periods in the pooling equilibrium and screening equilibrium for the relevant interval of values of ρ. What is the outsider’s decision concerning entry upon observation of the insider’s output level in period 1?

320

5. Suppose that the cost function and demand function in a Bentrand model are the same as in the Cournot model, but the two firms’ strategies are to choose prices rather than quantities. Solve for the Nash equilibrium and prove that it is Pareto optimal. 6. Consider the model in example 9.1. Assume that the probability for R = 16 is θ>0.5 and that for R = 4 is 1-θ when effort level is high. The probability for R = 4 is θ and that for R = 16 is 1-θ when effort level is low. The agent’s utility function is lnw - lne. Solve for the efficient contract. 7. Consider the model in example 9.3. Assume that the transaction efficiency coefficient of good y is k1 for M1 individuals of type 1 and is k2 for M2 individuals of type 2. M1 + M2 = M. Apply inframarginal analysis to solve the comparative statics of equilibrium. Note that the utility equalization condition no longer holds between the two types of different individuals and more structures with incomplete division of labor are possible. 8. Consider the two-sided moral hazard model in example 9.15. Assume that the parameters are modified as follows. Joint probability R C V 20 5 15 xy 20 10 10 x (1- y) 10 5 5 (1 - x) y 10 10 0 (1-x)(1-y) Solve for the general equilibrium and its inframarginal comparative statics. 9. Consider the model in example 9.11. Assume that good x is a producer good, and that utility equals the amount of good y consumed. The production function of y is y+ys = (x+kxd)0.5Ly and the production function of x is x+xs = Lx – a. Solve for the Nash bargaining equilibrium and its inframarginal comparative statics. 10. Assume that player i’s endowment of labor is ai in the model in the preceding exercise. Solve for the Nash bargaining equilibrium and analyze the effects of the relative values of threat points on the relative bargaining power of a player. 11. Assume that player i’s discount factor is δi in the model in example 9.5. Solve for the subgame perfect equilibrium in the alternating offer bargaining game. Analyze the effects of relative degree of impatience (the relative value of δ 1 and δ 2 ) and first mover’s advantage on the relative bargaining power of a player. 12. In the following bargaining models, what are the determinants of the relative bargaining power of a player? (a) The bargaining model in exercise 10; (b) The bargaining model with information asymmetry in example 9.12; (c) The alternating offer bargaining game in exercise 11. 13. Consider the model in example 3.2. Assume that the two governments are allowed to choose between the two trade regimes: Nash tariff bargaining and free trade. Suppose there is a cost coefficient c in terms of utility lose caused by the collection of information that is essential for sorting out the Nash bargaining solution. Work out the critical value of c below which the Nash bargaining solution is the general equilibrium. 14. Consider the strategic form of the Nash game in the prisoner’s dilemma model. Each of two criminals can choose the strategy “confess” or “not confess” when caught by police. Their payoffs for four possible outcomes of the game are listed as follows. Prisoner 2 Confess Not confess Player 1: Confess -5 -5 1 - 10 Not confess -10 1 0 0 where the first figure in each entry is the payoff to prisoner 1. Identify the Nash equilibrium.

321

15. (Yang, 2000b) Introduce two-sided moral hazard into the model in example 8.1. Assume that transaction efficiency coefficients are random variables, dependent on buyers’ efforts in reducing transaction risk. The coefficients are structure specific since monitoring efficiency differs between goods and labor. In structure D (see Fig. 8.1), the transaction efficiency coefficient of good i, ki = θi with probability sisj and ki = 0 with probability 1-sisj where si is the effort level of a buyer of good i = x, y. In structure E, the transaction efficiency coefficient of good y, ky = θy with probability rxsy and ky = 0 with probability 1-rxsy where ri is the effort level of a buyer of labor used to produce good i in avoiding transaction risk. The transaction efficiency coefficient of labor used to produce good x, tx = μx with probability rxsy and tx = 0 with probability 1-rxsy. In structure F, ky = θy with probability rysy and ky = 0 with probability 1rysy. Transaction efficiency coefficient of labor used to produce good y, ty = μy with probability rysy and tx = 0 with probability 1-rysy. θi and μi are parameters for good i and for labor used to produce good i, respectively. Solve for the inframarginal comparative statics of equilibrium. 16. (Yang and Yeh, 1996) Consider a model with two ex ante identical consumer-producers. Each of them can produce a final good y and an intermediate good x. Each person’s utility function is: U=ln[(y+kyd)s] where y and yd are the quantities of the final good self-provided and purchased, respectively. k is the trading efficiency coefficient. The production functions for the final and intermediate goods are yp≡y+ys=(x+kxd)Ly

⎧θ H with probability ρ H ⎩θ L with probability 1 - ρ H

if Lx=βH, then xp≡x+xs = ⎨

⎧θ H with probability ρ L ⎩θ L with probability 1 - ρ L

if Lx=βL, then xp≡x+xs = ⎨

where superscript s stands for the amount sold and x and xd are the quantities of the intermediate good self-provided and purchased, respectively, Li is the amount of labor allocated to produce good I = x, y. It is assumed that L>βH>βL>0, θH> θL>0, 1>ρH>ρL>0. Each individual is endowed with L units of time that can be allocated between working and leisure, so that the endowment constraint for each person is Lx+Ly+s= L, where s is time allocated for leisure. Solve for inframarginal comparative statics of general equilibrium. (Hint: the algebra is cumbersome and the answer can be found from Yang and Yeh, 1996.)

322

Index Abdel-Rahman, H., 392 Abraham, K., 556, 572 absolute price level, 545 accumulation of experience, 466 adaptive behavior, 479 adaptive decision, 490, 495 Adelman, I., 24, 419 administrative decentralization, 588 advantage absolute, 61 comparative, 61 adverse selection, 304 aggregate demand and supply, 146, 345, 545, 466 aggregate output, 568 aggregate real output, 568 aggregate reliability, 344 aggregate transformation, 547 aggregate variable, 545 Aghion, P., 15, 24, 181, 264, 355, 410, 443, 445, 468, 475, 479, 500, 551, 572, 617, 618, 627 Aiginger, K., 264 AK model, 427, 434 Akerlof, G., 304, 572 Alchian, A., 264, 543, 611 Alesina, A., 181, 198 Alizadeh, P., 198 allocation of resource, 123 alternating offer bargaining model, 291 Anant, T., 572 application of mathematics, 22 Arndt, H., 11, 24 Arnott, R., 392 Arrow, K., 132, 316, 469 Arthur, W., 500 Asian financial crisis, 352, 354 asymmetric relationships, 243 asymmetric structure of residual rights, 246 Autarky, 452, 454, 463 Author, A., 102 authoritarianism, 8 Azariadis, C., 75, 95 Babbage, C., 132 Bac, M., 264 Bacchetta, P., 355, 617, 618 Bacha, E., 198 backward deduction, 292 Baechler, J., 2, 8, 24, 56, 97, 317, 323, 356, 396, 419, 443 Bag, P.K., 264 Bai, C., 602, 611, 614 Baily, M., 75, 95 balanced incentives, 283 Balassa, B., 83, 95, 181, 196, 198 Baldwin, R., 141, 163, 168, 198 Ball, L., 556, 572 Banerjee, A., 180, 198, 355, 500, 617, 618 bang-bang control problem, 454, 458 Baran, P., 98 Bardhan, P., 500, 584 bargaining cost exogenous, 308 endogenous, 309

Barro, R., 21, 24, 51, 162, 163, 224, 247, 339, 356, 437, 439, 443, 446, 467, 468, 469, 471, 475, 555, 572 Barzel, Y., 15, 24, 234, 271, 283, 315, 316, 327, 339, 356, 357, 579, 580, 582 Basu, S., 572 Bauer, P., 60, 95, 198, 267 Baumol, W., 476 Baumgardner, J., 132, 236, 368, 391, 392, 393 Bayes equilibrium, 293 Bayes updating rule, 295, 486 Bazovsky, I., 356 Becker, G., 15, 24, 132, 138, 233, 234 Beckman, M., 501 Behrman, J., 11, 16, 24, 32 Beik, P., 579 Benhabib, J. , 468 Berger, P., 264, 572 Berle, 359 Besley, T., 504, 508 Bernard, A., 476 Bhagat, S., 264, 572, 573 Bhagwati, J., 11, 24, 101, 193 Bhaskar, V., 163 Bhattacharyya, S., 316 Binmore, K., 316 binomial distribution, 345 Birdzell, L., 2, 24, 74, 133, 237, 265, 316, 320, 356, 395, 396, 412, 419, 420, 443 Black, F., 550, 555, 572 Blanchard, O., 263, 356, 579, 623 Bliss, C., 11, 24 Blitch, C., 25 Block, W., 163 Blume, A., 163 Bolton, P., 15, 24, 234, 262, 264, 316, 500 Borjas, G., 181, 198 Borland, J., 15, 55, 102, 264, 451, 453, 473, 475, 477, 480, 532, 544 Boserup, E., 241 Bouin, O., 611. 613 boundary condition, 459 bounded rationality, 479, 480, 496 Bowen, H., 96 Boycko, M., 621 Braudel, F., 2, 24, 41, 56, 393, 419, 443, 476 Brown, G., 392 Brunner, K., 543 Bruton, H., 60, 95, 196, 198 Bruun, O., 588 Buchanan, J., 15, 16, 17, 24, 32, 74, 95, 132, 579, 580, 582 Burke, E., 581 Burtless, G., 198 business cycle, 552, 558, 564, 565, 568, 571 efficient, 553 Byrd, W., 589, 623 Caballero, R., 551, 572 calculation costs, 414 calculus of variations, 454 Calvo, G., 264 Canton, E., 572 Cao, Y., 611 Capie, F., 5, 55

644

capital mobility, 618 capitalist institutions, 2, 5, 7, 16 Caroli, E., 181 Carter, M., 234, 264 Case, A., 444 central marketplace, 376 centralized pricing mechanism, 116 certain equivalent wealth, 277, 281 CES function, 123 Chandler, A., 24, 136, 234, 419, 423, 443, 476 Chang, C., 609, 627 Chang, G., 273, 498 Che, J., 626 Chen, A., 614 Chen, B., 443, 471, 476 Chen, Y., 616 Chenery, H., 3, 24, 168, 196, 198, 199, 204, 224, 419, 472, 473, 476 Cheng, T., 590, 623 Cheng, W., 55, 96, 198, 316, 435, 534 Cheung, S., 15, 24, 245, 246, 261, 264, 267, 270, 283, 316, 317, 327, 339, 356, 357, 580, 584 Chiang, A., 228 Cho, D., 436, 443 Chow, G., 475 Chu, C., 240 Ciccone, A., 141, 163 CIF, 44, 87, 182 circular causation, 163, 398 circulation of money, 566 classical contracts, 333 classical mainstream economics, 1, 13 classical theory of industrialization, 397 Cline, W., 198 Clower, R., 543 Coase theorem, 313 Coase, R., 15, 24, 75, 95, 132, 139, 238, 246, 261, 264, 267, 270, 316, 327, 334, 354, 357 coastal economy, 44, 54 coastal region,39 Coate, S., 508 cobweb model, 355, 619 Cole, W., 580 collective actions, 301 Colwell, P., 391, 392 Comment, R., 264, 572, 573 commercialization, 221, 400 commitment game, 313 commodity money, 531 circulation volume of, 542 value of, 542 comparative advantage acquired, 146 endogenous, 17, 102, 103, 106, 122, 170, 176, 222, 346, 466, 467 dynamic, 453 evolution, 452 endowment, 87 exogenous, 170, 176 exogenous technology, 63 exogenous endowment, 88 comparative dynamics inframarginal, 72, 122, 175, 379, 494, 523 marginal, 122, 259 comparative statics of

decisions, 126 inframarginal, 113 marginal, 113 competitiveness, 85 complete insurance, 346 composition of trade, 455 computation cost, 486 configuration, 65, 108, 248 occupation, 65 Conlisk, J., 476, 480, 500 constitutional order, 16 consumption variety management cost of, 226 contract, 452, 453, 558 control problem, 454, 457 control rights asymmetric distribution of, 242 control variables, 454 convergence absolute, 435 conditional, 435 β-convergence, 435, 436 convincing cost, 297 Conybeare, J., 96 Cook, L., 589 Cooper, R., 316 coordination cost, 233 coordination failure, 290, 556 aggregate risk of, 330 risk of, 331 coordination reliability, 329, 332 Cooter, R., 316 corner equilibrium Pareto optimum dynamic, 518, 564 Pareto optimum, 119 corner solution, 107, 454 corruption, 604 costate variables, 454 costs in broadening potential connections, 332 costs in deepening incumbent relationships, 332 costs of specifying property rights, 339 Craft, N., 10, 443, 580 creative destruction, 409 credit market, 294, 297 credit system, 569 crisis of success, 8 Crosby, A., 41 Cypher, J., 198 Dasgupta, P., 146, 162, 163, 428, 436, 439, 443, 446, 468 Deane, P., 580 Deardorff, A., 95 Deaton, A., 444, 527, 551, 572 Debreu, G., 22, 96, 99 decision horizon, 452, 564 endogenous, 525 degree of externality, 339 endogenous, 283 degree of industrialization., 367 degree of market competition, 340 degree of monetization, 533 degree of roundaboutness, 403 degree of urbanization,45 degree of vagueness of property right, 339 Dehejia, V., 101, 193 Deininger, K., 181, 198, 201, 578 Dellas, H., 551, 572

Delong, B., 476 Demsetz, H., 264, 356, 611 Dernburger, R., 611 destructive creation, 74 development economics, 472 classical, 1, 3, 14, 15 high, 15, 397 neoclassical, 8, 9, 10, 11, 16 new, 15 scientific approach to, 19 development phenomena, 127 development strategy, 194 development trap, 194 deviation, 456 Dewatripont, M., 234, 264, 274, 313, 317, 579, 623 Diamond, C., 41, 236, 278, 509, 527 dichotomy between investment and consumption, 506 Diderot, D., 102 Dietz, J., 198 differential of land price, 380 dilemma between justice and efficiency, 604 dilemma of Pareto optimality, 497 Din, M., 168, 198 Ding, G., 602 Dinopoulos, E., 572 disaggregate variable, 545 discount factor, 291 continuously compounded, 430 discount rate, 564 subjective, 430 discounted dynamic shadow price, 454 diseconomies of specialization, 452 distance between a pair of neighbours, 451 distortions, 565 division of labor, 37, 661 qualitative aspect of, 18 economies of evolution in, 449 economies of, 73, 106, 140, 178, 208 evolution of, 459, 464, 466, 472 exogenous, 122 endogenous, 451, 452 level of, 72, 221, 346, 467, 472, 358 network effect of, 372, 384, 442 network size of, 18, 373, 384, 545 structure of, 66, 502 Dixit, A., 15, 18, 62, 95, 140, 141, 145, 163, 185, 198, 225, 230, 234, 316, 356, 427 Dodzin, S., 31 Domar, E., 426 Dornbusch, F., 95 double coincidence of demand and supply, 530 Dowrick, S., 476 driving mechanisms for transition, 593 DS formula, 145 Du, J., 572, 576 dual land system, 604 dual structure, 22, 194, 372 dual track approach, 600, 604, 617 dual urban-rural structure, 380 Dydley, S., 96 durability, 555 durable producer good, 552, 556 Dybvig, P., 508

645

dynamic equilibrium, 464 market structure, 456 dynamic integer programming, 458 dynamic organism, 492 dynamic programming, 292 Easton, S., 162, 163, 224, 247, 467 economic development, capitalist, 2, 3, 7 positive analysis of, 19 state planned, 11 economic organism, 373 economics of property rights, 14 economies of agglomeration, 52, 384 type I, 363, 372 type II, 365,372 economies of complementarity, 148, 418 economies of roundabout production type A, 247 type B, 247 type C, 247, 402 economies of scale (see scale effect), 140, 428, 442 external, 140 internal, 140 specialization, 260, 414, 418, 452, 453, 464 specialized learning by doing, 553, 558 education, 51 efficiency allocation, 77, 128 in delimiting rights to contracting, 358 in enforcing a contract, 358 organization, 128 wage model, 556, 575 efficient contract, 279 Eichberger, J., 263, 264 Eichengreen, B., 6, 7 Ekelund, R., 79, 95 elasticity of demand own price, 144 elasticity of substitution, 123 Elvin, M., 395 emergence of a new industry, 403 emergence of cities, 371 emergence of middlemen, 230 emergence of new links, 399 emergence of new machines, 395, 441 emergence of new technology, 229 Emmanuel, A., 198 empirical research, 21 endogenous absolute advantage, 14 economic structure, 222 business cycle, 555 economic growth, 15, 441 externality, 15, 328 interest rate, 509 land prices, 380 number of consumer goods, 225 number of producer goods, 149 neoclassical growth model, 428 policy regime, 44 principal-agent relationship, 283 risk of mass unemployment, 545 specialization, 15, 305 trade regime, 79

enforcement of property rights, 332 entrepreneurship, 17 entry cost, 556 equilibrium comparative statics, 126 corner, 70, 115 general, 57, 66, 69, 70, 118 partial, 58 Pareto optimum corner, 119 Sequential, 295 Walrasian, 479, 485, 492 Eswaran, M., 316 Ethier, W., 18, 95, 140, 141, 148, 163, 165, 180, 230, 234, 427 Euler equation, 431 Evans, D., 198 evolution in number of goods, 427 evolution in number of intermediate goods, 441 evolutionary uncertainty, 495 ex post bargaining power, 312 exchange rate, 79 exogenous evolution of transaction efficiency, 448 exogenous growth, 426 expansion of the market, 466 expected monetary policy, 567 expected utilities, 276 experiment sequence, 489 experimentation costs, 479, 488 experts, 453 export oriented development pattern, 196 extent of openness, 54 extent of the market, 18, 41, 221, 345, 467 external economies, 443 horizontal, 164 vertical, 164 factor price equalization, 194 Fairbank, J., 24, 323, 470 Fan, G., 611, 613 Fang, W., 586 Farrell, J., 132, 316 Fauver, L., 264, 572, 573 Fei, J., 22, 24, 57, 96, 134, 163, 167, 181, 198, 393, 397, 472, 475, 616 fiat money, 536,566, 569, 571 financial crisis, 618 first welfare theorem, 76 first-order conditions, 454 Fischer, S., 567, 572 fixed learning cost, 207, 208 Flandreau, M, 6 Fleming, M., 18, 24, 154, 163, 164, 397, 419, 423, 476, 500 FOB, 44, 87, 182 Foreigh Diret Investment (FDI), 264 Frank, A., 198 Frank, C., 181, 198 free enterprise system, 359 free entry, 129 Freeman, R., 181, 198 Friedman, M., 164, 236, 504, 583, 584 Frye, T., 21, 162, 163, 224, 247, 339, 356, 467 Fudenberg, D., 316 Fujita, M., 15, 18, 24, 141, 168, 198, 363, 368, 390, 391, 392, 393 function of contracts, 452, 453

function of the market, 499 fundamentalism investment, 11 saving, 506 technology, 14 Furubotn, E., 316, 356, 583 futures market, 453, 558 horizon, 452 Gabisch, G., 572 Gale, D., 316 Gallup, J., 21, 35, 46, 49, 52, 54, 55, 162, 163, 180, 198, 224, 230, 467 Galor, O., 181, 198, 469, 476 game rule, 289 evolution of, 315 Gans, J., 163, 198 Garcia-Pena Losa, C., 181 Garth, S., 132 GDP density, 37 general equilibrium dynamic, 564 general price level, 566 geographical concentration of transactions, 373 geographical pattern of residence, 371 geography, 38 GHM model, 310 Gibbons, R., 15, 24, 262, 264, 316 Glendon, M., 3, 56 global capitalism, 5 globalization, 23 Gomory, R., 95, 96, 97, 198 Goodwin, R., 555, 572 Gordon, B., 363 Gordon, D., 75 government intervention, 565 gradualism, 579 Graham, S., 436, 443 Granick, D., 588 Gray, C., 599 Gray, J., 567, 572 Gray, L., 580, 599 Great Depression, 331, 546 Green, E., 543 Green, J., 316, 356 Greenwood, J., 181 Grier, K., 550, 572 Groenewegen, P., 2, 24, 132 gross domestic product (GDP), 77 gross national product (GNP), 77 Grossman, G., 15, 24, 94, 96, 140, 146, 181, 198, 264, 443, 446, 464,469, 475, 480, 505 Grossman, S., 316, 357, 500 Groves, T., 611 growth phenomena, 127 Gwartney, J. 163, 467 Hadley, G., 132 Hagen, E., 1 Hahn, F., 62, 132, 392 Hai, W., 611, 613 Hall, J., 2, 56 Hamilton, B., 132, 392 Hamiltonian function, 454 Hamiltonian, 454 Hammour, M., 551, 572 Hanstad, T., 603 Harris, J., 102, 395 Harrod, R., 426

646

Hart, O., 15, 24, 261, 264, 279, 316, 328, 357 Hartwell, R., 419 Hayek, F., 315, 316, 498, 500, 581, 583, 584, 585, 587, 623 He, Q., 590, 607, 615, 616, 623, 624, 625 Headrick, D., 6 Heckscher, E., 59, 60, 89, 95 Heckscher-Ohlin (HO) model, 87 Hegel, G., 395 Heijdra, B., 163, 165 Heisenberg, W., 21, 201 Hellman, J., 600 Helpman, E., 15, 24, 96, 140, 146, 316, 356, 443, 446, 464, 468, 475, 480, 505 Henderson, J., 376, 392 Hendley, K., 599 Hessian, 249 Hicks, J., 419, 555, 572 hidden action, 276 hidden information, 276 hinterland, 55 Hirschman, A., 11, 18, 24, 149, 163, 164, 198, 201, 397, 398, 419, 476, 500 HO theorem, 93, 192 Hoffman, P., 28 Hogbin, G., 392 holding-up, 307, 453 Holmstrom, B., 15, 24, 261, 262, 264, 268, 274, 281, 283, 316, 318, 357, 361 Hondai, S., 613 Hong, Y., 611 hourly wage, 326 Houston, J., 264, 572, 573 Houthakker, M., 14, 24, 26, 132, 234 Howitt, P., 15, 24, 410, 443, 445, 468, 475, 551, 572 Hua, S., 583 Huang, R., 4, 317, 396 Huang, Y., 611 Huang, Z., 601 Hughes, J., 419 human capital, 450, 452, 453, 557, 564 Hume, D., 31, 528 Hurwicz, L., 224, 316, 318 identical peers, 453 immiserizing development, 179 imperfect sequential rationality, 495 impersonal networking decision, 213 import substitution, 79 incentive compatibility, 350 incentive constraint, 282 incentive provision, 276 income distribution, 179, 194 income redistribution, 567 income share of the roundabout sector, 467 income share of transaction cost, 466 income trasfer, 567 incomplete contract, 310, 312 incomplete information, 293 incomplete insurance, 349, 353 incumbent trade partners, 339 index of malaria, 52 indirect utility function, 115 indivisibility, 555, 557

industrial linkage, 148, 163 backward, 164 externality of, 398 forward, 164 pecuniary externality of, 398 Industrial Revolution, 395, 399 industrialization, 153, 194 395, 418, 497 big push, 9, 154, 157, 398, 585 endogenous degree of, 158 balanced vs. unbalanced, 398 market led, 398 state planned, 398 export oriented big push, 498 inequality of income distribution, 77, 180 ratcheting process of, 181 inflation, 567 inflation-stagnation, 567 informal credit, 510 information gains, 479, 488 information updating, 490 information asymmetry, 293, 303, 453 degree of, 223 absolute, 496 lack of, 479, 486 organization, 488, 494, 496, 499 prior, 294, 295, 493 posterior, 493 inframarginal analysis, 15, 17, 107, 182 institution of the firm, 17, 242, 412 insurance, 326 integer problem, 546 interior extreme, 249 interior solution, 454 international trade emergence of, 224 interpersonal dependence, 222 interpersonal loan, 509 intertemporal trade, 504 investment in information, 488 investment, 576 invisible hand, 70 involuntary unemployment, 565 Jacobs, J., 393 Jansen, ?., 5 Jarrell, G., 264, 572, 573 Jefferson, G., 611 Jensen, M., 264 Jesen inequality, 276 Jevons, W., 543 Jian, T., 616 Jin, Y., 611, 613 Jin, H., 623 job-shifting cost, 553, 564 Johnson, D., 603 Johnson, H., 96 Jones, C., 198, 201, 428, 435, 439, 443, 446, 468, 476 Jones, E., 2, 41, 55, 56, 97, 133, 238, 356, 419 Jones, R., 95, 542 Jovanovic, B., 181, 468 Judd, K., 24, 140, 427, 443, 464, 468, 475, 480 Jullien, B., 500 Kaldor, N., 3, 24, 419, 423, 476 Kamarck, A., 41

Kanemoto, Y., 392 Kang, Y., 103 Kaplan, S., 264, 572, 573 Karman, A., 132, 392 Karoly, L., 181, 198 Katz, L., 181, 198, 556, 572 Katz, M., 132, 181 Kelley, A., 141, 168, 392 Kelly, M., 162, 163, 198, 420 Kemp, M., 198 Kendrick, D., 15, 392 Keren, M., 264 Keynes, J., 8, 10, , 525, 552, 572 Khandker, A., 168, 198 Kihlstrom, R., 316, 356 Kim, S., 132 Kim, Y-G., 163 Kindleberger, C., 7, 55, 149, 198, 267 King, G., 1 King, R., 436, 443, 543, 556, 572 King, S., 500 Kirby, W., 621 Kirzner, I., 476 Kiyotaki, N., 530, 543 Klerman, J., 181, 198 Knight, F., 25, 137, 260, 264 Knowledge of organization, 502 Kohli, U., 60, 96, 198, 199 Kormendi, R., 550, 572 Kornai, J., 24, 356, 583, 584, 587, 612, 623 Kotwal, A., 316 Kravis, I., 198 Kremer, M., 238, 263, 356, 362 Kreps, D., 264, 316, 479, 480, 495, 500 Kroc, R., 480 Krueger, A., 8, 11, 14, 16, 24, 31, 79, 96, 198 Krugman, P., 15, 18, 22, 23, 24, 85, 96, 97, 140, 141, 146, 162, 163, 168, 169, 181, 182, 197, 198, 234, 237, 363, 368, 376, 390, 391, 392, 393, 397, 419 Kubo, Y., 419, 423 Kuhn-Tucker theorem, 107 Kuo, S., 181, 198, 616 Kurz, M., 62, 132, 392 Kuznets, S., 3, 24, 134, 181, 198, 224, 409, 472, 473 Kydland, F., 556, 572 La Porta, R., 40, 594 labor shift model, 555 labor surplus, 472 Laffont, J., 316, 356 Lafontaine, F., 316 Lagrange, J., 1 laissez-faire, 497 land price differential, 365 land rental contract, 281 Landes, D., 24, 27, 29, 40, 42, 97, 356, 470 landlocked economy, 35, 44 Lang, L., 264, 572, 573 Lange, O., 356, 499, 500, 583, 623 Lardy, N., 582, 592, 597, 609, 612, 614, 623, 624, 625 Laslett, P., 2, 56 Lau, L., 596 Lavoisier, A., 1

647

law of reciprocal demand, 111 law of specialization, 111 Lawrence, R., 181 Lawson, R., 163, 467 Leamer, E, 96 learning ability of society, 448 learning by doing, 448, 452, 453, 464, 466 individual specific, 452 Lee, D., 41 Legros, P., 316, 356 Lehn, K., 356 Lenand, H., 508 Lenin, V., 9, 500, 586 Leontief, W., 96 Lerner, A., 87, 95 level of specialization, 105, 221, 346, 464 Levhari, D., 264 Levine, R., 436, 443 Levinsohn, J., 94, 96 Lewis, W., 1, 3, 11, 22, 24, 96, 98, 134, 149, 163, 167, 168, 181, 198, 199, 200, 264, 316, 393, 397, 472, 475, 504 Li, D., 602, 611, 623 Li, H., 181, 198 Li, P., 603, 612 Li, W., 623 Liebowitz, S., 95, 132 life expectancy, 51 Lilien, D., 555, 572 Lin, J., 273, 392, 435, 443, 471, 476, 603 linkage network, 153 Lio, M., 15, 30, 33, 138, 234, 239, 263, 316, 344, 348, 356, 368, 394, 399, 419, 424, 545 Lippman, S., 500 Lipsey, R., 198 Lipton, M., 356, 392 Little, I., 15 Liu, D., 264 Liu, M., 198, 202, 203, 270, 444 Liu, P-W., 147, 162, 163, 197, 247, 264, 419 Liu, Y., 588, 608 Livingstone, I., 11, 24 Lo, X., 583 local community, 339 location pattern of residences, 380 location pattern of transactions, 372, 384 Locay, L., 132 long term contracts, 453, 567 Long, J., 556, 572 Lopez, A., 46 Lopez-de-Silanes, F., 40, 594 Lorenz, H., 572 Loury, G., 508 Loveman, G., 264 Lucas, R., 24, 443, 444, 464, 505, 567, 572 Luo, S., 592 Luo, X., 584 MacFarlane, A., 2, 4, 24, 56, 316, 317, 356, 396, 419, 443 MacLeod, W., 264 Maddison, A., 471 Mailath, G., 163, 315

malarial intensity, 46 Malcomson, J., 264 Mankiw, N., 443, 446, 476, 556, 567, 572 Mann, M., 356, 419 Manne, H., 356 Manning, R., 479, 500 Mantel, R., 96, 99 Mao, Z., 588 Mao's socialist system, 588 Marcouiller, D., 316, 356 marginal analysis, 110, 175 dynamic, 431 marginal cost pricing rule, 75 marginal rate of transformation, 105 Margolis, S., 95, 132 market clearing, 115, 455, 457 market failure, 552 market integration, 223, 230 market socialism, 499, 584 market structures, 455 Marshall, A., 11, 13, 14, 24, 58, 114, 137, 140, 358, 363, 391, 392, 395, 401, 420, 443, 476, 505 Marx, K., 74, 505, 552 Mas-Colell, A., 96, 316, 356 Maskin, E., 15, 16, 24, 264, 274, 313, 316, 317, 579, 623 Matsuayma, K., 141, 163, 476 Matsui, A., 163 Mauss, M., 340, 359 maximum principle, 454 Maxwell, H., 102 Mayer, W., 96 McCall, J., 500 McGuirk, A., 422 McKenzie, L., 87, 95 McMillan, J., 579, 611, 623 McNeil, W., 2, 24, 28, 41, 56 measure, 115 Meckling, W., 264 medium of exchange, 533, 567 Meek, R., 132 Meguire, P., 550, 572 Meier, G., 11, 16, 24, 95, 196, 199, 201, 204 Meltzer, A., 543 Men, Q., 583, 584 Meng, X., 611, 613 Menger, C., 543 mercantilism, 79 Milgrom, P., 15, 24, 262, 264, 274, 281, 283, 316, 321, 328, 336, 354, 356, 361 Mill, J., 505 Mills, E., 132, 392 Minami, R., 613 Mirrless, J., 15 mixed strategies, 290 model of labor surplus, 397 Modigliani, F., 504 Mokyr, J., 2, 4, 15, 24, 29, 30, 32, 56, 74, 97, 238, 316, 317, 320, 323, 334, 346, 356, 358, 360, 396, 399, 412, 419, 420, 422, 443, 468, 470, 476, 581, 627 monetary policy irrelevance, 567 monetary policy, 567 money stock, 566 money substitute, 531

money supply, 567 monopoly power, 453, 464 Monteverde, K., 356 Moore, B., 264, 316, 357 moral hazard, 275, 279 two-sided, 310 Morgan, P., 479, 500 Morgan, T., 60, 96, 198, 199 Mori, T., 392 Morris, C., 419 Mueller, M., 601, 602 multilateral bargaining equilibrium, 453 multiple equilibria, 157 type I, 217 type II, 217 type III, 217 Mundlak, Y., 422 Munneke, H., 391, 392 Murakami, N., 264 Murphy, K., 15, 18, 24, 96, 132, 140, 141, 154, 158, 163, 181, 198, 199, 233, 234, 290, 392, 420, 476, 500, 556, 572 Murray, C., 46 Myrdal, G., 18, 24, 163, 164, 196, 198, 200, 476, 528 Naisbitt, J., 33 Nalebuff, B., 316 Naranjo, A., 264, 572, 573 Nardinelli, C., 391, 392, 393 Nash bargaining equilibrium, 300, 301 Nash bargaining game, 299 Nash equilibrium, 289, 290 pure strategy, 307 mixed strategy, 308 Nash game, 81 Nash product, 300 Nash tariff game, 289 Nash tariff negotiation, 82 Nash, J., 82, 96, 302 National Research Council, 439, 443 natural agents, 472 natural unemployment, 546, 549 Naughton, B., 605, 608, 611, 613, 623 Nee, V., 588, 606 Nelson, R., 196, 198, 200, 480, 500 neoclassical framework, 22 neoclassical law of demand, 113 neoclassical mainstream, 13 neoclassical marginal analysis, 12 neoclassical optimum decision, 212 Nettels, C., 580 Network effect, 69 networking, 23 new economic history school, 15 new political economics, 16 Newman, A., 180, 198, 316, 356 Ng, S., 58, 95, 238 Ng, Y-K., 15, 24, 132, 246, 264, 269, 356, 361, 392, 410, 419, 424, 451, 475, 480, 489, 500, 548, 556, 572 Nguyen, D., 476 Nolan, P., 608 nominal prices, 566 non-cyclical pattern of division of labor, 566 nonexclusivity, 341 nonlinear programming, 67, 107 nonrivalry, 341

648

non-strategic behavior, 271 Norberg, K., 28 Norman, V., 62, 95 normative analysis of economic development, 21 North, D., 2, 4, 13, 14, 15, 21, 24, 29, 33, 76, 133, 162, 163, 224, 235, 271, 272, 297, 316, 317, 319, 320, 323, 331, 356, 359, 392, 396, 400, 413, 422, 443, 469, 476, 579, 581, 582, 587, 594 Novice, 453 number of a person's partners, 451 number of a person's traded goods, 455 number of links, 395, 399 Nurkse, R., 18, 24, 149, 154, 163, 164, 397, 419, 476, 500 Nussbaum, F., 580 objective functional, 452, 454 ocean-navigable river, 39 Ofek, E., 264, 572, 573 Oh, S., 543 Ohlin, B., 59, 60, 89, 96 Oi, J., 588, 605, 606, 608, 609 Olson, M., 272, 400, 421, 581 open market operation, 567 openness, 51 opportunistic behaviour, 452, 453 optimum speed of learning by doing, 452 organization capital, 523 organization efficiency, 77, 128 organization structure, 114 organization utility, 549 O'Rourke, K., 7 Osborne, M., 82, 96, 316 Ostroy, J., 543 Otsuka, K., 264 outcomes, 289 Owen, T., 6, 599 Page, S., 392 Palma, B., 60, 95, 98, 181, 196, 198, 200 Panagariya, A., 198 panic flight of capital, 618 parallel connection, 332 Pareto improving policies, 565 Pareto optimum, 76, 496, 565 Pareto superior, 455 Parker, E., 611 Parkin, M., 543, 567, 572 partition of parameter space, 121 path dependence, 488 Patten, R., 527 pattern of individuals’ residences, 384 Paxson, C., 444 payoff functions, 289 pecuniary externalility, 164 Pei, M., 602 Pejovich, S., 316, 356, 583 Peng, Y., 606, 610 per capita GDP, 35 per capita real income, 78, 117 perfect Bayes equilibrium, 294 perfect recall, 488 Perkings, D., 588, 589 Perkins, F., 611, 613 Petty, W., 1, 24, 102, 132, 363, 392 Philips, U., 580 Phillips curve, 567

physical labor, 564 piece rate wage, 326 Pigou, A., 139, 238, 327 Pilon, R., 601, 602 Pincus, J., 96 Ping, X., 583 Pipe, ?., 356 Pistor, K., 16, 579, 597, 599, 600 Plato, 531 players, 289 Plosser, C., 543, 556, 572 pooling equilibrium, 296 population density, 37, 54 posterior probability, 295 potential trade partners, 339 Prebisch, R. 198 precautionary saving, 508 Prendergast, C., 316 Prescott, E., 556, 572 Prestowitz, C., 85, 96, 97 price control, 584 pricing cost, 479, 486 principal-agent model, 278 Printchett, L., 505 prisoners’ dilemma, 290 private property rights, 323 problems of economic development, 114 of resource allocation, 114 production concentration, 223 production function for the firm, 251 ex ante, 257 ex post, 257 production possibility frontier (PPF), 73 aggregate, 178 production roundaboutness, 520 productivity, 502 implications of business cycles and unemployment, 557 progress, 222, 571 profession, 455 Prosterman, R., 603 Puga, D., 141, 163, 168, 198, 204 purchasing power, 569 parity (PPP), 35, 79 Qian, Y., 70, 264, 316, 356, 579, 581, 582, 588, 590, 592, 597, 601, 602, 623, 627 Quah, D., 476 quality of institutions, 51 Quesnay, F., 1 Quigley, J., 376, 392 R&D based model, 436 Rabushka, A., 500 Radelet, S., 43, 45, 354, 356 Radner, R., 264 Rae, J., 132 Ram, R., 181, 198, 201 Ramey, G., 550, 572 Ramey, V., 550, 572 Ramsey model, 426, 429, 505 Ranis, G., 3, 22, 163, 167, 168, 181, 198, 393, 397, 475, 616 Rashid, S., 132, 168, 198 rate of growth of the extent of the market, 466 Rawski, T., 611 Ray, D., 16

real business cycle model, 556 real business cycle, 567 real variable, 566 Rebelo, S., 443, 468, 475 recession, 565, 569 recursive paradox, 480 Reingnum, J., 500 relational contracts, 333 relative land price, 390 relative price, 566 renegotiation, 312 Renis, G., 22, 24, 57, 96, 134, 198 rent seeking, 301 repeated game, 309 reputation, 310 residual returns, 243 resource allocation, 117 revenue grabbing, 602 Reynolds, B., 613 Reynolds, L., 7, 55, 419 Ricardian Model, 61, 63 Ricardo, D., 60, 61, 62, 71, 84, 95, 96, 97, 102, 129 Rice, R., 363, 372, 390, 392, 393, 394 Richardson, D., 96 Riezman, R., 96 rights specified in a contract, 335 rights to contracting, 335 risk aversion, 276 degree of, 277, 344 risk loving, 276 risk neutral, 276 risk of coordination failure, 326, 329, 339, 545 risk of mass unemployment, 331, 546 risk sharing, 276 Riskin, C., 500, 587, 588 Robbins, L., 24 Roberts, J., 15, 24, 261, 262, 264, 268, 316, 318, 321, 328, 336, 354, 356, 357 Robinson, S., 196 Rodrik, D., 181, 198 Roemer, J., 500, 572, 584 Roland, G., 264, 579, 580, 587, 590, 593, 596, 602, 617, 623, 626, 627 Romano, R., 316 Romer model, 437 Romer, P., 15, 18, 140, 427, 434, 435, 436, 437, 442, 443, 444, 445, 446, 464, 468, 469, 475, 476, 480, 505, 556 Ronnas, P., 606 Rosca, 511 Rosen, S., 14, 15, 17, 24, 74, 95, 132, 138, 234, 236, 258, 476 Rosenberg, N., 2, 24, 74, 133, 237, 265, 316, 320, 356, 395, 396, 412, 419, 420, 443, Rosengard, J., 527 Rosenstein-Rodan, P., 18, 24, 149, 154, 163, 164, 397, 398, 419, 423, 476, 500 Ross, T., 316 Rostow, W., 469, 476 rotating savings, 510 Rotemberg, J., 572 roundabout production chain, 399 roundabout productive costs, 467 roundaboutness, 399, 400

649

Rozman, ?., 5 Rubinstein, A., 82, 96, 316 rule of laws, 597 RY theorem, 194 Rybczynski, T., 96, 101 Sachs, J., 9, 10, 16, 21, 35, 43, 45, 46, 47, 49, 52, 54, 55, 85, 96, 141, 158, 162, 163, 165, 170, 180, 181, 198, 200, 224, 230, 316, 317, 339, 346, 354, 356, 396, 467, 471, 500, 579, 582, 585, 587, 589, 592, 593, 596, 597, 600, 602, 604, 605, 608, 610, 616, 623, 626 Sah, R., 263, 356, 362, 392 Saint-Paul, G., 551, 572 salability, 541 Sala-i-Martin, X., 24, 51, 435, 437, 439, 443, 446, 468, 469, 471, 475, 476 Sammuelson, P., 96, , 87, 94, 95, 96, 238, 555, 572, 584 Sappington, D., 264, 316 Sapsford, D., 198 Sargent, T., 567, 572 savings, 565, 576 Say's law, 574 scale effect, 230, 441, 442 type I, 146,428, 439 type II, 147, 162, 197, 428 type III, 391, 428 type IV, 428 type V, 439 Scharfstein, D., 15, 24, 262, 264, 316 Schleifer, A., 198 Schultz, T., 164, 476 Schumpeter, J., 74, 409, 572 Schurmann, H., 588 Schweizer, U., 132, 392 Scitovsky, T., 18, 24, 149, 154, 163, 164, 423, 476 Scott, A., 392 screening equilibrium, 296 second order conditions, 228 for dynamic equilibrium, 452 Seers, D., 11, 24 Segerstrom, P., 468, 476, 572 Seierstad, A.. 475 self-sufficiency, 221 self-sufficient activity, 472 Selten, R., 479, 500 Sen, A., 1, 11, 21, 24, 96, 198, 199, 273, 392 Sen, P., 20, 60 Sengenberger, W., 264 separating equilibrium, 296 sequential move game, 291 sequential rationality, 292 unbounded, 479 Servaes, H., 264, 572, 573 Shapiro, C., 132, 572, 575 sharecropping model, 280, 281 Shatz, H., 181, 198 Shea, J., 608 Sheahan, J., 163, 399 Shi, H., 15, 234, 239, 264, 399, 406, 409, 419, 423, 424, 480 Shleifer, A., 15, 21, 24, 40, 96, 140, 141, 154, 158, 162, 163, 199, 224, 247, 264, 290, 339, 356, 392, 420,

467, 476, 500, 551, 572, 573, 584, 594, 600, 623 shock dependent business cycle models, 555 shock therapy, 579 Shooman, M., 356 shortage, 584 of durables, 566 Sijin, S., 588 Simon, C., 236, 391, 392 simultaneous move game, 293 Singer, H., 198 Singh, N., 280, 316 size of firms, 419 size of market network, 339 Skaperdas, S., 316, 356 Skinner, A., 132 Skinner, J., 551, 572 Skousen, M., 584 Smith theorem, 57 Smith, A., 1, 14, 17, 24, 26, 40, 55, 57, 69, 79, 102, 135, 198, 221, 234, 363, 392, 395, 397, 399, 419, 470, 472, 473, 476, 506, 531, 553 Smithe, D., 225 Smithian decision rule, 213 framework, 62 law of demand, 113 macroeconomic analysis, 545 mechanism, 103 microeconomic analysis, 545 model, 103, 104 of industrialization, 399 Sobel, J., 163 social experimentation, 479, 479, 482, 496, 499 social learning process, 496 socialist economy, 566 soft budget constraint, 313, 583 Solinger, D., 588 Solow, R, 57, 146, 427, 443, 475, 505 Song, D-H., 596 Sonnenschein, H., 96, 99 source of economic growth, 464 Soviet style system, 583, 585 Soviet style social experiment, 13 space of parameters, 121 spill-over effects, 443 spontaneous privatization, 616 spot markets, 452 Spraos, J., 198 Squire, L., 181, 198, 201, 578 Srinivasan, T., 11, 15, 16, 24, 32, 445 SS theorem, 94, 193 stage game, 309 Stahl, I., 316 Starr, R., 543 Starrett, D., 543, 572 state opportunism, 16, 601 state ownership system, 358 state planning, 8 state predation, 602 state variables, 454 steady growth rate, 433 steady state, 432 Stern, R., 95 Stern, N., 11, 24 Stigler, G., 14, 24, 132, 258, 264, 267, 270, 421, 500

Stiglitz, J., 18, 24, 140, 141, 145, 163, 185, 225, 230, 234, 274, 280, 316, 354, 356, 362, 392, 427, 476, 527, 552, 556, 572, 575 Stocky, N. 469, 476 Stolper, W., 87, 94, 96 strategic behavior, 271 nonopportunistic, 302 strategic form, 289 strategy, 289 Streeten, P., 149, 163 structural changes, 153, 224, 409 structure of property rights in a socialist country, 358 Stubblebine, W., 15, 95, 132 Stulz, R., 264, 572, 573 subgame perfect equilibrium, 291, 292 subjective discount rate, 452 substitution between competition and enforcement accurancy, 335 sub-tropical economies, 37 Summers, L., 27, 273 Sun, G., 76, 119, 121, 173, 198, 234, 380, 392, 393, 399, 419, 424 super game, 309 superadditivity, 74 supply of fiat money, 566 surplus of agricultural products, 472 Sutcliffe, R., 163 Sveikauskas, L., 96 Sydsater, K., 475 symmetric multilateral monopolistic regime, 453 Syrquin, M., 196 system of production, 452 systematic monetary policy, 567 Tabuchi, T., 376, 392 Tamura, R., 132, 233, 476 tariff, 194 ad valorem, 79 tatonnement, 116, 118 Taylor, F., 499, 500, 583, 623 Taylor, J., 567 Taylower, G., 580 Technical conditions, 502 Teece, D., 356 temperate-zone, 39 Temple, J., 443 terms of trade, 194 theory of absence of ownership, 583 theory of complexity, 390 theory of indirect pricing, 246, 257 Thirwal, A., 149, 198 Thisse, J., 392 Thomas, R., 24, 271 Thompson, H., 181, 198 Thorp, R., 8 thought experiments, 19 threat point, 299 threshold learning cost, 553 Tichy, G., 264, 589 Tirole, J., 75, 264, 316, 356 Todaro, M., 58 Tollison, R., 79, 95 Topel, R., 556, 572 total cost-benefit analysis, 173, 175 Toye, J., 198 trade conflict, 302 trade dependence, 221, 467 trade pattern, 192

650

traditional economy, 472 transaction cost coefficient, 451 transaction cost, 62, 464 anticipated endogenous, 330 endogenous, 22, 63, 271, 276, 279, 308, 332, 443, 453 specific endogenous, 63, 271 exogenous, 271, 332 in delimiting rights to contracting, 335 in enforcing contract terms, 335 type A, 297 type B, 297 type I endogenous, 353 type II endogenous, 353 type III endogenous, 353 type IV endogenous, 354 transaction efficiency, 451, 459, 464, 467, 558, 564 transaction risk, 344 aggregate, 344, 346 transformation curve, 105 transition of constitutional rules, 597 transport costs, 41, 44 Trefler, D., 96, 100 tropical country, 37 Tucker, J., 102, 132, 395 Tullock, G., 550, 572 Turgot, A., 1, 2, 18, 24, 26, 132, 531 TVE, 605 unemployment rate, 568 unemployment, 564, 571 cyclical, 553 efficient, 553, 558 of physical labor, 564 unexpected monetary policy, 567 unfair distribution of gains, 301 unilateral laissez faire, 83 unilateral tariff, 83 urban area, 377 urbanization, 368 utility equalization, 112, 115, 455, 457 Uzawa, H., 96, 427 Vamvakidis, A., 31 Van Zandt, T., 264 Varian, H., 316, 356 variety of producer goods economies, 414 Venables, A., 15, 18, 24, 141, 163, 168, 169, 181, 182, 197, 198, 204, 392, 420 Vishny, R., 15, 24, 40, 96, 140, 141, 154, 158, 163, 198, 199, 264, 290, 392, 420, 476, 500, 572, 573, 584, 594 Vogel, E., 588 Vogt, W., 555, 572 voluntary unemployment, 565 von Mises, L., 10, 498, 500, 583, 584, 585, 623, 542, 543 von Thünen, J. H., 392 wage fund argument, 505 Walker, A., 21, 132, 162, 163, 395, 589, 605, 606, 608, 609 Walker, M., 224, 247, 467 Wallace, N., 567, 572 Walrasian pricing mechanism, 116, 118 regime, 103 Walras's law, 455

Wang, J., 21, 27, 103, 224, 237, 273, 339, 356, 400, 468, 505, 584, 589, 602, 604 Wang, Y., 602, 609, 611, 627 Wank, D., 588 Warner, A., 10, 21, 162, 163, 198, 224, 230, 339, 346, 356, 467, 471, 616 Wartenberg, C., 392 Weber, M., 2, 24, 28, 319, 419 Webster, A., 324 Weel, B., 135 Weibull, J., 315 Weil, D., 443, 446, 476 Weingast, B., 13, 29, 162, 163, 224, 272, 316, 323, 356, 467,, 579, 581, 582, 587, 590 Weisbach, M., 264, 163, 572 Weiss, A., 527 Weitzman, M., 500, 556, 572, 573, 576, 608 Welch, F., 181, 198 welfare scheme, 567 Wellisz, S., 264 Wen theorem, 107, 369, 453 Wen, G., 273, 498 Wen, M., 107, 132, 134, 234, 240, 451, 475, 477 Werner, A., 96 Whinston, M., 316, 356 Williamson, J., 7, 55, 198, 271, 336, 392 Williamson, O., 264, 316, 328, 356, 392, 453 Wills, I., 15, 21, 24, 27, 103, 224, 237, 273, 333, 339, 356, 360, 400, 468, 505, 545, 589, 602, 604 Wilson, R., 316, 479, 500 Wolf, C., 592 Wong, K., 420 Wong, C., 588 Wong, K-Y, 141, 163, 166 Woo, W., 16, 356, 582, 585, 589, 592, 593, 596, 597, 602, 604, 605, 608, 610, 611, 613, 616, 623, 626 Woodward, C., 580 World Bank, 16, 24, 26, 500, 587 Wright, G., 580 Wright, R., 530, 543 Wu, H., 611 Wu, L., 602, 604, 607, 623 Wu, Y., 611 Xu, C., 15, 16, 24, 317, 579, 608, 623 Yamey, B., 60, 95, 198, 267 Yan, Q., 602 Yang, D., 273 Yang, X., 15, 58, 103, 158, 170, 181, 224, 246, 305, 333, 380, 406, 451, 468, 471, 473, 475, 476, 477, 480, 512, 532, 545, 548, 556, 572, 585 Yang, Xu, 602 Yang-Heijdra formula, 144, 367 Yao theorem, 119, 347, 383, 456, 539 Yao, S., 119, 198 Yeh, Y., 316 Yellen, J., 556, 572 Yi, G., 583 Yoon, Y., 74 Young theorem, 14 Young, L., 316, 356

Young, Allyn, 12, 14, 17, 18, 24, 26, 58, 69, 96, 104, 111, 132, 135, 137, 140, 221, 222, 234, 251, 252, 260, 267, 270, 397, 399, 419, 421, 443, 468, 472, 476, 506 Young, Alwyn, 198, 443, 468, 469, 470, 475, 476, 607 Yu, B., 234 Zaleski, E., 9, 500, 586 Zeira, J., 181, 198 Zhang, D., 55, 170 Zhang, G., 609 Zhang, J., 181, 201, 203, 451, 475, 477 Zhang, X., 583 Zhao, Y., 305, 480, 489, 500, 502, 611 Zheng, 611 Zhou, L., 76, 121, 173, 198 Zhou, T., 586 Zhou, Y., 324 Zhou, Z., 616 Zhuravskaya, E., 590 Zou, H., 181, 198 Zweig, D., 605

651

References Abdel-Rahman, H. M. (1990), “Agglomeration Economies, Types and Sizes of Cities Journal of Urban Economics.27, 25-45. Abraham, K. and Katz, L. (1986), "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?", Journal of Political Economy, 94, 507-22. Adelman, I. (1961), Theories of Economic Growth and Development. Stanford, Calif., Stanford University Press. Adelman, Irma and Morris, C. (1967), Society, Politics and Economic Development: A Quantitative Approach, Baltimore, Johns Hopkins University Press. Aghion, P., Bacchetta, P., and Banerjee, A. (1998), "Capital Markets and the Instability of Open Economies", Working paper, presented at Harvard University and MIT Growth and Development Seminar. Aghion, P., Bolton, P., and Jullien, B. (1991), "Optimal Learning by Experimentation", Review of Economic Studies, 58, 621-54. Aghion, P., Caroli, E., and Garcia-Pena Losa, C. (1999), "Inequality and Economic Growth: the Perspective of the New Growth Theories,” Journal of Economic Literature, 37, 1615-60. Aghion, Philippe and Howitt, Peter (1992), “A Model of Growth Through Creative Destruction”, Econometrica, 60, 323-351. Aghion, P. and Howitt, P (1998), Endogenous Growth Theory, Cambridge, MIT Press. Aghion P. and Saint-Paul, G. (1991), “On the Virtue of Bad Times: An Analysis of the Interaction between Economic Fluctuations and Productivity Growth”, CEPR Discussion Paper, No.578. Aghion, Philippe and Tirole, Jean (1997), "Formal and Real Authority in Organizations". Journal of Political Economy. Vol. 105 (1). p 129. February. Aiginger, K. and Tichy, G., (1991), "Small Firms and the Merger Mania", Small Business Economics 3, No. 2 (1991), 83-102. Akerlof , G. (1970), “The Market for Lemons: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics, 89, 488-500. Akerlof, G. and Yellen, J. (1985), "A Near-Rational Model of the Business Cycle, with Wage and Price Inertia", Quarterly Journal of Economics, Suppl., 100, 823-38. Alchian, A. (1977), "Why Money?", Journal of Money, Credit and Banking, 9, 131-40. Alchian, A. and Demsetz, H. (1972), "Production, Information Costs, and Economic Organization", American Economic Review, 62, 77795. Alesina, A. and Rodrik, D. (1994), "Distributive Politics and Economic Growth," Quarterly Journal of Economics, 109, 465-90. Alizadeh, Parvin (1984), “Trade, Industrialization, and the Visible Hand,” Journal of Development Studies? Anonymous (1701), Consideration on the East-India Trade, in J. R. McCulloch, ed. A Select Collection of Early English Tracts on Commerce, London, 1856, reissued, Cambridge, Cambridge University, 1954. Arndt, H. (1989), Economic Development: The History of an Idea. Chicago, University of Chicago Press. Arnott, R. (1979), “Optimal City Size in a Spatial Economy,” Journal of Urban Economics, 6, 65-89. Arrow, K. J. (1962), "The Economic Implications of Learning by Doing", Review of Economic Studies, 29, 155-73. Arrow, K. (1979), "The Division of Labor in the Economy, the Polity, and Society", in G. O'Driscoll, Jr. ed., Adam Smith and Modern Political Economy, Ames, Iowa, Iowa State University Press. Arrow, K. (1985), “The Economics of Agency. " In J. Pratt and R. Zeckhauser (eds.), Principals and Agents: The Structure of Business, pp. 37-51. Boston, Harvard Business School Press. Arrow, K., Ng, Y-K. and Yang, X. eds. (1998), Increasing Returns and Economic Analysis, London, Macmillan. Arrow, K., Enthoven, A., Hurwicz, and Uzawa, H. eds. (1958), Studies in Linear and Nonlinear Programming, Stanford, Stanford University Press. Arthur W. Brian (1994), Increasing Returns and Path Dependence in the Economy, Ann Arbor, the University Michigan Press. Azariadis, C. (1975), “Implicit Contracts and Underemployment Equilibrium,” Journal of Political Economy, 83, 1183-1202. Babbage, C. (1832), On the Economy of Machinery and Manufactures, 4th enlarged edition of 1835, reissued in 1977, New York, M. Kelly. Bac, M. (1996), "Corruption and Supervision Costs in Hierarchies," Journal of Comparative Economics, 22, 99-118. Bacha, Edmar L. (1978), “An Interpretation of Unequal Exchange from Prebisch-Singer to Emmanuel,” Journal of Development Economics. Baechler, Jean (1976), The Origins of Capitalism, Translated by Barr Cooper, Oxford, Blackwell. Baechler, Jean, Hall, John A., and Mann, Michael (1997), eds. Europe and the Rise of Capitalism. New York, Blackwell. Bag, P. K. (1997), "Controlling Corruption in Hierarchies," Journal of Comparative Economics, 25, 322-44. Bai, Chong-En, Li, David D., and Qian, Yingyi, Wang, Yijiang (1999), "Anonymous Banking and Financial Repression: How Does China's Reform Limit the Government's Predation without Reducing Its Revenue?" Mimeo, Stanford University. Baily, M. (1974), “Wages and Employment Under Uncertain Demand,” Review of Economic Studies, 41, 37-50. Balassa, B. (1980), The Process of Industrial Development and Alternative Development Strategies, Princeton University, International Finance Section, Essays in International Finance, No. 141. Balassa, B. (1986) “The Employment Effects of Trade in Manufactured Products between Developed and Developing Countries.” Journal of Policy Modeling, 8, 371-90. Balasubramanyam and S. Lall, eds., Current Issues in Development Economics, London, Macmillan, pp. 159-69. Baldwin, R. (1969), “The Case Against Infant-Industry Tariff Protection,” Journal of Polical Economy. 77, 295-305. Baldwin, Richard E, and Venables, Anthony J. (1995), “Regional Economic Integration,” in Grossman, Gene M. Rogoff, Kenneth, eds., Hanbook of International Economics. Volume 3. Amsterdam, New York and Oxford, Elsevier, North-Holland. Ball, L., Mankiw, N. and Romer, D. (1988), "The New Keynesian Economics and the Output-Inflation Tradeoff", Brookings Papers of Economic Activities, 1, 1-65. Banerjee, Abhijit V. (1992), “A Simple Model of Herd behavior”, The Quarterly Journal of Economics, 107, 797-817. Banerjee, A. and Besley, A. (1990), Moral Hazard, Limited Liability and Taxation: A Principal-Agent Model.. Oxford Economic Papers. 42, 46-60. Banerjee, A. and Newman, A. (1993), "Occupational Choice and the Process of Development," Journal of Political Economy, 101, 274-98. Baran, P. (1957), La economia politica del crecimiento, Mexico, F.C.E., 1969. Bardhan, P. (1970), Economic Growth, Development and Foreign Trade, New York, Wiley. Bardhan, P. and Roemer, J. eds. (1993), Market Socialism, the Current Debate, Oxford University Press. Bardhan, Pranab ed. (1989), The Economic Theory of Agrarian Institutions, Oxford, Clarendon Press.

627

Barro, R. (1991), "Economic Growth in a Cross-Section of Countries", Quarterly Journal of Economics, 106, 407-44. Barro, R. (1997), Determinants of Economic Growth, Cambridge, MA, MIT Press. Barro, R. and Sala-i-Martin, X. (1991), “Convergence Across States and Regions”, Brookings Papers on Economic Activities, # 1, 159-82. Barro, R. and Sala-i-Martin, X. (1992), “Convergence”, Journal of Political Economy, 100, 223-51. Barro, R. and Sala-i-Martin, X. (1995), Economic Growth, New York, McGraw-Hill. Barzel, Yoram. (1982), "Measurement Cost and the Organization of Markets", Journal of Law and Economics, 25, 27-48. Barzel, Y. (1985), “Transaction Costs: Are They Just Costs?” Journal of Institutional & Theoretical Economics. 141, 4-16. Barzel, Y. (1989), Economic Analysis of Property Rights, Cambridge, Cambridge University Press. Barzel, Y. (1997), "Property Rights and the Evolution of the State,” memeo. and “Third-party Enforcement and the State,” memeo. Department of Economics, University of Washington. Barzel, Yoram and Yu, Ben T. (1984), "The Effect of the Utilization Rate on the Division of Labor", Economic Inquiry, 22, 18-27. Basu, S. (1996), “Procyclical Productivity: Increasing Returns or Cyclical Utilization”, Quarterly Journal of Economics, 111, 719-750. Bauer, P. and Yamey, B. (1957), The Economics of Underdeveloped Countries, Chicargo, University of Chicargo Press. Baumgardner, J. R. (1988a), "The Division of Labor, Local Markets, and Worker Organization", Journal of Political Economy, 96, 509-27. Baumgardner, J. R. (1988b), "Physicians' Services and the Division of Labor across Local Markets." Journal of Political Economy. 96, 948-82. Baumol, W.J. (1996), “Productivity Growth, Convergence, and Welfare: What the Long-Run Data Show”, American Economic Review, 76(5), 1072-1085. Baxer, M. and King, R.G. (1995), “Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series”, NBER working paper No. 5022. Bazovsky, Igor (1961), Reliability Theory and Practice, Englewood Cliffs, Prentice-Hall. Beasley, W. G. (1995), The Rise of Modern Japan, New York, St. Martin's Press. Becker, Gary (1964), Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, New York, Columbia University Press. (1965), "A theory of the Allocation of Time", Economic Journal, 75, 497-517. (1981), A Treatise on the Family, Cambridge, Massachusetts, Harvard University Press. and Lewis, H.G. (1973) “On the Interaction Between the Quantity and Quality of Children,” Journal of Political Economy, 81, S279-88. Becker, G. and Murphy, K. (1992), "The Division of Labor, Coordination Costs, and Knowledge", Quarterly Journal of Economics, 107, 1137-60. Beckmann, M. (1968), Dynamic Programming of Economic Decisions, New York, Springer-Verlag. Behrman, J. and Srinivasan, T.N. (1995), "Introduction to Part 9." Vol. IIIB, in Behrman, J. and T.N. Srinivasan eds. Handbook of Development Economics, New York, Elsevier. Beik, Paul H. ed. (1970), The French Revolution. New York, Harper & Row. Benhabib, J. and Joranovic, B. (1991), “Externalities and Growth Accounting”, American Economic Review, 81, 82-113. Ben-Akiva, M. de Palma, A. and Thisse, J. (1989), “Spatial Competition with Differentiated Products.” Regional Science & Urban Economics. 19, 5-19. Berger, Philip, and Ofek, Eli (1995), "Diversification's Effect on Firm Value," Journal of Financial Economics, 37, 39-65. Berle, A. and Means, G. (1932), The Modern Corporation and Private Property, London, Macmillan. Bernard, A. and Jones, C.I. (1996), “Technology and Convergence”, Economic Journal, 106, 1037-1044. Besley, Timothy (1995), "Savings, Credit and Insurance." In J. Behrmand and T. N. Srinivasan, eds. Handbook of Development Economics, Vol. III, New York, Elsevier Science B. V. pp. 2125-2206. Besley, T., Coate, S. and Loury, G. (1993), "The Economics of Rotating Savings and Credit Associations." American Economic Review. 83, 792-810. Bhagat, Sanjay, Shleifer, Andrei and Vishny, Robert (1990), "Hostile Takeovers in the 1980s: The Return to Corporate Specialization," Brookings Papers on Economic Activity: Microeconomics, Special Issue, 1-72. Bhagwati, J. and Dehejia, V. (1994), “Freer Trade and Wages of the Unskilled: Is Marx Striking Again?” in Trade and Wages: Leveling Wages Down? ed. By J Bhagwati and M. Kosters. Washington, American Enterprise Institute. Bhagwati, Jagdish (1969), "Optimal Policies and Immiserizing Growth." American Economic Review. 59, 967-70. (1984), “The State of Development Theory,” American Economic Review. 74, 1-10. Bhaskar, V. (1995), "Noisy Communication and the Evolution of Cooperation," U. St. Andrews. Bhattacharyya, S. and Lafontaine, F. (1995), “Double Sided Moral Hazard and the Nature of Share Contracts,” RAND Journal of Economics, 26, pp. 761-81. Binmore, K., Osborne, M., Rubinstein, A. (1992). Noncooperative Models of Bargaining. New York, Elsevier Science. Black, F. (1979) Business Cycles in General Equilibrium, MIT Working Paper. Black, F. (1987), Business Cycles and Equilibrium, New York, Basil Blackwell. Black, F. (1995), Exploring General Equilibrium, MIT Press. Blanchard, Olivier. Economics of Post-Communism Transition, Oxford University Press, 1997. Blanchard, O. and Kremer, M. (1997), “Disorganization,” Quarterly Journal of Economics, 112, 1091-26. Blomstrom, M. and Wolff, E. (1997), “Growth in a Dual Economy”. World Development. 25, 1627-37. Bliss, C. (1989), “Trade and Development.” In Chenery and Srinivasan eds. Handbook of Development Economics, Vol. II, p. 1188. Blitch, C. P. (1983). “Allyn Young on Increasing Returns.” Journal of Post Keynesian Economics, vol. 5 (Spring), pp. 359-72. Blitch, C. P. (1995). Allyn Young: The Peripatetic Economist. London, Macmillan. Blume, A., Kim, Y-G. and Sobel, J. (1993), "Evolutionary Stability in Games of Communication," Games & Economic Behavior, 5, 547-75. Bolton, P. and Dewatripont, M. (1994), "The Firm as a Communication Network," Quarterly Journal of Economics, 109, 809-39. Bolton, P. and Dewatripont, M. (1995), "The Time and Budget Constraints of the Firm," European Economic Review, 39, 691-09. and (1994), "The Firm as a Communication Network." Quarterly Journal of Economics. 109, 809-39. Bolton, Patrick, and Scharfstein, David (1998), "Corporate Finance, the Theory of the Firm, and Organization," Journal of Economic Perspectives, 12, 95-114. Borjas, G., Freeman, R. and Katz, L. (1992), “How Much Do Immigration and Trade Affect Labor Market Outcomes?” Brookings Papers on Economic Activity. No. 1, 1-67. Borland, J. and Yang, X. (1992a), "Specialization and Money as a Medium for Exchange", Seminar Paper, Department of Economics, Monash University. and (1992b), "Specialization and a New Approach to Economic Organization and Growth", American Economic Review, 82, 386-91.

628

and (1995), "Specialization, Product Development, Evolution of the Institution of the Firm, and Economic Growth", Journal of Evolutionary Economics, 5, 19-42. Borland, Jeff and Eichberger, Jurgen (1998), "Organizational Form outside the Principal-agent Paradigm," Bulletin of Economic Research, 50, 201-27. Boserup, Ester (1975), “The Impact of Population Growth on Agricultural Output,” Quarterly Journal of Ecnomics, 89(2), 257-70. Bouin, Olivier (forthcoming), "Financial Discipline and State Enterprise Reform in China in the 1990s," in Olivier Bouin, Fabrizio Coricelli and Francoise Lemoine (ed.), Different Paths to a Market Economy: China and European Economies in Transition, OECD, Paris. Bowen, Harry P., Leamer, Edward E. and Sveikauskas, Leo (1987), “Multicountry, Multifactor Tests of the Factor Abundance Theory,” American Economic Review, 77(5), 791-809. Boycko, Maxim, Shleifer, Andre and Vishny, Robert (1995) Privatizing Russia. MIT Press. Boycko,, M., Shleifer, A. and Vishny, R. (1996), “A Theory of Privatization", Economic Journal. 106:309-19. Braudel, Fernand (1984), Civilization and Capitalism, 18th Century, translation from the French revised by Sian Reynolds. London, Collins. Braudel, Fernand (1972), The Mediterranean and the Mediterranean World in the Age of Philip II. New York, Harper & Row Braudel, Fernand (1981-84), Civilization and Capitalism, 15th-18th Century. London , Collins. 3 volumes. Braverman, A. and Stiglitz, J. (1982), “Sharecropping and the Interlinking of the Agrarian Markets,” American Economic Review, 72, 695-715. Brian, Arthur W. (1994), Increasing Returns and Path Dependence in the Economy, Ann Arbor, the University Michigan Press. Brown, R.L., Durbin, J. and Evans, J.M. (1975), “Techniques for Testing the Constancy of Regression Relationships Over Time” (with discussion), Journal of the Royal Statistical Society, Series B, 37, 149-92. Brunner, K. and Meltzer, A. (1971), "The Use of Money: Money in the Theory of an Exchange Economy", American Economic Review, 61, 784-805. Bruton, Henry (1998), “A Reconsideration of Import Substitution,” Journal of Economic Literature, 36, 903-36. Bruun, O. (1993), Business and Bureaucracy in a Chinese City, Chinese Research Monographs No. 43. Berkeley, Institute of East Asian Studies, University of California. Buchanan, James M. (1975), The Limits of Liberty: Between Anarchy and Leviathan. Chicago, University of Chicago Press. (1989), Explorations into Constitutional Economics. College Station, Texas A&M University Press. (1991), Constitutional Economics. Cambridge, Mass., Blackwell. Buchanan, J. (1994), "The Return to Increasing Returns," in Buchanan, J. and Yoon, Y. eds The Return to Increasing Returns, Ann Arbor, The University of Michigan Press. Buchanan, James M. and Tullock, Gordon (1965), The Calculus of Consent: Logical Foundations of Constitutional Democracy, Ann Arbor, University of Michigan Press. Buchanan, James M. and Stubblebine, W. Craig (1962), “Externality,” Economica, 29, 371-84. Burke, Edmund, (1790), Reflections on the French Revolution. ed. by W. Alison Phillips and Catherine Beatrice Phillips. Cambridge, Cambridge University Press, 1912. Burtless, Gary (1995), "International Trade and the Rise in Earnings Inequality." Journal of Economic Literature. 33, 800-16. Byrd, W. (1983), "Enterprise-Level Reforms in Chinese State-Owned Industry", American Economic Review, No. 73, pp. 329-32. Byrd, W. (1988), "The Impact of the Two-Tier Plan Market System in Chinese Industry", Journal of Comparative Economics, Vol. 11, No. 3, September 1987, pp. 295-308. Reprinted in Reynolds, Bruce L., Chinese Economic Reform: How Far, How Fast?, Academic Press, London. Byrd, William (1991), The Market Mechanism and Economic Reforms in China. New York, M.E. Sharpe. Caballero, R.J. and Hammour, M.L. (1994) “The Cleansing Effect of Recessions”, American Economic Review, vol. 84, 5, pp.1350-1368. Calvo, G. and Wellisz, S. (1978), "Supervision, Loss of Control and the Optimal Size of the Firm", Journal of Political Economy, 86, 94352. and (1979), "Hierarchy, Ability and Income Distribution", Journal of Political Economy, 87, 991-1010. Case, Anne and Deaton, Angus (1998), “Large Cash Transfers to the Elderly in South Africa.” Economic Journal. 108, 1330-61. Case, Anne and Deaton, Angus (1999a), “School Inputs and Educational Outcomes in South Africa.” Quarterly Journal of Economics. 114, 1047-84. Case, Anne and Deaton, Angus (1999b), “Household Resource Allocation in Stepfamilies: Darwin Reflects on the Plight of Cinderella.” American Economic Review. 89, 234-38. Canton, Erik (1997), Economic Growth and Business Cycles, Center for Economic Research, Tilburg University, Amsterdam, Thesis Publishers. Capie, Forrest H. (1983), "Tariff Protection and Economic Performance in the Nineteenth Century", reprinted in Forrest Capie, ed., Protection in the World Economy, (1992) Brookfield, Vermont, Edward Elgar Publishing Co. Carter, M. (1995), "Information and the Division of Labour: Implications for the Firm's Choice of Organisation," Economic Journal, 105, 385-97. Chandler, A. Jr. (1990), Scale and Scope the Dynamics of Industrial Capitalism, Cambridge, MA, Belknap Press of Harvard University Press. Chang, C. and Wang, Y. (1994). "The Nature of the Township Enterprises." Journal of Comparative Economics, 19, pp. 434-452. Chang, G. and Wen, G. (1998), "Food Availability Versus Consumption Efficiency: Causes of the Chinese Famine", China Economic Review, 9, 157-66. Che, Jiahua (1999), "From the Grabbing Hand to the Helping Hand", Working Paper, Department of Economics, University of Notre Dame. Che, Jiahua and Qian, Yingyi (1998), "Insecure Property Rights and Government Ownership of Firms." Quarterly Journal of Economics. 113, 467-96. Chen, B-L., Lin, J. and Yang, X. (1999): “Empirical Evidences for the Endogenous Growth Generated by Evolution in Division of Labor”, Development Discussion Paper, No. 671, Harvard Institute for International Development. Chen, Aimin (1994), "Chinese Industrial Structure in Transition: The Emergence of Stock-offering Firms," Comparative Economic Studies, Vol. 36, No. 4, Winter, pp. 1-19. Chen, Yinan and Zhou, Zhiren eds. (1996), Chuangye Zhifu Bushi Mong (It is not a Dream to Make a Fortune from Entrepreneurship), Hainan International News Center. Chenery, H. (1979), Structural Change and Development Policy, Oxford Univ. Press. Chenery, H., Robinson, S. and Syrquin, M. eds. (1986), Industrialization and Growth: A Comparative Studies, New York, Oxford University Press.

629

Cheng, T. (1991), "The Present and Future of China's Residential Registration System". Ph.D. Dissertation, Department of Sociology, NorthEast University. Cheng, W. (1998),“Specialization and the Emergence and the Value of Money”, In K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. (1999), “Division of Labor, Money, and Economic Progress”, Review of Development Economics, 3, 354-67. Cheng, W., Sachs, J. and Yang, X. (2000), “An Inframarginal Analysis of the Ricardian Model," Review of International Economics, 8, 208-20. (forthcoming), "A General Equilibrium Re-appraisal of the Stolper-Samuelson Theorem," Journal of Economics. (1999), "An Inframarginal Analysis of the Heckscher-Ohlin Model with Transaction Costs and Technological Comparative Advantage," Harvard Center for International Development Working Paper No. 9. Cheng, W., Liu, M. and Yang, X. (2000), “A Ricardo Model with Endogenous Comparative Advantage and Endogenous Trade Policy Regime," Economic Record, 76, 172-82. Cheung, S. (1968), “Private Property Rights and Sharecropping,” Journal of Political Economy Chicago, 76, 1117-22. (1969), The Theory of Share Tenancy, Chicago, University of Chicago Press. (1970), "The Structure of A Contract and the Theory of a Non-exclusive Resource", Journal of Law and Economics, 13, 49-70. (1974), "A Theory of Price Control," Journal of Law and Economics, 17, 53-71. (1983), "The Contractual Nature of the Firm", Journal of Law & Economics, 26, 1-21. (1989), "Privatization vs. Special Interests: The Experience of China's Economic Reforms," Cato Journal, 8, 585-96. (1996), "A Simplistic General Equilibrium Theory of Corruption," Contemporaty Economic Policy, 14, 1-5. Chiang, A. (1984), Fundamental Methods of Mathematical Economics, London, McGraw-Hill. Cho, D. and Graham, S. (1996), “The Other Side of Conditional Convergence.” Economics Letters, 50, 285-90. Chu, C. (1997), "Productivity, Investment in Infrastructure, and Population Size: Formalizing the Theory of Ester Boserup", Review of Development Economics, 1, 294-304. Chu, C. and Tsai, Y. (1998), "Productivity, Investment in Infrastructure, and Population Size: Formalizing the Theory of Ester Boserup", In K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. Chu, C. and Wang, C. (1998), "Economy of Specialization and Diseconomies of Externality", Journal of Public Economics. 69, 249-61. CIA. (1996), The World Factbook. Washington, D.C., Central Intelligence Agency. CIA. (1997), The World Factbook. http://www.odci.gov/cia/publications/factbook/index.html. Ciccone, A. and Matsuyama, K. (1996), “Start-up Costs and Pecuniary Externalities as Barriers to Economic Development,” Journal of Development Economics, 49, 33-59. Cline, William (1997), Trade and Income Distribution, Washington DC, Institute for International Economics. Clower, R. (1967), "A Reconsideration of the Microfoundations of Monetary Theory", Western Economic Journal, 6, 1-8. Coase, R. (1937), "The Nature of the Firm", Economica, 4, 386-405 Coase, Ronald (1946), “The Marginal Cost Controversy,” Economica, 13, 169-82. Coase, Ronald (1960), “The Problem of Social Cost,” Journal of Law and Economics, 3, 1-44. Coase, R. (1991), "The Nature of the Firm: Origin, Meaning, Influence", in Williamson. O. and Winter, S. (eds.), The Nature of the Firm, New York, Oxford University Press. Colwell, P. and Munneke, H. (1997), “The structure of urban land prices”, Journal of Urban Economics , 41, 321-36. Comment, Robert, and Jarrell, Gregg (1995), "Corporate Focus and Stock Returns," Journal of Financial Economics, 37, 67-87. Conlisk, John (1996), “Why Bounded Rationality?” The Journal of Economic Literature, 34, 669-700. Conybeare, John A. C. (1987), Trade Wars: The Theory and Practice of International Commercial Rivalry, New York, Colombia University Press. Cook, Linda, (1993), The Soviet Social Contract and Why It Failed: Welfare Policy and Workers' Politics from Brezhnev to Yeltsin, Harvard University Press, Cambridge, MA. Cooper, R. and Ross, T. W. (1985), “Produce Warranties and Double Moral Hazard,” RAND Journal of Economics, 16, pp. 103-13. Cooter, R. (1989), “The Coase Theorem,” The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate, and P. Newman, eds. London, The Macmillan Press, Vol. 1, 457-60. Crafts, N. (1996), “The First Industrial Revolution: A Guided Tour for Growth Economists” American Economic Review, Papers and Proceedings, 197-201. Crafts, N. (1997), “Endogenous Growth: Lessons for and from Economic History.” D. Kreps and K. Wallis eds. Advances in Economics and Econometrics: Theory and Applications, Vol. II. Cambridge, Cambridge University Press. Crosby, Alfred W. (1986), Ecological Imperialism: The Biological Expansion of Europe, 900-1900. Cambridge, Cambridge University Press. Curtin, Philip D. (1989), Death by Migration: Europe’s Encounter with the Tropical World in the Nineteenth Century. Cambridge, Cambridge University Press. Cypher, James and Dietz, James (1998), “Static and Dynamic Comparative Advantage: A Multi-period Analysis with Declining Terms of Trade,” Journal of Economic Issues, 32, 305-14. Dasgupta, Partha (1995), “The Population Problem: Theory and Evidence,” Journal of Economic Literature, 33, 1879-1902. Deane, Phyllis and Cole, William (1967), British Economic Growth, Cambridge, Cambridge University Press. Deardorff, Alan and Stern, Robert eds. (1994), The Stolper-Samuelson Theorem, Ann Arbor, University of Michigan Press. Deaton, A. (1990) “Saving in Developing Countries: Theory and Evidence”, World Bank Economic Review (Proceedings of the World Bank Annual Conference on Development Economics, 1989, 61-96. Deaton, A. (1991) “Saving and Liquidity Constraints”, Econometrica, 59, 1221-48. Deaton, A. and Paxson, C. (1998a) “Economies of Scale, Household Size, and the Demand for Food”, Journal of Political Economy,106, 897-930. Deaton, A. and Paxson, C. (1998b) “Aging and Inequality in Income and Health”, American Economic Review, 88, 248-53. Debreu, G. (1959), Theory of Value, Yale University Press, New Haven. Debreu, G. (1974), Excess Demand Functions. Journal of Mathematical Economics, 1, 15-21. Debreu, G. (1991), "The Mathematization of Economic Theory", American Economic Review, 81, 1-7. Deininger, K. and Squire, L. (1996), "A New Data Set Measuring Income Inequality," World Bank Economic Review, 10, 565-91. Dellas H. (1991) “Stabilization Policy and Long Term Growth: Are They Related?”, Mimeo, University of Maryland. Delong, B. (1988): “Productivity Growth, Convergence and Welfare: Comments”, American Economic Review, 78, 1138-1154. Demsetz, H. (1967), "Toward A Theory of Property Rights", American Economic Review, 57, 347-59. Demsetz, H. (1988), Ownership, Control, and the Firm, Oxford, Basil Blackwell.

630

Demsetz, H. and Lehn, K. (1985), "The Structure of Corporate Ownership: Causes and Consequences", Journal of Political Economy, 93, 1155-77. Department of Commerce (1972-1999), Statistical Abstract of the United States. Department of Commerce (1975), Historical Statistics of the United States. Dewatripont, Mathias (1988), "Commitment through Renegotiation-Proof Contracts with Third Parties." Review of Economic Studies. 55, 377-89. Dewatripont, M. and Maskin, E. (1995), "Contractual Contingencies and Renegotiation." Rand Journal of Economics. 26, 704-19. and (1995), "Credit and Efficiency in Centralized and Decentralized Economies," Review of Economic Studies, 62, 541-56. Dewatripont, M. and Roland, G. (1995), "The Design of Reform Packages under Uncertainty." American Economic Review. 85, 1207-23. and (1996), "Transition as a Process of Large Scale Institutional Change," in David Kreps and Kenneth Wallis (eds.), Advances in Economics and Econometrics: Theory and Applications, Cambridge, Cambridge University Press, 1996. Diamond, Charles and Simon, Curtis (1990), "Industrial Specialization and the Returns to Labor," Journal of Labor Economics, 8, 175-201. Diamond, D. W. and Dybvig, P. (1983), "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, 91, 401-19. Diderot, Denis (1713), Diderot Encyclopedia: the Complete Illustrations, New York, Abrams, 1978. Din, M. (1996), “International Capital Mobility and Development Policy in a Dual Economy,” Review of International Economics, 4, 185-201. Dixit, A. (1968), “The Optimal Development in the Labour Surplus Economy,” Review of Economic Studies, 35, 23-34. Dixit, A. (1969), “Marketable Surplus and Dualistic Development,” Journal of Economic Theory, August. Dixit, A. (1987), "Trade and Insurance with Moral Hazard," Journal of International Economics, 23, 201-20. Dixit, A. (1989), "Trade and Insurance with Imperfectly Observed Outcomes," Quarterly Journal of Economics, 104, 195-203. Dixit, A and Nalebuff, B. (1991), Thinking Strategically, New York, W. W. Norton & Company. Dixit, A. and Norman, V. (1980), Theory of International Trade, Cambridge, Cambridge University Press. Dixit, A. and Stiglitz, J. (1977), "Monopolistic Competition and Optimum Product Diversity", American Economic Review, 67, 297-308. Dodzin, Sergei and Vamvakidis, Athanasios (1999), "Trade and Industrialization in Developing Agricultural Economies." International Monetary Fund Working Paper. Domar, E. (1947), "Expansion and Employment", American Economic Review, 37, 34-55. Dornbusch, Fisher S. and Samuelson, Paul (1977), “Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods,” American Economics Review, 67(5), 823-39. Dowrick, S. and Nguyen, D.T. (1989), “OECD Comparative Economic Growth 1950-85: Catch-up and Convergence”, American Economic Review, 79, 1010-1030. Du, J. (2000), "Endogenous, Efficient Long-run Cyclical Unemployment, Endogenous Long-run Growth, and Division of Labor," Review of Development Economics, forthcoming. Dudley, Sarkar, P. (1986), “The Terms of Trade Experience of Britain Since the 19th Century,” Journal of Development Studies. Easterlin, R. (1981), Why Isn’t the Whole World Developed?” Journal of Economic History. March, 1-17. Easton, Stephen and Michael, Walker (1997), "Income, Growth, and Economic Freedom", American Economic Review, Papers and Proceedings, 87, 328-32. Eckholm, E. (1975), The Other Energy Crisis, Firewood, Washington, DC, Worldwatch Institute. Economic Literature. 33, 800-16. Eichberger, B. (1994), Game Theory for Economists, Academic Press. Eichengreen, B. and Flandreau, M. (1994), "The Geography of the Gold Standard." Discussion Paper 1050. London, Centre for Economic Policy Research, October. Ekelund, Robert, and Tollison, Robert (1981), Merchantilism as an Rent-seeking Society, College Station, TX, Texas A & M University Press. Elvin, Mark (1973), The Pattern of the Chinese Past. London, Eyre Methuen. Emmanuel, A. (1972), Unequal Exchange: A Study of the Imperialism of Trade, Eswaran, M. and Kotwal, A. (1985), “A Theory of Contractual Structure in Agriculture,” American Economic Review, 75, pp. 352-67. Ethier, W. (1979), "Internationally Decreasing Costs and World Trade", Journal of International Economics, 9, 1-24. Ethier, W. (1982), "National and International Returns to Scale in the Modern Theory of International Trade", American Economic Review, 72, 389-405. Ethier, Wilfred J (1988), Modern International Economics, second edition, New York: W. W. Norton & Company. Evans, David (1987), “The Long Run Determinants of North-South Terms of Trade and Some Recent Empirical Evidence,” World Development. 15 (5) 657-71. Fairbank, John King (1992), China: A New History. Cambridge, Mass., Belknap Press of Harvard University Press. Fama, E. and Jensen, M. (1983), "Separation of Ownership and Control", Journal of Law & Economics, 26, 301-27. Fan, Gang and Woo, Wing Thye (1996), "State Enterprise Reform as a Source of Macroeconomic Instability," Asian Economic Journal, November. Fang, Weizhong ed. (1984), Jinji Dashi Ji (Major Economic Events in the People's Republic of China, 1949-1980), Beijing, Chinese Social Science Press. Fang, Xinghai and Zhu, Tian (1999), "Institutional Imperfection and Transition Strategies," Economic Systems, 23, 331-48. Farrell, J. and Maskin, E. (1989), "Renegotiation in Repeated Games", Games and Economic Behaviour, 1, 327-60. Farrell, J. and Garth, S. (1985), "Standardization, Compatibility, and Innovation," Rand Journal of Economics, 16, 70-83. Fauver, Larry, Houston, Joel and Naranjo, Andy (1998), "Capital Market Development, Legal Systems and Value of Corporate Diversification: A Cros-Country Analysis," Working Paper, University of Florida. Fei, J. and Ranis, G. (1964), Development of the Labor Surplus Economy, Richard Irwin, Inc. Fei, John, Ranis, Gustav and Kuo, Shirley (1979), Growth with Equity : the Taiwan Case. New York, Oxford University Press. Fischer, S. (1977), "Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule", Journal of Political Economy, February, 85(1), 191-205. Fleming, Marcus (1955), “External Economies and the Doctrine of Balanced Growth,” Economic Journal, 65, 241-56. Frank, A. (1995), The Development of Underdevelopment. Aldershot, UK, Elgar. Frank, C. (1977), Foreign Trade and Domestic Aid. Washington, Brookings Institute. Friedman, Milton (1957), A Theory of the Consumption Function, Princeton, Princeton University Press. Friedman, M. (1962), Capitalism and Freedom, Chicago, The University of Chicago Press. Frye, Timothy and Shleifer, Andrei (1997), "The Invisible Hand and the Grabbing Hand.” American Economic Review, Papers and Proceedings, 87, 354-58. Fudenberg, D. and Tirole, J. (1983), "Sequential Bargaining with Incomplete Information", Review of Economic Studies, 50, 221-47.

631

Fudenberg, D. and Tirole, J. (1991), Game Theory, Cambridge, The MIT Press. Fujita, K., Krugman, P., and Venables, A. (1999), The Spatial Economy: Cities, Regions, and International Trade, Cambridge, MA, MIT Press. Fujita, M. (1988), “A Monopolistic Competition Model of Spatial Agglomeration: Differentiated Product Approach,” Regional Science & Urban Economics, 25, 505-28. Fujita, M. (1989), Urban Economic Theory: Land Use and City Size, New York, Cambridge University Press. Fujita, M. and Krugman, P. (1994), “On the Evolution of Hierarchical Urban Systems,” mimeograph, Department of Regional Science, University of Pennsylvania, Philadelphia, PA. Fujita, Masahisa and Krugman, Paul (1995), “When is the Economy Monocentric: von Thünen and Chamberlin Unified,” Regional Science & Urban Economics, 25, 505-28. Fujita, M. And Thissem, J.-F. (1996), "Economies of agglomeration", Journal of Japanese and International Economies, 10, 339-78. Fujita, M. and Mori, T. (1997), “Structural stability and evolution of urban systems”, Regional Science and Urban Economics , 27, 399-442. Furubotn, E. and Pejovich, S. (eds.) (1974), The Economics of Property Rights. Cambridge, Mass., Ballinger Publishing Company. Gabisch, G. and Lorenz, H. (1989), Business Cycle Theory: A Survey of Methods and Concepts, Berlin, Springer-Verlay. Gale, D. (1986), "Bargaining and Competition. Part I: Characterization and Part II: Existence", Econometrica, 54, 807-18. Gallup, John Luke (1998), “Agricultural Productivity and Geography,” Working Paper, HIID. Gallup, John and Sachs, Jeff (1998), “Geography and Economic Development,” in Pleskovic, Boris, and Joseph E. Stiglitz, eds., World Bank Annual Conference on Development Economics 1998. Washington, DC: The World Bank, pp. 127-178. Reprinted in International Regional Science Review, 22(2): 179-232.. Galor, O. (1996), “Convergence? Inferences from Theoretical Models”, Economic Journal, 106, 1056-1069. Galor, O. and Zeira, J. (1993), "Income Distribution and Macroeconomics," Review of Economic Studies, 87, 205-10. Gans, Joshua (1998), “ Industrialization Policy and the ‘Big Push’,” in K. Arrow, et al, eds. Increasing Returns and Economic Analysis, London, Macmillan. Ghatak, S. (1995), Introduction to Development Economics, London, Routledge. Gibbons, R. (1992), Game Theory for Applied Economist, Princeton University Press. Gibbons, Robert (1998), "Incentives in Organization," Journal of Economic Perspectives, 12, 115-32. Gillis, M., Perkins, D., Roemer, M., and Snodgrass, D.R. (1993) Economics of Development,London/New York, Norton. Gomory, Ralph E. (1994), “A Ricardo Model with Economies of Scale,” Journal of Economic Theory, 62, 394-419. Goodwin, R. (1951), "The Non-linear Accelerator and the Persistence to Markets Having Production Lags", Econometrica, 19, 1-17 Gorden, W. (1980), Institutional Economics, Austin, University of Texas Press. Gordon, B. (1975), Economic Analysis before Adam Smith, London, Macmillan. Gordon, D. (1974), “A Neo-classical Theory of Keynesian Unemployment,” Economic Inquiry, 12, 431-59. Granick, D. (1990), Chinese State Enterprises: A Regional Property Rights Analysis, Chicago, University of Chicago Press. Gray, Cheryl and Hendley, Kathryn (1997), "Developing Commercial Law in Transition Economies: Examples from Hungary and Russia." in Sachs, J. and Pistor, K. eds. The Rule of Law and Economic Reform in Russia, Westview Press. Gray, J. (1976), "Wage Indexation: A Macroeconomic Approach", Journal of Monetary Economics, 2, 221-35. Green, E. (1987), "Lending and the Smoothing of Uninsurable Income", in E. Prescott and N. Wallace (eds.), Contractual Arrangements for Intertemporal Trade, Minneapolis, University of Minnesota Press. Greenaway, D. (1992), “New Trade Theories and Developing Countries,” in V. Balasubramanyam and S. Lall, eds., Current Issues in Development Economics, London, Macmillan, pp. 159-69. Greenwood, J. and Jovanovic, B. (1990), "Financial Development, Growth, and the Distribution of Income," Journal of Political Economy, 98, 1076-1107. Grier, K.B. and Tullock, G. (1989) “An Empirical Analysis of Cross-National Economic Growth, 1951-80”, Journal of Monetary Economics, 24, pp.259-276. Groenewegen, Peter (1977), The Economics of A.R.J. Turgot, Martinus Nijhoff, Hague. Groenewegen, Peter (1987), "Division of Labor", in J. Eatwell, M. Milgate, and P. Newman eds. The New Palgrave A Dictionary of Economics, 901-7. Grossman, G. and Helpman, E. (1989), "Product Development and International Trade", Journal of Political Economy, 97, 1261-83. Grossman, G. and Helpman, E. (1990), "Comparative Advantage and Long-Run Growth", American Economic Review, 80, 796-815. Grossman, G. and Helpman, E. (1994), “Protection For Sale,” American Economic Review, 84, 833-50. Grossman, G. and Helpman, E. (1995a), "The Politics of Free-Trade Agreements," American Economic Review, 85(4),667-690. Grossman, G. and Helpman, E. (1995b), “Trade Wars and Trade Talks,” Journal of Political Economy, 1995, 103(4), 675-708. Grossman, G. and Helpman, E. (1995c), "Technology and Trade", in G. Grossman and K. Rogeff eds. Handbook of International Economics, Volume 3. Grossman, G. and Levinsohn, J. (1989), “Import Competition and the Stock Market Return to Capital,” American Economic Review, 79, 1065-87. Grossman, Gene (1998), “Imperfect Labor Contracts and International Trade,” memeo., Department of Economics, Princeton University. Grossman, Gene M. and Richardson, David J. (1986), "Strategic Trade Policy: A Survey of the Issues and Early Analysis." In Robert E. Baldwin and J. David Richardson, eds., International Trade and Finance, 3rd ed., 95-113. Boston, Little, Brown. Grossman, S (1989), The Informational Role of Prices, Cambridge, MIT Press. Grossman, S. and Hart, O. (1986), "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration", Journal of Political Economy, 94, 691-719. Grout, P. (1984), "Investment and Wages in the absence of Binding Contracts: A Nash Bargaining Approach", Econmetrica, 52, 449-60. Gwartney, J., Lawson, R., and Block, W. (1996), Economic Freedom of the World: 1975-1995. Vancouver, B.C., Fraser Institute. Gwartney, J. and Lawson, R. (1997), Economic Freedom of the World: 1997 Annual Report. Vancouver, B.C., Fraser Institute.Hadley, G. (1964), Nonlinear and Dynamic Programming, Reading, Addison-Wesley. Hadley, G. (1964), Nonlinear and Dynamic Programming, Reading, Addison-Wesley. Hagen, E. (1980), The Economics of Development. Irwin, Homewood. Hagen, E. (1958), Án Economic Justification of Protectionism” Quarterly Journal of Economics, 72 (4), 496-514. Hahn, F. (1971) "Equilibrium with Transaction Costs", Econometrica, 39, 417-39. Hall, John (1987), “State and Societies: the Miracle in Comparative Perspective, “ in Baechler, Hall, and Mann (eds.), Europe and the Rise of Capitalism, Cambridge, Blackwell. Harris, Joseph (1757), An Essay Upon Money and Coins. London, G. Hawkins, 1757-58.

632

Harrod, R. (1939), "An Essay in Dynamic Theory", Economic Journal, 49, 14 Hart, O. (1991), "Incomplete Contract and the Theory of the Firm ", in O. Williamson and S. Winter (eds.), The Nature of the Firm, New York, Oxford University Press. Hart, O. (1995), Firms, Contracts, and Financial Structure. Oxford, Clarendon Press. Hart, O. and Holmstrom, B. (1987), "The Theory of Contracts", in T. Bewley (ed.), Advances in Economic Theory, Cambridge, Cambridge University Press. Hart, O. and Moore, B. (1990), "Property Rights and the Nature of the Firm", Journal of Political Economy, 98, 1119-1158. Hart, O. and Moore, B. (1999), "Foundations of Incomplete Contracts", Review of Economic Studies, 66, 115-38. Hartwell, R. (1965), “The Causes of Industrial Revolution: An Essay in Methodology,” Economic History Review, 18. Hayek, F. (1940), "Socialist Calculation III: The Competitive 'Solution'," Economica, 7, 125-49. Hayek, F. (1944), The Road to Serfdom, Chicago, University of Chicago Press. Hayek, F. (1945), "The Use of Knowledge in Society", American Economic Review, 35, 519-30. Hayek, F. (1960), The Constitution of Liberty, Chicago, University of Chicago Press. Hayek, F. (1988), The Fatal Conceit: The Errors of Socialism, Chicago, University of Chicago Press. He, Qinglian (1997), The Primary Capital Accumulation in Contemporary China, Mirror Book, Hong Kong. Headrick, D. (1981), The Tools of Empire: Technology and European Imperialism in the Nineteenth Century, New York, Oxford University Press. Heckscher, E. (1919), "The Effect of Foreign Trade on the Distribution of Income", reprinted in Chater 13 in AEA Readings in the Theory of International Trade, Philadelphia, Blackiston, 1949. Hegel, G. W. F. (1821), Philosophy of Right, Trans. T.M. Knox, Oxford, Clarendon Press, 1962. Heisenberg, Werner (1971), p. 31. Physics and Beyong; Encounters and Conversations. Trans. Arnold Pomerans. New York, Harper & Row. Hellman, Joel (1997, p. 56), "Constitutions and Economic Reforms in the Post-Communist Transitions." in Sachs and Pistor The Rule of Law and Economic Reform in Russia, Boulder, Westview Press. Helpman, E. (1980), "International Trade in the Presence of Product Differentiation, Economies of Scale and Monopolistic Competition", Journal of International Economics, 11, 305-40. Helpman, E. (1992), "Endogenous Macroeconomic Growth", European Economic Review, 36, 237-67. Helpman, E. and Krugman, P. (1985), Market Structure and Foreign Trade, Cambridge, MIT Press. Helpman, Elhanan (1987), “Imperfect Competition and International Trade: Evidence from Fourteen Industrial Countries.” Journal of the Japanese and International Economics, 1, 62-81. Helpman, Elhanan and Laffont, Jean-Jacques (1975), “On Moral Hazard in General Equilibrium Theory,” Journal of Economic Theory, 10, 8-23. Henderson, J.V. (1974), “The Sizes and Types of Cities,” American Economic Review, 64, 640-57. Henderson, J.V. (1996), "Ways to Think about Urban Concentration: Neoclassical Urban Systems versus the New Economic Geography", International Regional Science Review 19(1-2), 31-36. Herberg, H., Kemp, M. and Tawada, M. (1982), "Further Implications of Variable Returns to Scale in General Equilibrium Theory", International Economic Review, 9, 261-72. Hicks, J. (1950), A Contribution to the Theory of the Trade Cycle, Oxford, Oxford University Press. Hicks, J. R. (1960), “Thoughts on the Theory of Capital.” Oxford Economic Papers, vol. 12 (June), pp. 123-32. Hicks, J. R. (1969), A Theory of Economic History. Oxford, Clarendon Press Hirschman, Albert (1958), The Strategy of Economic Development, New Haven, Yale University Press. Hirschman, A. (1968), “The Political Economy of Import Substituting Industrialization,” Quarterly Journal of Economics, 1968, in Haggard, Stephan, ed., The International Political Economy and the Developing Countries. Vol 1. Aldershot, U.K., Elgar. 1995. Hoffman, Philip and Norberg, Kathryn (eds) (1994), Fiscal Crises, Liberty, and Representative Government, 1450-1789. Stanford, Calif., Stanford University Press. Holborn, Hajo (1982), A history of Modern Germany. Princeton, Princeton Univ. Press. Holmstrom, Bengt, and Milgrom, Paul (1991), “Multitask Principal-Agent Analysis: Incentive Contracts, Asset Ownership, and Job Design,” Journal of Law, Economics, and Organization. 7, 24-51. Holmstrom, B. and Milgrom, P. (1994), " The Firm as an Incentive System", American Economic Review, 84, 972-91. Holmstrom, Bengt and Roberts, John (1998), “The Boundaries of the Firm Revisited,” Journal of Economic Perspectives, 12, 73-94. Houthakker, M. (1956), "Economics and Biology: Specialization and Speciation", Kyklos, 9, 181-89. Hua, Sheng, Zhang, Xuejuen, and Lo, Xiaopen (1988), "Ten Years in China's Reform: Looking Back, Reflection, and Prospect," Economic Research, No 9, 11, 12, Beijing. Huang, Ray (1991), Tzu Pen Chu I Yu Nien I Shih Chi (Capitalism). Taipei, Lien ching chu pan shih yeh kung ssu. Huang, Z. (1993), "Current Development of the Private Firms in the Mainland China," Economic Outlook, Vol. 8. No. 32, 87-91 Hughes, Jonathan (1970), Industrialization and Economic History, New York, McGraw-Hill. Hume, David (1748), Essays Moreal and Political (ed. By Eugene Rotwein) London, Nelson, 1955. Hummels, David, and Levinsohn, James (1995), “Monopolitic Competition and International Trade: Reconsidering the Evidence,” Quarterly Journal of Economics, 110, 799-836. Hurwicz, L. (1973), "The Design of Mechanisms for Resource Allocation," American Economic Review, 63, 1-30. International Franchise Association (1997), Franchise Opportunities Guide, Washington, D.C., International Franchise Association. Jacobs, Jane (1969), The Economy of Cities, New York, Random House. Jensen, M. and Meckling, W. (1976), "Theory of the Firm: Managerial Behaviour, Agency Costs, and Ownership Structure", Journal of Financial Economics, 3, 305-60. Jevons, W. (1893), Money and Mechanism of Exchange, New York, D. Appleton. Jian, Tianlun, Sachs, Jeffery and Warner, Andrew (1996), "Trends in Regional Inequality in China," China Economic Review, Vol. 7 No. 1, Spring, pp. 1-21. Jin, Hehui, Qian, Yingyi and Weingast, Barry (1999), "Regional Decentralization and Fiscal Incentives: Federalism, Chinese Style," Department of Economics, Stanford University, mimeo. Jin, Hehui and Qian, Yingyi (1998),"Public vs. Private Ownership of Firms: Evidence from Rural China." Quarterly Journal of Economics, August, 113(3), pp. 773-808. 52 Johnson, D. Gale, (1994), "Does China Have a Grain Problem?" China Economic Review, Vol. 5 No. 1, pp. 1-14. Johnson, Harry G. (1954), “Optimum Tariff and Retaliation,” Review of Economic Studies, 21(2), 142-53. Jones, C.I. (1995a), “Time Series Tests of Endogenous Growth Models”, Quarterly Journal of Economics, 110, 695-525. Jones, C.I. (1995b), “R & D-Based Models of Economic Growth”, Journal of Political Economy, 103, 759-784.

633

Jones, Charles I. (1998), Introduction to Economic Growth, New York, W. W. Norton & Company. Jones, Eric L. (1981), The European Miracle: Environments, Economies and Geopolitics in the History of Europe and Asia, Cambridge, Cambridge University Press. Jones, Ronald (1965), “The Structure of Simple General Equilibrium Models,” Journal of Political Economy, 73, 557-72. Jones, R. (1976), "The Origin and Development of Media of Exchange", Journal of Political Economy, 84, 757-75. Josephson, Matthew (1959), Edison; a Biography, New York, McGraw-Hill. Judd, K. (1985), "On the Performance of Patents”, Econometrica, 53, 579-85. Kaldor, N. (1957), “A Model of Economic Growth,” Economic Journal, 67, 591-624. Kaldor, N. (1967), Strategic Factors in Economic Development, Ithaca, Cornell University. Kamarck, Andrew M. (1976), The Tropics and Econoimc Development: a Provocative Inquiry into the Poverty of Nations, Baltimore, Johns Hopkins University Press (for the World Bank) Kamien, M. and Schwartz, N. (1981), Dynamic Optimization: the Calculus of Variations and Optimal Control in Economics and Management. New York, North Holland. Kanemoto, Y. (1980), Theory of Urban Externalities, Amsterdam, North-Holland. Kang, Youwei (1980), Zouxiang Shijie Chuengshu, Changsha, Hunan People's Press. Kaplan, Steven, and Weisbach, Michael (1992), "The Success of Acquisitions, Evidence from Divestitures," Journal of Finance, 47, 107-38. Karman, A. (1981), Competitive Equilibria in Spatial Economics, Cambridge, Oelgeshloger. Karoly, L. and Klerman, J. (1994), “Using Regional Data to Reexamine the Contribution of Demographic and Sectoral Changes to Increasing U.S. Wage Inequality.” in The Changing Distribution of Income in an Open US Economy, ed. by J. Bergstrand et al. Amsterdam, North-Holland. Katz, L. and Murphy, K. (1992), “Changes in Relative Wages, 1963-1987: Supply and Demand Factors. Quarterly Journal of Economics. 107, 35-78. Katz, M. and Shapiro, C. (1985), "Network Externalities, Competition, and Compatibility," American Economic Review, 75, 424-40. Katz, M. and Shapiro, C. (1986), "Technology Adoption in the Presence of Network Externalities," Journal of Political Economy, 94, 82241. Kelley, A. and Williamson, J. (1984), What Drives Third World City Growth, Princeton, Princeton University Press. Kelly, Morgan (1997), “The Dynamics of Smithian Growth”. Quarterly Journal of Economics, 112, 939-64. Kemp, Murray (1991), “Variable Returns to Scale, Non-uniqueness of Equilibrium and the Gains from International Trade.” Review of Economic Studies. 58, 807-16. Kendrick, D. A. (1978), The Planning of Industrial Investment Programs, Baltimore, Johns Hopkings University Press. Keren, M. and Levhari, D. (1982), "The Internal Organization of the Firm and the Shape of Average Costs", Bell Journal of Economics, 13, 474-86. Keynes, J. (1933), "National Self-Sufficiency." In the Collected Writings of John Maynard Keynes, Vol 21, London, Macmillan, 1982. Keynes, J. (1936), The General Theory of Employment, Interest and Money, London, Macmillan. Keynes, J. (1971), The Collected Writings of John Maynard Keynes, Vol 2 - The Economic Consequences of the Peace. London, Macmillan. Khandker, A. and Rashid, S. (1995), “Wage Subsidy and Full Employment in a Dual Economy with Open Unemployment and Surplus Labor,” Journal of Development Economics. 48, 205-23. Kihlstrom, Richard and Laffont, Jean-Jacques (1979), “A General Equilibrium Entrepreneurial Theory of Firm Formation Based on Risk Aversion,” Journal of Political Economy, 87, 719 Kim, S. (1989), "Labor Specialization and the Extent of the Market", Journal of Political Economy, 97, 692-705. Kim, Y-G. and Sobel, J. (1995), "An Evolutionary Approach to Pre-Play Communication," Econometrica, 63, 1181-93. Kindleberger, Charles P. (1973), The World in Depression - 1929-1939. Berkeley, University of California Press. King, R. and Plosser, C. (1984), "Money, Credit, and Prices in a Real Business Cycle", American Economic Review, 74, 363-80. King, R. and Plosser, C. (1986), "Money as the Mechanism of Exchange", Journal of Monetary Economics, 17, 93-115. King, R. G. and Levine, R. (1994), “Capital Fundamentalism, Economic Development, and Economic Growth.” Carnegie-Rochester Conference Series on Public Policy, 40, 259-92. King, Stephan P. (1995), “Search with Free-riders”, Journal of Economic Behavior & Organization, 26, 253-271. Kirby, William (1995), "China Unincorporated: Company Law and Business Enterprise in Twentieth Century China." Journal of Asian Studies, 54. Kirzner, Israel (1997), “Entrepreneurial Discovery and the Competitive Market Process: An Austrian Approach,” Journal of Economic Literature, 35, 60-85. Kiyotaki, N. and Wright, R. (1989), "On Money as a Medium of Exchange", Journal of Political Economy 97, 927-954. Kiyotaki, N. and Wright, R. (1993), "A Search-Theoretic Approach to Monetary Economics", American Economic Review 83, 63-77. Knight, F. (1921), Risk, Uncertainty and Profit. Chicago, Hart, Shaffner and Marx. Knight, F. (1925), "Decreasing Cost and Comparative Cost: A Rejoinder", Quarterly Journal of Economics, 39, 332-33. Kohli, Ulrich and Werner, Augustin (1998), “Accounting for South Korean GDP Growth: Index-Number and Econometric Estimates,” Pacific Economic Review, 3, 133-52. Koopman, T. R. (1957), Three Essays in the State of Economic Science, New York, McGraw-Hill. Kormendi, R.C. and Meguire, P.G. (1985), “Macroeconomic Determinants of Growth: Cross-Country Evidence”, Journal of Monetary Economics, 16, pp.141-163. Kornai, J. (1980), Economics of Shortage, Amsterdam, North-Holland. Kornai, J. (1991), The Road to a Free Economy, New York, Norton. Kornai, J. (1992), The Socialist System: The Political Economy of Communism, Princeton, Princeton University Press. Kornai, Janos.(1986), "The Hungarian Reform Process: Visions, Hopes, and Reality." Journal of Economic Literature, December, 24, pp. 1687-1737. Kravis, Irving and Lipsey, Robert (1981), “Prices and Terms of Trade for Developed Country Exports of Manufactured Goods,”National Bureau of Economic Research Working Paper, No. 774. Kremer, M. (1993), “Population growth and technological change: one million BC to 1990,” Quarterly Journal of Economics 108, 681716. _____ (1993), “The O-ring Theory of Economic Development,” Quarterly Journal of Economics 108, 551-75. Kreps, D. (1990), "Corporate Culture and Economic Theory", in J. Alt and K. Shepsle (eds.) Perspectives on Positive Political Economy, Cambridge, Cambridge University Press. Kreps, D. (1990), A Course in Microeconomic Theory, Princeton University Press.

634

Kreps, D. and Wilson, R. (1982), "Sequential Equilibria", Econometrica, 50, 863-94. Krueger, A. (1974), “The Political Economy of Rent-seeking Society,” American Economic Review, 64, 291-303. Krueger, A. (1986), “Aid in the Development Process,” World Bank Research Observer, January, 62-63. Krueger, A. (1995), "Policy Lessons from Development Experience since the Second World War," in J. Behrman and T.N. Srinivasan (eds.), Hand Book of Development Economics, Vol. III, 2498-550. Krueger, Anne (1984), “Trade Policies in Developing Countries,” in Handbook of International Economics, ed. R. Jones and P. Kenen. Krueger, Anne O. (1997), "Trade Policy and Economic Development: How We Learn." American Economic Review. 87, 1-22. Krugman, Paul (1979), "Increasing Returns, Monopolistic Competition, and International Trade", Journal of International Economics, 9, 469-479. Krugman, P. (1980), "Scale Economies, Product Differentiation, and the Pattern of Trade", American Economic Review, 70, 950-59. Krugman, P. (1981), "Intra-industry Specialization and the Gains from Trade", Journal of Political Economy, 89, 959-73. Krugman, P. (1991), Economics of Geography, Journal of Political Economy, 99, 483-502. Krugman, P. (1992), “Toward a Counter-Counter Revolution in Development Theory,” World Bank Observer, Supplement, 15.61. Krugman, P. (1994), "Complex Landscapes in Economic Geography," a paper presented at the meetings of the American Economic Association. Krugman, P. (1994a), “Europe Jobless, America Penniless?” Foreign Policy, 95, 19-34. Krugman, P. (1994b), “Competitiveness: A Dangerous Obsession,” Foreign Affairs, 73(2), 28-44. Krugman, P. (1994c), “Stolper-Samuelson and the Victory of Formal Economics,” in Alan Deardorff and Robert Stern eds. The Stolper-Samuelson Theorem, Ann Arbor, University of Michigan Press. Krugman, P. (1995), “Growing World Trade: Causes and Consequences.” Brookings Paper on Economic Activity, 1, 327-62. Krugman, P. (1995), Development, Geography, and Economic Theory, Cambridge, MIT Press. Krugman, P. and Lawrence, R. (1994), “Trade, Jobs and Wages. Scientific American. 270, 44-49. Krugman, P. and Venables, A.J. (1995), “Globalization and the Inequality of Nations,” Quarterly Journal of Economics, 110, 857-80. Krugman, P. and Venables, A.J. (1996), “Integration, specialization, and adjustment,” European Economic Review, 40, 959-67. Kubo, Y. (1985), "A Cross-country Comparison of Interindustry Linkages and the Role of Imported Intermediate Inputs", World Development, 13, 1287-98. Kurz, M. (1974), "Arrow-Debreu Equilibrium of an Exchange Economy with Transaction Costs", Econometrica, 42, 45-54. Kuznets, S. (1955), “Economic Growth and Income Inequality.” American Economic Review, March. Inverted-U Hypothesis of inequality Kuznets, S. (1966), Modern Economic Growth, New Haven, Yale Univ. Press. Kydland, F. and Prescott, E. (1982), "Time to Build and Aggregate Fluctuations", Econometrica, 50, 1345-70. La Porta, R., Lopez-de-Silanes, F., Shleifer, A., and Vishny, R. (forthcoming), "The Quality of Government", Journal of Law, Economics and Organization. Laffont, J. and Tirole, J. (1986), "Using Cost Observation to Regulate Firms", Journal of Political Economy, 94, 614-41. Landes, David (1998), The Wealth and Poverty of Nations. New York, W. W. Norton. Lang, Larry, and Stulz, Rene (1994), "Tobin's Q, Corporate Diversification and Firm Performance," Journal of Political Economics, 102, 1248-80. Lange, O. and Taylor, F. (1964), On the Economic Theory of Socialism. New York, McGraw Hill. Lange, O. (1970), Introduction to Economic Cybernetics, Pergamon Press, Oxford. Lardy, Nicholas (1998a), China's Unfinished Economic Revolution, Washington, D.C., The Brookings Institution. Lardy, Nicholas (1998b), "China's Unfinished Economic Experiment," in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Laslett, Peter (1988), “The European Family and Early Industrializatin,” in Baechler, Hall and Mann (eds.) Europe and the Rise of Capitalism, Cambridge, Blackwell. Lau, L. and Song, D-H. (1992), "Growth versus Privatization: An Alternative Strategy to Reduce the Public Enterprise Sector: The Experience Taiwan and South Korea", Working Paper, Department of Economics, Stanford University. Leamer, Edward E. (1984), Sources of International Comparative Advantage: Theory and Evidence, Cambridge, MA, MIT Press. Lee, Douglas (1957), Climate and Economic Development in the Tropics. New York, Harper for the Council on Foreign Relations. Legros, Patrick and Newman, Andrew (1996), “ Wealth Effects, Distribution, and the Theory of Organization,” Journal of Economic Theory, 70, 312-41 Leland, H. (1968), "Saving and Uncertainty: The Precautionary Demand for Saving." Quarterly Journal of Economics, 82, 465-73. Lenin, V. (1939), Imperialism, the Highest Stage of Capitalism, New York, International Publishers. Leontief, Wassily W. (1956), “Domestic Production and Foreign Trade: the American Capital Position Re-examined,” in Readings in International Economics, edited by Richard E. Caves and Harry G. Johnson. Homewood, Irwin, 1968. Lerner, A. P.(1952), “Factor Prices and International Trade,” Economica, 19(1), 1-15. Lewis, T. and Sappington, D. (1991), "Technological Change and the Boundaries of the Firm", American Economic Review, 81, 887-900. Lewis, W Arthur (1952), "World Production, Prices and Trade, 1870-1960". The International Political Economy and the Developing Countries. Vol 1. Haggard, S., ed., Elgar. 1995. Lewis, W Arthur (1954), "Economic Development with Unlimited Supplies of Labour"..Development Economics. Vol 1. Lal, Deepak, ed., Elgar, 1992. Lewis, W. (1955), The Theory of Economic Growth, London, Allen and Unwin. Lewis, W. (1984), “The State of Development Theory,” American Economic Review. 74, 1-10. Lewis, W. (1988), “The Roots of Development Theory,” Handbook of Development Economics. Vol I, 27-38. Li, David (1994), "The Behavior of Chinese State Enterprises under the Dual Influence of the Government and the Market," University of Michigan, manuscript. Li, David D. (1996), "A Theory of Ambiguous Property Rights in Transition Economies: The Case of the Chinese Non-State Sector." Journal of Comparative Economics, 23, 1-19. Li, Hongyi and Zou, Heng-fu (1998), "Income Inequality is not Harmful for Growth: Theory and Evidence." Review of Development Economics, 2, 318-34. Li, Junhui (1999), "Shunde de Zhuangzhi (The Transformation of the Ownership System in Shunde County)," Economic Highlights, No. 36, p. 3. Li, Wei (1997). "The Impact of Economic Reform on the Performance of Chinese State Enterprises, 1980-1989."Journal of Political Economy, 105(5), 1081-1106. Liebowitz, S. J. and Margolis, Stephen E. (1994), “Network Externality: An Uncommon Tragedy,” Journal of Economic Perspectives, 8, 133-50.

635

Lilien, D. (1982), "Sectoral Shifts and Cyclical Unemployment", Journal of Political Economy, 90, 777-93. Lin, J. Y. (1998), “The Current State of China's Economic Reforms,” in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Lin, J. Y. and Yang, D. (1998), “On the Causes of China's Agricultural Crisis and the Great Leap Famine,” China Economic Review. 9, 125-40. Lio, M. (1996), Three Assays on Increasing Returns and Specialization: A Contribution to New Classical Microeconomic Approach, Ph.D. Dissertation, Department of Economics, the National Taiwan University. Lio, M. (1998), “Uncertainty, Insurance, and Division of Labor,” Review of Development Economics, 2, 76-86. Lippman, Steven A. and McCall, John J. (1979), “The Economics of Job Search-A survey”, Economic Inquiry, 14, 155-189. Lipton, Michael (1977), Why Poor People Stay Poor, Lipton, Cambridge, Harvard University Press. Little, I. and Mirrless, J. (1980), Manual of Industrial Project Analysis in Developing Countries, Paris, OECD. Liu, Meng-Chun (1999) "Two Approaches to International Trade, Development and Import Protection," Ph.D. Dissertation, Department of Economics, Monash University. Liu, Pak-Wai and Yang, Xiaokai (2000) "The Theory of Irrelevance of the Size of the Firm," Journal of Economic Behavior and Organization, 42, 145-65. Liu, Yia-Ling, (1992), "Reform From Below: The Private Economy and Local Politics in the Rural Industrialization of Wenzhou," China Quarterly, 130, 293-316. Livingstone, I. (1983), “The Development of Development Economics,” O.D.I. Review, No. 2. Locay, L. (1990), "Economic Development and the Division of Production between Households and Markets", Journal of Political Economy, 98, 965-82. Long, J., Jr. and Plosser, C. (1983), "Real Business Cycles", Journal of Political Economy, 91, 39-69. Loveman, G. and Sengenberger, W. (1991), "The Re-emergence of Small-Scale Production: An International Comparison", Small Business Economics 3, No. 1, 1-38. Lucas, R., Jr. (1972), "Expectations and the Neutrality of Money", Journal of Economic Theory, 4, 103-24. Lucas, R., Jr. (1973), "International Evidence on Output-Inflation Tradeoffs", American Economic Review, 63, 326-34. Lucas, R., Jr. (1976), "Econometric Policy Evaluation: A Critique", Journal of Monetary Economics., Suppl. Series, 1, 19-46, 62. Lucas, R., Jr. (1980), "Equilibrium in a Pure Currency Economy", in J. Karenken and N. Wallace (eds.), Models of Monetary Economics, Minneapolis, Federal Reserve Bank of Minneapolis. Lucas, R., Jr. (1988), "On the Mechanics of Economic Development", Journal of Monetary Economics, 22, 3-42. Lucas, R., Jr. (1993), "Making a Miracle", Econometrica, 61, 251-72. Luo, Xiaopeng (1994), "Gaige yu Zhongguo Dalude Denji Chanquan (Reforms and Property Rights based on Ranking in Mainland China", Modern China Studies, No. 41, 31-45. MacFarlane, Alan (1988), “The Cradle of Capitalism: The Case of England,” in Baechler, Hall and Mann (eds.), Europe and the Rise of Capitalism, Cambridge, Blackwell. MacLeod, W. and Malcomson, J. (1988), "Reputation and Hierarchy in Dynamic Models of Employment," Journal of Political Economy, 96, 832-81. Maddison, Angus (1995), Monitoring the World Economy: 1820-1992. Paris, Organization of Economic Cooperation and Development. Mailath, George J. (1998), "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory." Journal of Economic Literature. 36, 1347-74. Mankiw, N. G. (1985), "Small Menu Costs and Large Business Cycles: A Macroeconomic Model", Quarterly Journal of Economics, May, 100(2), 529-38. Mankiw, N. G., Romer, D. and Weil, D.N. (1992), “A Contribution to the Empirics of Economic Growth.” Quartely Journal of Economics. 107, 407-37. Manne, H. (ed.) (1975), The Economics of Legal Relationships, St. Paul, West Publishing Company. Mantel, R. (1974), On the Characterization of Aggregate Excess Demand, Journal of Economic Theory, 7, 348-53. Mao, Zedong (1977a), Selected Works of Mao Zedong, Volume 5. Beijing, People's Press. Mao, Tse-tung (1977b), A Critique of Soviet Economics, Translated by Moss Roberts, annotated by Richard Levy, with an introduction by James Peck. New York, Monthly Review Press. Mao, Yushi (1999), "Zhengfu Ruhe Bangzu Qiye He Bangzu Jiuye (How Can the Government Assist Firms and Employment)?" Economic Highlights, No. 37, p. 1. Marcouiller, D. and Young, L. (1995), "The Black Hole of Graft: the Predatory State and the Informal Economy," American Economic Review, 85, 630-46. Marshall, Alfred (1890), Principles of Economics, 8th Edition, New York, Macmillan, 1948. Marx, Karl (1867), Capital, a Critique of Political Economy, Vols I-III, New York, International Publishers, 1967. Mas-Collell, A., Whinston, M., and Green, J. (1995), Microeconomic Theory, New Yourk, Oxford University Press. Maskin, Eric (forthcoming), “Recent Theoretical Work on the Soft Budget Constraint”, American Economic Review, Papers and Proceedings. Maskin, Eric and Tirole, Jean (1999a), "Unforeseen Contingencies, Property Rights, and Incomplete Contracts." Review of Economic Studies, 66, 83-114. Maskin, Eric and Tirole, Jean (1999b), "Two Remarks on the Property Rights Literature." Review of Economic Studies, 66, 139-50. Maskin, Eric and Xu, Chenggang (1999), “Soft Budget Constraint Theories: From Centralization to the Market”, Working Paper, Department of Economics, Harvard University. Matsui, A. (1991), Cheap-Talk and Cooperation in Society. " Journal of Economic Theory, 54, 245-58. Matsuyama, K. (1991), “Increasing Returns, Industrialization and Indeterminancy of Equilibria,” Quarterly Journal of Economics, 106, 651-67. Mauss, Marcel (1925), The Gift: The Form and Reason for Exchange in Archaic Societies, New York, W.W. Norton (1990) Maxwell, Henry (1721), Reasons Offered for Erecting a Bank in Ireland, the second edition, Dublin. Mayer, Wolfgang (1981), "Theoretical Considerations on Negotiated Tariff Adjustments." Oxford Economic Papers, 33, 135-53 Mayer, Wolfgang (1984), “Endogenous Tariff Formation,” American Economic Review, 74, 970-85. McGuirk, A. M. and Mundlak, Y. (1992). “The Transition of Punjab Agriculture: A Choice of Technique Approach.” American Journal of Agricultural Economics, vol. 74 (February), pp. 132-43. McKenzie, L. W. (1955), “Equality of Factor Prices in World Trade,” Econometrica, 23(3), 239-257. McMillan, John. (1996),"Markets in Transition," in David Kreps and Kenneth Wallis (eds.), Advances in Economics and Econometrics: Theory and Applications, Cambridge, Cambridge University Press.

636

McMillan, J., Whalley, J., and Zhu, L. (1989), "The Impact of China's Economic Reforms on Agricultural Productivity Growth", Journal of Political Economy, 97, 781-807. McNeil, W. (1974), The Shape of European History, Oxford, Oxford University Press. McNeill, William Hardy (1963), The Rise of the West: A History of the Human Community. Chicago, University of Chicago Press. Meek, R. and Skinner, A. (1973), "The Development of Adam Smith's Ideas on the Division of Labor," Economic Journal, 83, 1094-116. Meier, G. (1994), From Classical Economics to Development Economics. New York, St. Martin's Press. Meier, G. (1995), Leading Issues in Economic Development, New York, Oxford University Press. Meier, G. and Seers, Dudley (eds) (1984), Pioneers in Development. New York, Oxford University Press. Meier, Gerald (1994), ‘“The Progressive State” in Classical Economics,’ From Classical Economics to Development Economics, New York, St. Martin’s Press. Men Qinguo (1988), " On the Ownership Structure of Modern Corporation," Young Economists Forum, No 4, Tianjin. Meng, Xin and Perkins, France (1996), "The Destination of China's Enterprise Reform: A Case Study from a Labor Market Perspective," Australian National University, August. Menger, Carl (1871), Principles of Economics, translated by James Dingwall and Bert F. Hoselitz. New York, New York University Press. Michio, Nagai and Urrutia, Miguel (eds) (1985), Meiji Ishin: Restoration and Revolution, Tokyo, United Nations University. Milgrom, P. and Roberts, J. (1982), “Limit Pricing and Entry under Incomplete Information,” Econometrica, 40, 433-59. Milgrom, P. and Roberts, J. (1990), "Bargaining, Influence Costs, and the Organization of Economic Activity" in J. Alt and K. Shepsle (eds.), Perspectives on Positive Political Economy, Cambridge, Cambridge University Presspp. 57-89. Milgrom, P. and Roberts, J. (1992), Economics, Organization and Management, Englewood Cliffs, Prentice-Hall. Milgrom, P. and Roberts, J. (1994), "The Economics of Modern Manufacturing: Technology, Strategy and Organization," American Economic Review, 80, 511-28. Mill, John (1848), Principles of Political Economy, Harmondsworth, Penquin, 1970. Mills, E. S. (1967), “An Aggregative Model of Resource Allocation in a Metropolitan Area,” American Economic Review, 57, 197210. Mills, E. and Hamilton, B. (1984), Urban Economics, Glenview, Scott, Foresman and Company. Minami, Ryoshin and Hondai, Susumu (1995), "An Evaluation of the Enterprise Reform in China: Income Share of Labor and Profitability in the Machine Industry," Hitotsubashi Journal of Economics, Vol. 36, No. 2, December, pp. 125-143. Mitchell, B. R. (1998), International historical statistics : Europe, 1750-1993. London, Macmillan Reference; New York, N.Y., Stockton Press Modigliani, Franco (1989), The Collected Papers of Franco Modigliani. Vol 5. Saving, deficits, inflation, and financial theory. Modigliani, Franco, Edited by Simon Johnson Cambridge, Mass. and London, MIT Press. Mokyr, Joel (1990) The Lever of Richs: Technological Creativity and Economic Progress, New York, Oxford University Press. Mokyr, Joel, (1993), “The New Economic History and the Industrial Revolution,” in Mokyr, J. ed. The British Industrial Revolution: An economic perspective, Boulder and Oxford, Westview Press. Monteverde, K. and Teece, D.J. (1982), "Supplier Switching Costs and Vertical Integration in the Automobile Industry", Bell Journal of Economics, 13, pp. 206-13. Morgan, Peter and Manning, Richard (1985), “Optimal Search”, Econometrica, 53, 923-944. Morgan, T. (1970), “Trends in Terms of Trade, and Their Repercussion on Primary Products.” in Morris, C. and Adelman, I. (1988), Comparative Patterns of Economic Development, 1850-1914. Johns Hopkins Studies in Development series. Baltimore and London: Johns Hopkins University Press. Mueller, M. (1998), "China's Telecommunications Sector and the WTO: Can China Conform to the Telecom Regulatory Principles?" in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Murakami, Naoki, Liu, Deqiang, and Otsuka, K. (1996), “Market Reform, Division of Labor, and Increasing Advantage of Small-scale Enterprises: The Case of the Machine Tool Industry in China,” Journal of Comparative Economics, 23, 256-277 Murphy, K. and Welch, F. (1991), “The Role of International Trade in Wage Differentials.” in Workers and Their Wages: Changing Patterns in the United States. ed. by M. Kosters. Washitington, American Enterprise Institute. Murphy, K. and Topel, R. (1987), "The Evolution of Unemployment in the United States, 1968-1985", NBER Macroeconomics Annual, 2, 11-58. Murphy, K., Shleifer, A., and Vishny, R. (1989a), "Industrialization and the Big Push", Journal of Political Economy, 97, 1003-26. Murphy, K., Schleifer, A., and Vishny, R. (1989b), "Income Distribution, Market Size, and Industrialization", The Quarterly Journal of Economics, 104, 537-64. Murphy, K., Schleifer, A., and Vishny, R. (1991), "The Allocation of Talent: Implications for Growth", Quarterly Journal of Economics, 106, 503-530. Murphy, K., Shleifer, A. and Vishny, R. (1992), "The Transition to a Market Economy: Pitfalls of Partial Reform," The Quarterly Journal of Economics, August, 889-906. Murray, Christopher J. L. and Lopez, Alan D. (eds) (1996), The Global Burden of Disease. Cambridge, MA, Harvard University Press. Myrdal, Gunnar (1956), Development and Underdevelopment, National Bank of Egypt Fiftieth Anniversary Commemoration Lectures, Cairo (pp. 47-51). Myrdal, G. (1957), Economic Theory and the Underdeveloped Regions. London, Duckworth Naisbitt, John (1990), Megatrends 2000 : the New Directions for the 1990's. New York, Morrow. Nash, J. F. (1950), “The Bargaining Problem,” Econometrica, 18, 115-62. Nath, S.K. (1962), The Theory of Balanced Growth,” Oxford Economic Papers, 14(2), 138-53. National Research Council (1986), Population Growth and Economic Development: Policy Questions. Washington, DC, National Academy of Sciences Press. Naughton, Barry (1994a), "Chinese Institutional Innovation and Privatization from Below," American Economic Review, Vol. 84 Vol. 2, May, pp. 266-270. Naughton, Barry (1994b), "What is Distinctive about China's Economic Transition? State Enterprise Reform and Overall System Transformation," Journal of Comparative Economics, Vol. 18, No. 3, June, pp. 470-490. Naughton, Barry (1995), Growing Out of the Plan. Cambridge University Press, 1995. Nee, V. and Sijin, S. (1993), "Local Corporatism and Informal Privatization in China's Market Transition", Working Paper on Transitions from State Socialism No. 93-2. Einaudi Center for International Studies, Cornell. Nee, Victor (1996), "Changing Mechanisms of Stratification in China," American Journal of Sociology, Vol. 101 No. 4, January, pp.908-949.

637

Nelson, R. (1956), “A Theory of the Low Level of Equilibrium Trap in Under-developed Economies.” American Economic Review, 46, 894-908. Nelson, R. (1995), "Recent Evolutionary Theorizing About Economic Change", Journal of Economics Literature, 33, 48-90. Nettels, Curtis (1962), The Emergence of a National Economy, 1775-1815, New York. Ng, S. (1995), Economic Openness and Growth, Ph.D. dissertation, Department of Economics, Monash University. Ng, Y-K. (1986), Meseconomics, a Micro-macro Analysis, New York, Harvester Wheatsheaf. Ng, Y-K. (1992), "Business Confidence and Depression Prevention: A Mesoeconomic Perspective", American Economic Review, 82, 36571. Ng, Y-K. and Yang, X. (1997), "Specialization, Information, and Growth: a Sequential Equilibrium Analysis". Review of Development Economics. 1, 257-74. Ng, Y-K. and Yang, X. (2000), "Effects of Externality-Corrective Taxation on the Extent of the Market and Network Size of Division of Labor". Seminar Paper, Department of Economics, Monash University. Nolan, Peter (1993), State and Market in the Chinese Economy: Essays on Controversial Issues, MacMillan, London. North, Douglas (1958), "Ocean Freight Rates and Economic Development", Journal of Economic History, 18, 537-55. North, Douglas (1981a) Structure and Change in Economic History, chapter 12, New York, Norton. North, Douglas (1981b) “The Industrial Revolution Reconsidered,” in North, Structure and Change in Economic History, Norton. North, D. (1986), "Measuring the Transaction Sector in the American Economy", S. Eugerman and R. Gallman, eds,. Long Term Trends in the American Economy, Chicago, University of Chicago Press. North, D. (1987), "Institutions, Transaction Costs and Economic Growth", Economic Inquiry, 25, 419-28. North, D. (1990), Institutions, Institutional Change and Economic Performance, New York, Cambridge University Press. North, D. (1994), "Economic Performance through Time,” American Economic Review. 84, 359-68. North, D. (1997), "The Contribution of the New Institutional Economics to an Understanding of the Transition Problem." WIDER Annual Lectures, March. North, Douglass and Weingast, Barry (1989), “Constitutions and Commitment: The Evolution of Institutions Governing Public Choice in Seventeenth-Century England,” Journal of Economic History, XLIX, pp 803-32. North, Douglas and Robert Thomas (1970), “An Economic Theory of the Growth of the West World,” The Economic Review, 23, 117. Nurkse, R. (1952), Indivisibilities play a role in virtuous circles of development, but they are not essential. Nurkse, R. (1953), Problems of Capital Formation in Underdeveloped Countries, New York, Oxford University Press. Nussbaum, Frederick (1925) "American Tobacco and French Politics, 1783-1789," Political Science Quarterly, 40, 501-503. Oh, S. (1989), "A Theory of a Generally Acceptable Medium of Exchange and Barter", Journal of Monetary Economics, 23, 101-19. Ohlin, B. (1933), Interregional and International Trade, Cambridge, Harvard University Press. Oi, Jean (1986), "Commercializing China's Rural Cadres." Problems of Communism, 35, 1-15. Oi, Jean (1992) "Fiscal Reform and the Economic Foundations of Local State Corporatism in China." World Politics, October, 45(1). Oi, Jean (1995), "The Role of the Local Government in China's Transitional Economy," China Quarterly. 144, 1132-49. Olson, Mancur (1982), The Rise and Decline: Economic Growth, Stagflation, and Social Rigidities. New Haven, Yale University Press. Olson, Mancur (1996), “Distinguished Lecture on Economics in Government: Big Bills Left on the Sidewalk: Why Some Nations are Rich and others Poor,” Journal of Economic Perspectives 10(2). O'Rourke, K. and Williamson, J. (1994), "Late Nineteenth Century Anglo-American Factor-Price Convergence: Were Heckscher and Ohlin Right?" Journal of Economic History, 54, 892-916. Osborne, M. and Rubinstein, A. (1990), Bargaining and Markets, Boston, Academic Press. Ostroy, J. (1973), "The Informational Efficiency of Monetary Exchange", American Economic Review, 63, 597-610. Ostroy, J. and Starr, R. (1990), "The Transactions Role of Money", in B. Friedman and F. Hahn (eds.), Handbook of Monetary Economics, Volume 1, Amsterdam, North Holland. Owen, T. (1997), "Autocracy and the Rule of Law in Russian Economic History," in J. Sachs and K. Pistor eds. The Rule of Law and Economic Reform in Russia, Westview Press. Page, Scott E. (1999), "On the emergence of cities", Journal of Urban Economics, 45, 184-208. Palma, Babriel (1978), “Dependency: A Formal Theory of Underdevelopment or a Methodology for the Analysis of Concrete Situations of Underdevelopment?” World Development, 6, 899-902. Panagariya, Arvind (1983), “Variable Returns to Scale and the Heckscher-Ohlin and Factor-Price-Equalization Theorems.” World Economics. 119, 259-80. Parkin, M. (1986), "The Output-inflation Tradeoff when Prices are Costly to Change," Journal of Political Economy, 94, 200-24. Patten, R. H. and Rosengard, J.K. (1991), Progress with Profits: The Development of Rural Banking in Indonesia, San Francisco, CA, ICS Press. Paxson, C. (1999) “Parental Resources and Child Abuse and Neglect”, American Economic Review, 89, 239-44. Pei, M. (1998), "The Growth of Civil Society in China." in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Peng, Yusheng, (1992), "Wage Determination in Rural and Urban China: A Comparison of Public and Private Industrial Sectors," American Sociological Review, Vol. 57 No. 2, April, pp. 198-213. Perkins, D., ed. (1977), Rural Small-Scale Industry in China, Berkeley, University of California Press. Perkins, D. (1988), "Reforming China's Economic System", Journal of Economic Literature, Vol. XXVI, pp. 601-45. Perkins, Frances, Zheng, Yuxing and Cao, Yong (1993), "The Impact of Economic Reform on Productivity Growth in Chinese Industry: A Case of Xiamen Special Economic Zone," Asian Economic Journal, Vol. 7, No. 2, pp. 107-146. Petty, William (1671), Political Arithmetics, in C. H. Hull ed. Economic Writings of Sir. William Petty, reissued, New York, Augustus M. Kelly, 1963. Petty, William (1683), Another Essay on Political Arithmetics, in C. H. Hull ed. Economic Writings of Sir. William Petty, reissued, New York, M. Kelly, 1963. Philips, Ulrich (1929), Life and Labor in the Old South, Boston, Little, Brown, and Company. Pigou, A C. (1940), War Finance and Inflation. Neal, Larry, ed., Elgar Reference Collection. International Library of Macroeconomic and Financial History series, vol. 12. Aldershot, U.K., Elgar. Pilon, Roger (1998), "A Constitution of Liberty for China", China in The New Millennium: Market Reforms and Social Development, CATO Institute, Washington, D.C. Pincus, Jonathan J. (1975), “Pressure Groups and the Pattern of Tariffs,” Journal of Political Economy, 83, 757-78. Ping, Xinqiao (1988), "The Reform of the Ownership System, Property Rights, and Management," Pipe, R. (1999), Property and Freedom, New York, Alfred Knopf.

638

Pistor, K. (1997), "Company Law and Corporate Governance in Russia," in J. Sachs and K. Pistor eds. The Rule of Law and Economic Reform in Russia, Westview Press. Plato (380 BC) (1955), The Republic, Trans. H.D.P. Lee, Harmondsworth, Penguin Classics Prebisch, R. (1988), “Dependence, Interdependence and Development.” Cepal Review, 34, 197-205. Prendergast, Canice (forthcoming), "The Provision of Incentives in Firms," Journal of Economic Literature. Prescott, E. (1986), "Theory Ahead of Business Cycle Measurement", Federal Reserve Bank of Minneapolis Quarterly Review, 10, 9-22. Prestowitz, Clyde V. Jr et al. (1994), “The Fight over Competitiveness,” Foreign Affairs, 73(4), 186-197. Pritchett, L. (1997), “Ðivergence, Big Time,” Journal of Economic Perspectives, 11(3). Prosterman, Roy, Hanstad, Tim and Li, Ping (1996), "Can China Feed Itself?" Scientific American, November, pp. 90-96. Puga, Diego and Venables, Anthony (1998), "Agglomeration and Economic Development: Import Substitution vs. Trade Liberasation," Centre for Economic Performance Discussion Paper No. 377. London School of Economics. Qian, Y. (1994a), "Incentives and Loss of Control in an Optimal Hierarchy", Review of Economic Studies, 61(3), 527-44. Qian, Y. (1994b), "A Theory of Shortage in Socialist Economies based on the ‘Soft Budget Constraint’ ", American Economic Review, 84, 145-56. Qian, Yingyi (1999), "The Institutional Foundations of China's Market Transition", Annual Bank Conference on Development Economics. Qian, Y. (forthcoming), "The Process of China's Market Transition (1978-98), The Evolutionary, Historical, and Comparative Perspectives." Journal of Institutional and Theoretical Economics. Qian, Yingyi and Weingast, Barry R. (1997), "Federalism As a Commitment to Preserving Market Incentives." Journal of Economic Perspectives, Fall, 11(4), pp. 83-92. Qian, Yingyi and Roland, Gerard (1998), "Federalism and the Soft Budget Constraint." American Economic Review, December, 88(5), pp. 1143-1162. Qian, Yingyi, Roland, Gerard and Xu, Chenggang (1999) "Coordinating Changes in M-form and U-form Organizations." Mimeo, Stanford University. Quah, D. (1993), “Galton‘s Fallacy and Tests of The Convergence Hypothesis”, Scandinavian Journal of Economics, 95(4), 427-443. Quah, D. (1996), “Twin Peaks: Growth and Convergence in Models of Distribution Dynamics”, Economic Journal, 100, 1045-1055. Quigley, John M. (1998), "Urban Diversity and Eonomic Growth", Journal of Economic Perspectives, 2(2), 1998, 127-138. Rabushka, A. (1987), The New China: Comparative Economic Development in Mainland China, Taiwan, and Hong Kong, Westview Press, Colorado, 1987. Radelet, Steven and Sachs, Jeff (1998a), “The Onset of the East Asian Financial Crisis,” Paper presented in the National Bureau of Economic Research Currency Crisis Conference. Radelet, Steven and Sach, Jeff (1998b) “Shipping Costs, Manufactured Exports, and Economic Growth,” mimeo, HIID. Radner, R. (1992), "Hierarchy: The Economics of Managing", Journal of Economic Literature, 30, 1382-1415. Radner, R. (1993), "The Organization of Decentralized Information Processing ", Econometrica, 61, 1109-46. Rae, J. (1834), Statement of Some New Principles on the Subject of Political Economy, reissued, New York, M. Kelly, 1964. Ram, Rati (1997), "Level of Economic Development and Income Inequality: Evidence from the Postwar Developed World," Southern Economic Journal. 64, 576-83. Ramey G. and Ramey, V. (1995) “Cross-Country Evidence on the Link between Volatility and Growth”, American Economic Review, 85, 1138-1151. Ramsey (1928), "A Mathematical Theory of Saving", Economic Journal, 38, 543-59. Ranis, G. (1988), “Analytics of Development: Dualism,” in Handbook of Development Economics, ed. H. Chenery and T. Srinivasan, Vol. 1, pp. 74-92. Rashid, Salim (1986), "Adam Smith and the Division of Labor: a Historical View", Scottish Journal of Political Economy, 33, 292-97. Rawski, Thomas (1986), "Overview: Industry and Transport," in U.S. Congress, Joint Economic Committee, China's Economy Looks Toward the Year 2000: Volume 1. The Four Modernizations, May. Ray, Debraj (1998), Development Economics, Princeton, Princeton Uni. Press. Rebelo, S. (1991), "Long Run Policy Analysis and Long Run Growth", Journal of Political Economy, 99, 500-21. Reingnum, Jennifer F. (1982), “Strategic Search Theory”, International Economics Review, 23, 1-17. Reynolds, Bruce (ed.) (1987), Reform in China: Challenges and Choices, M.E. Sharpe, New York. Reynolds, L. (1985), Economic Growth in the Third World, 1850-1980. New Haven, Yale University Press. Ricardo, D. (1817), The Principle of Political Economy and Taxation, London, Gaernsey Press, 1973. Riezman, Raymond (1982), "Tariff Retaliation from a Strategic Viewpoint," Southern Economic Journal, 48, 583-93. Riskin, C. (1971), "Small Industry and the Chinese Model of Development," China Quarterly, 46, 245-73. Riskin, Carl (1987), China's Political Economy: The Quest for Development Since 1949, Studies of the East Asian Institute of Columbia University, Oxford University Press, 1987. Robbins, L. (1968), The Theory of Economic Development in the History of Economic Thought. London, Macmillan, New York, St. Martin's P. Roland, Gerard (2000), Politics, Markets and Firms: Transition and Economics, Cambridge, MA, MIT Press. Romano, R. E. (1994), “Double Moral Hazard and Resale Price Maintenance,” RAND Journal of Economics, 25, pp. 455-66. Romer, P. (1986), "Increasing Returns and Long Run Growth", Journal of Political Economy, 94, 1002-37. Romer, P. (1987), “Growth Based on Increasing Returns Due to Specialization.” American Economic Review Papers and Proceedings. 77, 56-72. Romer, P. (1990), "Endogenous Technological Change", Journal of Political Economy, 98, S71-S102. Romer, P. (1993), "The Origins of Endogenous Growth", Journal of Economic Perspectives, 8, 3-22. Ronnas, Per (1993), "Township Enterprises in Sichuan and Zhejiang: Establishment and Capital Generation," National Workshop on Rural Industrialization in Post-Reform China, Beijing, China, October. Rosen, S. (1978), “Substitution and the Division of Labor,” Economica, 45, 235-50. Rosen, S. (1983), “Specialization and Human Capital,” Journal of Labor Economics, 1, 43-49. Rosenberg, N. and Birdzell, L. E. (1986), How the West Grew Rich: Economic Transformation of the Industrial World, New York, Basic Books. Rosenstein-Rodan, P. (1943), Problems of industrialization in Eastern and Southeastern Europe, Economic Journal, June-September issue. Rostow,W.W. (1960), The Stages of Economic Growth: A Non-Communist Manifesto, Cambridge, Cambridge University Press. Rotemberg, Julio, (1987), "The New Keynesian Micro Foundations", in Stanley Fischer, ed. NBER Macroeconomics Annual, 1987, Cambridge, MA, MIT Press. Rubinstein, A. (1982), "Perfect Equilibrium in a Bargaining Model", Econometrica, 50, 97-108.

639

Rubinstein, A. (1985), "A Bargaining Model with Incomplete Information", Econometrica 53, 1151-72. Rybczynski, T. M. (1955), “Factor Endowments and Relative Commodity Prices,” Economica, 22, 336-41. Sachs, Jeffrey D. (1986) “Managing the LDC Debt Crisis,” Brookings Paper, 397-443. (1987) “U.S. Commercial Banks and the Developing Country Debt Crisis," with H. Huizinga, Brookings Papers on Economic Activitv, No. 2. (1988), Review Essay: 'Recent Studies of the Latin American Debt Crisis'," Latin American Research Review, Vol. XXIII, no. 3 , pp. 170-179. (1989) "Political and Economic Determinants of Budget Deficits in the Industrial Democracies," with N. Roubini, European Economic Review 33, No. 5 pp. 903-938 North-Holland (1992) "Privatization in Russia : Some Lessons from Eastern Europe American Economic Review, Spring. (1992) "Transition from a Planned Economy to a Market Economy," in Social and Ethical Aspects of Economics: A Colloquium in the Vatican. (1993) "An Update on Reform in Eastern Europe and Russia," China Economic Review, Volume 4, Number 2. (1994) Understanding 'Shock Therapy'," Social Market Foundation Occasional Paper No. 7, London. (1995) "The Age of Global Capitalism," Foreign Policy, Number 98, Spring. (1996a), “Globalization and the U.S. Labor Market.” The American Economic Review: Papers and Proceedings, May. (1996b), “The Tankers Are Turning - Sachs on Competitiveness,” World Link, September/October 1996 (1996c), “On the Tigers Trail, - Sachs on Competitiveness,” World Link, November/December. Sachs, J. (1996d), "Notes on the Life Cycle of State-led Industrilization," Japan and the World Economy. 8, 153-74. (1997) “Globalization is the Driving Force for Growth in the U.S.,” The Rising Tide: The Leading Minds of Business and Economics Chart a Course Toward Higher Growth and Prosperity, John Wiley and Sons, Inc. (1998), Lecture Notes for Capitalist Economic Development. Department of Economics, Harvard University. Sachs, J. and Pistor, K. (1997), "Introduction: Progress, Pitfalls, Scenarios, and Lost Opportunities," in J. Sachs and K. Pistor eds. The Rule of Law and Economic Reform in Russia, Westview Press. Sachs, J. and Shartz, H. (1994), “Trade and Jobs in US Manufactures. Brookings Papers on Activity. No. 1. 1-84. and (1997), The Rule of Law and Economic Reform in Russia, Westview Press. Sachs, J. and Warner, A. (1997), "Fundamental Sources of Long-Run Growth.” American Economic Review, Papers and Proceedings, 87, 184-88. and (1995), “Economic Reform and the Process of Global Integration,” Brookings Papers on Economic Activity, 1. Sachs, J. and Woo, W.T.(1994), "Structural Factors in the Economic Reforms of China, Eastern Europe, and the Former Soviet Union", Economic Policy, 18, April. Sachs, J. and Woo, W.T. (1996) “China's Transition Experience,", Transition: The Newsletter About Reforming Economies, vol. 7, nos 3-4, March-April. The World Bank Transition Economics Division. and (1999), "Understanding China's Economic Performance", Journal of Policy Reforms, forthcoming. Sachs, J. and Yang, X. (1999), "Gradual Spread of Market-Led Industrialization.” Harvard Center for International Development Working Paper No. 11. Sachs, J., Woo, W. and Parker, S. (1997), Economies in Transition: Comparing Asia and Europe. MIT Press. Sachs, J., Yang, X. and Zhang, D. (1999a), "Trade Pattern and Economic Development when Endogenous and Exogenous Comparative Advantages Coexist.” Harvard Center for International Development Working Paper No. 3. , , and (1999b), "Patterns of Trade and Economic Development in the Model of Monopolistic Competition.” Harvard Center for International Development Working Paper No. 14 Sachs, J. and Warner, A. (1995), Natural Resources and Economic Growth. Cambridge MA, Harvard University mimeo (January). Sah, R and Stiglitz, J. (1988), "Committees, Hierarchies and Polyarchies", The Economic Journal, 98, 451-70. Sah, R. (1991), “Fallibility in Human Organizations and Political Systems,” Journal of Economic Perspectives, 5, 67-88. Sah, R. and Stiglitz, J. (1984), “The Economics of Price Scissors,” American Economic Review, 74, 125-38. Sah, R. and Stiglitz, J. (1986), “The Architecture of Economic Systems,” American Economic Review, 76, 716-27. Sah, Raj and Stiglitz, Joseph. (1991), "The Quality of Managers in Centralized versus Decentralized Organizations", Quarterly Journal of Economics. 106, 289-95. Sala-i-Martin, X. (1996), “The Classical Approach to Convergence Analysis”, Economic Journal, 106, 1019-1036. Samuelson, P. (1939), "Interactions Between the Multiplier Analysis and the Principle of Acceleration", Review of Economic Statistics, 21, 75-78. Samuelson, P.A. (1948), “International Trade and the Equalisation of Factor Prices,” Economic Journal, 58(230), 163-84. Samuelson, P. A. (1953), “Prices of Factors and Goods in General Equilibrium”, Review of Economic Studies, 21(1), 1-20. Sapsford, D. (1985), “The Statistical Debate on the Net Barter Terms of Trade Between Primary Commodities and Manufactures,” Economic Journal, 95, 781-88. Sargent, T. and Wallace, N. (1975), "`Rational Expectations,' the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political of Economy, 83, 241-54. Schultz, T. W., ed. (1974), Economics of the Family : Marriage, Children, and Human Capital, Chicago, the University of Chicago Press. Schultz, T. W. (1993), Origins of Increasing Returns, Cambridge, MA, Blackwell. Schumpeter, J. (1934), The Theory of Economic Development, New York, Oxford University Press. (1939), Business Cycles, New York, McGraw-Hill. Schurmann, H. (1968), Ideology and Organization in Communist China, Berkeley, University of California Press. Schweizer, U. (1986), "General Equilibrium in Space," in J. J. Gabszewicz et. al, Location Theory. London, Harwood,. Scitovsky, T. (1954), "Two Concepts of External Economies," Journal of Political Economy, 62, 143-51. Scott, A.J. (1988), Metropolis: from the division of labor to urban form, University of California Press. Segal, I. (1999), "A Theory of Incomplete Contracts," Review of Economic Studies, 66, 57-82. Segerstrom, P. (1998), "Endogenous Growth without Scale Effects", American Economic Review, 88, 1290-1310. Segerstrom, P., Anant, T., and Dinopoulos, E. (1990), "A Schumpeterian Model of the Product Life Cycle", American Economic Review, 80, 1077-91. Seierstad, A. and Sydsater, K. (1987), Optimal Control Theory with Economic Applications, Amsterdam, North-Holland. Sen, Amartya K. (1977), “Starvation and Exchange Entitlements: A General Approach and Its Application to the Great Bengal Famine.” Cambridge Journal of Economics, No. 2, 33-59. Sen, A.K. (1981) Poverty and Famines: An Essay on Entitlement and Deprivation, Oxford, Clarendon. Sen, A.K. (1983), “Development: Which Way Now?” Economic Journal, 93, 742-62.

640

Sen, A.K. (1988), "The Concept of Development,” Handbook of Development Economics, I, Chapter 1, Amsterdam, North-Holland. Sen, Partha (1998), “Terms of Trade and Welfare for a Developing Economy with an Imperfectly Competitive Sector,” Review of Development Economics, 2, 87-93. Servaes, Henri (1996), "The Value of Diversification During the Conglomerate," Journal of Finance, 51, 1201-25. Shapiro, C. and Stiglitz, J. (1984), “Equilibrium Umnemployment as a Worker Discipline Device,” American Economic Review, 74, 433-44. Shea, Jia-Dong and Yang, Ya-Hwei (1994), "Taiwan's Financial System and the Allocation of Investment Funds," in Joel Aberbach, David Dollar and Kenneth Sokoloff (ed.), The Role of State in Taiwan's Development, M.E. Sharpe, Armonk, N.Y., pp. 193-230. Sheahan, J. (1958), “International Specialization and the Concept of Balanced Growth,” Quarterly Journal of Economics, 52, 183-97. Shi, H. (1994), "Implications of Imperfect Competition and Specialization on Business Cycles and Economic Structure", Ph.D. Dissertation, Department of Economics, Monash University. Shi, H. and Yang, X. (1995), "A New Theory of Industrialization", Journal of Comparative Economics, 20, 171-89. and (1998), "Centralised Hierarchy within a Firm vs. Decentralised Hierarchy in the Market ", in K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. Shleifer, A. (1986), "Implementation Cycles", Journal of Political Economy, 94, 1163-1190. Shleifer, A. (1994), "Establishing Property Rights," Paper presented in World Bank Annual Conference on Development Economics. Shleifer, Andrei (1998), "State versus Private Ownership," Journal of Economic Perspectives, 12, 133-50. Shleifer, A. and Vishny, R. (1992), "Pervasive Shortages Under Socialism," RAND Journal of Economics, 23, 237-46. Shleifer, A. and Vishny, R. (1993), "The Politics of Market Socialism," Working Paper, Department of Economics, Harvard University. Shooman, Martin (1968), Probabilistic Reliability: An Engineering Approach, McGraw-Hill Book Company, New York. Simon, Curtis and Nardinelli, Clark (1996) “The Talk of the Town: Human Capital, Information, and the Growth of English Cities, 18611961”. Explorations of Economic History, 33, 384-413. Singer, H. W. (1984), “The Terms of Trade Controversy and the Evolution of Soft Financing,” in Pionnerrs in Development, ed. Meier, Gerald and Seers Singh, Nirvikar (1989), “Theories of Sharecropping,” in Pranab Bardhan ed. The Economic Theory of Agrarian Institutions, Oxford, Clarendon Press. Skaperdas, S. (1992), "Cooperation, Conflict, and Power in the Absence of Property Rights ", American Economic Reiview, 82, 720-39. Skinner, J. (1988) “Risky Income, Life Cycle Consumption, and Precautionary Savings”, Journal of Monetary Economics, 22, pp.237255. Skousen, Mark (1997), "The Perseverance of Paul Samuelson's Economics." Journal Economic Perspective, 11, 137-53 Smith, Adam (1776), An Inquiry into the Nature and Causes of the Wealth of Nations. Reprint, edited by E. Cannan. Chicago, University of Chicago Press, 1976. Smith, Sheila and Toye, John (1979), “Three Stories About Trade and Poor Economies,” Journal of Development Studies. Smythe, D. (1994), "Book Review: Specialization and Economic Organization: A New Classical Microeconomic Framework," Journal of Economic Literature, 32, 691-92. Solinger, D. (1992), "Urban Entrepreneurs and the State: The Merger of State and Society," pp. 121-42 in State and Society in China: The Consequences of Reform, edited by A. Rosenbaum. Boulder, Westview Press. Solow, R. (1956), "A Contribution to the Theory of Economic Growth", Quarterly Journal of Economics, 70, 65-94 Sonnenschein, H. (1973), “Do Walras’ identity and continuity characterize the class of community excess demand functions?” Journal of Economic Theory, 6, 345-54. Spence, M. A. (1976), "Product Selection, Fixed Costs, and Monopolistic Competition", Review of Economic Studies, 43, 217-36. Spraos, John (1983), Inequalising Trade: a study of traditional north/south specialisation in the context of terms of trade concepts, New York, Oxford University Press. Srinivasan, T. N. (1964), "Optimum Savings in a Two-Sector Model of Growth", Econometrica, 32, 358-74. St. Catherines Ont., Info Press (1999), The Franchise Annual. St. Catherines Ont., Info Press Stahl, I. (1972), Bargaining Theory, Stockholm: Economic Research Institute, Stockholm School of Economics. Starrett, D. (1973), "Inefficiency and the Demand for Money in a Sequence Economy", Review of Economic Studies, 40, 289-303. Stern, N. (1989), “Survey of Development,” Economic Journal, 99, 597-685. Stigler, G. (1951), "The Division of Labor is Limited by the Extent of the Market", Journal of Political Economy, 59, 185-93. Stigler, George J. (1961), “The Economics of Information”, Journal of Political Economy, 69, 213-225. Stigler, George (1976) “The Successes and Failures of Professor Smith”. Journal of Political Economy, 84, 1199-1213. P. 1209 Stiglitz, J. (1974) “Incentives and Risk-sharing in Sharecropping,” Review of Economic Studies, 41, 219-55. Stiglitz, J. (1986), "The New Development Economic,” World Development, 14, 257-65. Stiglitz, J. (1988), “Economic Organization, Information and Development,” in H. Chenery and T.N. Srinivasan (eds.) Handbook of Development Economics, Amsterdam, North-Holland, Vol. I. Stiglitz, J. (1989), “Rational Peasants, Efficient Institutions, and a Theory of Rural Organization: Methodological Remarks for Development Economics,” in Bardhan, P. ed. The Economic Theory of Agrarian Institutions, Oxford, Clarendon Press. Stiglitz, J. (1992), "Capital Markets and Economic Fluctuations in Capitalist Economies", European Economic Review, 36, 269-306. Stiglitz, Joseph (1998), “Sound Finance and Sustainable Development in Asia,” Keynote Address to the Asia Development Forum, The World Bank Group. Stiglitz, Joseph and Weiss, A. (1986), “Credit Rationing and Collateral", in J. Edwards and Mayer, C. (eds.), Recent Development in Corporate Finance, Cambridge, Cambridge University Press. Stokey, N. (1991), "Human Capital, Product Quality, and Growth", Quarterly Journal of Economics, 106, 587-616. Stolper, Wolfgang and Sammuelson, Paul (1941), “Protection and Real Wages,” Review of Economic Studies, 9, 58-73. Streeten, P. (1959), “Unbalanced Growth,” Oxford Economic Papers, 6, 167-90. Summer, L. (1992), “The Challenges of Development,” Finance & Development, March, pp 6-8. Summers, A. and Heston, A. (1988), “Penn World Tables Mark 5: 1950-1988,” Quarterly Journal of Economics, 340-67. Sun, Guangzhen (1999), Increasing Returns, Roundabout Production and Urbanization: A General Equilibrium Analysis of the Division of Labor. Ph.D. Dissertation, Department of Economics, Monash University. Sun, Guangzhen (2000), “The Size of the Firm and Social Division of Labour.” Australian Economic Papers. 39, 263-77. Sun, G. and Lio, M. (1996), "A General Equilibrium Model Endogenizing the Level of Division of Labor and Variety of Producer Goods", Working Paper, Department of Economics, Monash University. Sun, G., Yang, X, and Yao, S. (1999), "Theoretical Foundation of Economic Development Based on Networking Decisions in the Competitive Market", Harvard Center for International Development Working Paper No. 17. Sutcliffe, R. (1964), “Balanced and Unbalanced Growth,” Quarterly Journal of Economics, 79, 62-43.

641

Swan, T. W. (1956), "Economic Growth and Capital Accumulation", Economic Record, 32, 334-61. Tabuchi, Takatoshi (1998), "Urban Agglomeration and Dispersion: a Synthesis of Alonso and Krugman", Tamura, R. (1991), "Income Convergence in an Endogenous Growth Model", Journal of Political Economy, 99, 522-40. Tamura, R. (1992), "Efficient Equilibrium Convergence: Heterogeneity and Growth", Journal of Economic Theory, 58, 355-76. Taylor, J. (1980), "Aggregate Dynamics and Staggered Contracts", Journal of Political Economy, February, 88, 1-23. Taylower, George (1932), "Wholesale Commodity Prices at Charleston, South Carolina, 1732-1792", Journal of Economic and Business History, 4, 367. Temple, J. (1999), “The New Growth Evidence,” Journal of Economic Literature, 37, 112-56. Thirwal, A. (1986), “A General Model of Growth and Development of Kaldorian Lines,” Oxford Economic Papers. Thirwall, A.P. (1994), Growth and Development:With Special Reference to Developing Economies, London, Macmillan. Thompson, Henry (1995), "Free Trade and Income Redistribution in Some Developing and Newly Industrialized Countries." Open Economies Review, 6, 265-80. Thorp, R. eds (1984), Latin America in the 1930s: The Role of the Periphery in World Crisis. New York, St. Martin's. Tirole, J. (1986), "Hierarchies and Bureaucracies: On the Role of Collusion in Organizations," Journal of Law and Economic Organization, 2, 181-214. Tirole, J. (1989), The Theory of Industrial Organization, Cambridge, The MIT Press. Tirole, Jean (1999), "Incomplete Contracts: Where Do We Stand?" Econometrica, 67, 741-81. Todaro, M (1969), “A Model of Labor Migration and Urban Unemployment” American Economic Review, 59 (1), 138-48. Trefler, Daniel (1993), “International Factor Price Differences: Leontief was Right!” Journal of Political Economy, 10(6), 961-87. Trefler, Daniel (1995), "The Case of the Missing Trade and Other Mysteries." American Economic Review. 85, 1029-46. Tucker, Josiah (1755), The Elements of Commerce and Theory of Taxes, London. Tucker, Josiah (1774), Four Tracts on Political and Commercial Subjects, Gloucester, R. Taikes. Turgot, A.R.J. (1751), Lettre a Madame de Graffigny sur les lettres d'une Peruvienne, in G. Schelle, ed. Oeuvres de Turgot et Documents le concernant, Vol. I, Paris, F. Alcan, 1913. Turgot, A.R.J. (1766), Reflections on the Production and Distribution of Wealth, in P. D. Groenewegen, ed. The Economics of A.R.J. Turgot, The Hague, Nijjhoff, 1977. United Nation’s Economic Commission for Latin America (ECLA) (1950), The Economic Devleopment of Latin America and Its Principal Problems. Uzawa, H. (1959), “Prices of the Factors of Production in International Trade,” Econometrica, 27(3), 448-468. Uzawa, H. (1965), Optimum Technical Change in an Aggregative Model of Economic Growth, Review of Economic Studies, 6, 18-31. Van Zandt, T. (1995), "Hierarchical Computation of the Resource Allocation Problem," European Economic Review, 39, 700-8. Varian, Hal (1993), Microeconomic Analysis, New York, Norton. Vogel, E. (1989), One Step Ahead in China: Guangdong Under Reform, Cambridge, Harvard University Press. Vogt, W. (1969), "Fluktuationen in einer washsenden Wirtschaft under klassischen Bedingungen", in Bombach, G. (ed.), Wachstum, Einkommensverteilung und wirtschaftliches Gleichgewicht, Berlin, Duncker und Humblot. von Mises, L. (1922), Socialism: An Economic and Sociological Analysis, Indianapolis, Liberty Classics, reprinted in 1981. von Mises, Ludwig (1924), The Theory of Money and Credit, London, Jonathan Cape Ltd., 1934 von Thünen, J. H. (1826), Der Isolierte Staat in Bezierhung auf landwrirtschaft und Nationalekonomie, The Isolated State. (Carla M. Wartenberg, Trans.) New York, Pergamon, 1966. Hamburg. Walder, A. (1986), "The Informal Dimension of Enterprise Financial Reforms", pp. 630-45 in The Chinese Economy Toward the Year 2000, Joint Economic Committee, U.S. Congress. Washington D.C., U.S. Government Printing Office. Walder, A. (1989), "Factory and Manager in an Era of Reform", The China Quarterly, No. 118, June pp. 242-264. Walder, A. (1992), "Local Bargaining Relationships and Urban Industrial Finance," pp. 308-33 in Bureaucracy, Politics, and Decision Making in Post Mao China, edited by K. Lieberthal and D. Lampton, Berkeley, University of California Press. Walder, Andrew (1995), "China's Transitional Economy: Interpreting its Significance." China Quarterly, December 1995, 144, pp. 963-979. Walker, Amasa (1874), Science of Wealth: A Manual of Political Economy, Boston, Little Brown, New York, by Kraus Reprint, 1969. Wallace, N. (1980), "The Overlapping Generations Model of Fiat Money", in J. Karenken and N. Wallace (eds.) Models of Monetary Economics, Minneapolis, Federal Reserve Bank of Minneapolis. Wank, D. (1993), From State Socialism to Community Capitalism: State Power, Social Structure, and Private Enterprise in a Chinese City, Unpublished Ph. Dissertation, Department of Sociology, Harvard University. Wartenberg, C. M. (1966), von Thünen’s Isolated State, London, Pergamon. Weber, Max (1927), General Economic History, translated by Frank H. Knight. New York, Greenberg. Weber, Max (1961), The Protestant Ethic and the Spirit of Capitalism, Routledge, Chapman & Hall. Weber, Max (1968), Economy and Society, An Outline of Interpretive Sociology.Edited by Guenther Roth and Claus Wittich. Translators: Ephraim Fischoff [and others]. New York, Bedminster Press. Webster, A. ed. (1990) Structural Change in the World Economy, London, Routledge. Weibull, Jorgen (1995), Evolutionary Game Theory, Cambridge, MA, MIT Press. Weitzman Martin L. (1979), “Optimal Search for the Best Alternative”, Econometrica, 47, 641-654. Weitzman, M. (1982), "Increasing Returns and the Foundations of Unemployment Theory", The Economic Journal, 92, 787-804. Weitzman, M. (1994), "Monopolistic Competition with Endogenous Specialization", Review of Economic Studies, 61, 45-56. Weitzman, M. (1998), "Recombinant Growth", Quarterly Journal of Economics, 113, 331-60. Weitzman, Martin and Xu, Chenggang (1994), "Chinese Township Village Enterprises as Vaguely Defined Cooperatives." Journal of Comparative Economics, September 1994, 18, pp. 121-145. Wen, M. (1997a), “Infrastructure and Evolution in Division of Labor”, Review of Development Economics,1,191-206. Wen, M. (1997b), Division of Labor in Economic Development, Ph.D. dissertation, Department of Economics, Monash University. Wen, M. (1998), “An Analytical Framework of Consumer-Producers, Economies of Specialisation and Transaction Costs,” in K. Arrow, Y-K. Ng, X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. West, E.G. (1964), "Adam Smith's Two Views of the Division of Labor," Economica, 3, 23-32. WHO. (1997a), “World Malaria Situation in 1994, Part I,” WHO Weekly Epidemiological Record 36, 269-74. Williamson, J. G (1993), "Economic Convergence: Placing Post-famine Ireland in Comparative Perspective." Discussion Paper No. 1654. Cambridge, MA, Harvard Institute of Economic Research (September). Williamson, J. G. (1992), "The Evolution of Global Labor Markets in the First and Second World Since 1830: Background Evidence and Hypotheses." SAE Working Paper 36, Cambridge, MA, National Bureau of Economic Research (February). (1998), "Globalization, Labor Markets and Policy Backlash in the Past," Journal of Economic Perspectives, 12, 51-72.

642

Williamson, O. (1967), "Hierarchical Control and Optimum Firm Size", Journal of Political Economics, 75, 123-38. Williamson, O. (1985), Economic Institutions of Capitalism, New York, The Free Press. Wong, C. (1985), "Material Allocation and Decentralization: Impact of the Local Sector on Industrial Reform," in The Political Economy of Reform in Post Mao China, edited by E. Perry and C. Wong, Cambridge, Harvard University Press. Wong, C. (1986a), "The Economics of Shortage and Problems of Reform in Chinese Industry", Journal of Comparative Economics, 10, 36387. Wong, C. (1986b), "Ownership and Control in Chinese Industry: The Maoist Legacy and Prospects for the 1980s", pp. 571-602 in The Chinese Economy Toward the Year 2000, Joint Economic Committee, U.S. Congress. Washington D.C., U.S. Government Printing Office. Wong, K-Y. and Yang, X. (1994), "An Extended Dixit-Stiglitz Model with the Tradeoff Between Economies of Scale and Transaction Costs," Seminar Paper, Department of Economics, Monash University. and (1998), "An Extended Ethier Model with the Tradeoff Between Economies of Scale and Transaction Costs," in K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan, forthcoming. Woo, Wing Thye, Hai, Wen, Jin, Yibiao and Fan, Gang (1994), "How Successful Has the Chinese Enterprise Reform Been?" Journal of Comparative Economics, June, 18(3), pp. 410-37. Woodward, C. (1951), Origins of the New South, 1877-1913. New York World Bank (1992), Development Report 1992. Environment and Resource Problems. New York, Oxford University Press. World Bank (1997), Development Report 1997: The State in a Changing World. New York, Oxford University Press. World Bank (1981-1999), World Development Report, Various issues, Washington, DC, World Bank. Wu, Jieh-min (1998), Local Property Rights Regime in Socialist Reform: A Case Study of China's Informal Privatization. Ph. D. Dissertation, Department of Political Science, Columbia University. Xing, Yujing (1999), "Renminbi Ziben Xiangmo Keduihuan (Is Liberalization of Capital Account of China Urgent)", Economic Highlights, No. 38, p. 2. Yang, X. (1984): Jingji Kongzhilun Chubu (Introduction to Economic Cybernetics, in Chinese), Changsha: Hunan People's Press. Yang, X. (1988), "A Microeconomic Approach to Modeling the Division of Labor Based on Increasing Returns to Specialization", Ph.D. Dissertation, Dept. of Economics, Princeton University. Yang, X. (1991), "Development, Structure Change, and Urbanization," Journal of Development Economics, 34, 199-222. (1994), "Endogenous vs. Exogenous Comparative Advantages and Economies of Specialization vs. Economies of Scale", Journal of Economics, 60, 29-54. (1996), "A New Theory of Demand and the Emergence of International Trade from Domestic Trade", Pacific Economic Review, 1, 215-17. (1998), Economics and China's Economy, Beijing Zhaocheng Press, China. (1999), "The Division of Labor, Investment, and Capital", Metroeconomica. 50, 301-24. (2000a), Economics: New Classical Versus Neoclassical Frameworks. Cambridge, MA., Blackwell. (2000b), “Incomplete Contingent Labor Contract, Asymmetric Residual Rights and Authority, and the Theory of the Firm.” Seminar Paper, Department of Economics, Monash University Yang, X. and Borland, J. (1991a), "A Microeconomic Mechanism for Economic Growth", Journal of Political Economy, 99, 460-82. and (1991b), "The Evolution of Trade and Economic Growth", Mimeo, University of Melbourne. and (1992), "Specialization and Money as a Medium of Exchange", Department of Economics Seminar Paper No. 8/92, Monash University. Yang, X. and Heijdra, B. (1993), "Monopolistic Competition and Optimum Product Diversity: Comment", American Economic Review, 83, 295-301. Yang, X. and Hogbin, G. (1990), "The Optimum Hierarchy", China Economic Review, 2, 125-40. Yang, X. and Ng, Y-K. (1993), Specialization and Economic Organization, a New Classical Microeconomic Framework, Amsterdam, North-Holland. Yang, X. and Ng, Y-K. (1995), "Theory of the Firm and Structure of Residual Rights", Journal of Economic Behavior and Organization, 26, 107-28. Yang, X. and Ng, S. (1998), “Specialization and Division of Labor: a Survey,” in K. Arrow, Y-K. Ng, and Xiaokai Yang (eds.), Increasing Returns and Economic Analysis, London, Macmillan. Yang, X. and Rice, R. (1994), "An Equilibrium Model Endogenizing the Emergence of a Dual Structure between the Urban and Rural Sectors", Journal of Urban Economics, Vol. 25, 346-68. Yang, X. and Shi, H. (1992), "Specialization and Product Diversity," American Economic Review, 82, 392-98. Yang, X. and Wills, I. (1990), "A Model Formalizing the Theory of Property Rights", Journal of Comparative Economics, 14, 177-98. Yang, X. and Yeh, Y. (1996), "A General Equilibrium Model with Endogenous Principal-agent Relationship," Department of Economics Seminar Paper, Monash University. Yang, X., Wang, J., and Wills, I. (1992), "Economic Growth, Commercialization, and Institutional Changes in Rural China, 1979-1987", China Economic Review, 3, 1-37. Yang, X. and Zhang, D. (1999), "International Trade and Income Distribution," Harvard Center for International Development Working Paper No. 18. Yang, X. and Zhao, Y. (1998), " Endogenous Transaction Costs and Evolution of Division of Labor," Monash University, Department of Economics Working Paper. Ye, Xingqing (1999), “Another Detriment of Urbanization ,” Economic Highlights, No. 365, p. 1, Dec. 31. Yellen, J. L. (1984), "Efficiency Wage Models of Unemployment", American Economic Review, 74, 200-05. Yi, Gang (1988), "The Efficiency of the Market and the Delimiting of Property Rights," China: Development and Reform, No 12, Beijing. Young, Allyn (1928), "Increasing Returns and Economic Progress", The Economic Journal, 38, 527-42. Young, Alwyn (1991), "Learning by Doing and the Effects of International Trade", Quarterly Journal of Economics, 106, 369-406. Young, Alwyn (1993), “Invention and Bounded Learning by Doing”, Journal of Political Economy, 101, 443-472. Young, Alwyn (1998), "Growth without Scale Effects,” Journal of Political Economy, 106, 41-63. Young, Leslie (1991), “Heckscher-Ohlin Trade Theory with Variable Returns to Scale.” Journal of International Economics.” 31, 183-90. Zaleski, E. (1980), Stalinist Planning for Economic Growth, 1933-1952, University of North Carolina Press. Zhang, D. (1999), "Inframarginal Analysis of Asymmetric Models with Increasing Returns," Ph.D. Dissertation, Wuhan University, Center for Advanced Economic Studies. Zhang, Gang, (1993), "Government Intervention versus Marketisation in China's Rural Industries: The Role of Local Governments," National Workshop on Rural Industrialization in Post-Reform China, Beijing, China, October.

643

Zhang, J. (1997), "Evolution in Division of Labor and Macroeconomic Policies”, Review of Development Economics, 1, 236-45. Zhang, Weiying (1999), The Theory of the Firm and China's Enterprise Reforms (Qiye Lilun Yu Zhongguo Qiye Gaige). Peking University Press. Zhang, Yongsheng (2000), Irrelevance of the Size of the Firm: Theory and Empirical Evidence, Ph.D. Dissertation, Department of Economics, Renmin University. Zhao, Y. (1999), " Information, Evolution of the Institution of the Firm, and the Optimal Decision Horizon", Review of Development Economics, 3, 336-53. Zhou, Lin, Sun, Guangzhen, and Yang, Xiaokai (1998), “General Equilibria in Large Economies with Endogenous Structure of Division of Labor,” Working Paper, Department of Economics, Monash University. Zhou, Qiren (1999), "Ba Chuangye Huangdao Diyiwei Lai, Ba Jiuye Huangdao Dierwei Qu (Put Founding Firms before Finding Employment)", Economic Highlights, No. 37, p. 1. Zhou, Taihe (1984), ed., Dangdai Zhongguo de Jingji Tizhi Gaige (Economic System Reforms in Contemporary China). Beijing, China Social Science Press. Zhuravskaya, Ekaterina (1998), "Incentives to Provide Local Public Goods: Fiscal Federalism, Russian Style."Mimeo, Harvard University. Zweig, David (1991), "Rural Industry: Constraining the Leading Growth Sector in China's Economy," Joint Economic Committee, U.S. Congress, China's Economics Dilemmas in the 1990s: The Problems of Reforms, Modernization, and Interdependence, April.

644

References Abdel-Rahman, H. M. (1990), “Agglomeration Economies, Types and Sizes of Cities Journal of Urban Economics.27, 25-45. Abraham, K. and Katz, L. (1986), "Cyclical Unemployment: Sectoral Shifts or Aggregate Disturbances?", Journal of Political Economy, 94, 507-22. Adelman, I. (1961), Theories of Economic Growth and Development. Stanford, Calif., Stanford University Press. Adelman, Irma and Morris, C. (1967), Society, Politics and Economic Development: A Quantitative Approach, Baltimore, Johns Hopkins University Press. Aghion, P., Bacchetta, P., and Banerjee, A. (1998), "Capital Markets and the Instability of Open Economies", Working paper, presented at Harvard University and MIT Growth and Development Seminar. Aghion, P., Bolton, P., and Jullien, B. (1991), "Optimal Learning by Experimentation", Review of Economic Studies, 58, 621-54. Aghion, P., Caroli, E., and Garcia-Pena Losa, C. (1999), "Inequality and Economic Growth: the Perspective of the New Growth Theories,” Journal of Economic Literature, 37, 1615-60. Aghion, Philippe and Howitt, Peter (1992), “A Model of Growth Through Creative Destruction”, Econometrica, 60, 323-351. Aghion, P. and Howitt, P (1998), Endogenous Growth Theory, Cambridge, MIT Press. Aghion P. and Saint-Paul, G. (1991), “On the Virtue of Bad Times: An Analysis of the Interaction between Economic Fluctuations and Productivity Growth”, CEPR Discussion Paper, No.578. Aghion, Philippe and Tirole, Jean (1997), "Formal and Real Authority in Organizations". Journal of Political Economy. Vol. 105 (1). p 129. February. Aiginger, K. and Tichy, G., (1991), "Small Firms and the Merger Mania", Small Business Economics 3, No. 2 (1991), 83-102. Akerlof , G. (1970), “The Market for Lemons: Quality Uncertainty and the Market Mechanism,” Quarterly Journal of Economics, 89, 488-500. Akerlof, G. and Yellen, J. (1985), "A Near-Rational Model of the Business Cycle, with Wage and Price Inertia", Quarterly Journal of Economics, Suppl., 100, 823-38. Alchian, A. (1977), "Why Money?", Journal of Money, Credit and Banking, 9, 131-40. Alchian, A. and Demsetz, H. (1972), "Production, Information Costs, and Economic Organization", American Economic Review, 62, 77795. Alesina, A. and Rodrik, D. (1994), "Distributive Politics and Economic Growth," Quarterly Journal of Economics, 109, 465-90. Alizadeh, Parvin (1984), “Trade, Industrialization, and the Visible Hand,” Journal of Development Studies? Anonymous (1701), Consideration on the East-India Trade, in J. R. McCulloch, ed. A Select Collection of Early English Tracts on Commerce, London, 1856, reissued, Cambridge, Cambridge University, 1954. Arndt, H. (1989), Economic Development: The History of an Idea. Chicago, University of Chicago Press. Arnott, R. (1979), “Optimal City Size in a Spatial Economy,” Journal of Urban Economics, 6, 65-89. Arrow, K. J. (1962), "The Economic Implications of Learning by Doing", Review of Economic Studies, 29, 155-73. Arrow, K. (1979), "The Division of Labor in the Economy, the Polity, and Society", in G. O'Driscoll, Jr. ed., Adam Smith and Modern Political Economy, Ames, Iowa, Iowa State University Press. Arrow, K. (1985), “The Economics of Agency. " In J. Pratt and R. Zeckhauser (eds.), Principals and Agents: The Structure of Business, pp. 37-51. Boston, Harvard Business School Press. Arrow, K., Ng, Y-K. and Yang, X. eds. (1998), Increasing Returns and Economic Analysis, London, Macmillan. Arrow, K., Enthoven, A., Hurwicz, and Uzawa, H. eds. (1958), Studies in Linear and Nonlinear Programming, Stanford, Stanford University Press. Arthur W. Brian (1994), Increasing Returns and Path Dependence in the Economy, Ann Arbor, the University Michigan Press. Azariadis, C. (1975), “Implicit Contracts and Underemployment Equilibrium,” Journal of Political Economy, 83, 1183-1202. Babbage, C. (1832), On the Economy of Machinery and Manufactures, 4th enlarged edition of 1835, reissued in 1977, New York, M. Kelly. Bac, M. (1996), "Corruption and Supervision Costs in Hierarchies," Journal of Comparative Economics, 22, 99-118. Bacha, Edmar L. (1978), “An Interpretation of Unequal Exchange from Prebisch-Singer to Emmanuel,” Journal of Development Economics. Baechler, Jean (1976), The Origins of Capitalism, Translated by Barr Cooper, Oxford, Blackwell. Baechler, Jean, Hall, John A., and Mann, Michael (1997), eds. Europe and the Rise of Capitalism. New York, Blackwell. Bag, P. K. (1997), "Controlling Corruption in Hierarchies," Journal of Comparative Economics, 25, 322-44. Bai, Chong-En, Li, David D., and Qian, Yingyi, Wang, Yijiang (1999), "Anonymous Banking and Financial Repression: How Does China's Reform Limit the Government's Predation without Reducing Its Revenue?" Mimeo, Stanford University. Baily, M. (1974), “Wages and Employment Under Uncertain Demand,” Review of Economic Studies, 41, 37-50. Balassa, B. (1980), The Process of Industrial Development and Alternative Development Strategies, Princeton University, International Finance Section, Essays in International Finance, No. 141. Balassa, B. (1986) “The Employment Effects of Trade in Manufactured Products between Developed and Developing Countries.” Journal of Policy Modeling, 8, 371-90. Balasubramanyam and S. Lall, eds., Current Issues in Development Economics, London, Macmillan, pp. 159-69. Baldwin, R. (1969), “The Case Against Infant-Industry Tariff Protection,” Journal of Polical Economy. 77, 295-305. Baldwin, Richard E, and Venables, Anthony J. (1995), “Regional Economic Integration,” in Grossman, Gene M. Rogoff, Kenneth, eds., Hanbook of International Economics. Volume 3. Amsterdam, New York and Oxford, Elsevier, North-Holland. Ball, L., Mankiw, N. and Romer, D. (1988), "The New Keynesian Economics and the Output-Inflation Tradeoff", Brookings Papers of Economic Activities, 1, 1-65. Banerjee, Abhijit V. (1992), “A Simple Model of Herd behavior”, The Quarterly Journal of Economics, 107, 797-817. Banerjee, A. and Besley, A. (1990), Moral Hazard, Limited Liability and Taxation: A Principal-Agent Model.. Oxford Economic Papers. 42, 46-60. Banerjee, A. and Newman, A. (1993), "Occupational Choice and the Process of Development," Journal of Political Economy, 101, 274-98. Baran, P. (1957), La economia politica del crecimiento, Mexico, F.C.E., 1969. Bardhan, P. (1970), Economic Growth, Development and Foreign Trade, New York, Wiley. Bardhan, P. and Roemer, J. eds. (1993), Market Socialism, the Current Debate, Oxford University Press. Bardhan, Pranab ed. (1989), The Economic Theory of Agrarian Institutions, Oxford, Clarendon Press.

627

Barro, R. (1991), "Economic Growth in a Cross-Section of Countries", Quarterly Journal of Economics, 106, 407-44. Barro, R. (1997), Determinants of Economic Growth, Cambridge, MA, MIT Press. Barro, R. and Sala-i-Martin, X. (1991), “Convergence Across States and Regions”, Brookings Papers on Economic Activities, # 1, 159-82. Barro, R. and Sala-i-Martin, X. (1992), “Convergence”, Journal of Political Economy, 100, 223-51. Barro, R. and Sala-i-Martin, X. (1995), Economic Growth, New York, McGraw-Hill. Barzel, Yoram. (1982), "Measurement Cost and the Organization of Markets", Journal of Law and Economics, 25, 27-48. Barzel, Y. (1985), “Transaction Costs: Are They Just Costs?” Journal of Institutional & Theoretical Economics. 141, 4-16. Barzel, Y. (1989), Economic Analysis of Property Rights, Cambridge, Cambridge University Press. Barzel, Y. (1997), "Property Rights and the Evolution of the State,” memeo. and “Third-party Enforcement and the State,” memeo. Department of Economics, University of Washington. Barzel, Yoram and Yu, Ben T. (1984), "The Effect of the Utilization Rate on the Division of Labor", Economic Inquiry, 22, 18-27. Basu, S. (1996), “Procyclical Productivity: Increasing Returns or Cyclical Utilization”, Quarterly Journal of Economics, 111, 719-750. Bauer, P. and Yamey, B. (1957), The Economics of Underdeveloped Countries, Chicargo, University of Chicargo Press. Baumgardner, J. R. (1988a), "The Division of Labor, Local Markets, and Worker Organization", Journal of Political Economy, 96, 509-27. Baumgardner, J. R. (1988b), "Physicians' Services and the Division of Labor across Local Markets." Journal of Political Economy. 96, 948-82. Baumol, W.J. (1996), “Productivity Growth, Convergence, and Welfare: What the Long-Run Data Show”, American Economic Review, 76(5), 1072-1085. Baxer, M. and King, R.G. (1995), “Measuring Business Cycles: Approximate Band-Pass Filters for Economic Time Series”, NBER working paper No. 5022. Bazovsky, Igor (1961), Reliability Theory and Practice, Englewood Cliffs, Prentice-Hall. Beasley, W. G. (1995), The Rise of Modern Japan, New York, St. Martin's Press. Becker, Gary (1964), Human Capital: A Theoretical and Empirical Analysis, with Special Reference to Education, New York, Columbia University Press. (1965), "A theory of the Allocation of Time", Economic Journal, 75, 497-517. (1981), A Treatise on the Family, Cambridge, Massachusetts, Harvard University Press. and Lewis, H.G. (1973) “On the Interaction Between the Quantity and Quality of Children,” Journal of Political Economy, 81, S279-88. Becker, G. and Murphy, K. (1992), "The Division of Labor, Coordination Costs, and Knowledge", Quarterly Journal of Economics, 107, 1137-60. Beckmann, M. (1968), Dynamic Programming of Economic Decisions, New York, Springer-Verlag. Behrman, J. and Srinivasan, T.N. (1995), "Introduction to Part 9." Vol. IIIB, in Behrman, J. and T.N. Srinivasan eds. Handbook of Development Economics, New York, Elsevier. Beik, Paul H. ed. (1970), The French Revolution. New York, Harper & Row. Benhabib, J. and Joranovic, B. (1991), “Externalities and Growth Accounting”, American Economic Review, 81, 82-113. Ben-Akiva, M. de Palma, A. and Thisse, J. (1989), “Spatial Competition with Differentiated Products.” Regional Science & Urban Economics. 19, 5-19. Berger, Philip, and Ofek, Eli (1995), "Diversification's Effect on Firm Value," Journal of Financial Economics, 37, 39-65. Berle, A. and Means, G. (1932), The Modern Corporation and Private Property, London, Macmillan. Bernard, A. and Jones, C.I. (1996), “Technology and Convergence”, Economic Journal, 106, 1037-1044. Besley, Timothy (1995), "Savings, Credit and Insurance." In J. Behrmand and T. N. Srinivasan, eds. Handbook of Development Economics, Vol. III, New York, Elsevier Science B. V. pp. 2125-2206. Besley, T., Coate, S. and Loury, G. (1993), "The Economics of Rotating Savings and Credit Associations." American Economic Review. 83, 792-810. Bhagat, Sanjay, Shleifer, Andrei and Vishny, Robert (1990), "Hostile Takeovers in the 1980s: The Return to Corporate Specialization," Brookings Papers on Economic Activity: Microeconomics, Special Issue, 1-72. Bhagwati, J. and Dehejia, V. (1994), “Freer Trade and Wages of the Unskilled: Is Marx Striking Again?” in Trade and Wages: Leveling Wages Down? ed. By J Bhagwati and M. Kosters. Washington, American Enterprise Institute. Bhagwati, Jagdish (1969), "Optimal Policies and Immiserizing Growth." American Economic Review. 59, 967-70. (1984), “The State of Development Theory,” American Economic Review. 74, 1-10. Bhaskar, V. (1995), "Noisy Communication and the Evolution of Cooperation," U. St. Andrews. Bhattacharyya, S. and Lafontaine, F. (1995), “Double Sided Moral Hazard and the Nature of Share Contracts,” RAND Journal of Economics, 26, pp. 761-81. Binmore, K., Osborne, M., Rubinstein, A. (1992). Noncooperative Models of Bargaining. New York, Elsevier Science. Black, F. (1979) Business Cycles in General Equilibrium, MIT Working Paper. Black, F. (1987), Business Cycles and Equilibrium, New York, Basil Blackwell. Black, F. (1995), Exploring General Equilibrium, MIT Press. Blanchard, Olivier. Economics of Post-Communism Transition, Oxford University Press, 1997. Blanchard, O. and Kremer, M. (1997), “Disorganization,” Quarterly Journal of Economics, 112, 1091-26. Blomstrom, M. and Wolff, E. (1997), “Growth in a Dual Economy”. World Development. 25, 1627-37. Bliss, C. (1989), “Trade and Development.” In Chenery and Srinivasan eds. Handbook of Development Economics, Vol. II, p. 1188. Blitch, C. P. (1983). “Allyn Young on Increasing Returns.” Journal of Post Keynesian Economics, vol. 5 (Spring), pp. 359-72. Blitch, C. P. (1995). Allyn Young: The Peripatetic Economist. London, Macmillan. Blume, A., Kim, Y-G. and Sobel, J. (1993), "Evolutionary Stability in Games of Communication," Games & Economic Behavior, 5, 547-75. Bolton, P. and Dewatripont, M. (1994), "The Firm as a Communication Network," Quarterly Journal of Economics, 109, 809-39. Bolton, P. and Dewatripont, M. (1995), "The Time and Budget Constraints of the Firm," European Economic Review, 39, 691-09. and (1994), "The Firm as a Communication Network." Quarterly Journal of Economics. 109, 809-39. Bolton, Patrick, and Scharfstein, David (1998), "Corporate Finance, the Theory of the Firm, and Organization," Journal of Economic Perspectives, 12, 95-114. Borjas, G., Freeman, R. and Katz, L. (1992), “How Much Do Immigration and Trade Affect Labor Market Outcomes?” Brookings Papers on Economic Activity. No. 1, 1-67. Borland, J. and Yang, X. (1992a), "Specialization and Money as a Medium for Exchange", Seminar Paper, Department of Economics, Monash University. and (1992b), "Specialization and a New Approach to Economic Organization and Growth", American Economic Review, 82, 386-91.

628

and (1995), "Specialization, Product Development, Evolution of the Institution of the Firm, and Economic Growth", Journal of Evolutionary Economics, 5, 19-42. Borland, Jeff and Eichberger, Jurgen (1998), "Organizational Form outside the Principal-agent Paradigm," Bulletin of Economic Research, 50, 201-27. Boserup, Ester (1975), “The Impact of Population Growth on Agricultural Output,” Quarterly Journal of Ecnomics, 89(2), 257-70. Bouin, Olivier (forthcoming), "Financial Discipline and State Enterprise Reform in China in the 1990s," in Olivier Bouin, Fabrizio Coricelli and Francoise Lemoine (ed.), Different Paths to a Market Economy: China and European Economies in Transition, OECD, Paris. Boycko, Maxim, Shleifer, Andre and Vishny, Robert (1995) Privatizing Russia. MIT Press. Boycko,, M., Shleifer, A. and Vishny, R. (1996), “A Theory of Privatization", Economic Journal. 106:309-19. Braudel, Fernand (1984), Civilization and Capitalism, 18th Century, translation from the French revised by Sian Reynolds. London, Collins. Braudel, Fernand (1972), The Mediterranean and the Mediterranean World in the Age of Philip II. New York, Harper & Row Braudel, Fernand (1981-84), Civilization and Capitalism, 15th-18th Century. London , Collins. 3 volumes. Braverman, A. and Stiglitz, J. (1982), “Sharecropping and the Interlinking of the Agrarian Markets,” American Economic Review, 72, 695-715. Brian, Arthur W. (1994), Increasing Returns and Path Dependence in the Economy, Ann Arbor, the University Michigan Press. Brown, R.L., Durbin, J. and Evans, J.M. (1975), “Techniques for Testing the Constancy of Regression Relationships Over Time” (with discussion), Journal of the Royal Statistical Society, Series B, 37, 149-92. Brunner, K. and Meltzer, A. (1971), "The Use of Money: Money in the Theory of an Exchange Economy", American Economic Review, 61, 784-805. Bruton, Henry (1998), “A Reconsideration of Import Substitution,” Journal of Economic Literature, 36, 903-36. Bruun, O. (1993), Business and Bureaucracy in a Chinese City, Chinese Research Monographs No. 43. Berkeley, Institute of East Asian Studies, University of California. Buchanan, James M. (1975), The Limits of Liberty: Between Anarchy and Leviathan. Chicago, University of Chicago Press. (1989), Explorations into Constitutional Economics. College Station, Texas A&M University Press. (1991), Constitutional Economics. Cambridge, Mass., Blackwell. Buchanan, J. (1994), "The Return to Increasing Returns," in Buchanan, J. and Yoon, Y. eds The Return to Increasing Returns, Ann Arbor, The University of Michigan Press. Buchanan, James M. and Tullock, Gordon (1965), The Calculus of Consent: Logical Foundations of Constitutional Democracy, Ann Arbor, University of Michigan Press. Buchanan, James M. and Stubblebine, W. Craig (1962), “Externality,” Economica, 29, 371-84. Burke, Edmund, (1790), Reflections on the French Revolution. ed. by W. Alison Phillips and Catherine Beatrice Phillips. Cambridge, Cambridge University Press, 1912. Burtless, Gary (1995), "International Trade and the Rise in Earnings Inequality." Journal of Economic Literature. 33, 800-16. Byrd, W. (1983), "Enterprise-Level Reforms in Chinese State-Owned Industry", American Economic Review, No. 73, pp. 329-32. Byrd, W. (1988), "The Impact of the Two-Tier Plan Market System in Chinese Industry", Journal of Comparative Economics, Vol. 11, No. 3, September 1987, pp. 295-308. Reprinted in Reynolds, Bruce L., Chinese Economic Reform: How Far, How Fast?, Academic Press, London. Byrd, William (1991), The Market Mechanism and Economic Reforms in China. New York, M.E. Sharpe. Caballero, R.J. and Hammour, M.L. (1994) “The Cleansing Effect of Recessions”, American Economic Review, vol. 84, 5, pp.1350-1368. Calvo, G. and Wellisz, S. (1978), "Supervision, Loss of Control and the Optimal Size of the Firm", Journal of Political Economy, 86, 94352. and (1979), "Hierarchy, Ability and Income Distribution", Journal of Political Economy, 87, 991-1010. Case, Anne and Deaton, Angus (1998), “Large Cash Transfers to the Elderly in South Africa.” Economic Journal. 108, 1330-61. Case, Anne and Deaton, Angus (1999a), “School Inputs and Educational Outcomes in South Africa.” Quarterly Journal of Economics. 114, 1047-84. Case, Anne and Deaton, Angus (1999b), “Household Resource Allocation in Stepfamilies: Darwin Reflects on the Plight of Cinderella.” American Economic Review. 89, 234-38. Canton, Erik (1997), Economic Growth and Business Cycles, Center for Economic Research, Tilburg University, Amsterdam, Thesis Publishers. Capie, Forrest H. (1983), "Tariff Protection and Economic Performance in the Nineteenth Century", reprinted in Forrest Capie, ed., Protection in the World Economy, (1992) Brookfield, Vermont, Edward Elgar Publishing Co. Carter, M. (1995), "Information and the Division of Labour: Implications for the Firm's Choice of Organisation," Economic Journal, 105, 385-97. Chandler, A. Jr. (1990), Scale and Scope the Dynamics of Industrial Capitalism, Cambridge, MA, Belknap Press of Harvard University Press. Chang, C. and Wang, Y. (1994). "The Nature of the Township Enterprises." Journal of Comparative Economics, 19, pp. 434-452. Chang, G. and Wen, G. (1998), "Food Availability Versus Consumption Efficiency: Causes of the Chinese Famine", China Economic Review, 9, 157-66. Che, Jiahua (1999), "From the Grabbing Hand to the Helping Hand", Working Paper, Department of Economics, University of Notre Dame. Che, Jiahua and Qian, Yingyi (1998), "Insecure Property Rights and Government Ownership of Firms." Quarterly Journal of Economics. 113, 467-96. Chen, B-L., Lin, J. and Yang, X. (1999): “Empirical Evidences for the Endogenous Growth Generated by Evolution in Division of Labor”, Development Discussion Paper, No. 671, Harvard Institute for International Development. Chen, Aimin (1994), "Chinese Industrial Structure in Transition: The Emergence of Stock-offering Firms," Comparative Economic Studies, Vol. 36, No. 4, Winter, pp. 1-19. Chen, Yinan and Zhou, Zhiren eds. (1996), Chuangye Zhifu Bushi Mong (It is not a Dream to Make a Fortune from Entrepreneurship), Hainan International News Center. Chenery, H. (1979), Structural Change and Development Policy, Oxford Univ. Press. Chenery, H., Robinson, S. and Syrquin, M. eds. (1986), Industrialization and Growth: A Comparative Studies, New York, Oxford University Press. Cheng, T. (1991), "The Present and Future of China's Residential Registration System". Ph.D. Dissertation, Department of Sociology, NorthEast University.

629

Cheng, W. (1998),“Specialization and the Emergence and the Value of Money”, In K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. (1999), “Division of Labor, Money, and Economic Progress”, Review of Development Economics, 3, 354-67. Cheng, W., Sachs, J. and Yang, X. (2000), “An Inframarginal Analysis of the Ricardian Model," Review of International Economics, 8, 208-20. (forthcoming), "A General Equilibrium Re-appraisal of the Stolper-Samuelson Theorem," Journal of Economics. (1999), "An Inframarginal Analysis of the Heckscher-Ohlin Model with Transaction Costs and Technological Comparative Advantage," Harvard Center for International Development Working Paper No. 9. Cheng, W., Liu, M. and Yang, X. (2000), “A Ricardo Model with Endogenous Comparative Advantage and Endogenous Trade Policy Regime," Economic Record, 76, 172-82. Cheung, S. (1968), “Private Property Rights and Sharecropping,” Journal of Political Economy Chicago, 76, 1117-22. (1969), The Theory of Share Tenancy, Chicago, University of Chicago Press. (1970), "The Structure of A Contract and the Theory of a Non-exclusive Resource", Journal of Law and Economics, 13, 49-70. (1974), "A Theory of Price Control," Journal of Law and Economics, 17, 53-71. (1983), "The Contractual Nature of the Firm", Journal of Law & Economics, 26, 1-21. (1989), "Privatization vs. Special Interests: The Experience of China's Economic Reforms," Cato Journal, 8, 585-96. (1996), "A Simplistic General Equilibrium Theory of Corruption," Contemporaty Economic Policy, 14, 1-5. Chiang, A. (1984), Fundamental Methods of Mathematical Economics, London, McGraw-Hill. Cho, D. and Graham, S. (1996), “The Other Side of Conditional Convergence.” Economics Letters, 50, 285-90. Chu, C. (1997), "Productivity, Investment in Infrastructure, and Population Size: Formalizing the Theory of Ester Boserup", Review of Development Economics, 1, 294-304. Chu, C. and Tsai, Y. (1998), "Productivity, Investment in Infrastructure, and Population Size: Formalizing the Theory of Ester Boserup", In K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. Chu, C. and Wang, C. (1998), "Economy of Specialization and Diseconomies of Externality", Journal of Public Economics. 69, 249-61. CIA. (1996), The World Factbook. Washington, D.C., Central Intelligence Agency. CIA. (1997), The World Factbook. http://www.odci.gov/cia/publications/factbook/index.html. Ciccone, A. and Matsuyama, K. (1996), “Start-up Costs and Pecuniary Externalities as Barriers to Economic Development,” Journal of Development Economics, 49, 33-59. Cline, William (1997), Trade and Income Distribution, Washington DC, Institute for International Economics. Clower, R. (1967), "A Reconsideration of the Microfoundations of Monetary Theory", Western Economic Journal, 6, 1-8. Coase, R. (1937), "The Nature of the Firm", Economica, 4, 386-405 Coase, Ronald (1946), “The Marginal Cost Controversy,” Economica, 13, 169-82. Coase, Ronald (1960), “The Problem of Social Cost,” Journal of Law and Economics, 3, 1-44. Coase, R. (1991), "The Nature of the Firm: Origin, Meaning, Influence", in Williamson. O. and Winter, S. (eds.), The Nature of the Firm, New York, Oxford University Press. Colwell, P. and Munneke, H. (1997), “The structure of urban land prices”, Journal of Urban Economics , 41, 321-36. Comment, Robert, and Jarrell, Gregg (1995), "Corporate Focus and Stock Returns," Journal of Financial Economics, 37, 67-87. Conlisk, John (1996), “Why Bounded Rationality?” The Journal of Economic Literature, 34, 669-700. Conybeare, John A. C. (1987), Trade Wars: The Theory and Practice of International Commercial Rivalry, New York, Colombia University Press. Cook, Linda, (1993), The Soviet Social Contract and Why It Failed: Welfare Policy and Workers' Politics from Brezhnev to Yeltsin, Harvard University Press, Cambridge, MA. Cooper, R. and Ross, T. W. (1985), “Produce Warranties and Double Moral Hazard,” RAND Journal of Economics, 16, pp. 103-13. Cooter, R. (1989), “The Coase Theorem,” The New Palgrave: A Dictionary of Economics, J. Eatwell, M. Milgate, and P. Newman, eds. London, The Macmillan Press, Vol. 1, 457-60. Crafts, N. (1996), “The First Industrial Revolution: A Guided Tour for Growth Economists” American Economic Review, Papers and Proceedings, 197-201. Crafts, N. (1997), “Endogenous Growth: Lessons for and from Economic History.” D. Kreps and K. Wallis eds. Advances in Economics and Econometrics: Theory and Applications, Vol. II. Cambridge, Cambridge University Press. Crosby, Alfred W. (1986), Ecological Imperialism: The Biological Expansion of Europe, 900-1900. Cambridge, Cambridge University Press. Curtin, Philip D. (1989), Death by Migration: Europe’s Encounter with the Tropical World in the Nineteenth Century. Cambridge, Cambridge University Press. Cypher, James and Dietz, James (1998), “Static and Dynamic Comparative Advantage: A Multi-period Analysis with Declining Terms of Trade,” Journal of Economic Issues, 32, 305-14. Dasgupta, Partha (1995), “The Population Problem: Theory and Evidence,” Journal of Economic Literature, 33, 1879-1902. Deane, Phyllis and Cole, William (1967), British Economic Growth, Cambridge, Cambridge University Press. Deardorff, Alan and Stern, Robert eds. (1994), The Stolper-Samuelson Theorem, Ann Arbor, University of Michigan Press. Deaton, A. (1990) “Saving in Developing Countries: Theory and Evidence”, World Bank Economic Review (Proceedings of the World Bank Annual Conference on Development Economics, 1989, 61-96. Deaton, A. (1991) “Saving and Liquidity Constraints”, Econometrica, 59, 1221-48. Deaton, A. and Paxson, C. (1998a) “Economies of Scale, Household Size, and the Demand for Food”, Journal of Political Economy,106, 897-930. Deaton, A. and Paxson, C. (1998b) “Aging and Inequality in Income and Health”, American Economic Review, 88, 248-53. Debreu, G. (1959), Theory of Value, Yale University Press, New Haven. Debreu, G. (1974), Excess Demand Functions. Journal of Mathematical Economics, 1, 15-21. Debreu, G. (1991), "The Mathematization of Economic Theory", American Economic Review, 81, 1-7. Deininger, K. and Squire, L. (1996), "A New Data Set Measuring Income Inequality," World Bank Economic Review, 10, 565-91. Dellas H. (1991) “Stabilization Policy and Long Term Growth: Are They Related?”, Mimeo, University of Maryland. Delong, B. (1988): “Productivity Growth, Convergence and Welfare: Comments”, American Economic Review, 78, 1138-1154. Demsetz, H. (1967), "Toward A Theory of Property Rights", American Economic Review, 57, 347-59. Demsetz, H. (1988), Ownership, Control, and the Firm, Oxford, Basil Blackwell. Demsetz, H. and Lehn, K. (1985), "The Structure of Corporate Ownership: Causes and Consequences", Journal of Political Economy, 93, 1155-77. Department of Commerce (1972-1999), Statistical Abstract of the United States.

630

Department of Commerce (1975), Historical Statistics of the United States. Dewatripont, Mathias (1988), "Commitment through Renegotiation-Proof Contracts with Third Parties." Review of Economic Studies. 55, 377-89. Dewatripont, M. and Maskin, E. (1995), "Contractual Contingencies and Renegotiation." Rand Journal of Economics. 26, 704-19. and (1995), "Credit and Efficiency in Centralized and Decentralized Economies," Review of Economic Studies, 62, 541-56. Dewatripont, M. and Roland, G. (1995), "The Design of Reform Packages under Uncertainty." American Economic Review. 85, 1207-23. and (1996), "Transition as a Process of Large Scale Institutional Change," in David Kreps and Kenneth Wallis (eds.), Advances in Economics and Econometrics: Theory and Applications, Cambridge, Cambridge University Press, 1996. Diamond, Charles and Simon, Curtis (1990), "Industrial Specialization and the Returns to Labor," Journal of Labor Economics, 8, 175-201. Diamond, D. W. and Dybvig, P. (1983), "Bank Runs, Deposit Insurance, and Liquidity," Journal of Political Economy, 91, 401-19. Diderot, Denis (1713), Diderot Encyclopedia: the Complete Illustrations, New York, Abrams, 1978. Din, M. (1996), “International Capital Mobility and Development Policy in a Dual Economy,” Review of International Economics, 4, 185-201. Dixit, A. (1968), “The Optimal Development in the Labour Surplus Economy,” Review of Economic Studies, 35, 23-34. Dixit, A. (1969), “Marketable Surplus and Dualistic Development,” Journal of Economic Theory, August. Dixit, A. (1987), "Trade and Insurance with Moral Hazard," Journal of International Economics, 23, 201-20. Dixit, A. (1989), "Trade and Insurance with Imperfectly Observed Outcomes," Quarterly Journal of Economics, 104, 195-203. Dixit, A and Nalebuff, B. (1991), Thinking Strategically, New York, W. W. Norton & Company. Dixit, A. and Norman, V. (1980), Theory of International Trade, Cambridge, Cambridge University Press. Dixit, A. and Stiglitz, J. (1977), "Monopolistic Competition and Optimum Product Diversity", American Economic Review, 67, 297-308. Dodzin, Sergei and Vamvakidis, Athanasios (1999), "Trade and Industrialization in Developing Agricultural Economies." International Monetary Fund Working Paper. Domar, E. (1947), "Expansion and Employment", American Economic Review, 37, 34-55. Dornbusch, Fisher S. and Samuelson, Paul (1977), “Comparative Advantage, Trade, and Payments in a Ricardian Model with a Continuum of Goods,” American Economics Review, 67(5), 823-39. Dowrick, S. and Nguyen, D.T. (1989), “OECD Comparative Economic Growth 1950-85: Catch-up and Convergence”, American Economic Review, 79, 1010-1030. Du, J. (2000), "Endogenous, Efficient Long-run Cyclical Unemployment, Endogenous Long-run Growth, and Division of Labor," Review of Development Economics, forthcoming. Dudley, Sarkar, P. (1986), “The Terms of Trade Experience of Britain Since the 19th Century,” Journal of Development Studies. Easterlin, R. (1981), Why Isn’t the Whole World Developed?” Journal of Economic History. March, 1-17. Easton, Stephen and Michael, Walker (1997), "Income, Growth, and Economic Freedom", American Economic Review, Papers and Proceedings, 87, 328-32. Eckholm, E. (1975), The Other Energy Crisis, Firewood, Washington, DC, Worldwatch Institute. Economic Literature. 33, 800-16. Eichberger, B. (1994), Game Theory for Economists, Academic Press. Eichengreen, B. and Flandreau, M. (1994), "The Geography of the Gold Standard." Discussion Paper 1050. London, Centre for Economic Policy Research, October. Ekelund, Robert, and Tollison, Robert (1981), Merchantilism as an Rent-seeking Society, College Station, TX, Texas A & M University Press. Elvin, Mark (1973), The Pattern of the Chinese Past. London, Eyre Methuen. Emmanuel, A. (1972), Unequal Exchange: A Study of the Imperialism of Trade, Eswaran, M. and Kotwal, A. (1985), “A Theory of Contractual Structure in Agriculture,” American Economic Review, 75, pp. 352-67. Ethier, W. (1979), "Internationally Decreasing Costs and World Trade", Journal of International Economics, 9, 1-24. Ethier, W. (1982), "National and International Returns to Scale in the Modern Theory of International Trade", American Economic Review, 72, 389-405. Evans, David (1987), “The Long Run Determinants of North-South Terms of Trade and Some Recent Empirical Evidence,” World Development. 15 (5) 657-71. Fairbank, John King (1992), China: A New History. Cambridge, Mass., Belknap Press of Harvard University Press. Fama, E. and Jensen, M. (1983), "Separation of Ownership and Control", Journal of Law & Economics, 26, 301-27. Fan, Gang and Woo, Wing Thye (1996), "State Enterprise Reform as a Source of Macroeconomic Instability," Asian Economic Journal, November. Fang, Weizhong ed. (1984), Jinji Dashi Ji (Major Economic Events in the People's Republic of China, 1949-1980), Beijing, Chinese Social Science Press. Fang, Xinghai and Zhu, Tian (1999), "Institutional Imperfection and Transition Strategies," Economic Systems, 23, 331-48. Farrell, J. and Maskin, E. (1989), "Renegotiation in Repeated Games", Games and Economic Behaviour, 1, 327-60. Farrell, J. and Garth, S. (1985), "Standardization, Compatibility, and Innovation," Rand Journal of Economics, 16, 70-83. Fauver, Larry, Houston, Joel and Naranjo, Andy (1998), "Capital Market Development, Legal Systems and Value of Corporate Diversification: A Cros-Country Analysis," Working Paper, University of Florida. Fei, J. and Ranis, G. (1964), Development of the Labor Surplus Economy, Richard Irwin, Inc. Fei, John, Ranis, Gustav and Kuo, Shirley (1979), Growth with Equity : the Taiwan Case. New York, Oxford University Press. Fischer, S. (1977), "Long-Term Contracts, Rational Expectations, and the Optimal Money Supply Rule", Journal of Political Economy, February, 85(1), 191-205. Fleming, Marcus (1955), “External Economies and the Doctrine of Balanced Growth,” Economic Journal, 65, 241-56. Frank, A. (1995), The Development of Underdevelopment. Aldershot, UK, Elgar. Frank, C. (1977), Foreign Trade and Domestic Aid. Washington, Brookings Institute. Friedman, Milton (1957), A Theory of the Consumption Function, Princeton, Princeton University Press. Friedman, M. (1962), Capitalism and Freedom, Chicago, The University of Chicago Press. Frye, Timothy and Shleifer, Andrei (1997), "The Invisible Hand and the Grabbing Hand.” American Economic Review, Papers and Proceedings, 87, 354-58. Fudenberg, D. and Tirole, J. (1983), "Sequential Bargaining with Incomplete Information", Review of Economic Studies, 50, 221-47. Fudenberg, D. and Tirole, J. (1991), Game Theory, Cambridge, The MIT Press. Fujita, K., Krugman, P., and Venables, A. (1999), The Spatial Economy: Cities, Regions, and International Trade, Cambridge, MA, MIT Press.

631

Fujita, M. (1988), “A Monopolistic Competition Model of Spatial Agglomeration: Differentiated Product Approach,” Regional Science & Urban Economics, 25, 505-28. Fujita, M. (1989), Urban Economic Theory: Land Use and City Size, New York, Cambridge University Press. Fujita, M. and Krugman, P. (1994), “On the Evolution of Hierarchical Urban Systems,” mimeograph, Department of Regional Science, University of Pennsylvania, Philadelphia, PA. Fujita, Masahisa and Krugman, Paul (1995), “When is the Economy Monocentric: von Thünen and Chamberlin Unified,” Regional Science & Urban Economics, 25, 505-28. Fujita, M. And Thissem, J.-F. (1996), "Economies of agglomeration", Journal of Japanese and International Economies, 10, 339-78. Fujita, M. and Mori, T. (1997), “Structural stability and evolution of urban systems”, Regional Science and Urban Economics , 27, 399-442. Furubotn, E. and Pejovich, S. (eds.) (1974), The Economics of Property Rights. Cambridge, Mass., Ballinger Publishing Company. Gabisch, G. and Lorenz, H. (1989), Business Cycle Theory: A Survey of Methods and Concepts, Berlin, Springer-Verlay. Gale, D. (1986), "Bargaining and Competition. Part I: Characterization and Part II: Existence", Econometrica, 54, 807-18. Gallup, John Luke (1998), “Agricultural Productivity and Geography,” Working Paper, HIID. Gallup, John and Sachs, Jeff (1998), “Geography and Economic Development,” in Pleskovic, Boris, and Joseph E. Stiglitz, eds., World Bank Annual Conference on Development Economics 1998. Washington, DC: The World Bank, pp. 127-178. Reprinted in International Regional Science Review, 22(2): 179-232.. Galor, O. (1996), “Convergence? Inferences from Theoretical Models”, Economic Journal, 106, 1056-1069. Galor, O. and Zeira, J. (1993), "Income Distribution and Macroeconomics," Review of Economic Studies, 87, 205-10. Gans, Joshua (1998), “ Industrialization Policy and the ‘Big Push’,” in K. Arrow, et al, eds. Increasing Returns and Economic Analysis, London, Macmillan. Ghatak, S. (1995), Introduction to Development Economics, London, Routledge. Gibbons, R. (1992), Game Theory for Applied Economist, Princeton University Press. Gibbons, Robert (1998), "Incentives in Organization," Journal of Economic Perspectives, 12, 115-32. Gillis, M., Perkins, D., Roemer, M., and Snodgrass, D.R. (1993) Economics of Development,London/New York, Norton. Gomory, Ralph E. (1994), “A Ricardo Model with Economies of Scale,” Journal of Economic Theory, 62, 394-419. Goodwin, R. (1951), "The Non-linear Accelerator and the Persistence to Markets Having Production Lags", Econometrica, 19, 1-17 Gorden, W. (1980), Institutional Economics, Austin, University of Texas Press. Gordon, B. (1975), Economic Analysis before Adam Smith, London, Macmillan. Gordon, D. (1974), “A Neo-classical Theory of Keynesian Unemployment,” Economic Inquiry, 12, 431-59. Granick, D. (1990), Chinese State Enterprises: A Regional Property Rights Analysis, Chicago, University of Chicago Press. Gray, Cheryl and Hendley, Kathryn (1997), "Developing Commercial Law in Transition Economies: Examples from Hungary and Russia." in Sachs, J. and Pistor, K. eds. The Rule of Law and Economic Reform in Russia, Westview Press. Gray, J. (1976), "Wage Indexation: A Macroeconomic Approach", Journal of Monetary Economics, 2, 221-35. Green, E. (1987), "Lending and the Smoothing of Uninsurable Income", in E. Prescott and N. Wallace (eds.), Contractual Arrangements for Intertemporal Trade, Minneapolis, University of Minnesota Press. Greenaway, D. (1992), “New Trade Theories and Developing Countries,” in V. Balasubramanyam and S. Lall, eds., Current Issues in Development Economics, London, Macmillan, pp. 159-69. Greenwood, J. and Jovanovic, B. (1990), "Financial Development, Growth, and the Distribution of Income," Journal of Political Economy, 98, 1076-1107. Grier, K.B. and Tullock, G. (1989) “An Empirical Analysis of Cross-National Economic Growth, 1951-80”, Journal of Monetary Economics, 24, pp.259-276. Groenewegen, Peter (1977), The Economics of A.R.J. Turgot, Martinus Nijhoff, Hague. Groenewegen, Peter (1987), "Division of Labor", in J. Eatwell, M. Milgate, and P. Newman eds. The New Palgrave A Dictionary of Economics, 901-7. Grossman, G. and Helpman, E. (1989), "Product Development and International Trade", Journal of Political Economy, 97, 1261-83. Grossman, G. and Helpman, E. (1990), "Comparative Advantage and Long-Run Growth", American Economic Review, 80, 796-815. Grossman, G. and Helpman, E. (1994), “Protection For Sale,” American Economic Review, 84, 833-50. Grossman, G. and Helpman, E. (1995a), "The Politics of Free-Trade Agreements," American Economic Review, 85(4),667-690. Grossman, G. and Helpman, E. (1995b), “Trade Wars and Trade Talks,” Journal of Political Economy, 1995, 103(4), 675-708. Grossman, G. and Helpman, E. (1995c), "Technology and Trade", in G. Grossman and K. Rogeff eds. Handbook of International Economics, Volume 3. Grossman, G. and Levinsohn, J. (1989), “Import Competition and the Stock Market Return to Capital,” American Economic Review, 79, 1065-87. Grossman, Gene (1998), “Imperfect Labor Contracts and International Trade,” memeo., Department of Economics, Princeton University. Grossman, Gene M. and Richardson, David J. (1986), "Strategic Trade Policy: A Survey of the Issues and Early Analysis." In Robert E. Baldwin and J. David Richardson, eds., International Trade and Finance, 3rd ed., 95-113. Boston, Little, Brown. Grossman, S (1989), The Informational Role of Prices, Cambridge, MIT Press. Grossman, S. and Hart, O. (1986), "The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration", Journal of Political Economy, 94, 691-719. Grout, P. (1984), "Investment and Wages in the absence of Binding Contracts: A Nash Bargaining Approach", Econmetrica, 52, 449-60. Gwartney, J., Lawson, R., and Block, W. (1996), Economic Freedom of the World: 1975-1995. Vancouver, B.C., Fraser Institute. Gwartney, J. and Lawson, R. (1997), Economic Freedom of the World: 1997 Annual Report. Vancouver, B.C., Fraser Institute.Hadley, G. (1964), Nonlinear and Dynamic Programming, Reading, Addison-Wesley. Hadley, G. (1964), Nonlinear and Dynamic Programming, Reading, Addison-Wesley. Hagen, E. (1980), The Economics of Development. Irwin, Homewood. Hagen, E. (1958), Án Economic Justification of Protectionism” Quarterly Journal of Economics, 72 (4), 496-514. Hahn, F. (1971) "Equilibrium with Transaction Costs", Econometrica, 39, 417-39. Hall, John (1987), “State and Societies: the Miracle in Comparative Perspective, “ in Baechler, Hall, and Mann (eds.), Europe and the Rise of Capitalism, Cambridge, Blackwell. Harris, Joseph (1757), An Essay Upon Money and Coins. London, G. Hawkins, 1757-58. Harrod, R. (1939), "An Essay in Dynamic Theory", Economic Journal, 49, 14 Hart, O. (1991), "Incomplete Contract and the Theory of the Firm ", in O. Williamson and S. Winter (eds.), The Nature of the Firm, New York, Oxford University Press.

632

Hart, O. (1995), Firms, Contracts, and Financial Structure. Oxford, Clarendon Press. Hart, O. and Holmstrom, B. (1987), "The Theory of Contracts", in T. Bewley (ed.), Advances in Economic Theory, Cambridge, Cambridge University Press. Hart, O. and Moore, B. (1990), "Property Rights and the Nature of the Firm", Journal of Political Economy, 98, 1119-1158. Hart, O. and Moore, B. (1999), "Foundations of Incomplete Contracts", Review of Economic Studies, 66, 115-38. Hartwell, R. (1965), “The Causes of Industrial Revolution: An Essay in Methodology,” Economic History Review, 18. Hayek, F. (1940), "Socialist Calculation III: The Competitive 'Solution'," Economica, 7, 125-49. Hayek, F. (1944), The Road to Serfdom, Chicago, University of Chicago Press. Hayek, F. (1945), "The Use of Knowledge in Society", American Economic Review, 35, 519-30. Hayek, F. (1960), The Constitution of Liberty, Chicago, University of Chicago Press. Hayek, F. (1988), The Fatal Conceit: The Errors of Socialism, Chicago, University of Chicago Press. He, Qinglian (1997), The Primary Capital Accumulation in Contemporary China, Mirror Book, Hong Kong. Headrick, D. (1981), The Tools of Empire: Technology and European Imperialism in the Nineteenth Century, New York, Oxford University Press. Heckscher, E. (1919), "The Effect of Foreign Trade on the Distribution of Income", reprinted in Chater 13 in AEA Readings in the Theory of International Trade, Philadelphia, Blackiston, 1949. Hegel, G. W. F. (1821), Philosophy of Right, Trans. T.M. Knox, Oxford, Clarendon Press, 1962. Heisenberg, Werner (1971), p. 31. Physics and Beyong; Encounters and Conversations. Trans. Arnold Pomerans. New York, Harper & Row. Hellman, Joel (1997, p. 56), "Constitutions and Economic Reforms in the Post-Communist Transitions." in Sachs and Pistor The Rule of Law and Economic Reform in Russia, Boulder, Westview Press. Helpman, E. (1980), "International Trade in the Presence of Product Differentiation, Economies of Scale and Monopolistic Competition", Journal of International Economics, 11, 305-40. Helpman, E. (1992), "Endogenous Macroeconomic Growth", European Economic Review, 36, 237-67. Helpman, E. and Krugman, P. (1985), Market Structure and Foreign Trade, Cambridge, MIT Press. Helpman, Elhanan (1987), “Imperfect Competition and International Trade: Evidence from Fourteen Industrial Countries.” Journal of the Japanese and International Economics, 1, 62-81. Helpman, Elhanan and Laffont, Jean-Jacques (1975), “On Moral Hazard in General Equilibrium Theory,” Journal of Economic Theory, 10, 8-23. Henderson, J.V. (1974), “The Sizes and Types of Cities,” American Economic Review, 64, 640-57. Henderson, J.V. (1996), "Ways to Think about Urban Concentration: Neoclassical Urban Systems versus the New Economic Geography", International Regional Science Review 19(1-2), 31-36. Herberg, H., Kemp, M. and Tawada, M. (1982), "Further Implications of Variable Returns to Scale in General Equilibrium Theory", International Economic Review, 9, 261-72. Hicks, J. (1950), A Contribution to the Theory of the Trade Cycle, Oxford, Oxford University Press. Hicks, J. R. (1960), “Thoughts on the Theory of Capital.” Oxford Economic Papers, vol. 12 (June), pp. 123-32. Hicks, J. R. (1969), A Theory of Economic History. Oxford, Clarendon Press Hirschman, Albert (1958), The Strategy of Economic Development, New Haven, Yale University Press. Hirschman, A. (1968), “The Political Economy of Import Substituting Industrialization,” Quarterly Journal of Economics, 1968, in Haggard, Stephan, ed., The International Political Economy and the Developing Countries. Vol 1. Aldershot, U.K., Elgar. 1995. Hoffman, Philip and Norberg, Kathryn (eds) (1994), Fiscal Crises, Liberty, and Representative Government, 1450-1789. Stanford, Calif., Stanford University Press. Holborn, Hajo (1982), A history of Modern Germany. Princeton, Princeton Univ. Press. Holmstrom, Bengt, and Milgrom, Paul (1991), “Multitask Principal-Agent Analysis: Incentive Contracts, Asset Ownership, and Job Design,” Journal of Law, Economics, and Organization. 7, 24-51. Holmstrom, B. and Milgrom, P. (1994), " The Firm as an Incentive System", American Economic Review, 84, 972-91. Holmstrom, Bengt and Roberts, John (1998), “The Boundaries of the Firm Revisited,” Journal of Economic Perspectives, 12, 73-94. Houthakker, M. (1956), "Economics and Biology: Specialization and Speciation", Kyklos, 9, 181-89. Hua, Sheng, Zhang, Xuejuen, and Lo, Xiaopen (1988), "Ten Years in China's Reform: Looking Back, Reflection, and Prospect," Economic Research, No 9, 11, 12, Beijing. Huang, Ray (1991), Tzu Pen Chu I Yu Nien I Shih Chi (Capitalism). Taipei, Lien ching chu pan shih yeh kung ssu. Huang, Z. (1993), "Current Development of the Private Firms in the Mainland China," Economic Outlook, Vol. 8. No. 32, 87-91 Hughes, Jonathan (1970), Industrialization and Economic History, New York, McGraw-Hill. Hume, David (1748), Essays Moreal and Political (ed. By Eugene Rotwein) London, Nelson, 1955. Hummels, David, and Levinsohn, James (1995), “Monopolitic Competition and International Trade: Reconsidering the Evidence,” Quarterly Journal of Economics, 110, 799-836. Hurwicz, L. (1973), "The Design of Mechanisms for Resource Allocation," American Economic Review, 63, 1-30. International Franchise Association (1997), Franchise Opportunities Guide, Washington, D.C., International Franchise Association. Jacobs, Jane (1969), The Economy of Cities, New York, Random House. Jensen, M. and Meckling, W. (1976), "Theory of the Firm: Managerial Behaviour, Agency Costs, and Ownership Structure", Journal of Financial Economics, 3, 305-60. Jevons, W. (1893), Money and Mechanism of Exchange, New York, D. Appleton. Jian, Tianlun, Sachs, Jeffery and Warner, Andrew (1996), "Trends in Regional Inequality in China," China Economic Review, Vol. 7 No. 1, Spring, pp. 1-21. Jin, Hehui, Qian, Yingyi and Weingast, Barry (1999), "Regional Decentralization and Fiscal Incentives: Federalism, Chinese Style," Department of Economics, Stanford University, mimeo. Jin, Hehui and Qian, Yingyi (1998),"Public vs. Private Ownership of Firms: Evidence from Rural China." Quarterly Journal of Economics, August, 113(3), pp. 773-808. 52 Johnson, D. Gale, (1994), "Does China Have a Grain Problem?" China Economic Review, Vol. 5 No. 1, pp. 1-14. Johnson, Harry G. (1954), “Optimum Tariff and Retaliation,” Review of Economic Studies, 21(2), 142-53. Jones, C.I. (1995a), “Time Series Tests of Endogenous Growth Models”, Quarterly Journal of Economics, 110, 695-525. Jones, C.I. (1995b), “R & D-Based Models of Economic Growth”, Journal of Political Economy, 103, 759-784. Jones, Charles I. (1998), Introduction to Economic Growth, New York, W. W. Norton & Company. Jones, Eric L. (1981), The European Miracle: Environments, Economies and Geopolitics in the History of Europe and Asia, Cambridge, Cambridge University Press.

633

Jones, Ronald (1965), “The Structure of Simple General Equilibrium Models,” Journal of Political Economy, 73, 557-72. Jones, R. (1976), "The Origin and Development of Media of Exchange", Journal of Political Economy, 84, 757-75. Josephson, Matthew (1959), Edison; a Biography, New York, McGraw-Hill. Judd, K. (1985), "On the Performance of Patents”, Econometrica, 53, 579-85. Kaldor, N. (1957), “A Model of Economic Growth,” Economic Journal, 67, 591-624. Kaldor, N. (1967), Strategic Factors in Economic Development, Ithaca, Cornell University. Kamarck, Andrew M. (1976), The Tropics and Econoimc Development: a Provocative Inquiry into the Poverty of Nations, Baltimore, Johns Hopkins University Press (for the World Bank) Kamien, M. and Schwartz, N. (1981), Dynamic Optimization: the Calculus of Variations and Optimal Control in Economics and Management. New York, North Holland. Kanemoto, Y. (1980), Theory of Urban Externalities, Amsterdam, North-Holland. Kang, Youwei (1980), Zouxiang Shijie Chuengshu, Changsha, Hunan People's Press. Kaplan, Steven, and Weisbach, Michael (1992), "The Success of Acquisitions, Evidence from Divestitures," Journal of Finance, 47, 107-38. Karman, A. (1981), Competitive Equilibria in Spatial Economics, Cambridge, Oelgeshloger. Karoly, L. and Klerman, J. (1994), “Using Regional Data to Reexamine the Contribution of Demographic and Sectoral Changes to Increasing U.S. Wage Inequality.” in The Changing Distribution of Income in an Open US Economy, ed. by J. Bergstrand et al. Amsterdam, North-Holland. Katz, L. and Murphy, K. (1992), “Changes in Relative Wages, 1963-1987: Supply and Demand Factors. Quarterly Journal of Economics. 107, 35-78. Katz, M. and Shapiro, C. (1985), "Network Externalities, Competition, and Compatibility," American Economic Review, 75, 424-40. Katz, M. and Shapiro, C. (1986), "Technology Adoption in the Presence of Network Externalities," Journal of Political Economy, 94, 82241. Kelley, A. and Williamson, J. (1984), What Drives Third World City Growth, Princeton, Princeton University Press. Kelly, Morgan (1997), “The Dynamics of Smithian Growth”. Quarterly Journal of Economics, 112, 939-64. Kemp, Murray (1991), “Variable Returns to Scale, Non-uniqueness of Equilibrium and the Gains from International Trade.” Review of Economic Studies. 58, 807-16. Kendrick, D. A. (1978), The Planning of Industrial Investment Programs, Baltimore, Johns Hopkings University Press. Keren, M. and Levhari, D. (1982), "The Internal Organization of the Firm and the Shape of Average Costs", Bell Journal of Economics, 13, 474-86. Keynes, J. (1933), "National Self-Sufficiency." In the Collected Writings of John Maynard Keynes, Vol 21, London, Macmillan, 1982. Keynes, J. (1936), The General Theory of Employment, Interest and Money, London, Macmillan. Keynes, J. (1971), The Collected Writings of John Maynard Keynes, Vol 2 - The Economic Consequences of the Peace. London, Macmillan. Khandker, A. and Rashid, S. (1995), “Wage Subsidy and Full Employment in a Dual Economy with Open Unemployment and Surplus Labor,” Journal of Development Economics. 48, 205-23. Kihlstrom, Richard and Laffont, Jean-Jacques (1979), “A General Equilibrium Entrepreneurial Theory of Firm Formation Based on Risk Aversion,” Journal of Political Economy, 87, 719 Kim, S. (1989), "Labor Specialization and the Extent of the Market", Journal of Political Economy, 97, 692-705. Kim, Y-G. and Sobel, J. (1995), "An Evolutionary Approach to Pre-Play Communication," Econometrica, 63, 1181-93. Kindleberger, Charles P. (1973), The World in Depression - 1929-1939. Berkeley, University of California Press. King, R. and Plosser, C. (1984), "Money, Credit, and Prices in a Real Business Cycle", American Economic Review, 74, 363-80. King, R. and Plosser, C. (1986), "Money as the Mechanism of Exchange", Journal of Monetary Economics, 17, 93-115. King, R. G. and Levine, R. (1994), “Capital Fundamentalism, Economic Development, and Economic Growth.” Carnegie-Rochester Conference Series on Public Policy, 40, 259-92. King, Stephan P. (1995), “Search with Free-riders”, Journal of Economic Behavior & Organization, 26, 253-271. Kirby, William (1995), "China Unincorporated: Company Law and Business Enterprise in Twentieth Century China." Journal of Asian Studies, 54. Kirzner, Israel (1997), “Entrepreneurial Discovery and the Competitive Market Process: An Austrian Approach,” Journal of Economic Literature, 35, 60-85. Kiyotaki, N. and Wright, R. (1989), "On Money as a Medium of Exchange", Journal of Political Economy 97, 927-954. Kiyotaki, N. and Wright, R. (1993), "A Search-Theoretic Approach to Monetary Economics", American Economic Review 83, 63-77. Knight, F. (1921), Risk, Uncertainty and Profit. Chicago, Hart, Shaffner and Marx. Knight, F. (1925), "Decreasing Cost and Comparative Cost: A Rejoinder", Quarterly Journal of Economics, 39, 332-33. Kohli, Ulrich and Werner, Augustin (1998), “Accounting for South Korean GDP Growth: Index-Number and Econometric Estimates,” Pacific Economic Review, 3, 133-52. Koopman, T. R. (1957), Three Essays in the State of Economic Science, New York, McGraw-Hill. Kormendi, R.C. and Meguire, P.G. (1985), “Macroeconomic Determinants of Growth: Cross-Country Evidence”, Journal of Monetary Economics, 16, pp.141-163. Kornai, J. (1980), Economics of Shortage, Amsterdam, North-Holland. Kornai, J. (1991), The Road to a Free Economy, New York, Norton. Kornai, J. (1992), The Socialist System: The Political Economy of Communism, Princeton, Princeton University Press. Kornai, Janos.(1986), "The Hungarian Reform Process: Visions, Hopes, and Reality." Journal of Economic Literature, December, 24, pp. 1687-1737. Kravis, Irving and Lipsey, Robert (1981), “Prices and Terms of Trade for Developed Country Exports of Manufactured Goods,”National Bureau of Economic Research Working Paper, No. 774. Kremer, M. (1993), “Population growth and technological change: one million BC to 1990,” Quarterly Journal of Economics 108, 681716. _____ (1993), “The O-ring Theory of Economic Development,” Quarterly Journal of Economics 108, 551-75. Kreps, D. (1990), "Corporate Culture and Economic Theory", in J. Alt and K. Shepsle (eds.) Perspectives on Positive Political Economy, Cambridge, Cambridge University Press. Kreps, D. (1990), A Course in Microeconomic Theory, Princeton University Press. Kreps, D. and Wilson, R. (1982), "Sequential Equilibria", Econometrica, 50, 863-94. Krueger, A. (1974), “The Political Economy of Rent-seeking Society,” American Economic Review, 64, 291-303. Krueger, A. (1986), “Aid in the Development Process,” World Bank Research Observer, January, 62-63.

634

Krueger, A. (1995), "Policy Lessons from Development Experience since the Second World War," in J. Behrman and T.N. Srinivasan (eds.), Hand Book of Development Economics, Vol. III, 2498-550. Krueger, Anne (1984), “Trade Policies in Developing Countries,” in Handbook of International Economics, ed. R. Jones and P. Kenen. Krueger, Anne O. (1997), "Trade Policy and Economic Development: How We Learn." American Economic Review. 87, 1-22. Krugman, Paul (1979), "Increasing Returns, Monopolistic Competition, and International Trade", Journal of International Economics, 9, 469-479. Krugman, P. (1980), "Scale Economies, Product Differentiation, and the Pattern of Trade", American Economic Review, 70, 950-59. Krugman, P. (1981), "Intra-industry Specialization and the Gains from Trade", Journal of Political Economy, 89, 959-73. Krugman, P. (1991), Economics of Geography, Journal of Political Economy, 99, 483-502. Krugman, P. (1992), “Toward a Counter-Counter Revolution in Development Theory,” World Bank Observer, Supplement, 15.61. Krugman, P. (1994), "Complex Landscapes in Economic Geography," a paper presented at the meetings of the American Economic Association. Krugman, P. (1994a), “Europe Jobless, America Penniless?” Foreign Policy, 95, 19-34. Krugman, P. (1994b), “Competitiveness: A Dangerous Obsession,” Foreign Affairs, 73(2), 28-44. Krugman, P. (1994c), “Stolper-Samuelson and the Victory of Formal Economics,” in Alan Deardorff and Robert Stern eds. The Stolper-Samuelson Theorem, Ann Arbor, University of Michigan Press. Krugman, P. (1995), “Growing World Trade: Causes and Consequences.” Brookings Paper on Economic Activity, 1, 327-62. Krugman, P. (1995), Development, Geography, and Economic Theory, Cambridge, MIT Press. Krugman, P. and Lawrence, R. (1994), “Trade, Jobs and Wages. Scientific American. 270, 44-49. Krugman, P. and Venables, A.J. (1995), “Globalization and the Inequality of Nations,” Quarterly Journal of Economics, 110, 857-80. Krugman, P. and Venables, A.J. (1996), “Integration, specialization, and adjustment,” European Economic Review, 40, 959-67. Kubo, Y. (1985), "A Cross-country Comparison of Interindustry Linkages and the Role of Imported Intermediate Inputs", World Development, 13, 1287-98. Kurz, M. (1974), "Arrow-Debreu Equilibrium of an Exchange Economy with Transaction Costs", Econometrica, 42, 45-54. Kuznets, S. (1955), “Economic Growth and Income Inequality.” American Economic Review, March. Inverted-U Hypothesis of inequality Kuznets, S. (1966), Modern Economic Growth, New Haven, Yale Univ. Press. Kydland, F. and Prescott, E. (1982), "Time to Build and Aggregate Fluctuations", Econometrica, 50, 1345-70. La Porta, R., Lopez-de-Silanes, F., Shleifer, A., and Vishny, R. (forthcoming), "The Quality of Government", Journal of Law, Economics and Organization. Laffont, J. and Tirole, J. (1986), "Using Cost Observation to Regulate Firms", Journal of Political Economy, 94, 614-41. Landes, David (1998), The Wealth and Poverty of Nations. New York, W. W. Norton. Lang, Larry, and Stulz, Rene (1994), "Tobin's Q, Corporate Diversification and Firm Performance," Journal of Political Economics, 102, 1248-80. Lange, O. and Taylor, F. (1964), On the Economic Theory of Socialism. New York, McGraw Hill. Lange, O. (1970), Introduction to Economic Cybernetics, Pergamon Press, Oxford. Lardy, Nicholas (1998a), China's Unfinished Economic Revolution, Washington, D.C., The Brookings Institution. Lardy, Nicholas (1998b), "China's Unfinished Economic Experiment," in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Laslett, Peter (1988), “The European Family and Early Industrializatin,” in Baechler, Hall and Mann (eds.) Europe and the Rise of Capitalism, Cambridge, Blackwell. Lau, L. and Song, D-H. (1992), "Growth versus Privatization: An Alternative Strategy to Reduce the Public Enterprise Sector: The Experience Taiwan and South Korea", Working Paper, Department of Economics, Stanford University. Leamer, Edward E. (1984), Sources of International Comparative Advantage: Theory and Evidence, Cambridge, MA, MIT Press. Lee, Douglas (1957), Climate and Economic Development in the Tropics. New York, Harper for the Council on Foreign Relations. Legros, Patrick and Newman, Andrew (1996), “ Wealth Effects, Distribution, and the Theory of Organization,” Journal of Economic Theory, 70, 312-41 Leland, H. (1968), "Saving and Uncertainty: The Precautionary Demand for Saving." Quarterly Journal of Economics, 82, 465-73. Lenin, V. (1939), Imperialism, the Highest Stage of Capitalism, New York, International Publishers. Leontief, Wassily W. (1956), “Domestic Production and Foreign Trade: the American Capital Position Re-examined,” in Readings in International Economics, edited by Richard E. Caves and Harry G. Johnson. Homewood, Irwin, 1968. Lerner, A. P.(1952), “Factor Prices and International Trade,” Economica, 19(1), 1-15. Lewis, T. and Sappington, D. (1991), "Technological Change and the Boundaries of the Firm", American Economic Review, 81, 887-900. Lewis, W Arthur (1952), "World Production, Prices and Trade, 1870-1960". The International Political Economy and the Developing Countries. Vol 1. Haggard, S., ed., Elgar. 1995. Lewis, W Arthur (1954), "Economic Development with Unlimited Supplies of Labour"..Development Economics. Vol 1. Lal, Deepak, ed., Elgar, 1992. Lewis, W. (1955), The Theory of Economic Growth, London, Allen and Unwin. Lewis, W. (1984), “The State of Development Theory,” American Economic Review. 74, 1-10. Lewis, W. (1988), “The Roots of Development Theory,” Handbook of Development Economics. Vol I, 27-38. Li, David (1994), "The Behavior of Chinese State Enterprises under the Dual Influence of the Government and the Market," University of Michigan, manuscript. Li, David D. (1996), "A Theory of Ambiguous Property Rights in Transition Economies: The Case of the Chinese Non-State Sector." Journal of Comparative Economics, 23, 1-19. Li, Hongyi and Zou, Heng-fu (1998), "Income Inequality is not Harmful for Growth: Theory and Evidence." Review of Development Economics, 2, 318-34. Li, Junhui (1999), "Shunde de Zhuangzhi (The Transformation of the Ownership System in Shunde County)," Economic Highlights, No. 36, p. 3. Li, Wei (1997). "The Impact of Economic Reform on the Performance of Chinese State Enterprises, 1980-1989."Journal of Political Economy, 105(5), 1081-1106. Liebowitz, S. J. and Margolis, Stephen E. (1994), “Network Externality: An Uncommon Tragedy,” Journal of Economic Perspectives, 8, 133-50. Lilien, D. (1982), "Sectoral Shifts and Cyclical Unemployment", Journal of Political Economy, 90, 777-93. Lin, J. Y. (1998), “The Current State of China's Economic Reforms,” in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute.

635

Lin, J. Y. and Yang, D. (1998), “On the Causes of China's Agricultural Crisis and the Great Leap Famine,” China Economic Review. 9, 125-40. Lio, M. (1996), Three Assays on Increasing Returns and Specialization: A Contribution to New Classical Microeconomic Approach, Ph.D. Dissertation, Department of Economics, the National Taiwan University. Lio, M. (1998), “Uncertainty, Insurance, and Division of Labor,” Review of Development Economics, 2, 76-86. Lippman, Steven A. and McCall, John J. (1979), “The Economics of Job Search-A survey”, Economic Inquiry, 14, 155-189. Lipton, Michael (1977), Why Poor People Stay Poor, Lipton, Cambridge, Harvard University Press. Little, I. and Mirrless, J. (1980), Manual of Industrial Project Analysis in Developing Countries, Paris, OECD. Liu, Meng-Chun (1999) "Two Approaches to International Trade, Development and Import Protection," Ph.D. Dissertation, Department of Economics, Monash University. Liu, Pak-Wai and Yang, Xiaokai (2000) "The Theory of Irrelevance of the Size of the Firm," Journal of Economic Behavior and Organization, 42, 145-65. Liu, Yia-Ling, (1992), "Reform From Below: The Private Economy and Local Politics in the Rural Industrialization of Wenzhou," China Quarterly, 130, 293-316. Livingstone, I. (1983), “The Development of Development Economics,” O.D.I. Review, No. 2. Locay, L. (1990), "Economic Development and the Division of Production between Households and Markets", Journal of Political Economy, 98, 965-82. Long, J., Jr. and Plosser, C. (1983), "Real Business Cycles", Journal of Political Economy, 91, 39-69. Loveman, G. and Sengenberger, W. (1991), "The Re-emergence of Small-Scale Production: An International Comparison", Small Business Economics 3, No. 1, 1-38. Lucas, R., Jr. (1972), "Expectations and the Neutrality of Money", Journal of Economic Theory, 4, 103-24. Lucas, R., Jr. (1973), "International Evidence on Output-Inflation Tradeoffs", American Economic Review, 63, 326-34. Lucas, R., Jr. (1976), "Econometric Policy Evaluation: A Critique", Journal of Monetary Economics., Suppl. Series, 1, 19-46, 62. Lucas, R., Jr. (1980), "Equilibrium in a Pure Currency Economy", in J. Karenken and N. Wallace (eds.), Models of Monetary Economics, Minneapolis, Federal Reserve Bank of Minneapolis. Lucas, R., Jr. (1988), "On the Mechanics of Economic Development", Journal of Monetary Economics, 22, 3-42. Lucas, R., Jr. (1993), "Making a Miracle", Econometrica, 61, 251-72. Luo, Xiaopeng (1994), "Gaige yu Zhongguo Dalude Denji Chanquan (Reforms and Property Rights based on Ranking in Mainland China", Modern China Studies, No. 41, 31-45. MacFarlane, Alan (1988), “The Cradle of Capitalism: The Case of England,” in Baechler, Hall and Mann (eds.), Europe and the Rise of Capitalism, Cambridge, Blackwell. MacLeod, W. and Malcomson, J. (1988), "Reputation and Hierarchy in Dynamic Models of Employment," Journal of Political Economy, 96, 832-81. Maddison, Angus (1995), Monitoring the World Economy: 1820-1992. Paris, Organization of Economic Cooperation and Development. Mailath, George J. (1998), "Do People Play Nash Equilibrium? Lessons from Evolutionary Game Theory." Journal of Economic Literature. 36, 1347-74. Mankiw, N. G. (1985), "Small Menu Costs and Large Business Cycles: A Macroeconomic Model", Quarterly Journal of Economics, May, 100(2), 529-38. Mankiw, N. G., Romer, D. and Weil, D.N. (1992), “A Contribution to the Empirics of Economic Growth.” Quartely Journal of Economics. 107, 407-37. Manne, H. (ed.) (1975), The Economics of Legal Relationships, St. Paul, West Publishing Company. Mantel, R. (1974), On the Characterization of Aggregate Excess Demand, Journal of Economic Theory, 7, 348-53. Mao, Zedong (1977a), Selected Works of Mao Zedong, Volume 5. Beijing, People's Press. Mao, Tse-tung (1977b), A Critique of Soviet Economics, Translated by Moss Roberts, annotated by Richard Levy, with an introduction by James Peck. New York, Monthly Review Press. Mao, Yushi (1999), "Zhengfu Ruhe Bangzu Qiye He Bangzu Jiuye (How Can the Government Assist Firms and Employment)?" Economic Highlights, No. 37, p. 1. Marcouiller, D. and Young, L. (1995), "The Black Hole of Graft: the Predatory State and the Informal Economy," American Economic Review, 85, 630-46. Marshall, Alfred (1890), Principles of Economics, 8th Edition, New York, Macmillan, 1948. Marx, Karl (1867), Capital, a Critique of Political Economy, Vols I-III, New York, International Publishers, 1967. Mas-Collell, A., Whinston, M., and Green, J. (1995), Microeconomic Theory, New Yourk, Oxford University Press. Maskin, Eric (forthcoming), “Recent Theoretical Work on the Soft Budget Constraint”, American Economic Review, Papers and Proceedings. Maskin, Eric and Tirole, Jean (1999a), "Unforeseen Contingencies, Property Rights, and Incomplete Contracts." Review of Economic Studies, 66, 83-114. Maskin, Eric and Tirole, Jean (1999b), "Two Remarks on the Property Rights Literature." Review of Economic Studies, 66, 139-50. Maskin, Eric and Xu, Chenggang (1999), “Soft Budget Constraint Theories: From Centralization to the Market”, Working Paper, Department of Economics, Harvard University. Matsui, A. (1991), Cheap-Talk and Cooperation in Society. " Journal of Economic Theory, 54, 245-58. Matsuyama, K. (1991), “Increasing Returns, Industrialization and Indeterminancy of Equilibria,” Quarterly Journal of Economics, 106, 651-67. Mauss, Marcel (1925), The Gift: The Form and Reason for Exchange in Archaic Societies, New York, W.W. Norton (1990) Maxwell, Henry (1721), Reasons Offered for Erecting a Bank in Ireland, the second edition, Dublin. Mayer, Wolfgang (1981), "Theoretical Considerations on Negotiated Tariff Adjustments." Oxford Economic Papers, 33, 135-53 Mayer, Wolfgang (1984), “Endogenous Tariff Formation,” American Economic Review, 74, 970-85. McGuirk, A. M. and Mundlak, Y. (1992). “The Transition of Punjab Agriculture: A Choice of Technique Approach.” American Journal of Agricultural Economics, vol. 74 (February), pp. 132-43. McKenzie, L. W. (1955), “Equality of Factor Prices in World Trade,” Econometrica, 23(3), 239-257. McMillan, John. (1996),"Markets in Transition," in David Kreps and Kenneth Wallis (eds.), Advances in Economics and Econometrics: Theory and Applications, Cambridge, Cambridge University Press. McMillan, J., Whalley, J., and Zhu, L. (1989), "The Impact of China's Economic Reforms on Agricultural Productivity Growth", Journal of Political Economy, 97, 781-807. McNeil, W. (1974), The Shape of European History, Oxford, Oxford University Press.

636

McNeill, William Hardy (1963), The Rise of the West: A History of the Human Community. Chicago, University of Chicago Press. Meek, R. and Skinner, A. (1973), "The Development of Adam Smith's Ideas on the Division of Labor," Economic Journal, 83, 1094-116. Meier, G. (1994), From Classical Economics to Development Economics. New York, St. Martin's Press. Meier, G. (1995), Leading Issues in Economic Development, New York, Oxford University Press. Meier, G. and Seers, Dudley (eds) (1984), Pioneers in Development. New York, Oxford University Press. Meier, Gerald (1994), ‘“The Progressive State” in Classical Economics,’ From Classical Economics to Development Economics, New York, St. Martin’s Press. Men Qinguo (1988), " On the Ownership Structure of Modern Corporation," Young Economists Forum, No 4, Tianjin. Meng, Xin and Perkins, France (1996), "The Destination of China's Enterprise Reform: A Case Study from a Labor Market Perspective," Australian National University, August. Menger, Carl (1871), Principles of Economics, translated by James Dingwall and Bert F. Hoselitz. New York, New York University Press. Michio, Nagai and Urrutia, Miguel (eds) (1985), Meiji Ishin: Restoration and Revolution, Tokyo, United Nations University. Milgrom, P. and Roberts, J. (1982), “Limit Pricing and Entry under Incomplete Information,” Econometrica, 40, 433-59. Milgrom, P. and Roberts, J. (1990), "Bargaining, Influence Costs, and the Organization of Economic Activity" in J. Alt and K. Shepsle (eds.), Perspectives on Positive Political Economy, Cambridge, Cambridge University Presspp. 57-89. Milgrom, P. and Roberts, J. (1992), Economics, Organization and Management, Englewood Cliffs, Prentice-Hall. Milgrom, P. and Roberts, J. (1994), "The Economics of Modern Manufacturing: Technology, Strategy and Organization," American Economic Review, 80, 511-28. Mill, John (1848), Principles of Political Economy, Harmondsworth, Penquin, 1970. Mills, E. S. (1967), “An Aggregative Model of Resource Allocation in a Metropolitan Area,” American Economic Review, 57, 197210. Mills, E. and Hamilton, B. (1984), Urban Economics, Glenview, Scott, Foresman and Company. Minami, Ryoshin and Hondai, Susumu (1995), "An Evaluation of the Enterprise Reform in China: Income Share of Labor and Profitability in the Machine Industry," Hitotsubashi Journal of Economics, Vol. 36, No. 2, December, pp. 125-143. Mitchell, B. R. (1998), International historical statistics : Europe, 1750-1993. London, Macmillan Reference; New York, N.Y., Stockton Press Modigliani, Franco (1989), The Collected Papers of Franco Modigliani. Vol 5. Saving, deficits, inflation, and financial theory. Modigliani, Franco, Edited by Simon Johnson Cambridge, Mass. and London, MIT Press. Mokyr, Joel (1990) The Lever of Richs: Technological Creativity and Economic Progress, New York, Oxford University Press. Mokyr, Joel, (1993), “The New Economic History and the Industrial Revolution,” in Mokyr, J. ed. The British Industrial Revolution: An economic perspective, Boulder and Oxford, Westview Press. Monteverde, K. and Teece, D.J. (1982), "Supplier Switching Costs and Vertical Integration in the Automobile Industry", Bell Journal of Economics, 13, pp. 206-13. Morgan, Peter and Manning, Richard (1985), “Optimal Search”, Econometrica, 53, 923-944. Morgan, T. (1970), “Trends in Terms of Trade, and Their Repercussion on Primary Products.” in Morris, C. and Adelman, I. (1988), Comparative Patterns of Economic Development, 1850-1914. Johns Hopkins Studies in Development series. Baltimore and London: Johns Hopkins University Press. Mueller, M. (1998), "China's Telecommunications Sector and the WTO: Can China Conform to the Telecom Regulatory Principles?" in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Murakami, Naoki, Liu, Deqiang, and Otsuka, K. (1996), “Market Reform, Division of Labor, and Increasing Advantage of Small-scale Enterprises: The Case of the Machine Tool Industry in China,” Journal of Comparative Economics, 23, 256-277 Murphy, K. and Welch, F. (1991), “The Role of International Trade in Wage Differentials.” in Workers and Their Wages: Changing Patterns in the United States. ed. by M. Kosters. Washitington, American Enterprise Institute. Murphy, K. and Topel, R. (1987), "The Evolution of Unemployment in the United States, 1968-1985", NBER Macroeconomics Annual, 2, 11-58. Murphy, K., Shleifer, A., and Vishny, R. (1989a), "Industrialization and the Big Push", Journal of Political Economy, 97, 1003-26. Murphy, K., Schleifer, A., and Vishny, R. (1989b), "Income Distribution, Market Size, and Industrialization", The Quarterly Journal of Economics, 104, 537-64. Murphy, K., Schleifer, A., and Vishny, R. (1991), "The Allocation of Talent: Implications for Growth", Quarterly Journal of Economics, 106, 503-530. Murphy, K., Shleifer, A. and Vishny, R. (1992), "The Transition to a Market Economy: Pitfalls of Partial Reform," The Quarterly Journal of Economics, August, 889-906. Murray, Christopher J. L. and Lopez, Alan D. (eds) (1996), The Global Burden of Disease. Cambridge, MA, Harvard University Press. Myrdal, Gunnar (1956), Development and Underdevelopment, National Bank of Egypt Fiftieth Anniversary Commemoration Lectures, Cairo (pp. 47-51). Myrdal, G. (1957), Economic Theory and the Underdeveloped Regions. London, Duckworth Naisbitt, John (1990), Megatrends 2000 : the New Directions for the 1990's. New York, Morrow. Nash, J. F. (1950), “The Bargaining Problem,” Econometrica, 18, 115-62. Nath, S.K. (1962), The Theory of Balanced Growth,” Oxford Economic Papers, 14(2), 138-53. National Research Council (1986), Population Growth and Economic Development: Policy Questions. Washington, DC, National Academy of Sciences Press. Naughton, Barry (1994a), "Chinese Institutional Innovation and Privatization from Below," American Economic Review, Vol. 84 Vol. 2, May, pp. 266-270. Naughton, Barry (1994b), "What is Distinctive about China's Economic Transition? State Enterprise Reform and Overall System Transformation," Journal of Comparative Economics, Vol. 18, No. 3, June, pp. 470-490. Naughton, Barry (1995), Growing Out of the Plan. Cambridge University Press, 1995. Nee, V. and Sijin, S. (1993), "Local Corporatism and Informal Privatization in China's Market Transition", Working Paper on Transitions from State Socialism No. 93-2. Einaudi Center for International Studies, Cornell. Nee, Victor (1996), "Changing Mechanisms of Stratification in China," American Journal of Sociology, Vol. 101 No. 4, January, pp.908-949. Nelson, R. (1956), “A Theory of the Low Level of Equilibrium Trap in Under-developed Economies.” American Economic Review, 46, 894-908. Nelson, R. (1995), "Recent Evolutionary Theorizing About Economic Change", Journal of Economics Literature, 33, 48-90. Nettels, Curtis (1962), The Emergence of a National Economy, 1775-1815, New York.

637

Ng, S. (1995), Economic Openness and Growth, Ph.D. dissertation, Department of Economics, Monash University. Ng, Y-K. (1986), Meseconomics, a Micro-macro Analysis, New York, Harvester Wheatsheaf. Ng, Y-K. (1992), "Business Confidence and Depression Prevention: A Mesoeconomic Perspective", American Economic Review, 82, 36571. Ng, Y-K. and Yang, X. (1997), "Specialization, Information, and Growth: a Sequential Equilibrium Analysis". Review of Development Economics. 1, 257-74. Ng, Y-K. and Yang, X. (2000), "Effects of Externality-Corrective Taxation on the Extent of the Market and Network Size of Division of Labor". Seminar Paper, Department of Economics, Monash University. Nolan, Peter (1993), State and Market in the Chinese Economy: Essays on Controversial Issues, MacMillan, London. North, Douglas (1958), "Ocean Freight Rates and Economic Development", Journal of Economic History, 18, 537-55. North, Douglas (1981a) Structure and Change in Economic History, chapter 12, New York, Norton. North, Douglas (1981b) “The Industrial Revolution Reconsidered,” in North, Structure and Change in Economic History, Norton. North, D. (1986), "Measuring the Transaction Sector in the American Economy", S. Eugerman and R. Gallman, eds,. Long Term Trends in the American Economy, Chicago, University of Chicago Press. North, D. (1987), "Institutions, Transaction Costs and Economic Growth", Economic Inquiry, 25, 419-28. North, D. (1990), Institutions, Institutional Change and Economic Performance, New York, Cambridge University Press. North, D. (1994), "Economic Performance through Time,” American Economic Review. 84, 359-68. North, D. (1997), "The Contribution of the New Institutional Economics to an Understanding of the Transition Problem." WIDER Annual Lectures, March. North, Douglass and Weingast, Barry (1989), “Constitutions and Commitment: The Evolution of Institutions Governing Public Choice in Seventeenth-Century England,” Journal of Economic History, XLIX, pp 803-32. North, Douglas and Robert Thomas (1970), “An Economic Theory of the Growth of the West World,” The Economic Review, 23, 117. Nurkse, R. (1952), Indivisibilities play a role in virtuous circles of development, but they are not essential. Nurkse, R. (1953), Problems of Capital Formation in Underdeveloped Countries, New York, Oxford University Press. Nussbaum, Frederick (1925) "American Tobacco and French Politics, 1783-1789," Political Science Quarterly, 40, 501-503. Oh, S. (1989), "A Theory of a Generally Acceptable Medium of Exchange and Barter", Journal of Monetary Economics, 23, 101-19. Ohlin, B. (1933), Interregional and International Trade, Cambridge, Harvard University Press. Oi, Jean (1986), "Commercializing China's Rural Cadres." Problems of Communism, 35, 1-15. Oi, Jean (1992) "Fiscal Reform and the Economic Foundations of Local State Corporatism in China." World Politics, October, 45(1). Oi, Jean (1995), "The Role of the Local Government in China's Transitional Economy," China Quarterly. 144, 1132-49. Olson, Mancur (1982), The Rise and Decline: Economic Growth, Stagflation, and Social Rigidities. New Haven, Yale University Press. Olson, Mancur (1996), “Distinguished Lecture on Economics in Government: Big Bills Left on the Sidewalk: Why Some Nations are Rich and others Poor,” Journal of Economic Perspectives 10(2). O'Rourke, K. and Williamson, J. (1994), "Late Nineteenth Century Anglo-American Factor-Price Convergence: Were Heckscher and Ohlin Right?" Journal of Economic History, 54, 892-916. Osborne, M. and Rubinstein, A. (1990), Bargaining and Markets, Boston, Academic Press. Ostroy, J. (1973), "The Informational Efficiency of Monetary Exchange", American Economic Review, 63, 597-610. Ostroy, J. and Starr, R. (1990), "The Transactions Role of Money", in B. Friedman and F. Hahn (eds.), Handbook of Monetary Economics, Volume 1, Amsterdam, North Holland. Owen, T. (1997), "Autocracy and the Rule of Law in Russian Economic History," in J. Sachs and K. Pistor eds. The Rule of Law and Economic Reform in Russia, Westview Press. Page, Scott E. (1999), "On the emergence of cities", Journal of Urban Economics, 45, 184-208. Palma, Babriel (1978), “Dependency: A Formal Theory of Underdevelopment or a Methodology for the Analysis of Concrete Situations of Underdevelopment?” World Development, 6, 899-902. Panagariya, Arvind (1983), “Variable Returns to Scale and the Heckscher-Ohlin and Factor-Price-Equalization Theorems.” World Economics. 119, 259-80. Parkin, M. (1986), "The Output-inflation Tradeoff when Prices are Costly to Change," Journal of Political Economy, 94, 200-24. Patten, R. H. and Rosengard, J.K. (1991), Progress with Profits: The Development of Rural Banking in Indonesia, San Francisco, CA, ICS Press. Paxson, C. (1999) “Parental Resources and Child Abuse and Neglect”, American Economic Review, 89, 239-44. Pei, M. (1998), "The Growth of Civil Society in China." in James Dorn, eds. China in the New Millennium: Market Reforms and Social Development, Washington, D.C., CATO Institute. Peng, Yusheng, (1992), "Wage Determination in Rural and Urban China: A Comparison of Public and Private Industrial Sectors," American Sociological Review, Vol. 57 No. 2, April, pp. 198-213. Perkins, D., ed. (1977), Rural Small-Scale Industry in China, Berkeley, University of California Press. Perkins, D. (1988), "Reforming China's Economic System", Journal of Economic Literature, Vol. XXVI, pp. 601-45. Perkins, Frances, Zheng, Yuxing and Cao, Yong (1993), "The Impact of Economic Reform on Productivity Growth in Chinese Industry: A Case of Xiamen Special Economic Zone," Asian Economic Journal, Vol. 7, No. 2, pp. 107-146. Petty, William (1671), Political Arithmetics, in C. H. Hull ed. Economic Writings of Sir. William Petty, reissued, New York, Augustus M. Kelly, 1963. Petty, William (1683), Another Essay on Political Arithmetics, in C. H. Hull ed. Economic Writings of Sir. William Petty, reissued, New York, M. Kelly, 1963. Philips, Ulrich (1929), Life and Labor in the Old South, Boston, Little, Brown, and Company. Pigou, A C. (1940), War Finance and Inflation. Neal, Larry, ed., Elgar Reference Collection. International Library of Macroeconomic and Financial History series, vol. 12. Aldershot, U.K., Elgar. Pilon, Roger (1998), "A Constitution of Liberty for China", China in The New Millennium: Market Reforms and Social Development, CATO Institute, Washington, D.C. Pincus, Jonathan J. (1975), “Pressure Groups and the Pattern of Tariffs,” Journal of Political Economy, 83, 757-78. Ping, Xinqiao (1988), "The Reform of the Ownership System, Property Rights, and Management," Pipe, R. (1999), Property and Freedom, New York, Alfred Knopf. Pistor, K. (1997), "Company Law and Corporate Governance in Russia," in J. Sachs and K. Pistor eds. The Rule of Law and Economic Reform in Russia, Westview Press. Plato (380 BC) (1955), The Republic, Trans. H.D.P. Lee, Harmondsworth, Penguin Classics Prebisch, R. (1988), “Dependence, Interdependence and Development.” Cepal Review, 34, 197-205.

638

Prendergast, Canice (forthcoming), "The Provision of Incentives in Firms," Journal of Economic Literature. Prescott, E. (1986), "Theory Ahead of Business Cycle Measurement", Federal Reserve Bank of Minneapolis Quarterly Review, 10, 9-22. Prestowitz, Clyde V. Jr et al. (1994), “The Fight over Competitiveness,” Foreign Affairs, 73(4), 186-197. Pritchett, L. (1997), “Ðivergence, Big Time,” Journal of Economic Perspectives, 11(3). Prosterman, Roy, Hanstad, Tim and Li, Ping (1996), "Can China Feed Itself?" Scientific American, November, pp. 90-96. Puga, Diego and Venables, Anthony (1998), "Agglomeration and Economic Development: Import Substitution vs. Trade Liberasation," Centre for Economic Performance Discussion Paper No. 377. London School of Economics. Qian, Y. (1994a), "Incentives and Loss of Control in an Optimal Hierarchy", Review of Economic Studies, 61(3), 527-44. Qian, Y. (1994b), "A Theory of Shortage in Socialist Economies based on the ‘Soft Budget Constraint’ ", American Economic Review, 84, 145-56. Qian, Yingyi (1999), "The Institutional Foundations of China's Market Transition", Annual Bank Conference on Development Economics. Qian, Y. (forthcoming), "The Process of China's Market Transition (1978-98), The Evolutionary, Historical, and Comparative Perspectives." Journal of Institutional and Theoretical Economics. Qian, Yingyi and Weingast, Barry R. (1997), "Federalism As a Commitment to Preserving Market Incentives." Journal of Economic Perspectives, Fall, 11(4), pp. 83-92. Qian, Yingyi and Roland, Gerard (1998), "Federalism and the Soft Budget Constraint." American Economic Review, December, 88(5), pp. 1143-1162. Qian, Yingyi, Roland, Gerard and Xu, Chenggang (1999) "Coordinating Changes in M-form and U-form Organizations." Mimeo, Stanford University. Quah, D. (1993), “Galton‘s Fallacy and Tests of The Convergence Hypothesis”, Scandinavian Journal of Economics, 95(4), 427-443. Quah, D. (1996), “Twin Peaks: Growth and Convergence in Models of Distribution Dynamics”, Economic Journal, 100, 1045-1055. Quigley, John M. (1998), "Urban Diversity and Eonomic Growth", Journal of Economic Perspectives, 2(2), 1998, 127-138. Rabushka, A. (1987), The New China: Comparative Economic Development in Mainland China, Taiwan, and Hong Kong, Westview Press, Colorado, 1987. Radelet, Steven and Sachs, Jeff (1998a), “The Onset of the East Asian Financial Crisis,” Paper presented in the National Bureau of Economic Research Currency Crisis Conference. Radelet, Steven and Sach, Jeff (1998b) “Shipping Costs, Manufactured Exports, and Economic Growth,” mimeo, HIID. Radner, R. (1992), "Hierarchy: The Economics of Managing", Journal of Economic Literature, 30, 1382-1415. Radner, R. (1993), "The Organization of Decentralized Information Processing ", Econometrica, 61, 1109-46. Rae, J. (1834), Statement of Some New Principles on the Subject of Political Economy, reissued, New York, M. Kelly, 1964. Ram, Rati (1997), "Level of Economic Development and Income Inequality: Evidence from the Postwar Developed World," Southern Economic Journal. 64, 576-83. Ramey G. and Ramey, V. (1995) “Cross-Country Evidence on the Link between Volatility and Growth”, American Economic Review, 85, 1138-1151. Ramsey (1928), "A Mathematical Theory of Saving", Economic Journal, 38, 543-59. Ranis, G. (1988), “Analytics of Development: Dualism,” in Handbook of Development Economics, ed. H. Chenery and T. Srinivasan, Vol. 1, pp. 74-92. Rashid, Salim (1986), "Adam Smith and the Division of Labor: a Historical View", Scottish Journal of Political Economy, 33, 292-97. Rawski, Thomas (1986), "Overview: Industry and Transport," in U.S. Congress, Joint Economic Committee, China's Economy Looks Toward the Year 2000: Volume 1. The Four Modernizations, May. Ray, Debraj (1998), Development Economics, Princeton, Princeton Uni. Press. Rebelo, S. (1991), "Long Run Policy Analysis and Long Run Growth", Journal of Political Economy, 99, 500-21. Reingnum, Jennifer F. (1982), “Strategic Search Theory”, International Economics Review, 23, 1-17. Reynolds, Bruce (ed.) (1987), Reform in China: Challenges and Choices, M.E. Sharpe, New York. Reynolds, L. (1985), Economic Growth in the Third World, 1850-1980. New Haven, Yale University Press. Ricardo, D. (1817), The Principle of Political Economy and Taxation, London, Gaernsey Press, 1973. Riezman, Raymond (1982), "Tariff Retaliation from a Strategic Viewpoint," Southern Economic Journal, 48, 583-93. Riskin, C. (1971), "Small Industry and the Chinese Model of Development," China Quarterly, 46, 245-73. Riskin, Carl (1987), China's Political Economy: The Quest for Development Since 1949, Studies of the East Asian Institute of Columbia University, Oxford University Press, 1987. Robbins, L. (1968), The Theory of Economic Development in the History of Economic Thought. London, Macmillan, New York, St. Martin's P. Roland, Gerard (2000), Politics, Markets and Firms: Transition and Economics, Cambridge, MA, MIT Press. Romano, R. E. (1994), “Double Moral Hazard and Resale Price Maintenance,” RAND Journal of Economics, 25, pp. 455-66. Romer, P. (1986), "Increasing Returns and Long Run Growth", Journal of Political Economy, 94, 1002-37. Romer, P. (1987), “Growth Based on Increasing Returns Due to Specialization.” American Economic Review Papers and Proceedings. 77, 56-72. Romer, P. (1990), "Endogenous Technological Change", Journal of Political Economy, 98, S71-S102. Romer, P. (1993), "The Origins of Endogenous Growth", Journal of Economic Perspectives, 8, 3-22. Ronnas, Per (1993), "Township Enterprises in Sichuan and Zhejiang: Establishment and Capital Generation," National Workshop on Rural Industrialization in Post-Reform China, Beijing, China, October. Rosen, S. (1978), “Substitution and the Division of Labor,” Economica, 45, 235-50. Rosen, S. (1983), “Specialization and Human Capital,” Journal of Labor Economics, 1, 43-49. Rosenberg, N. and Birdzell, L. E. (1986), How the West Grew Rich: Economic Transformation of the Industrial World, New York, Basic Books. Rosenstein-Rodan, P. (1943), Problems of industrialization in Eastern and Southeastern Europe, Economic Journal, June-September issue. Rostow,W.W. (1960), The Stages of Economic Growth: A Non-Communist Manifesto, Cambridge, Cambridge University Press. Rotemberg, Julio, (1987), "The New Keynesian Micro Foundations", in Stanley Fischer, ed. NBER Macroeconomics Annual, 1987, Cambridge, MA, MIT Press. Rubinstein, A. (1982), "Perfect Equilibrium in a Bargaining Model", Econometrica, 50, 97-108. Rubinstein, A. (1985), "A Bargaining Model with Incomplete Information", Econometrica 53, 1151-72. Rybczynski, T. M. (1955), “Factor Endowments and Relative Commodity Prices,” Economica, 22, 336-41. Sachs, Jeffrey D. (1986) “Managing the LDC Debt Crisis,” Brookings Paper, 397-443.

639

(1987) “U.S. Commercial Banks and the Developing Country Debt Crisis," with H. Huizinga, Brookings Papers on Economic Activitv, No. 2. (1988), Review Essay: 'Recent Studies of the Latin American Debt Crisis'," Latin American Research Review, Vol. XXIII, no. 3 , pp. 170-179. (1989) "Political and Economic Determinants of Budget Deficits in the Industrial Democracies," with N. Roubini, European Economic Review 33, No. 5 pp. 903-938 North-Holland (1992) "Privatization in Russia : Some Lessons from Eastern Europe American Economic Review, Spring. (1992) "Transition from a Planned Economy to a Market Economy," in Social and Ethical Aspects of Economics: A Colloquium in the Vatican. (1993) "An Update on Reform in Eastern Europe and Russia," China Economic Review, Volume 4, Number 2. (1994) Understanding 'Shock Therapy'," Social Market Foundation Occasional Paper No. 7, London. (1995) "The Age of Global Capitalism," Foreign Policy, Number 98, Spring. (1996a), “Globalization and the U.S. Labor Market.” The American Economic Review: Papers and Proceedings, May. (1996b), “The Tankers Are Turning - Sachs on Competitiveness,” World Link, September/October 1996 (1996c), “On the Tigers Trail, - Sachs on Competitiveness,” World Link, November/December. Sachs, J. (1996d), "Notes on the Life Cycle of State-led Industrilization," Japan and the World Economy. 8, 153-74. (1997) “Globalization is the Driving Force for Growth in the U.S.,” The Rising Tide: The Leading Minds of Business and Economics Chart a Course Toward Higher Growth and Prosperity, John Wiley and Sons, Inc. (1998), Lecture Notes for Capitalist Economic Development. Department of Economics, Harvard University. Sachs, J. and Pistor, K. (1997), "Introduction: Progress, Pitfalls, Scenarios, and Lost Opportunities," in J. Sachs and K. Pistor eds. The Rule of Law and Economic Reform in Russia, Westview Press. Sachs, J. and Shartz, H. (1994), “Trade and Jobs in US Manufactures. Brookings Papers on Activity. No. 1. 1-84. and (1997), The Rule of Law and Economic Reform in Russia, Westview Press. Sachs, J. and Warner, A. (1997), "Fundamental Sources of Long-Run Growth.” American Economic Review, Papers and Proceedings, 87, 184-88. and (1995), “Economic Reform and the Process of Global Integration,” Brookings Papers on Economic Activity, 1. Sachs, J. and Woo, W.T.(1994), "Structural Factors in the Economic Reforms of China, Eastern Europe, and the Former Soviet Union", Economic Policy, 18, April. Sachs, J. and Woo, W.T. (1996) “China's Transition Experience,", Transition: The Newsletter About Reforming Economies, vol. 7, nos 3-4, March-April. The World Bank Transition Economics Division. and (1999), "Understanding China's Economic Performance", Journal of Policy Reforms, forthcoming. Sachs, J. and Yang, X. (1999), "Gradual Spread of Market-Led Industrialization.” Harvard Center for International Development Working Paper No. 11. Sachs, J., Woo, W. and Parker, S. (1997), Economies in Transition: Comparing Asia and Europe. MIT Press. Sachs, J., Yang, X. and Zhang, D. (1999a), "Trade Pattern and Economic Development when Endogenous and Exogenous Comparative Advantages Coexist.” Harvard Center for International Development Working Paper No. 3. , , and (1999b), "Patterns of Trade and Economic Development in the Model of Monopolistic Competition.” Harvard Center for International Development Working Paper No. 14 Sachs, J. and Warner, A. (1995), Natural Resources and Economic Growth. Cambridge MA, Harvard University mimeo (January). Sah, R and Stiglitz, J. (1988), "Committees, Hierarchies and Polyarchies", The Economic Journal, 98, 451-70. Sah, R. (1991), “Fallibility in Human Organizations and Political Systems,” Journal of Economic Perspectives, 5, 67-88. Sah, R. and Stiglitz, J. (1984), “The Economics of Price Scissors,” American Economic Review, 74, 125-38. Sah, R. and Stiglitz, J. (1986), “The Architecture of Economic Systems,” American Economic Review, 76, 716-27. Sah, Raj and Stiglitz, Joseph. (1991), "The Quality of Managers in Centralized versus Decentralized Organizations", Quarterly Journal of Economics. 106, 289-95. Sala-i-Martin, X. (1996), “The Classical Approach to Convergence Analysis”, Economic Journal, 106, 1019-1036. Samuelson, P. (1939), "Interactions Between the Multiplier Analysis and the Principle of Acceleration", Review of Economic Statistics, 21, 75-78. Samuelson, P.A. (1948), “International Trade and the Equalisation of Factor Prices,” Economic Journal, 58(230), 163-84. Samuelson, P. A. (1953), “Prices of Factors and Goods in General Equilibrium”, Review of Economic Studies, 21(1), 1-20. Sapsford, D. (1985), “The Statistical Debate on the Net Barter Terms of Trade Between Primary Commodities and Manufactures,” Economic Journal, 95, 781-88. Sargent, T. and Wallace, N. (1975), "`Rational Expectations,' the Optimal Monetary Instrument, and the Optimal Money Supply Rule," Journal of Political of Economy, 83, 241-54. Schultz, T. W., ed. (1974), Economics of the Family : Marriage, Children, and Human Capital, Chicago, the University of Chicago Press. Schultz, T. W. (1993), Origins of Increasing Returns, Cambridge, MA, Blackwell. Schumpeter, J. (1934), The Theory of Economic Development, New York, Oxford University Press. (1939), Business Cycles, New York, McGraw-Hill. Schurmann, H. (1968), Ideology and Organization in Communist China, Berkeley, University of California Press. Schweizer, U. (1986), "General Equilibrium in Space," in J. J. Gabszewicz et. al, Location Theory. London, Harwood,. Scitovsky, T. (1954), "Two Concepts of External Economies," Journal of Political Economy, 62, 143-51. Scott, A.J. (1988), Metropolis: from the division of labor to urban form, University of California Press. Segal, I. (1999), "A Theory of Incomplete Contracts," Review of Economic Studies, 66, 57-82. Segerstrom, P. (1998), "Endogenous Growth without Scale Effects", American Economic Review, 88, 1290-1310. Segerstrom, P., Anant, T., and Dinopoulos, E. (1990), "A Schumpeterian Model of the Product Life Cycle", American Economic Review, 80, 1077-91. Seierstad, A. and Sydsater, K. (1987), Optimal Control Theory with Economic Applications, Amsterdam, North-Holland. Sen, Amartya K. (1977), “Starvation and Exchange Entitlements: A General Approach and Its Application to the Great Bengal Famine.” Cambridge Journal of Economics, No. 2, 33-59. Sen, A.K. (1981) Poverty and Famines: An Essay on Entitlement and Deprivation, Oxford, Clarendon. Sen, A.K. (1983), “Development: Which Way Now?” Economic Journal, 93, 742-62. Sen, A.K. (1988), "The Concept of Development,” Handbook of Development Economics, I, Chapter 1, Amsterdam, North-Holland. Sen, Partha (1998), “Terms of Trade and Welfare for a Developing Economy with an Imperfectly Competitive Sector,” Review of Development Economics, 2, 87-93.

640

Servaes, Henri (1996), "The Value of Diversification During the Conglomerate," Journal of Finance, 51, 1201-25. Shapiro, C. and Stiglitz, J. (1984), “Equilibrium Umnemployment as a Worker Discipline Device,” American Economic Review, 74, 433-44. Shea, Jia-Dong and Yang, Ya-Hwei (1994), "Taiwan's Financial System and the Allocation of Investment Funds," in Joel Aberbach, David Dollar and Kenneth Sokoloff (ed.), The Role of State in Taiwan's Development, M.E. Sharpe, Armonk, N.Y., pp. 193-230. Sheahan, J. (1958), “International Specialization and the Concept of Balanced Growth,” Quarterly Journal of Economics, 52, 183-97. Shi, H. (1994), "Implications of Imperfect Competition and Specialization on Business Cycles and Economic Structure", Ph.D. Dissertation, Department of Economics, Monash University. Shi, H. and Yang, X. (1995), "A New Theory of Industrialization", Journal of Comparative Economics, 20, 171-89. and (1998), "Centralised Hierarchy within a Firm vs. Decentralised Hierarchy in the Market ", in K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. Shleifer, A. (1986), "Implementation Cycles", Journal of Political Economy, 94, 1163-1190. Shleifer, A. (1994), "Establishing Property Rights," Paper presented in World Bank Annual Conference on Development Economics. Shleifer, Andrei (1998), "State versus Private Ownership," Journal of Economic Perspectives, 12, 133-50. Shleifer, A. and Vishny, R. (1992), "Pervasive Shortages Under Socialism," RAND Journal of Economics, 23, 237-46. Shleifer, A. and Vishny, R. (1993), "The Politics of Market Socialism," Working Paper, Department of Economics, Harvard University. Shooman, Martin (1968), Probabilistic Reliability: An Engineering Approach, McGraw-Hill Book Company, New York. Simon, Curtis and Nardinelli, Clark (1996) “The Talk of the Town: Human Capital, Information, and the Growth of English Cities, 18611961”. Explorations of Economic History, 33, 384-413. Singer, H. W. (1984), “The Terms of Trade Controversy and the Evolution of Soft Financing,” in Pionnerrs in Development, ed. Meier, Gerald and Seers Singh, Nirvikar (1989), “Theories of Sharecropping,” in Pranab Bardhan ed. The Economic Theory of Agrarian Institutions, Oxford, Clarendon Press. Skaperdas, S. (1992), "Cooperation, Conflict, and Power in the Absence of Property Rights ", American Economic Reiview, 82, 720-39. Skinner, J. (1988) “Risky Income, Life Cycle Consumption, and Precautionary Savings”, Journal of Monetary Economics, 22, pp.237255. Skousen, Mark (1997), "The Perseverance of Paul Samuelson's Economics." Journal Economic Perspective, 11, 137-53 Smith, Adam (1776), An Inquiry into the Nature and Causes of the Wealth of Nations. Reprint, edited by E. Cannan. Chicago, University of Chicago Press, 1976. Smith, Sheila and Toye, John (1979), “Three Stories About Trade and Poor Economies,” Journal of Development Studies. Smythe, D. (1994), "Book Review: Specialization and Economic Organization: A New Classical Microeconomic Framework," Journal of Economic Literature, 32, 691-92. Solinger, D. (1992), "Urban Entrepreneurs and the State: The Merger of State and Society," pp. 121-42 in State and Society in China: The Consequences of Reform, edited by A. Rosenbaum. Boulder, Westview Press. Solow, R. (1956), "A Contribution to the Theory of Economic Growth", Quarterly Journal of Economics, 70, 65-94 Sonnenschein, H. (1973), “Do Walras’ identity and continuity characterize the class of community excess demand functions?” Journal of Economic Theory, 6, 345-54. Spence, M. A. (1976), "Product Selection, Fixed Costs, and Monopolistic Competition", Review of Economic Studies, 43, 217-36. Spraos, John (1983), Inequalising Trade: a study of traditional north/south specialisation in the context of terms of trade concepts, New York, Oxford University Press. Srinivasan, T. N. (1964), "Optimum Savings in a Two-Sector Model of Growth", Econometrica, 32, 358-74. St. Catherines Ont., Info Press (1999), The Franchise Annual. St. Catherines Ont., Info Press Stahl, I. (1972), Bargaining Theory, Stockholm: Economic Research Institute, Stockholm School of Economics. Starrett, D. (1973), "Inefficiency and the Demand for Money in a Sequence Economy", Review of Economic Studies, 40, 289-303. Stern, N. (1989), “Survey of Development,” Economic Journal, 99, 597-685. Stigler, G. (1951), "The Division of Labor is Limited by the Extent of the Market", Journal of Political Economy, 59, 185-93. Stigler, George J. (1961), “The Economics of Information”, Journal of Political Economy, 69, 213-225. Stigler, George (1976) “The Successes and Failures of Professor Smith”. Journal of Political Economy, 84, 1199-1213. P. 1209 Stiglitz, J. (1974) “Incentives and Risk-sharing in Sharecropping,” Review of Economic Studies, 41, 219-55. Stiglitz, J. (1986), "The New Development Economic,” World Development, 14, 257-65. Stiglitz, J. (1988), “Economic Organization, Information and Development,” in H. Chenery and T.N. Srinivasan (eds.) Handbook of Development Economics, Amsterdam, North-Holland, Vol. I. Stiglitz, J. (1989), “Rational Peasants, Efficient Institutions, and a Theory of Rural Organization: Methodological Remarks for Development Economics,” in Bardhan, P. ed. The Economic Theory of Agrarian Institutions, Oxford, Clarendon Press. Stiglitz, J. (1992), "Capital Markets and Economic Fluctuations in Capitalist Economies", European Economic Review, 36, 269-306. Stiglitz, Joseph (1998), “Sound Finance and Sustainable Development in Asia,” Keynote Address to the Asia Development Forum, The World Bank Group. Stiglitz, Joseph and Weiss, A. (1986), “Credit Rationing and Collateral", in J. Edwards and Mayer, C. (eds.), Recent Development in Corporate Finance, Cambridge, Cambridge University Press. Stokey, N. (1991), "Human Capital, Product Quality, and Growth", Quarterly Journal of Economics, 106, 587-616. Stolper, Wolfgang and Sammuelson, Paul (1941), “Protection and Real Wages,” Review of Economic Studies, 9, 58-73. Streetern, P. (1956), “Unbalanced Growth,” Oxford Economic Papers, 6, 167-90. Summer, L. (1992), “The Challenges of Development,” Finance & Development, March, pp 6-8. Summers, A. and Heston, A. (1988), “Penn World Tables Mark 5: 1950-1988,” Quarterly Journal of Economics, 340-67. Sun, Guangzhen (1999), Increasing Returns, Roundabout Production and Urbanization: A General Equilibrium Analysis of the Division of Labor. Ph.D. Dissertation, Department of Economics, Monash University. Sun, Guangzhen (2000), “The Size of the Firm and Social Division of Labour.” Australian Economic Papers. 39, 263-77. Sun, G. and Lio, M. (1996), "A General Equilibrium Model Endogenizing the Level of Division of Labor and Variety of Producer Goods", Working Paper, Department of Economics, Monash University. Sun, G., Yang, X, and Yao, S. (1999), "Theoretical Foundation of Economic Development Based on Networking Decisions in the Competitive Market", Harvard Center for International Development Working Paper No. 17. Sutcliffe, R. (1964), “Balanced and Unbalanced Growth,” Quarterly Journal of Economics, 79, 62-43. Swan, T. W. (1956), "Economic Growth and Capital Accumulation", Economic Record, 32, 334-61. Tabuchi, Takatoshi (1998), "Urban Agglomeration and Dispersion: a Synthesis of Alonso and Krugman", Tamura, R. (1991), "Income Convergence in an Endogenous Growth Model", Journal of Political Economy, 99, 522-40.

641

Tamura, R. (1992), "Efficient Equilibrium Convergence: Heterogeneity and Growth", Journal of Economic Theory, 58, 355-76. Taylor, J. (1980), "Aggregate Dynamics and Staggered Contracts", Journal of Political Economy, February, 88, 1-23. Taylower, George (1932), "Wholesale Commodity Prices at Charleston, South Carolina, 1732-1792", Journal of Economic and Business History, 4, 367. Temple, J. (1999), “The New Growth Evidence,” Journal of Economic Literature, 37, 112-56. Thirwal, A. (1986), “A General Model of Growth and Development of Kaldorian Lines,” Oxford Economic Papers. Thirwall, A.P. (1994), Growth and Development:With Special Reference to Developing Economies, London, Macmillan. Thompson, Henry (1995), "Free Trade and Income Redistribution in Some Developing and Newly Industrialized Countries." Open Economies Review, 6, 265-80. Thorp, R. eds (1984), Latin America in the 1930s: The Role of the Periphery in World Crisis. New York, St. Martin's. Tirole, J. (1986), "Hierarchies and Bureaucracies: On the Role of Collusion in Organizations," Journal of Law and Economic Organization, 2, 181-214. Tirole, J. (1989), The Theory of Industrial Organization, Cambridge, The MIT Press. Tirole, Jean (1999), "Incomplete Contracts: Where Do We Stand?" Econometrica, 67, 741-81. Todaro, M (1969), “A Model of Labor Migration and Urban Unemployment” American Economic Review, 59 (1), 138-48. Trefler, Daniel (1993), “International Factor Price Differences: Leontief was Right!” Journal of Political Economy, 10(6), 961-87. Trefler, Daniel (1995), "The Case of the Missing Trade and Other Mysteries." American Economic Review. 85, 1029-46. Tucker, Josiah (1755), The Elements of Commerce and Theory of Taxes, London. Tucker, Josiah (1774), Four Tracts on Political and Commercial Subjects, Gloucester, R. Taikes. Turgot, A.R.J. (1751), Lettre a Madame de Graffigny sur les lettres d'une Peruvienne, in G. Schelle, ed. Oeuvres de Turgot et Documents le concernant, Vol. I, Paris, F. Alcan, 1913. Turgot, A.R.J. (1766), Reflections on the Production and Distribution of Wealth, in P. D. Groenewegen, ed. The Economics of A.R.J. Turgot, The Hague, Nijjhoff, 1977. United Nation’s Economic Commission for Latin America (ECLA) (1950), The Economic Devleopment of Latin America and Its Principal Problems. Uzawa, H. (1959), “Prices of the Factors of Production in International Trade,” Econometrica, 27(3), 448-468. Uzawa, H. (1965), Optimum Technical Change in an Aggregative Model of Economic Growth, Review of Economic Studies, 6, 18-31. Van Zandt, T. (1995), "Hierarchical Computation of the Resource Allocation Problem," European Economic Review, 39, 700-8. Varian, Hal (1993), Microeconomic Analysis, New York, Norton. Vogel, E. (1989), One Step Ahead in China: Guangdong Under Reform, Cambridge, Harvard University Press. Vogt, W. (1969), "Fluktuationen in einer washsenden Wirtschaft under klassischen Bedingungen", in Bombach, G. (ed.), Wachstum, Einkommensverteilung und wirtschaftliches Gleichgewicht, Berlin, Duncker und Humblot. von Mises, L. (1922), Socialism: An Economic and Sociological Analysis, Indianapolis, Liberty Classics, reprinted in 1981. von Mises, Ludwig (1924), The Theory of Money and Credit, London, Jonathan Cape Ltd., 1934 von Thünen, J. H. (1826), Der Isolierte Staat in Bezierhung auf landwrirtschaft und Nationalekonomie, The Isolated State. (Carla M. Wartenberg, Trans.) New York, Pergamon, 1966. Hamburg. Walder, A. (1986), "The Informal Dimension of Enterprise Financial Reforms", pp. 630-45 in The Chinese Economy Toward the Year 2000, Joint Economic Committee, U.S. Congress. Washington D.C., U.S. Government Printing Office. Walder, A. (1989), "Factory and Manager in an Era of Reform", The China Quarterly, No. 118, June pp. 242-264. Walder, A. (1992), "Local Bargaining Relationships and Urban Industrial Finance," pp. 308-33 in Bureaucracy, Politics, and Decision Making in Post Mao China, edited by K. Lieberthal and D. Lampton, Berkeley, University of California Press. Walder, Andrew (1995), "China's Transitional Economy: Interpreting its Significance." China Quarterly, December 1995, 144, pp. 963-979. Walker, Amasa (1874), Science of Wealth: A Manual of Political Economy, Boston, Little Brown, New York, by Kraus Reprint, 1969. Wallace, N. (1980), "The Overlapping Generations Model of Fiat Money", in J. Karenken and N. Wallace (eds.) Models of Monetary Economics, Minneapolis, Federal Reserve Bank of Minneapolis. Wank, D. (1993), From State Socialism to Community Capitalism: State Power, Social Structure, and Private Enterprise in a Chinese City, Unpublished Ph. Dissertation, Department of Sociology, Harvard University. Wartenberg, C. M. (1966), von Thünen’s Isolated State, London, Pergamon. Weber, Max (1927), General Economic History, translated by Frank H. Knight. New York, Greenberg. Weber, Max (1961), The Protestant Ethic and the Spirit of Capitalism, Routledge, Chapman & Hall. Weber, Max (1968), Economy and Society, An Outline of Interpretive Sociology.Edited by Guenther Roth and Claus Wittich. Translators: Ephraim Fischoff [and others]. New York, Bedminster Press. Webster, A. ed. (1990) Structural Change in the World Economy, London, Routledge. Weibull, Jorgen (1995), Evolutionary Game Theory, Cambridge, MA, MIT Press. Weitzman Martin L. (1979), “Optimal Search for the Best Alternative”, Econometrica, 47, 641-654. Weitzman, M. (1982), "Increasing Returns and the Foundations of Unemployment Theory", The Economic Journal, 92, 787-804. Weitzman, M. (1994), "Monopolistic Competition with Endogenous Specialization", Review of Economic Studies, 61, 45-56. Weitzman, M. (1998), "Recombinant Growth", Quarterly Journal of Economics, 113, 331-60. Weitzman, Martin and Xu, Chenggang (1994), "Chinese Township Village Enterprises as Vaguely Defined Cooperatives." Journal of Comparative Economics, September 1994, 18, pp. 121-145. Wen, M. (1997), “Infrastructure and Evolution in Division of Labor”, Review of Development Economics,1,191-206. Wen, M. (1997), Division of Labor in Economic Development, Ph.D. dissertation, Department of Economics, Monash University. Wen, M. (1998), “An Analytical Framework of Consumer-Producers, Economies of Specialisation and Transaction Costs,” in K. Arrow, Y-K. Ng, X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan. West, E.G. (1964), "Adam Smith's Two Views of the Division of Labor," Economica, 3, 23-32. WHO. (1997a), “World Malaria Situation in 1994, Part I,” WHO Weekly Epidemiological Record 36, 269-74. Williamson, J. G (1993), "Economic Convergence: Placing Post-famine Ireland in Comparative Perspective." Discussion Paper No. 1654. Cambridge, MA, Harvard Institute of Economic Research (September). Williamson, J. G. (1992), "The Evolution of Global Labor Markets in the First and Second World Since 1830: Background Evidence and Hypotheses." SAE Working Paper 36, Cambridge, MA, National Bureau of Economic Research (February). (1998), "Globalization, Labor Markets and Policy Backlash in the Past," Journal of Economic Perspectives, 12, 51-72. Williamson, O. (1967), "Hierarchical Control and Optimum Firm Size", Journal of Political Economics, 75, 123-38. Williamson, O. (1985), Economic Institutions of Capitalism, New York, The Free Press.

642

Wong, C. (1985), "Material Allocation and Decentralization: Impact of the Local Sector on Industrial Reform," in The Political Economy of Reform in Post Mao China, edited by E. Perry and C. Wong, Cambridge, Harvard University Press. Wong, C. (1986a), "The Economics of Shortage and Problems of Reform in Chinese Industry", Journal of Comparative Economics, 10, 36387. Wong, C. (1986b), "Ownership and Control in Chinese Industry: The Maoist Legacy and Prospects for the 1980s", pp. 571-602 in The Chinese Economy Toward the Year 2000, Joint Economic Committee, U.S. Congress. Washington D.C., U.S. Government Printing Office. Wong, K-Y. and Yang, X. (1994), "An Extended Dixit-Stiglitz Model with the Tradeoff Between Economies of Scale and Transaction Costs," Seminar Paper, Department of Economics, Monash University. and (1998), "An Extended Ethier Model with the Tradeoff Between Economies of Scale and Transaction Costs," in K. Arrow, Y-K. Ng, and X. Yang eds. Increasing Returns and Economic Analysis, London, Macmillan, forthcoming. Woo, Wing Thye, Hai, Wen, Jin, Yibiao and Fan, Gang (1994), "How Successful Has the Chinese Enterprise Reform Been?" Journal of Comparative Economics, June, 18(3), pp. 410-37. Woodward, C. (1951), Origins of the New South, 1877-1913. New York World Bank (1992), Development Report 1992. Environment and Resource Problems. New York, Oxford University Press. World Bank (1997), Development Report 1997: The State in a Changing World. New York, Oxford University Press. World Bank (1981-1999), World Development Report, Various issues, Washington, DC, World Bank. Wu, Jieh-min (1998), Local Property Rights Regime in Socialist Reform: A Case Study of China's Informal Privatization. Ph. D. Dissertation, Department of Political Science, Columbia University. Xing, Yujing (1999), "Renminbi Ziben Xiangmo Keduihuan (Is Liberalization of Capital Account of China Urgent)", Economic Highlights, No. 38, p. 2. Yang, X. (1991), "Development, Structure Change, and Urbanization," Journal of Development Economics, 34, 199-222. (1994), "Endogenous vs. Exogenous Comparative Advantages and Economies of Specialization vs. Economies of Scale", Journal of Economics, 60, 29-54. (1996), "A New Theory of Demand and the Emergence of International Trade from Domestic Trade", Pacific Economic Review, 1, 215-17. (1998), Economics and China's Economy, Beijing Zhaocheng Press, China. (1999), "The Division of Labor, Investment, and Capital", Metroeconomica. 50, 301-24. (2000a), Economics: New Classical Versus Neoclassical Frameworks. Cambridge, MA., Blackwell. (2000b), “Incomplete Contingent Labor Contract, Asymmetric Residual Rights and Authority, and the Theory of the Firm.” Seminar Paper, Department of Economics, Monash University Yang, X. and Borland, J. (1991a), "A Microeconomic Mechanism for Economic Growth", Journal of Political Economy, 99, 460-82. and (1991b), "The Evolution of Trade and Economic Growth", Mimeo, University of Melbourne. and (1992), "Specialization and Money as a Medium of Exchange", Department of Economics Seminar Paper No. 8/92, Monash University. Yang, X. and Heijdra, B. (1993), "Monopolistic Competition and Optimum Product Diversity: Comment", American Economic Review, 83, 295-301. Yang, X. and Hogbin, G. (1990), "The Optimum Hierarchy", China Economic Review, 2, 125-40. Yang, X. and Ng, Y-K. (1993), Specialization and Economic Organization, a New Classical Microeconomic Framework, Amsterdam, North-Holland. Yang, X. and Ng, Y-K. (1995), "Theory of the Firm and Structure of Residual Rights", Journal of Economic Behavior and Organization, 26, 107-28. Yang, X. and Ng, S. (1998), “Specialization and Division of Labor: a Survey,” in K. Arrow, Y-K. Ng, and Xiaokai Yang (eds.), Increasing Returns and Economic Analysis, London, Macmillan. Yang, X. and Rice, R. (1994), "An Equilibrium Model Endogenizing the Emergence of a Dual Structure between the Urban and Rural Sectors", Journal of Urban Economics, Vol. 25, 346-68. Yang, X. and Shi, H. (1992), "Specialization and Product Diversity," American Economic Review, 82, 392-98. Yang, X. and Wills, I. (1990), "A Model Formalizing the Theory of Property Rights", Journal of Comparative Economics, 14, 177-98. Yang, X. and Yeh, Y. (1996), "A General Equilibrium Model with Endogenous Principal-agent Relationship," Department of Economics Seminar Paper, Monash University. Yang, X., Wang, J., and Wills, I. (1992), "Economic Growth, Commercialization, and Institutional Changes in Rural China, 1979-1987", China Economic Review, 3, 1-37. Yang, X. and Zhang, D. (1999), "International Trade and Income Distribution," Harvard Center for International Development Working Paper No. 18. Yang, X. and Zhao, Y. (1998), " Endogenous Transaction Costs and Evolution of Division of Labor," Monash University, Department of Economics Working Paper. Ye, Xingqing (1999), “Another Detriment of Urbanization ,” Economic Highlights, No. 365, p. 1, Dec. 31. Yellen, J. L. (1984), "Efficiency Wage Models of Unemployment", American Economic Review, 74, 200-05. Yi, Gang (1988), "The Efficiency of the Market and the Delimiting of Property Rights," China: Development and Reform, No 12, Beijing. Young, Allyn (1928), "Increasing Returns and Economic Progress", The Economic Journal, 38, 527-42. Young, Alwyn (1991), "Learning by Doing and the Effects of International Trade", Quarterly Journal of Economics, 106, 369-406. Young, Alwyn (1993), “Invention and Bounded Learning by Doing”, Journal of Political Economy, 101, 443-472. Young, Alwyn (1998), "Growth without Scale Effects,” Journal of Political Economy, 106, 41-63. Young, Leslie (1991), “Heckscher-Ohlin Trade Theory with Variable Returns to Scale.” Journal of International Economics.” 31, 183-90. Zaleski, E. (1980), Stalinist Planning for Economic Growth, 1933-1952, University of North Carolina Press. Zhang, D. (1999), "Inframarginal Analysis of Asymmetric Models with Increasing Returns," Ph.D. Dissertation, Wuhan University, Center for Advanced Economic Studies. Zhang, Gang, (1993), "Government Intervention versus Marketisation in China's Rural Industries: The Role of Local Governments," National Workshop on Rural Industrialization in Post-Reform China, Beijing, China, October. Zhang, J. (1997), "Evolution in Division of Labor and Macroeconomic Policies”, Review of Development Economics, 1, 236-45. Zhang, Weiying (1999), The Theory of the Firm and China's Enterprise Reforms (Qiye Lilun Yu Zhongguo Qiye Gaige). Peking University Press. Zhang, Yongsheng (2000), Irrelevance of the Size of the Firm: Theory and Empirical Evidence, Ph.D. Dissertation, Department of Economics, Renmin University.

643

Zhao, Y. (1999), " Information, Evolution of the Institution of the Firm, and the Optimal Decision Horizon", Review of Development Economics, 3, 336-53. Zhou, Lin, Sun, Guangzhen, and Yang, Xiaokai (1998), “General Equilibria in Large Economies with Endogenous Structure of Division of Labor,” Working Paper, Department of Economics, Monash University. Zhou, Qiren (1999), "Ba Chuangye Huangdao Diyiwei Lai, Ba Jiuye Huangdao Dierwei Qu (Put Founding Firms before Finding Employment)", Economic Highlights, No. 37, p. 1. Zhou, Taihe (1984), ed., Dangdai Zhongguo de Jingji Tizhi Gaige (Economic System Reforms in Contemporary China). Beijing, China Social Science Press. Zhuravskaya, Ekaterina (1998), "Incentives to Provide Local Public Goods: Fiscal Federalism, Russian Style."Mimeo, Harvard University. Zweig, David (1991), "Rural Industry: Constraining the Leading Growth Sector in China's Economy," Joint Economic Committee, U.S. Congress, China's Economics Dilemmas in the 1990s: The Problems of Reforms, Modernization, and Interdependence, April.

644