Intermediate microeconomic analysis 0060421851

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Intermediate Microeconomic Analysis A. My rick Freeman III BOWDOIN COLLEGE

1H17 HARPER & ROW, PUBLISHERS, New York Cambridge, Philadelphia, San Francisco, London, Mexico City, Sao Paulo, Sydney

Sponsoring Editor: David Forgione Project Editor: Eleanor Castellano Designer: T. R. Funderburk Manager of New Book Production: Kewal K. Sharma Compositor: ComCom Division of Haddon Craftsmen, Inc. Printer and Binder: R. R. Donnelley & Sons Company Art Studio: Vantage Art, Inc. Intermediate Microeconomic Analysis Copyright © 1983 by A. Myrick Freeman, III All rights reserved. Printed in the United States of America. No part of this book may be used or reproduced in any manner whatsoever without written permission, except in the case of brief quotations embodied in critical articles and reviews. For information address Harper & Row, Publishers, Inc., 10 East 53d Street, New York, NY 10022. Library of Congress Cataloging in Publication Data Freeman, A. Myrick, 1936Intermediate microeconomic analysis. Includes index. 1. Microeconomics. HB172.F73 1983 ISBN 0-06-042185-1

I. Title. 338.5

82-25856

V

Contents

PREFACE

xi

ALTERNATIVE COURSE SYLLABI

xv

PART I. 1.

2.

Introduction

i

What Is Economics?

3

THE SUBJECT MATTER OF ECONOMICS

3

THEORY AND MODELS IN MICROECONOMICS

11

THE COMPETITIVE MARKET SYSTEM: AN OVERVIEW

14

SUMMARY

16

KEY CONCEPTS

16

QUESTIONS AND PROBLEMS

17

SUPPLEMENTARY READINGS

17

Analytical Concepts: Optimization, Equilibrium, and Comparative Statics

19

LANGUAGES FOR ANALYSIS

20

OPTIMIZATION

23

EQUILIBRIUM COMPARATIVE STATIC ANALYSIS

28 32

SUMMARY

34

KEY CONCEPTS QUESTIONS AND PROBLEMS

35 33

SUPPLEMENTARY READINGS

36

MATHEMATICAL APPENDIX TO CHAPTER 2

36 v

Contents

VI

PART II. 3.

4.

The Economic Problem: Allocating Scarce Resources

The Allocation of Resources in Production

43

THE PRODUCTION FUNCTION PRODUCTION WITH TWO GOODS THE PRODUCTION POSSIBILITIES FRONTIER SUMMARY KEY CONCEPTS QUESTIONS AND PROBLEMS MATHEMATICAL APPENDIX TO CHAPTER 3

44 57 60 64 64 64 66

Preferences and the Allocation of Goods to Individuals

68

PREFERENCE ORDERINGS

68

A SIMPLE TWO-PERSON ECONOMY

QUESTIONS AND PROBLEMS

76 79 80 80

Resource Allocation and Economic Efficiency

81

THE CRITERION OF ECONOMIC EFFICIENCY

82 82 87 90 90 90 91

SUMMARY KEY CONCEPTS

5.

THE CONDITIONS FOR PARETO OPTIMALITY EFFICIENCY AND PRICES SUMMARY KEY CONCEPTS QUESTIONS AND PROBLEMS SUPPLEMENTARY READINGS

PART III. 6.

7.

41

The Competitive Market System

93

An Introduction to Markets and Exchange

95

CONDITIONS FOR EFFECTIVE MARKETS MARKET STRUCTURES SUMMARY KEY CONCEPTS QUESTIONS AND PROBLEMS SUPPLEMENTARY READINGS

96 102 104 105 105 105

Individual Preferences and the Theory of Demand

106

PREFERENCE FORMATION AND CONSUMER SOVEREIGNTY

107

THE INDIVIDUAL’S EQUILIBRIUM

110

THE COMPARATIVE STATICS OF INDIVIDUAL DEMAND

H8

vii

Contents

8.

9.

CHANGES IN PRICE: A CLOSER LOOK

134

UTILITY THEORY AND DEMAND: AN ALTERNATIVE APPROACH

143

SUMMARY

150

KEY CONCEPTS

151

QUESTIONS AND PROBLEMS

151

SUPPLEMENTARY READINGS

152

MATHEMATICAL APPENDIX TO CHAPTER 7

153

Market Demand: Topics and Applications

156

THE MARKET DEMAND FUNCTION

156

PRICE ELASTICITY AND MARGINAL REVENUE

159

MEASURING DEMAND

170

CONSUMER SURPLUS AND WELFARE MEASUREMENT

176

INDEX NUMBERS

184

IMPLICIT PRICES

189

ADDITIONAL CONSTRAINTS ON CHOICE

194

SUMMARY

201

KEY CONCEPTS

202

QUESTIONS AND PROBLEMS

202

SUPPLEMENTARY READINGS

205

MATHEMATICAL APPENDIX TO CHAPTER 8

206

The Theory of the Firm and Production

209

THE NATURE AND BEHAVIOR OF THE FIRM

209

OPTIMUM PRODUCTION PROCESSES

215

SOME PRODUCTION FUNCTIONS AND THEIR PROPERTIES

222

TECHNOLOGICAL CHANGE AND PRODUCTIVITY GROWTH

232

SOME ECONOMICS OF NATIONAL DEFENSE

237

SUMMARY

239

KEY CONCEPTS

240

QUESTIONS AND PROBLEMS

240

SUPPLEMENTARY READINGS

242

MATHEMATICAL APPENDIX TO CHAPTER 9

242

10. The Analysis of Costs

245

CONCEPTS OF COSTS FROM THE PRODUCTION FUNCTION TO COST CURVES

245 250

MEASURING COST FUNCTIONS AND RETURNS TO SCALE

268

APPLICATIONS

271

SUMMARY

275

KEY CONCEPTS

276

viii

Contents

11.

12.

13.

14.

QUESTIONS AND PROBLEMS

277

SUPPLEMENTARY READINGS

278

MATHEMATICAL APPENDIX TO CHAPTER 10

279

Price and Output in Competitive Markets

280

INTRODUCTION

280

THE THEORY OF THE FIRM

281

THE INDUSTRY

287

COMPETITION AND ECONOMIC EFFICIENCY

293

SOME COMPARATIVE STATIC ANALYSES

295

SUMMARY

300

KEY CONCEPTS

301

QUESTIONS AND PROBLEMS

301

SUPPLEMENTARY READINGS

305

MATHEMATICAL APPENDIX TO CHAPTER 11

305

Marginal Productivity and Factor Prices in Competition

306

MARGINAL PRODUCTIVITY AND INCOME DISTRIBUTION

306

THE DEMAND FOR A FACTOR

311

FACTOR SUPPLY

316

SOME APPLICATIONS

338

MARGINAL PRODUCTIVITY THEORY: AN EVALUATION

347

SUMMARY

349

KEY CONCEPTS

350

QUESTIONS AND PROBLEMS

350

SUPPLEMENTARY READINGS

352

Capital Markets: Savings, Investment, and Allocation over Time

353

WHAT IS CAPITAL?

353

THE ARITHMETIC OF CAPITAL AND TIME

355

THE PRESENT VALUE CRITERION FOR INVESTMENT

358

THE MARKET FOR LOANABLE FUNDS

361

SOME APPLICATIONS AND EXTENSIONS

374

SUMMARY

377

KEY CONCEPTS

378

QUESTIONS AND PROBLEMS

378

SUPPLEMENTARY READINGS

380

The General Equilibrium of the Competitive Economy

381

INTRODUCTION

38i

THE MODEL

382

A COMPARATIVE STATIC APPLICATION

3S7

Contents

IX

SUMMARY QUESTIONS AND PROBLEMS SUPPLEMENTARY READINGS

PART IV. 15.

16.

18.

391

Prices and Quantities in Monopoly Markets

393

INTRODUCTION MONOPOLY IN THE PRODUCT MARKET THE MONOPOLIST’S DEMAND FOR FACTORS MONOPSONY: THE SINGLE BUYER WITH MARKET POWER BILATERAL MONOPOLY SUMMARY KEY CONCEPTS QUESTIONS AND PROBLEMS SUPPLEMENTARY READINGS MATHEMATICAL APPENDIX TO CHAPTER 15

393 394 418 420 427 428 428 429 431 432

Oligopoly and Monopolistic Competition: The Economics of Interdependence

436

INTRODUCTION MODELS OF INTERDEPENDENCE MONOPOLISTIC COMPETITION

436 438 455

SUMMARY KEY CONCEPTS QUESTIONS AND PROBLEMS SUPPLEMENTARY READINGS MATHEMATICAL APPENDIX TO CHAPTER 16

460 460 460 462 462

PART V. 17.

Market Power

388 389 389

Welfare Economics

465

Welfare Economics: Competition and Efficiency

467

COMPETITION AND PARETO OPTIMALITY

468

MARKET FAILURE THE MANY PARETO OPTIMUMS SUMMARY KEY CONCEPTS QUESTIONS AND PROBLEMS

472 485 488 489 489

Equity and Social Welfare

491

SOCIAL WELFARE FUNCTIONS THE PRINCIPLES OF APPLIED WELFARE ECONOMICS THE MARKET SYSTEM AND WELFARE

491 505 513

X

Contents

SUMMARY

516

KEY CONCEPTS

517

QUESTIONS AND PROBLEMS

518

SUPPLEMENTARY READINGS

519

Glossary

52i

Answers to End-of-Chapter Questions

529

Index of Names

547

Index of Subjects

549

Preface

There are four key features of this book that I believe make it different from and better than other microeconomic texts and in combination will make it attractive to teachers of the intermediate micro course. First, Intermediate Microeconomic Analysis emphasizes economic reasoning as a process for deriving testable hypotheses about economic behavior and empirically relevant behavioral relationships such as demand and supply functions. The method employed for deriving these relationships is comparative statics. Second, throughout the book there is continuing discussion of the normative analysis of the outcomes of economic processes, especially the proposition that perfect competi¬ tion leads to Pareto optimality. The topics considered include the concept of consumer surplus as a basis for measuring changes in individual welfare, economic efficiency, the social cost of monopoly, and the normative implications of marginal productivity theory. There is also an extensive discussion of efficiency and equity in the two chapters on welfare economics. Third, I show that microeconomics is not just about prices and market equilibria, but also about how societies deal with their resource allocation problems in general. In order to emphasize this point, I have followed a different set of organizing principles from those governing most current textbooks. In Chapters 3 to 5 I have introduced just enough production theory and preference theory to derive the production box, the production possibilities curve, and the exchange box for a two-person, two-good, two-factor economy. This model makes it possible to describe the three tasks that any economic system must accomplish: determining what to produce, how to produce it, and who gets the output. This discussion of the resource allocation problem is general in that there is no reference to any specific form of economic institution. Next, I examine economic efficiency as a basis for evaluating alternative resource xi

Xll

Preface

allocations, the nature of shadow prices and their role in achieving an efficient alloca¬ tion, and the market system as an institution for translating shadow prices into market signals to guide the economic choices of individuals and firms. After the stage has been set and the economic problem posed in this way, I then consider preference and demand theory, production and cost theory, perfect competition, factor prices, monopoly, and so forth. My experience in teaching intermediate microeconomics by following this organiza¬ tion has been successful. The early chapters provide a context within which the students can deal with the specifics of demand theory, production theory, and so forth. And they have a clearer picture of the basic normative issues concerning efficiency and equity as they come across topics such as consumer sovereignty, consumer surplus, perfect competition, and market power. However, in view of the fact that not all instructors may care to follow this order of the material, I have provided alternative syllabi for utilizing this text for teaching a more conventionally organized course. These syllabi are presented after this Preface. The fourth key feature of this text is an effort to draw some of the major connections between microeconomic analysis and macroeconomics. Specifically, the chapter on capital and the interest rate includes a model of individual savings behavior in which the choice between saving and consumption today is shown to be a function of the interest rate and income. The simple Keynesian consumption function is shown as a special case of this model in which the substitution and income effects of an interest rate change cancel out. And the positive marginal propensity to save out of current income follows from the fact that future consumption is a normal good. Second, the demand for funds to pursue investment projects is shown to depend not only on the interest rate but also upon expectations about the future monetary returns from invest¬ ment. The Keynesian theory emphasizes the variability of these expectations. Finally there is a discussion of unemployment in the context of a model of the market for labor in which the wage rate serves to equate the quantity demanded and the quantity supplied. In organizing and writing this book, I have tried to convey the idea that microeco¬ nomics is not just a set of analytical techniques and theorems. Rather, it is a valuable way of achieving a better understanding of the functioning of modern capitalist econo¬ mies. Microeconomics also provides a way of analyzing economic problems in a variety of other economic institutional settings, for example, planning and resource allocation problems in socialist economies, resource allocation to the public sector, and so forth. I have also raised several issues that are not always treated in conventional microeco¬ nomics texts. These issues include the question of how individual preferences are formed and influenced and the implications of preference modification for the positive and normative analysis of demand; the nature of the firm, the reasons for its existence, and alternative views concerning the behavior of the firm as an economic institution; the role of property rights and transactions costs in market economies; and the norma¬ tive implications of the marginal productivity theory of factor prices. The exposition in this book is primarily verbal and graphical. I have resorted to simple algebra in explaining some relationships such as the individual’s budget con-

Xlll

Preface

straint and as a shorthand notation for expressing behavioral relationships such as demand and supply functions. Short mathematical appendixes to many of the chapters show the use of the calculus in deriving some of the principal relationships and hypothe¬ ses. These appendixes are optional. My thanks go to those individuals who helped me during the preparation of this book, especially my editor, John Greenman, and several colleagues, for their valuable advice; Richard K. Hay, who read a preliminary version of the manuscript and made significant suggestions; and Richard Dye, Peter Gottschalk, Robert Haveman, and Philip Sorenson, for their comments on parts of the manuscript. The great effort and care given by Jini Linkovich in typing the manuscript through several drafts are much appreciated. A. Georgetown, Maine December 1982

Myrick Freeman,

III

Alternative Course Syllabi

A key feature of this book is the presentation of the general problem of resource allocation and distribution in a two-person, two-good, two-factor economy before the detailed treatment of demand, production, competition, and so forth. I recognize that many instructors will prefer to retain the conventional organization of the material in which the general equilibrium model is introduced at the end of the course primarily as a basis for the analysis of Pareto optimality and welfare economics. For this reason, I have also prepared alternative sequences of reading assignments for those who wish to follow the conventional organization with either demand theory first or, as some instructors prefer, production theory first. The book has been written so that either alternative sequence can be followed without serious loss of continuity.

CONVENTIONAL ORGANIZATION WITH DEMAND THEORY FIRST Introduction Chapter 1. What Is Economics? Chapter 2. Some Analytical Concepts Chapter 6. Markets and Exchange

Competitive Markets Chapter 4, Preferences, section on “Preference Orderings” (an introduction to indifference curves) Chapter 7. Preferences and Demand Chapter 8. Market Demand; Topics Chapter 3, Production, section on “The Production Function’ (an introduction to isoquants) xv

XVI

Alternative Course Syllabi

Chapter Chapter Chapter Chapter Chapter

9. The Firm and Production 10. Cost 11. Prices and Outputs in Competition 12. Marginal Productivity and Factor Prices 13. Capital

Market Power Chapter 15. Monopoly Chapter 16. Oligopoly and Monopolistic Competition

General Equilibrium and Welfare Chapter 3, Production, sections on “Production with Two Goods” and “The Production Possibilities Frontier” Chapter 4, Preferences, section on “A Simple Two-Person Economy” Chapter 5. Economic Efficiency Chapter 14. The General Equilibrium of a Competitive Economy Chapter 17. Competition and Efficiency Chapter 18. Equity and Social Welfare

CONVENTIONAL ORGANIZATION WITH PRODUCTION THEORY FIRST Introduction Chapter 1. What Is Economics? Chapter 2. Some Analytical Concepts Chapter 6. Markets and Exchange

Competitive Markets Chapter 3, Production, section on “The Production Function” (an introduction to isoquants) Chapter 9. The Firm and Production Chapter 4, Preferences, section on “Preference Orderings” (an introduction to indifference curves) Chapter 7. Preferences and Demand Chapter 8. Market Demand; Topics Chapter 10. Cost Chapter 11. Prices and Outputs in Competition Chapter 12. Marginal Productivity and Factor Prices Chapter 13. Capital

Market Power Chapter 15. Monopoly Chapter 16. Oligopoly and Monopolistic Competition

XVH

Alternative Course Syllabi

General Equilibrium and Welfare Chapter 3, Production, section on “Production with Two Goods," and “The Production Possibilities Frontier” Chapter 4, Preferences, section on “A Simple Two-Person Economy” Chapter Chapter Chapter Chapter

5. Economic Efficiency 14. The General Equilibrium of a Competitive Economy 17. Competition and Efficiency 18. Equity and Social Welfare

PARTI_ Introduction

CHAPTER 1 What Is Economics?

In this introductory chapter we consider three topics. First, we ask. What is the scope of economics as a subject for intellectual inquiry? How is the subject defined? What are the central questions studied by economists? And, What kinds of things does one have to study and learn about in order to be called an economist? Second, we discuss the methods of economic reasoning. How is economic theory developed? How is good theory distinguished from bad theory? These questions involve us in a discussion of models, prediction, and the testing of theory. Third, we briefly discuss the most signifi¬ cant conclusion stemming from microeconomic reasoning on the functioning of eco¬ nomic systems. This conclusion, which has important ideological implications, is a statement on the virtues of a competitive market system as a means of organizing economic activity. Thus it is important to understand the reasoning that lies behind this conclusion and any limitations or qualifications concerning its applicability to a modern economy.

THE SUBJECT MATTER OF ECONOMICS Some Definitions of Economics A number of short one-sentence definitions of economics have been offered through the years. But economics is simply too rich a subject to have its essence captured in a single sentence. Although each of these definitions highlights some aspect of economics as a subject, each is unsatisfactory as a complete description of what economics is about. By reviewing and discussing some of these definitions and their limitations, we can reach a clearer understanding of economics. One person has proposed to define the subject of economics as “whatever economists 3

4

Introduction

do.” This is a pragmatic, if circular, approach to answering the question—What is economics? But it suggests that some insight into the nature of economics might be gained by looking at what kinds of activities economists are involved in. In a recent listing of job openings for economists with advanced degrees about half the available positions were in teaching and research at colleges and universities. The remainder were with manufacturing firms, financial institutions, consulting firms, and government agencies that wanted economists to perform functions such as: Apply cost-effectiveness analysis to mental health services programs; Analyze economic development projects for the Navajo tribe; Assist developing countries in the formulation and evaluation of food policies; Study the impact of labor legislation; Perform benefit-cost analyses of air pollution control legislation; Assist in the analysis of the impacts of nuclear reactor accidents and carbon-dioxide-induced climate change; Analyze the cost of capital, rates of return, revenue requirements, and prices in the communications industry; Study banking practices and their effects on financial markets; Provide forecasts of energy supply and demand and assess new energy technologies. What do these activities have in common? Most deal with the implications of scarcity and means of coping with it by making better use of available resources. Many involve the evaluation of alternatives and making choices among alternative courses of action. And some deal with the setting of prices and the effects of price on supply and demand. Let us consider these common elements in more detail.

Prices. Economics has been defined by some as the study of price. By this definition the core of economic theory is the theory of the determination of prices in markets through the interaction of supply and demand. For them, microeconomic theory is synonymous with price theory, which is reflected in the titles of several prominent textbooks on the subject. But equating price theory and economic theory seems to imply that there can be no economic theory for societies that do not have market systems (e.g., some traditional or primitive societies) or for societies that set prices by administrative fiat (e.g., the Communist bloc socialist countries). This definition also implies that economic theory has nothing to say on the question of what percentage of a society’s resources should be controlled by the government through taxing and spending or how a government’s budget should be allocated across different expenditure categories. Clearly, then, there is more to economics than the study of prices and markets. Scarcity and Resource Allocation.

A widely quoted definition of economics was offered by Lord Robbins in his influential book, An Essay on the Nature and Significance of Economic Science (1935). He defined economics as the study of the allocation of scarce resources among competing ends. This definition has several good features. First, because scarcity or limits on the abundance of productive resources is a basic feature

5

What Is Economics?

of human existence, economics as defined by Robbins applies to all societies, whether or not they use markets to allocate resources. Also this definition focuses on an aspect of human behavior in many contexts rather than on particular types of behavior, for example, consumption or production. Where there is scarcity, people must economize; that is, they must try to make the best of any situation. Thus economics involves the study of economizing behavior in a wide variety of settings. Finally, this definition points out the central role of choice in an economy. Without scarcity, there is no need to make choices. All things are possible. It is the alternative ends and the alternative means to their attainment that make choice both possible and necessary. Thus economic theory necessarily involves a theory of choice.

Choosing from Among Alternatives. This has led some economists to advocate that economics be defined as the science of choice. The theory of choice begins with the assumption that people have well-defined objectives—they know what they want. Each individual must choose from among an array of alternative activities that contrib¬ ute in varying degrees to his or her objectives. But each person faces constraints or limits on the extent to which each activity can be engaged in. These constraints reflect the scarcity of resources. The logic of choice dictates that individuals choose those alternatives that make the largest contribution to the attainment of their objectives. This logic will be developed more fully in Chapter 2. A substantial part of economic theory involves the application of this logic to problems such as consumer demand, production theory, and the theory of the firm. Thus the logic of choice plays a very important role in economic theory. Some economists have advocated applying the theory of choice to a wide range of topics, including having children, engaging in criminal activity, going to church, select¬ ing a mate in marriage, and ending one’s life.1 Whether the application of the theory of choice to some of these areas will improve our understanding of human behavior remains to be seen.

Social Organization and Economic Activity. The definition of economics in terms of the theory of choice focuses on the behavior of individuals and away from the consequences of the interactions of individuals in different economic settings. The definition of economics offered by Frank Knight has the virtue of calling attention to the social dimension of economic behavior. Knight defined economics as dealing with “the social organization of economic activity.”2 Economic activity means what people do to meet their material needs and wants. These activities include the production of goods and services, their distribution, and their use and consumption by individuals. Thus activities such as going to church may contribute to spiritual welfare and, accord¬ ing to some, might be better understood by the application of the economic theory of

‘See, for example, Gary S. Becker, The Economic Approach to Human Behavior (Chicago: University of Chicago Press, 1976) and Robert L. Crouch, Human Behavior: An Economic Approach (North Scituate, Mass.: Duxbury Press, 1979). 2Frank H. Knight, The Economic Organization (New York: Harper & Row, 1951), p. 6.

6

Introduction

choice. But because they do not contribute to material welfare and comfort, they are not economic activities, at least in Knight’s view. The term “social organization” emphasizes the varieties of interaction among in¬ dividuals. Robinson Crusoe faced the problem of allocating his scarce resources (time, tools, and materials) among competing ends (food, shelter, and warmth). The economic theory of choice could be applied to the study of his behavior. But at least until he met up with Friday, there were no interactions. The economics of Robinson Crusoe is not a social science. With two or more people in an economy there are opportunities for division of labor and specialization that may increase productivity and the ability to satisfy material needs and wants. Division of labor and specialization creates the need to coordinate and manage economic activity. And there must be some means for dividing rights to the output from productive activity.

Economic Institutions. Society must devise a set of institutions to deal with these problems. An economic institution can be described in terms of the rules and obliga¬ tions it imposes on its members and the rights and privileges it accords them. There are many types of social institutions for managing economic relationships. A system of markets is a social institution. The rights and privileges accorded to individuals include the right of ownership and the right to enter into exchange transactions with others. The family is a social institution defined by, among other things, the responsibil¬ ity of parents to care for and nurture their children. The government is a social institution. It may have the power to tax its citizens and the responsibility of disposing of the proceeds of taxation in accordance with the preferences of its citizens as they are expressed through some political mechanism. Many primitive and traditional soci¬ eties tended to rely on the extended family or the tribe as a social institution for organizing and managing economic activity. The socialist command economies rely primarily on the government to coordinate economic activity. A variety of economic institutions can coexist within any given society at a point in time. There has never been a society in which all economic activity has been coordinated through markets. And even the socialist command economies rely to some extent on market institutions. In summary, economic activity involves the allocation of scarce resources among competing ends. The really important and interesting economic problems, however, arise because of the social dimension of economic activity. My definition of the subject emphasizes these two aspects of the study of economics. Definition: Economics is the study of the nature and peiformance of the social institutions that have evolved to manage and coordinate the economizing behavior of the members of society. In Western societies and Japan a market system has emerged as the dominant form of social institution for economic management and coordination. Thus understanding the functioning of markets and the determination of prices within markets is a very important part of economics. Finally, whatever the economic institution, the behavior of individuals within that institutional setting can be analyzed with the economic theory of choice. Their behaviors can best be understood as the purposeful responses

7

What Is Economics?

to the opportunities and constraints on choice presented by the given economic insti¬ tution.

Micro Versus Macro Most students of economics learn very early that macroeconomics deals with aggregate measures of economic activity such as the national income, the average price level, and the rate of unemployment of labor. With this point in mind, one could distinguish between the concerns of macroeconomics and microeconomics in several ways. For example, Macroeconomics is concerned with explaining the level of national output, whereas microeconomics seeks to explain the composition of output (guns vs. butter; automobiles vs. refrigerators). Macroeconomics seeks to understand the determinants of the price level, that is, the average of all prices in the economy; whereas microeconomics is concerned with the relative prices of specific goods. From these examples it appears that macroeconomics and microeconomics are sepa¬ rate and distinct areas of study with little or no overlap. But this is not really the case. What distinguishes microeconomics from much of macroeconomic analysis is the former’s emphasis on understanding the economic behavior of individuals who respond to different incentives and constraints in a given institutional setting. In microeconom¬ ics the analysis of the behavior of aggregate variables such as market demand and industry supply is firmly rooted in the analysis of the behavior of individual buyers and supplying firms. This should also be true of the analysis of macroeconomic variables such as the price level and the employment rate. In other words, to be effective, macroeconomic analysis must be built on a foundation of the microeconomic analysis of the individuals and firms making up the aggregate. For example, unemployment implies that there are some workers who are willing to supply labor at the going wage rate but that there are no buyers for their labor services. A macroanalysis of unemploy¬ ment must, among other things, come to grips with the question of why the wage rate is not bid down until the quantity demanded is equal to the quantity supplied. Also macroanalysis suggests that a major source of the variability in national output and employment is variation in the rate at which businesses invest in new productive facilities. Explanations of this variability must begin with an examination of what influences an individual firm’s decisions to invest in new capital. In this book we develop some of the basic microanalytical tools with which the microfoundations of macroeconomics can be built.

The Three Functions of Economic Institutions The economic institutions of any society must provide a means of settling three ques¬ tions: (1) What ends will be satisfied by the use of society’s scarce resources—What goods will be produced (the “What?” question)? (2) What techniques will be used in

8

Introduction

combining society’s scarce resources for the production of valued goods (the “How? question)? (3) How will the goods and services produced by the economy be distributed among the members of society (the “For whom?” question)?

What to Produce? Consider the question of whether available resources should be used to produce more radios or more TV sets. In the market economies of the Western developed nations this question would be decided by the managers of radio and TV manufacturing firms as they responded to the price and cost signals generated in the markets for their products. In other words, the question would be settled through the market system as a social institution. Alternatively, in a socialist command economy the question would be settled within the bureaucracy on the basis of priorities deter¬ mined by the hierarchy controlling that economy. Even in a market economy some decisions as to what to produce are at least influenced by governmental and political institutions. The question of whether to produce large or small, fuel-efficient cars has been influenced by government regula¬ tions that govern fuel efficiency standards and air pollution emissions standards, as well as by the market signal of rising gasoline prices. Decisions such as whether to produce nuclear submarines or urban mass transit systems or whether to use public lands for parks or for mineral resource development are made by the government—a political institution. However, even these decisions may be influenced by market forces as reflected in costs and demands for certain kinds of services. Even in the Western capitalist economies many economic decisions about what to produce are made neither by government nor through market institutions. For exam¬ ple, a university must decide how to allocate its resources among the production of new knowledge through research, the transmission of knowledge through classroom teach¬ ing, and the provision of extracurricular activities such as intercollegiate athletics. Also, families must make decisions such as whether to have children and whether family members should engage in home production (e.g., child care, housework, and meal preparation) or in paid work through the labor market. The family is a very complex institution from an economic perspective. Economic decisions are likely to be in¬ fluenced by social and cultural norms and traditions concerning sex roles and the division of authority within the family. How to Produce It? Observation and experience confirm that from a technological point of view there are many ways to “skin a cat.” Any good can be produced through the application of a variety of alternative techniques that differ primarily in the propor¬ tions in which they employ labor and capital. Perhaps the most extreme example is in large-scale earth-moving construction projects such as dams, roads, and irrigation and drainage systems. In the labor abundant and capital scarce economies of China and India such projects are often carried out by using large numbers of people who employ only the most primitive tools. In contrast, in the United States relatively few people are needed to perform the same tasks by using large-scale earth-moving machines. There are similar differences in the use of labor and capital in farming when countries such as France, the United States, and Japan are compared.

9

What Is Economics?

In the capitalist economies the choice of technique is usually made through the market system as an economic institution. Producers consider the relative scarcities of labor and capital as reflected by their market prices. But even in the capitalist econo¬ mies, governments sometimes impose restrictions or dictate choices concerning produc¬ tion techniques. For example, the U.S. government has banned the use of oil as a fuel in new electric-generating plants and even requires that some oil-burning plants switch to coal as a fuel. These decisions reflect a view that the market, if left to its own devices, would make wrong choices; that is, the market would fail as an economic decision¬ making institution.

For Whom? In a market economy the question of for whom are goods produced is governed largely by the distribution of income. Those individuals who want a good badly enough and have the income to make their demands effective have their demands satisfied by the market. The distribution of income in turn depends on the distribution of the ownership of the factors of production, labor, capital, and land and the prices paid for the services of these factors. These prices are themselves determined in the market system. In the capitalist nations, governments often intervene to modify the answers to this question that are produced by the market system. This intervention can take two forms: (1) The government can use its powers to levy taxes and make transfer payments to redistribute income or purchasing power directly from one individual family to another. (2) The government can command resources through taxation to produce goods and services such as police and fire protection, medical care, education. These goods and services are typically not sold through markets but, rather, are made available on some other basis. The family is also an important economic institution for determining who gets to consume the output of the economy. In many societies today, and in the capitalist nations in earlier times, the family was the predominant institution for transferring goods from the productive members of the economy to those whose own productive activity was impaired by age. Primary responsibility for the economic well-being of the elderly lay with their adult children. Even at present in most societies the family is the primary institution for transferring goods to children who are too young to provide for them¬ selves. However, the government’s increasing role in making provisions for the economic well-being of the elderly and children reflects a weakening of the family as an economic institution. The forces governing the distribution of economic well-being within the nuclear family are complex. Until recently, economists were primarily concerned with gaining a better understanding of the role of the market system in answering the for whom question. But more work is currently being done on the economics of the household and the functioning of the family as an economic institution.

Positive and Normative Analysis In the study of the social organization of economic activity economists can undertake either positive analysis or normative analysis.

10

Introduction

Definition: Positive analysis has the objectives of developing a better understanding of how particular economic institutions work and of explaining their functioning.

Definition: Normative analysis has the objective of evaluating the performance of

alternative economic institutions or given institutions under alternative conditions. This is called normative analysis because it involves the establishment of some norm or criterion for evaluation. In the simplest terms, positive analysis is concerned with what is, whereas normative analysis is concerned with what ought to be. The results of positive analysis consist of models of economic institutions and processes and predictions about observable phenomena. The statements and predictions of positive analysis can in principle be verified through observation. We will have more to say about models and predictions in the next section. In contrast, normative statements are based on value judgments that have no scientific basis. They are not verifiable. For example, the theory of consumer demand provides an explanation of individuals’ responses to a change in the price of a commodity, other things being equal. This theory yields the prediction that the imposition of a tax on the sale of, say, whiskey, will lead to an increase in its price and a decrease in the quantity of whiskey purchased. This is positive analysis. If one were to say that the price of whiskey is too low because it encourages excessive drinking, this would be a normative statement. A temperance worker might agree with this statement. But others could say with equal conviction that the price of whiskey is too high. There is no logical or objective basis for determining whether either or both of these statements are false, because they are based implicitly on different value judgments about the consumption of alcohol and the appropriate role of government in influencing individual choice. In normative analysis alternative states of the world are compared and ranked. This comparison is based on objective features of these alternative states. But if the alternatives are to be ranked, a criterion must be established. Formally, a criterion is a rule, perhaps a functional relationship, by which different states can be ranked. The two criteria most relevant to microeconomic analysis are efficiency and equity. Efficiency can be defined in several ways, for example, the size of aggregate output or net national product. Equity refers to the way in which income or output is distributed among individuals. The efficiency criterion evaluates the size of the economic pie; the equity criterion looks at the way in which the pie is sliced. People can differ in their views on what constitutes fairness in the distribution of income and on the relative importance to be given to equity versus efficiency when the two criteria are in conflict. Many, if not most, of the differences in opinion regarding economic policy can be traced to differences in value judgments concerning objectives. Most of this book is devoted to positive analysis—to the development of models and theories to explain the functioning of economic institutions. But the evaluation of the performance of economic systems is also an important task for microeconomic analysis. The last chapter is devoted to the problems of evaluating economic outcomes in terms of their efficiency and equity impacts.

11

What Is Economics?

THEORY AND MODELS IN MICROECONOMICS One of the principal objectives of this text is to show how the major results of positive microeconomic analysis have been arrived at through the processes of logical reasoning —deduction and inference. For this reason we turn now to a discussion of the methods of economic reasoning. Method refers to the set of rules and procedures scientists adopt when they commence to investigate some phenomenon. These rules should tell them something about what they are trying to accomplish by their work; in a very general sense, how to go about it; and finally, how to evaluate the results when they are finished. Specifically, method refers to the logical principles that determine when to accept and when to reject a proposition as a valid part of the body of scientific knowledge. Although textbooks often refer to “the scientific method,” there is by no means complete agreement among scientists on all aspects of appropriate method. In fact, controversies over methodological issues are often among the most long lasting and bitter of scholarly debates. The purpose here is neither to start nor end such a debate. Rather, it is to state as simply as possible those methodological principles that have guided the development, testing, and application of the microeconomic theory pre¬ sented in this text. The positive analysis of economic phenomena and the development of economic theory proceeds through several steps.

Defining the Question The first step, naturally, is the selection of a problem or phenomenon that has not been fully or adequately explained. In one sense this is easy because there is so much still to learn. But in another sense it is hard because the way that the problem is defined influences all subsequent steps. In some formulations the problem might prove impossi¬ ble to solve, whereas other forms of statements of the problem might be trivially easy. Becoming a good theorist is partly a matter of developing the necessary judgment and experience in asking the right questions and in stating the problem in a meaningful but manageable form.

Building the Model The second step is the construction of a model of the phenomenon under study. A model is a simplified and scaled-down version of the real thing. It includes the essential details and relationships but omits extraneous features and unnecessary detail. For example, models of ships do not typically include tiny replicas of each fastening and fitting. Rather, they have only enough detail to convey the essential elements of the ship; and what is considered essential by the model builder depends on the purposes of the model. Models for testing the hydrodynamic properties of the hull concentrate on reproducing the external hull shape and the weight distribution characteristics to the exclusion of all other detail. Similarly, the models used in economic analysis will

12

Introduction

take different forms, depending on their purpose and the nature of the problem they are meant to address. The process of model building begins with the adoption (or the development, if necessary) of a language for expressing the main features of the model. This language must include a set of definitions and concepts that are as unambiguous as possible. For example, the analysis of the supply of a good to a market involves definitions of the terms “output,” “factors of production,” “technology,” and “cost.” These concepts may be defined and related in purely verbal terms or with the aid of graphical and geometric language or in more abstract mathematical symbols. In economics much of the language is already in existence, and this step is implicit rather than explicit. Learning this language is one of the main tasks for beginning students in economics. The chosen language is then used to construct a set of relationships between concepts or between the variables of the model. These relationships are based on assumptions and postulates that concern the behavior of actors in the model, the opportunities and constraints they face, and other structural relationships. For example, the theory of supply is based on the assumption that producers strive to maximize their profit and that there is a technological relationship between inputs and outputs that has certain properties.

Deducing Conclusions The next step is the manipulation of the model and its relationships to produce conclu¬ sions. This manipulation is a logical process of deduction which can be carried out verbally, graphically, or mathematically. Because they are deduced from the model, the conclusions can only be accepted as true within the context of the model and the language used. They furnish a basis for determining whether or not the model is useful. The conclusions must take the form of hypotheses or predictions that can be compared with observations of the real world in order to provide a test of a model. Definition: A hypothesis is a conditional statement that is derived from a model for

the purpose of testing the model. A hypothesis typically takes the following form: If A, all other things held constant, then B. Here, A refers to the conditions under which the hypothesis is thought to be valid, and B refers to the expected consequences of those conditions. A hypothesis is “true” in the sense that it follows logically from the model; but it is highly tentative in the sense that it may or may not be consistent with observation. This comparison of hypothesis and reality is the distinguishing feature of scientific investigation. A hypothesis can also be interpreted as a prediction of what will be found by observation under certain conditions. A prediction is not a forecast. A forecast is an unconditional statement about the future, such as, “It will rain tomorrow.” A predic¬ tion differs from a forecast in two respects: (1) It need not refer to the future. (2) It must include a statement of the conditions under which the prediction is expected to hold. A prediction about the weather could take the following form. “If the sky is

13

What Is Economics?

cloudy, if the wind is from the northeast, and if the barometer is falling, then rain will occur. This prediction is derived from a model relating cloud conditions, movements of air masses, and barometric pressure. It applies to all situations, past, present, and future, in which the stated conditions hold. And it is a hypothesis about the nature of the relationship among these variables.

Testing the Model One of the controversial questions in methodology is, What constitutes an appropriate test of a model? Clearly, a model must pass the test of internal consistency and logic. That is, there must be no logical errors in moving from the definitions and assumptions of the model to its conclusions and predictions. But internal consistency and logic are only necessary conditions, not sufficient conditions for accepting a model. A model can be internally consistent and logical but be of no value in explaining real-world phenomena.3 It is sometimes argued that models should be rejected if their assumptions are too “unrealistic.” But aside from being ambiguous on the question of how much lack of realism is too much, this argument seems to be based on a misunderstanding of the role of assumptions in model building. In order to be useful, models must be unrealis¬ tic. They must abstract from reality by making simplifying assumptions. Ideally, the¬ ory should have sufficient detail and precision to handle all possible variations and exceptions, make accurate numerical predictions, and have sufficient generality to be applicable in a variety of situations. Yet these properties to a large extent are mutu¬ ally exclusive. Generality means loss of precision; yet detail means reduction in appli¬ cability and an increase in the cumbersomeness of the model. Lack of detail and lack of reality in models go hand in hand. In fact, models by definition are unrealistic. A completely realistic model would be an exact reproduction of reality and would for¬ feit any usefulness as such by its zealous attention to realism. It would be too com¬ prehensive to comprehend. A model’s success depends on its ability to capture the essential elements of a complex reality by making simplifying but nondistorting as¬ sumptions. The best way to test the success of a model in capturing the essentials is to compare its predictions with observed phenomena. The ultimate test of the model is whether its predictions are consistent with reality; that is, whether when the conditions A are observed, B is also observed. For if A is observed without B, the model has not adequately captured the true relationship between A and B. The testing of hypotheses and predictions against reality is usually a statistical process carried out in accordance with rules that are derived mathematically. Two important points to remember about this process are: (1) Hypothesis testing requires more than a superficial search for a few historical cases that are consistent with the hypothesis. Rather, statistical testing of hypotheses requires a search of all known cases

Tor example, see the kinked demand curve model of Chapter 16.

14

Introduction

or a random sample of known cases to determine, if possible, whether the predicted result occurred more often than can be attributed to pure chance. (2) Hypotheses can be rejected on the basis of statistical tests, but they can never be accepted. The best that can be said is “not rejected.” The nature of the test is such that other better and undiscovered models cannot be ruled out as alternative explanations of the observed relationships; and there is always a slim possibility that the apparent successful test of the hypothesis was due to pure chance. After gathering appropriate data by observation and measurement, one may find that the predictions of the model are not consistent with reality. In this case the model in its present form must be discarded as a description of reality. At this point the process of model building can become iterative. Hypothesis testing is a source of information about the problem being investigated. This information can be used to redefine the problem or to alter the structure of assumptions and postulates in the model itself. Revised models may produce alternative hypotheses and predictions which then can be tested against observation. Models that produce hypotheses that have not been refuted by observation gain the status of theories. All too often one hears, “That sounds fine in theory but it won’t work in practice.” Such statements are probably the result of two facts: (1) a misunderstand¬ ing of the term theory and the process of theorizing and (2) a reaction to those who place too much faith on the predictive and explanatory power of existing theory. A theory that will not work in practice must be one whose hypotheses and predictions are not supported by the empirical evidence. Theories that do not work in this sense must be discarded. The only acceptable theories are those that actually do work. On the second point, the economic world is changing as fast as it is being investigated. This means that the specific features and quantitative relationships of economic models must also be adjusted to reflect this changing reality. More comprehensive models may be able to incorporate the variables causing these changes. But generality and compre¬ hensiveness in models is not an unmixed blessing. The development of theories and investigation of hypotheses have not proceeded so far that one can think of having anything like complete explanations of economic life. In subsequent chapters some extremely unrealistic models of economies will be built, unrealistic because of both what is left out of the model and what is said about what remains in the model. These models represent the main body of conventional microeco¬ nomic theory. But since it has been argued here that theories must be tested, we will devote some space to presenting empirical evidence that relates to the predictions of models.

THE COMPETITIVE MARKET SYSTEM: AN OVERVIEW Economists at least since Adam Smith (author of Inquiry into the Nature and Causes of the Wealth Nations, first published in 1776) have marveled at the apparent ease with which the capitalist economies with their decentralized market systems carry out the

15

What Is Economics?

complex tasks of coordinating economic activity. On the one hand, we observe large numbers of households with different tastes and preferences that are provided with a myriad of different goods and services by a multitude of individuals, small businesses, and corporations involved in production and distribution. This is a very complex, interdependent economic system. On the other hand, however, it appears to operate for the most part without any direction or management from above. Rather, the orderly functioning of the system is accomplished through the decentralized decision making of many individuals and firms. The two central questions for which microeconomic analysis has sought answers concern different aspects of this ability of markets to produce order out of apparent chaos. They are: (1) “What produces this order and how is it maintained?” This is a question for positive analysis; that is, it seeks an explanation for the functioning of the market system. (2) Is the outcome of this market system in some sense good? Will the independent maximizing behavior of each consumer and producer in a market economy result in an allocation of resources that, in a normative sense, maximizes the well-being of society as a whole? A major purpose of this text is to show how economists have attempted to answer these questions. Economists have based their answers on the belief that human behavior in the aggregate can be understood as the response of rational, self-interested individu¬ als to the opportunities and constraints presented by their environment. In other words, individuals are assumed to be striving to maximize their well-being as they make decisions about what goods to consume, how much to save, and how much to work. Managers of firms are assumed to make production and supply decisions in an effort to maximize their profits. Economists have then proceeded to develop models of market systems with which it is possible to analyze the implications of maximizing behavior on the part of produc¬ ers and consumers. These models show that when producers and households attempt to maximize profit and well-being, and when they utilize the opportunities for exchange and the information on prices provided by a system of markets, the economy will tend to an equilibrium position. In this sense the outcome of market interactions is orderly. This result will be established more rigorously in Chapter 14. These models also show that when all markets are perfectly competitive, the resulting equilibrium is one in which it is not possible to make any individual in the economy better off without simultaneously making someone else worse off. In other words, there is no way to alter the equilibrium of the economy for one person’s benefit without imposing a loss on another individual. In this sense the outcome of a competitive market system is good. This might be called the “principle conclusion” of microeco¬ nomic theory. This conclusion and the analysis leading to it have important ideological implications. They provide the economic justification for laissez-faire capitalism as well as for certain forms of government intervention into the market system, for example, the regulation of the prices charged by electric utilities. We will show how this conclu¬ sion is derived and discuss its limitations and policy implications in Chapter 17. Establishing, analyzing, and criticizing these conclusions have been a major focus

16

Introduction

of economic research at least since Adam Smith. In this book we will first formulate the general problem of economic organization and choice faced by all societies. We will then study the solution of the problem through the institution of a system of competitive markets. Both positive and normative aspects of the analysis will be em¬ phasized. The text will include discussions of some criticisms of both the positive analytical components of the model and the normative evaluations of the outcomes of market processes.

SUMMARY Economics is the study of the social organization of economic activity. Economic activity involves the allocation of scarce resources to competing material wants or objectives. Major emphasis in economic research has been given to explaining the role of markets and prices in allocating resources and coordinating economic activity. Many societies have evolved a system of markets to carry out the three coordination and resource allocation functions of deciding what to produce, how to produce it, and for whom goods and services are produced. However, other social institutions such as the family and the government also play roles in the economy. The study of economic processes involves both positive and normative analysis. Positive analysis seeks to explain patterns of economic activity by developing simplified models of economic processes. These models are tested by comparing their predictions with observations of the real world. Normative analysis seeks to provide an evaluation of the outcomes of economic processes by using some criterion such as efficiency or equity to rank alternative economic states. Economists have long wondered how a market economy maintains order and whether the outcome of market processes is good in some sense. The positive analysis of market systems has shown that when all firms and individuals in the system attempt to maximize their profit or well-being, the market provides opportunities for exchange and information in the form of prices. The exchange opportunities and price informa¬ tion provide the mechanisms of coordination that lead the market system toward an equilibrium. And if all markets are competitive, this equilibrium is good in the sense that no individual could better his or her position except at the expense of someone else’s economic welfare.

KEY CONCEPTS Economics Economic institutions Positive analysis Normative analysis Models

Hypothesis Prediction Theory Testing models

17

What Is Economics?

QUESTIONS AND PROBLEMS For Basic Review 1. Define and explain the economic significance of each of the key concepts. 2 * Classify each of the following statements as either a positive statement or a normative statement: a. Smoking tobacco causes cancer. b. Smoking tobacco is bad.

.

c. U.S. oil producers will increase their output of crude oil if the price of oil rises. d. U.S. producers of crude oil should produce more oil. 3. What are the three major functions of an economic system? 4 What is meant by the term “economic institution”? Give some examples of economic institutions and describe the role each plays in helping the economy carry out its three basic functions. 5. * How is an economic model to be judged good or bad, or perhaps it is better to say, useful or not useful?

.

6.

Discuss the relationships between microeconomics and macroeconomics as fields of study.

For Discussion 1. * Briefly outline the various approaches to defining economics as a subject. Discuss whether the following statements properly belong within the scope of economics as a subject: a. The allocation of land between farming and residential development. b. The allocation of land between growing timber and wilderness preservation. c. The allocation of time to various activities in a monastery that provides for its own food, clothing, and so on. d. The decision to marry and the choice of a mate. e. Once married, the decision as to whether to have children. f. The division of responsibilities within a family for child rearing, household work, and work outside the household. 2 * Suppose an economist presented you with a model that led to the hypothesis that if the tax rate on income from wages and salaries were raised, people would work longer hours. How would you go about testing the model?

.

SUPPLEMENTARY READINGS Blaug, Mark. The Methodology of Economics. Cambridge: Cambridge University Press, 1980, Chapters 1 to 5, 15.

*Answers to questions marked with an asterisk appear at the end of the book in the answer section.

18

Introduction

Friedman, Milton. The Methodology of Positive Economics, in Essays in Positive Economics. Chicago: University of Chicago Press, 1953. Knight, Frank H. The Economic Organization. New York: Harper & Row, 1951, Chapter 1. Nagel, Ernest. Assumptions in Economic Theory. American Economic Review, May 1963, 53(2), 211-219. Robbins, Lionel. An Essay on the Nature and Significance of Economic Science. Lon¬ don: Macmillan, 1935. Stigler, George J. The Theory of Price (3d ed.). New York: Macmillan, 1966, Chapter

1.

CHAPTER 2 Analytical Concepts: Optimization, Equilibrium, and Comparative Statics

T

-■*he purpose of this chapter is to introduce several important analytical concepts that will play a central role in the development of the theory in subsequent chapters. Most of microeconomic theory is built on the assumption that the individual agents or actors within the economic system (producers, consumers, suppliers of factors) all act in a rational, purposeful manner. In other words, economic agents are assumed to have some objective or goal and to plan their actions to achieve their objectives. Thus a major component of model building in microeconomics is modeling rational behavior in given circumstances. From this perspective, rational behavior can be viewed as attempting to maximize some objective, given certain circumstances such as the scarcity of re¬ sources that place constraints on the ability to achieve these objectives. This process is known as optimization. Developing a full understanding of the logic of optimization is important in learning microeconomic theory. As a general rule we do not observe economies to move rapidly and erratically from one pattern of production and consumption to another. Rather, economies appear to have some degree of stability in their patterns of microeconomic activity. This tendency toward stability can be modeled as a process of reaching and maintaining a position of equilibrium. Economic change involves changes in the conditions that determine an equilibrium position and the creation of forces that tend to move the economy toward the new equilibrium. The analysis of equilibrium positions and the comparison of equilibriums as economic conditions change constitute the principal techniques for generating testable predictions about economic phenomena. These techniques will be described in the sections titled, “Equilibrium” and “Comparative Statics.” All these topics can be discussed in verbal terms, with graphical models, or in terms of mathemat¬ ical relationships. These are alternative languages for expressing analytical concepts. We turn now to a discussion of languages to be used in economic analysis. 19

20

Introduction

LANGUAGES FOR ANALYSIS Virtually all the important concepts and relationships of microeconomics can be ex¬ pressed verbally, that is, without resorting to geometry or mathematics. Yet just as a sentence or paragraph can be translated from English into French, economic relation¬ ships can be translated from verbal language into the symbolic mathematical languages of graphs, geometry, and algebra. Mathematical languages often make it possible to express certain ideas with greater precision and economy. And as models and relation¬ ships become more complex, it is usually easier to perform the necessary manipulations to deduce hypotheses and predictions when models are expressed in a mathematical language. However, no matter how complex these manipulations, it should still be possible to present the essential features of the results of the analysis in verbal form. In this book we will rely primarily on verbal and graphical expositions of the material. We will also use the functional notation of algebra as a shorthand means of expressing certain relationships. Examples of more advanced mathematical analysis, primarily the calculus, are relegated to mathematical appendices to various chapters. These appendices are optional, and a clear understanding of the material in the text can be obtained without resorting to them. The mathematical appendices may help to show that mathematics is a powerful language, especially for the analysis of maximiza¬ tion and optimization problems. But there is a danger in excessive reliance on mathe¬ matics, particularly where complex economic concepts and relationships must be trans¬ lated into the necessarily simplified and abstract notation of mathematics.

Verbal Analysis We will illustrate the three alternative languages by stating the familiar law of demand, first verbally, then graphically, and finally, in algebraic functional notation. The law of demand states: For any commodity that can be purchased in a market, the quantity demanded in a given period of time varies inversely with the price, other things equal.

In other words, at higher prices, lower quantities will be demanded, and vice versa. Before showing how this law can be stated in other languages, there are several points to consider on the nature and derivation of this law. First, as we will show in Chapter 7, this law can be deduced from a model of individual behavior following the procedures outlined in Chapter 1. The model is one of optimization based on the assumption that individuals maximize their well-being subject to constraints on their spending. This means that the law can be stated as a prediction or hypothesis: If the price of a good changes, other things equal, the quantity demanded of the good will change in the opposite direction. The model also shows that the quantity demanded of a good depends on the incomes of individuals and on the prices of other goods that are available in the market. But the phrase “other things equal” means that the law applies only to those situations where only the price of the good in question is changed.

21

Analytical Concepts

Second, this hypothesis has been tested by observing the relationship between quan¬ tity and price for many different goods in a wide variety of circumstances and historical settings. Some examples of tests of the hypotheses of demand theory will be presented in Chapter 8. Because of its overwhelming success in these tests, the model has taken on the status of a theory, and the hypothesis of the downward-sloping demand curve has come to be accepted as the law of demand. The third point is the importance of the phrase “other things equal.” This phrase limits the applicability of the law to those instances in which the price of the good changes, but there are no changes in any of the other variables that might influence the quantity demanded, in particular, the incomes of buyers and the prices of other goods. This phrase helps to define the circumstances in which the law of demand is presumed to be valid and the conditions that must hold when the hypothesis is tested. If, for example, an increase in the price of X were accompanied by an increase in the incomes of individuals, we might observe an increase in the quantity demanded. If we observed an increase in the quantity demanded, this would not mean that the law of demand was invalid, only that it could not be applied when other things such as income were not equal or unchanged. The phrase implies that the law of demand is a statement on the effect of a change in price on quantity demanded; it is not a statement on the combined effects of changing prices and incomes on the quantity demanded. The phrase “other things equal” (or its Latin equivalent, ceteris paribus) will be used frequently in this text to limit the circumstances under which hypotheses and predictions are held to be true.

Graphical Analysis The translation of the law of demand into the language of graphs is shown in Figure 2.1. The vertical axis measures the price of the good, and the horizontal axis mea¬ sures the quantity demanded per period of time. The downward-sloping demand curve shows that the quantity demanded increases as the price decreases, and vice versa. Because there are no scales or numerical units on the horizontal or vertical

Figure 2.1

The Downward-Sloping Demand Curve and the Law of Demand.

22

Introduction

axes of this figure, it does not convey any information about the magnitude of the change in quantity. Like the verbal statement of the law of demand, the figure is only a qualitative statement about the direction of change. Suppose that through empirical research the following data had been obtained on the relationship between the price of X and the quantity demanded, other things equal. Price of X

Quantity demanded per period

5

0

4

20

3

40

2

60

1

80

0

100

This relationship can be graphed as in Figure 2.2. And quantitative statements can be made about the magnitude of the change in quantity for a given change of price. In this simple example a $1 increase in price leads to a 20-unit decrease in the quantity demanded. Also, the quantities demanded at other prices (e.g., at a price of $3.50) can be found from the graph (30 units).

Algebra An algebraic statement of the law of demand is = f(Px)

Figure 2.2

X per period The Demand Curve as a Graph of Price and Quantity Data.

23

Analytical Concepts

where XD = quantity demanded of good X per period Px = price of X This states that there is a functional dependence of XD on Px, that is, Px is the independent variable and XD is the dependent variable. The functional notation /(•) indicates that the precise nature of this relationship is unspecified. To convey the full statement of the law of demand, one should add that/(-) is an inverse relationship. This functional relationship might also be written as XD = XD(Px)

where XD(-) indicates that this is a demand relationship. As previously discussed, in the model from which the law of demand is deduced the quantity demanded also depends on incomes and the prices of other goods. A more general algebraic statement of the demand relationship would incorporate these other variables: ■D

= XD(PX, Py, M)

Py and M are held constant by assumption when the relationship between the quantity demanded of X and its price is analyzed and when the demand curves of Figures 2.1 and 2.2 are drawn. We will use asterisks (*) to indicate which variables are held constant in any specific analysis. For example, the law of demand applies when XD — X D(Px P y, M )

On the basis of empirical research it may be possible to derive a specific equation that describes the quantitative dependence of the quantity demanded on price. The demand relationship plotted in Figure 2.2 has the following form: = a

bP,

As can be verified by examining the graph or the preceding tabular data, a = 100,

b = 20

and xn = 100 - 20P, With this expression it is possible to make numerical predictions about the quantity demanded at alternative prices. What will the quantity demanded be if the price is $2.25?

OPTIMIZATION Most of the positive and normative analytical questions in microeconomics can be formulated as optimization or maximization problems. An example of an optimization problem in normative analysis is the determination of a maximum of social welfare. One could define a variable called social welfare and postulate that social welfare depends

24

Introduction

on (is a function of) the quantities of certain goods produced by the economy. The analytical problem is to maximize social welfare by choosing the appropriate levels of output for the goods that contribute to social welfare. At a more mundane level, consider a government official who is charged with maximizing the net economic benefits to be derived from developing the water resources of a river basin. The possible outputs include water for irrigation, water for drinking and other human uses, recrea¬ tion opportunities, and reduced damages from floods. The problem for the official is to choose the levels of all the possible outputs from development of the river basin so as to maximize net economic benefits. After a maximization problem of this sort has been formulated and solved by using appropriate mathematical techniques, the econo¬ mist can give a prescription or recommendation to policymakers concerning what actions to take to achieve their stated objectives. Recall from Chapter 1 that the objective of positive analysis is to make predictions about economic phenomena. Because economics is a social science, we must, therefore, typically seek to make predictions about human behavior. A basic postulate of econom¬ ics is that human behavior can best be understood as the response of rational, selfinterested people to the constraints and opportunities provided by their economic environment. Rational behavior can in most circumstances be interpreted to mean maximizing behavior. Thus the positive analysis of human economic behavior can be approached by using the following steps: 1. Define the variable to be maximized. For an individual this is his or her own well-being or utility. A producer is assumed to strive to maximize profit. The thing to be maximized is called the maximand. The maximand must be a function of variables that are under the control of the individual. 2. Specify the functional relationship between the maximand and the variables that are under the control of the individual. This relationship is called the objective function. It gives the maximand as a function of variables under control of the economic agent whose behavior is being analyzed. These variables are called choice variables. 3. Solve for the optimizing or maximizing values of the choice variables. If the precise form of the objective function is known, the solution of the maximum problem will give the numerical values for the choice variables. But if only the general form of the objective function is known, the solution to the problem will be a set of maximum conditions that must be satisfied if a given solution is to be a maximum.

.

4 Examine the economic implications of the maximum conditions. The economic implications involve considerations of equilibrium and comparative statics, concepts that will be explained in the next two sections.

The Logic of Maximization Maximization without Constraints. The simplest form of the maximization problem is one in which the maximand is a function of only one variable and there are no limits

25

Analytical Concepts

or constraints on the values that the choice variable can take. Verbally, this type of problem can be stated as: Choose a numerical value for the variable X so as to maximize the numerical value of Y where the numerical value of Y depends on X. In algebraic notation this problem is written as follows: Maximize Y — f(X)

The variable Y could refer to a simple concept such as welfare or utility; or it could refer to a compound variable such as profit (defined as total revenue minus total cost) or net benefit (defined as total benefit minus total cost). In the latter case Y refers to the net benefit or net return to the variable X. Suppose that the relationship between Y and X is as shown in Table 2.1. The first two columns of this table are portrayed graphically in Figure 2.3(a). The table and the figures show that as X increases from 0 to 40, Y increases but at a decreasing rate. As X increases past 40, Y decreases. Therefore Y reaches a maximum when X is 40. This is the solution to the maximization problem. The logic of maximization can be seen more clearly if we examine how Y changes as X increases. This analysis of the relationship between changes in one variable and changes in another is central to much of microeconomic theory. It is known as marginal analysis. The third column of Table 2.1 gives the change in Y for each 10-unit change in X. Each entry in the third column is oriented halfway between the beginning and end points of the intervals for X and Y to show that it refers to the change over the whole interval. The fourth column of Table 2.1 indicates the change in Y for a one-unit change in X as estimated at the midpoint of the interval.

Table 2.1

The Relationship Between Y and X The marginal net return to X in units of Y

The value for X 0 10

The value for Y

30

150

60

+ 70

+7

+ 50

+5

+ 30

+3

+ 10

+i

-10

-1

-30

-3

70 120

50

(AY/ AX)

0

20

40

The change in Y(AY)

0

160 150 120

26

Introduction

Figure 2.3

The Graph of Y as a Function of X and the Marginal Net Return of X.

Definition: The marginal net return to X is the change in Y for a one-unit change in X. Graphically, the marginal net return is the slope of the curve showing the relation¬ ship between Y and X. The marginal net return to X is plotted in Figure 2.3(b). As X increases from 0 to 40, the marginal net return to X is positive but decreasing. When X reaches the value of 40, the marginal net return to X is 0. The last small increase in X adds nothing to the value of Y. At this point Y is at a maximum.

27

Analytical Concepts

The First Rule for Maximization: When the maximand is the function of only one variable, maximization requires that the choice variable be increased as long as its marginal net return is positive. The maximum is achieved when the marginal net yield has decreased to zero.1

Maximization with Constraints. A more common form of the maximization prob¬ lem in microeconomic analysis is one in which the maximand is a function of two or more choice variables and in which there exists some constraint or limit on the values that the choice variables can take. Such a constraint is a reflection of economic scarcity. Suppose that Robinson Crusoe has decided to allocate 4 hours per day of his scarce time to hunting birds for food. He can hunt in either the woods or the fields or divide his time in some manner between these two areas. He wishes to maximize the number of birds caught per day. Suppose that the returns in the form of birds caught for different total hours of hunting in each area are as shown in Table 2.2. How should he allocate his hunting time in the woods and fields? One way to find the solution to this constrained maximization problem is by trial and error, that is, to find the total number of birds for all possible combinations of hunting times in the two areas. For example, with 0 hours in the woods and 4 hours in the fields the total return is 5 birds. For 1 hour in the woods and 3 hours in the fields the total return is 13 birds. A less tedious approach, based on marginal analysis, is to allocate the first hour to the area with the highest marginal net return. The marginal net returns are also shown in Table 2.2. Because the marginal net return of the first hour of time is greater in the

Table 2.2

Robinson Crusoe’s Hunting Productivity Fields

Woods

Hours

Birds

0

0

Marginal net return

Hours

Birds

0

0

1

3

2

5

3

6

4

5

+3

+7

1

7

+2

+5 2

12

3

15

+1

+3

-1

+i 4

16

-2

-i 5

15

Marginal net return

5

3

'This rule is derived using the calculus in the Mathematical Appendix to this chapter.

28

Introduction

woods ( + 7 vs. +3), at least 1 hour should be spent hunting in the woods. Each successive hour should be spent in the area with the highest remaining marginal net return until the total available time has been exhausted. The highest attainable total return, 18 birds, occurs when 3 hours are spent in the woods and 1 hour in the fields. Notice that in this allocation of hunting time the marginal net returns of hunting activity in the two areas are equal. The Second Rule for Maximization: When the maximand is a function of more than one choice variable and when there are constraints on the values that the choice variables can take, maximization requires that the marginal net returns in all activities be equal.2 Whenever the marginal net returns of the two activities are unequal, it is possible to increase the total return by reallocating the scarce resource away from the activity with the lower net return and toward the activity with the higher net return. In the case of the Robinson Crusoe example suppose the marginal net returns in the woods and fields were six and four birds, respectively. Reallocating one unit of time from the fields to the woods would increase total return by two birds (—4 + 6). Only when the marginal net returns are equal is it not possible to find some reallocation that would increase total return. Suppose now that Robinson Crusoe decides to allocate 9 hours per day to hunting. The allocation that equalizes the marginal net returns is 5 hours in the woods and 4 hours in the fields. But notice that the marginal net returns of the last hour spent in each area are negative. Actually, the maximum possible return of birds is 22 per day which can be obtained when only 7 hours per day are spent hunting (4 hours in the woods and 3 hours in the fields). In this case the constraint of 9 hours per day is not binding; that is, the objective function can be maximized without using the maximum number of hours allowed by the constraint. If the constraint is not binding, then a variation of the first rule for maximization should be followed: Where possible, carry all activities out to the level where their marginal net returns are equal to 0. These two rules for maximization in one form or another underlie our analysis of individual behavior in Chapters 7, 8, 12, and 13 and the behavior of firms in Chapters 9, 11, 12, 15, and 16. By the end of the book the student should seethe common threads of logic running through all our models of behavior and choice where maximizing behavior is assumed and should be able to apply this logic to maximization problems in other settings as well.

EQUILIBRIUM In general terms an equilibrium means a state of balance between opposing forces such that there is no tendency for movement or change. This definition can be applied to economic models.

This rule is derived using the calculus in the Mathematical Appendix to this chapter.

29

Analytical Concepts

Definition: An economic system is said to be in equilibrium when there is no tendency for any of the variables of the system to change. For example, an individual is said to be in equilibrium with respect to her consump¬ tion pattern when she has no incentive to alter her pattern of consumption. If she had not attained the consumption pattern that maximized her well-being (subject to the constraints of limited income, etc.), she would have an incentive to change her con¬ sumption. Therefore an individual can be in equilibrium only if she has achieved the appropriate solution to her maximization problem. The concept of equilibrium also applies to models of industries and markets. These models focus on the interaction of maximizing individuals and firms. All the agents in a model must be in equilibrium with respect to their own maximizing problem in order for the larger model to be in equilibrium. But usually additional conditions must also be satisfied for the full model to be an equilibrium. This point can be illustrated with a simple model of a market for a good. We will state this model and its equilibrium conditions in verbal terms and then show how the same conclusion can be stated graphically and algebraically.

The Equilibrium of a Market A Verbal Analysis. According to the law of demand, the quantity demanded by buyers in a market varies inversely with the market price, other things such as buyers’ incomes held constant. Assume also that the quantity supplied to the market varies directly with the market price, other things such as the prices of the factor inputs held constant. In other words, as the price increases, suppliers act to increase the quantity supplied to the market. The equilibrium condition for the market is that the quantity demanded be equal to the quantity supplied. If the market price is such that the quantity demanded exceeds the quantity supplied, the equilibrium condition is not satisfied. The market price must be increased so as to reduce the quantity demanded and to increase the quantity supplied, thus bringing them into equality with each other.

A Graphical Model.

A graphical version of the model is shown in Figure 2.4. The downward-sloping demand curve portrays the inverse relationship between the price and quantity demanded. The upward-sloping supply curve shows that the quantity supplied is greater at a higher market price. For both the demand and supply curves other things such as income and factor prices are assumed constant. Because buyers and sellers face the same price in the market, the quantity demanded can equal the quantity supplied only where the demand curve and the supply curve intersect. In equilibrium both the market price and the market quantity are determined simultane¬ ously.

Algebraic Analysis. An algebraic statement of the model makes it possible to consider more variables in an explicit manner. It also enables us to see more clearly which variables are determined within the model (endogenous variables) and which variables

30

Introduction

are determined outside the model and taken as given in the solution of the model (exogenous variables). In the verbal and geometric version of the market model income was assumed to be constant so that the model could focus on the effect of price on the quantity demanded. Now let us assume that the quantity demanded also depends on income (M)—at higher incomes more is demanded. This can be expressed in algebraic notation as XD = XD (Px, M)

Similarly, factor prices (PF) affect the quantity supplied. At higher factor prices produc¬ tion is more expensive and less is supplied at any given price of output. In algebraic notation (Px, PF)

Finally, in equilibrium quantity demanded must equal quantity supplied, or Xs = XD

This is a system of three equations in three unknowns, Px, XD, and Xs. These are the endogenous variables of the model whose values are to be determined. M and PF are exogenous variables whose values must be given in order to solve the model. If they were to change, the equilibrium of the model would change. Suppose that empirical research had enabled us to determine the exact form of the supply and demand equations. For example, suppose that the demand and supply relationships are:

31

Analytical Concepts

(i) XD = a — bPx + cM (ii) Xs = d + eP x — fP F (iii) The small letters are the parameters of the model that help to determine its properties. Each parameter can be given an economic interpretation. For example, the minus sign on b shows that if Px increases, XD decreases. The positive sign on c shows that an increase in M will increase the quantity demanded. The positive sign on e means that increases in product price lead to increases in the quantity supplied. An an increase in the prices of factor inputs will make production of X more costly and lead producers to supply less, other things including the price of X held constant. Using (iii) to set (i) and (ii) equal to each other gives a — bPx + cM — d + ePx — fPF

This can be solved for the equilibrium value of Px: a ~ d + cM + fPF

Px =

(2.i)

e + b

This is known as a “reduced form” equation. Definition: A reduced form equation expresses an endogenous variable of the model as a function of the model’s parameters and its exogenous variables. A similar reduced form equation can be found for the equilibrium value of X. Alternatively, the equilibrium value of X can be found by substituting the solution for Px into the demand and supply equations. Thus the equilibrium price and quantity depend on the parameters and the values of the exogenous variables of the model.3 3For example, suppose that the parameters and coefficients of the model have the following values: a = 100

d = 0

M = $20

b = 20

e = 20 PF = $10

c = 10

/ = 2

Plugging these values into the reduced form equation for Px gives 100 - 0 + 10 X 20 + 20 Px = 20 + 20 =

$8

Plugging this into the demand equation gives XD = 100 - 20 X 8 + 10.20 = 140

Also,

Xs = 0 + 20 X 8 — 2.10 = 140

32

Introduction

It can reasonably be doubted that any real-world economy ever reaches and main¬ tains a true equilibrium. It is probably better to interpret the term equilibrium to be a property of models rather than of real economic systems. Nevertheless equilibrium can be a useful concept for economic analysis, at least if it is possible to identify the forces in a real-world economy that tend to move the economic system toward a given equilibrium position. Then equilibrium can be interpreted as a target. And if the position (or at least the general direction) of the target can be determined, the direction of movement of the economic system can be predicted. Consider again our model of the market for good X. Suppose that the price of X is below the equilibrium price, say, Pxl, as shown in Figure 2.4. Given this price, the quantity demanded is greater than the quantity supplied. The market is not in equilib¬ rium. Some buyers must be out of equilibrium in the sense that at the market price they wish to buy more than is physically available. Suppose that those people with un¬ satisfied demands begin to offer prices above Pxl in an effort to bid away some of the good from other buyers. Also, suppliers must be turning away potential customers because they are unwilling to supply more than As,atthe initial market price of PX1. Suppliers may realize that they can increase their revenues by charging higher prices. These two forces will tend to push up the market price as long as, at any given price, the quantity demanded exceeds the quantity supplied. If the market price is above the equilibrium price, the quantity supplied exceeds the quantity demanded. Suppliers will have unsold goods; and at least some suppliers will offer to sell them at prices below the going market price. Thus if price is above the equilibrium and there is excess supply, market forces will tend to push the price down. The upward pressure on price when there is excess demand and the downward pressure on price when there is excess supply tend to push the market price toward the equilib¬ rium price. If the equilibrium is constantly changing because of changes in the exogenous varia¬ bles of the model, these forces may never make the market price exactly equal to the equilibrium price at any instant in time; but they will always work to move the market price toward the ever-shifting target. If we can determine the direction in which the equilibrium target has shifted, we can predict the direction of changes in the endoge¬ nous variables of the model.

COMPARATIVE STATIC ANALYSIS In the first chapter we mentioned that economic knowledge was advanced by deducing and testing hypotheses about the behavior of economic systems. Comparative static analysis is one of the most fruitful approaches to using models to make predictions and to deduce hypotheses. Comparative static analysis of a model involves the comparison of two static equilibrium positions that differ because of changes in one or more of the exogenous variables in the model.

33

Analytical Concepts

Definition: Comparative static analysis is the prediction of the change in an endoge¬ nous variable of the model as a consequence of a postulated change in one of the exogenous variables of the model. At the level of theoretical analysis, comparative static analysis can only predict the direction of change in certain variables. But if statistical techniques have been used to estimate the parameters of a model, it may be possible to predict the magnitude of the change in an endogenous variable as well. Models are tested by comparing the predic¬ tions of comparative static analyses with the observed changes in variables when the conditions of the model are observed to hold. As a simple example of comparative static analysis, consider the model of the market for X developed in the preceding section. One can ask of the model: What will happen to the price of X if the incomes of consumers increase? Verbally, if incomes increase, at any given market price consumers will wish to purchase a larger quantity. This increase in the quantity demanded will tend to bid up the price. The comparative static prediction can be stated as follows: If consumer incomes increase, other things equal, market price will increase, and the quantity demanded will increase.

A graphical version of the model is shown in Figure 2.5. With the original income level the demand curve is D, and the equilibrium is at Pxl and V,. The increase in income will lead to an increase in the quantity demanded at any given price. In other words, the demand curve will shift out and to the right to D2. This curve intersects the supply curve at a higher price, PX2, and a higher quantity, X2. Again, the direc¬ tion of the change in price can be predicted from analysis of the simple model.

X per period Figure 2.5

The Comparative Static Analysis of a Shift in Demand.

34

Introduction

If the model can be expressed algebraically as in equations (i) to (iii) of the preceding section, and if the parameters of the model are known, the magnitude as well as the direction of change can be predicted. The reduced form equation gives Px as a function of the parameters and exogenous variables. The change in price can be predicted by solving this equation for Px with the original and new values for income (M) on the assumption that the values for the parameters do not change.4 Can you predict the direction of the changes in Px and X when Ph increases? Much of the analysis in this textbook involves using verbal and graphical models to deduce qualitative comparative static hypotheses. In each case it the functional forms and parameters of the models were known, it would also be possible to make predictions about the magnitude as well as the direction of the changes in the endoge¬ nous variables.

SUMMARY The principal conclusions of microeconomics can be arrived at through verbal reason¬ ing, graphical analysis, or mathematical reasoning. Many of the major conclusions of microeconomic theory are reached by assuming that economic agents are striving to maximize something such as well-being or profit and then deducing the implications of maximizing behavior. When an individual’s objective function contains only one choice variable and there are no binding constraints on choice, the first rule of maximi¬ zation calls for choosing that level of the choice variable where its marginal net return is zero. Where the objective function contains more than one choice variable and when there are constraints on the range of choice, the second rule of maximization requires that the choice variables be chosen so that the marginal net returns of all the variables are equal to each other. An economic system is in equilibrium when there is no tendency for any variables in the system to change. A model of an economic system can be solved to determine the equilibrium position of the model. The position of equilibrium depends on the conditions of the model and the values for exogenous variables. When conditions are postulated to change, the equilibrium of the model changes. Comparative static analysis is the comparison of different equilibrium positions under varying conditions. It is the basis for deducing hypotheses and predictions about the direction and magnitude of changes in economic variables.

KEY CONCEPTS Maximand Objective function

Exogenous and endogenous variables Optimization

4An example is shown in the Mathematical Appendix to this chapter.

35

Analytical Concepts

Marginal net return Maximization without constraints Constrained maximization with two or more variables

Comparative static analysis Other things equal

QUESTIONS AND PROBLEMS For Basic Review 1. 2.

Define and explain the economic significance of each of the key concepts. Explain the role and significance of the assumption of maximizing behavior in the construction of economic models. State the two rules for maximization. Provide a verbal explanation or proof of the validity of each of these rules. 3. * Provide a verbal translation of the following algebraic statements: a. X$ = Xs(Px, PF)

b. x , = x jpx, p;}

Problems 1. A college student who is cramming for final exams has only 5 hours of study time remaining. His goal is to get as high an average grade as possible in three subjects: economics, mathematics, and government. He must decide how to allocate his time among the subjects. According to the best estimates he can make, his grade in each subject will depend on the time allocated to it according to the following schedule: Economics Hours of stud) 0 1 2 3 5

Mathematics Grade 25 50 60 67 73 77

Hours of study 0 1 2 3 4 5

Government Grade 40 55 65 74 80 83

Hours of study 0 1 2 3 4 5

Grade 78 88 94 98 99 100

a. How should the student allocate his time? Study economics_, study mathematics_, study government_Explain how you got your answer. b. What is the marginal net return in terms of grade average of the sixth hour of study? 2.* You are given the following information. The equations for the quantity demanded and quantity supplied are: XD = 1000 - 50Px -V- 10Py

36

Introduction

Y5 = 75 + 25Px - 50PF PY = $10 PF = $5

3.

a. Plot the supply and demand curves and find the equilibrium price and quantity of X. (Alternatively, use algebraic analysis to find the equilibrium values.) b. Predict the direction of the changes in Px and X given that P Y increases. Explain your reasoning. c. Predict the magnitude of the changes in Px and X given that PY increases to $17.50. (The answer can be found by either graphical or algebraic analysis.) d. Predict the direction of the changes in Px and X given that PF increases. Explain your reasoning. e. Predict the magnitude of the changes in Px and X given that PF increases to $6.50. (The answer can be found by either graphical or algebraic analy¬ sis.) Use the comparative static model of the market developed in this chapter to deduce the consequences of a decrease in factor prices on the equilibrium price and output. Discuss how you would go about conducting an empirical test of this prediction.

SUPPLEMENTARY READINGS Elenderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach (3d ed.). New York: McGraw-Hill, 1980, Appendix, pp. 358-395. Samuelson, Paul A. The Foundations of Economic Analysis. Cambridge, Mass.: Har¬ vard University Press, 1947, Chapters 1, 2, 3. Silberberg, Eugene. The Structure of Economics: A Mathematical Analysis. New York: McGraw-Hill, 1978, Chapter 1.

MATHEMATICAL APPENDIX TO CHAPTER 2 The mathematical appendices to the various chapters present mathematical derivations of some of the principal conclusions of the text.

Functional Notation The simplest version of the law of demand is Xd = XD {Px) dPx

< 0

The inequality makes explicit the inverse relationship between Px and XD.

37

Analytical Concepts

The general statement of the law of demand is XD — XD (Px, P y, M)

sPx

dPY dX, dM

|

0

> 0

The partial derivatives show the change in the dependent variable for a small change in each independent variable, holding all other variables constant (other things equal).

Maximization The calculus is well suited to the analysis of maximization problems. When there is only one choice variable and there are no constraints on its value, maximization requires that the first derivative of the objective function be set equal to zero. The second-order condition is that the second derivative be negative. The problem is to maximize Y = f(X) where Y is the maximand and f(X) is the objective function. The solution is dY first-order condition:- = 0

dX d2Y

second-order condition: -

< 0

dX2 This requires that the derivative of the objective function be decreasing in the region of the solution. The relationship shown in Table 2.1 and Figure 2.2 of the text is Y = 8X - 0.1X2 The solution to the maximum problem is dY - = 8 - 0.2X = 0 dX X = 40 d2Y

0.2 < 0

dX2 The problem of constrained maximization can be solved through the device of the Lagrangian multiplier. The basic structure of the problem is

38

Introduction

Maximize: Z — f(X, 7) Subject to: g(X, 7) = 0

The example of the text fits this structure if the maximand Z is assumed to be birds caught, X and 7 are hours spent hunting in the fields and the woods, respectively, and the total hours spent hunting cannot exceed T. Thus the constraint would be g(X, Y) = T - X - Y = 0 The technique is to form a new expression that incorporates the constraint Maximize: Zx = f(X, Y) — A. (T — X — Y)

If the constraint is satisfied, the second term in parentheses is zero and Zx = Z. The maximum of this expression can be found by taking the first partial derivatives with respect to X, Y, and X and setting them equal to zero. dZ _ = - + X = 0 aY dX aZ d zx = - + X = 0

dZx

(i) (ii) (iii)

dY dZx

dY = T — X — Y

dX

Condition (iii) states that the constraint must be satisfied. The first two conditions can be reduced by substitution to aZ

_ aZ

dX

a7

These two terms are the marginal net returns to X and Y, respectively, both measured in units of Z. They must be equal to each other. For a discussion of the second-order conditions, see James M. Henderson and Richard E. Quandt, Microeconomic Theory: A Mathematical Approach (3d ed.). New York: McGraw-Hill, 1980, Appendix.

The Comparative Statics of the Market Model As shown in the text, the reduced form equation for Px is n

Fx —

a — d + cM + fPF ~ e + b

The predicted change in Px for a given change in M, AM, is found from XPx — PX2 — P xi where Pxl is given by the reduced form equation and PX2 is found by substituting (M + AM) for M in that equation. That is, n P X2

a — d + c(M + AM) + JPF e + b

39

Analytical Concepts

This gives A Pi¬

et — d

c

c

f

- + -M + —- A M + —--PF e + b e + b e + b e + b a — d c M-—— P. e + b e + b e + b c

AM

e + b

Because of the positive signs on all the terms in this expression, we can say that

e + b

and therefore any change in M must be accompanied by a change in Px in the same direction. Similarly, the reduced form expression for X could be used to predict the magnitude of the change in the equilibrium quantity. The calculus often provides a more direct route for deducing comparative static hypotheses. The partial derivative of a reduced form equation gives the change in the endogenous variable as a function of the relevant exogenous variable. In this case, given the reduced form equation, tpx

dM

=

c

e + b

PARTII The Economic Problem: Allocating Scarce Resources

CHAPTER 3 The Allocation of Resources in Production

A we saw in Chapter 1, all societies must have some form of economic institution for carrying out three tasks: deciding what to produce, how to produce it, and who gets the output. The purpose of this and the next two chapters is to develop a simple model for the analysis of these three aspects of the general resource allocation problem faced by all societies. The model is descriptive and cannot be used to make predictions about behavior or outcomes. Nevertheless it will prove to be useful in clarifying what conditions limit or constrain the range of choices about what is produced and how. It will also provide a basis for evaluating alternative outcomes as either good or bad, or at least as better or worse. In this chapter we will show that society’s range of alternatives is limited by the available supply of factor inputs for production and the available technology for converting inputs into outputs. In the next chapter we will assume that the way economic systems perform the resource allocation task should be judged in terms of how well they are able to satisfy individuals’ preferences or demands for goods; and we will develop a model for describing and analyzing those preferences. Then in Chapter 5 we will show that any society must satisfy three conditions of economic efficiency if it is to be considered as doing a satisfactory job in performing its resource allocation functions. The analysis proceeds without any reference to particular forms of economic institu¬ tions such as decentralized markets, centralized planning and command, or cooperative and communal sharing. The model of production, preferences, and choice can be applied to the economic problem facing any society. And the conditions of economic efficiency that emerge from the analysis have universal applicability. A major component of the model is the production possibilities frontier. 43

44

The Economic Problem: Allocating Scarce Resources

Definition: A production possibilities frontier is a locus of maximum attainable pro¬ duction combinations. It shows the maximum amount of one good that an economy can produce for any given level of production of the other goods. Figure 3.1 shows a production possibility frontier for a very simple economy in which there are only two goods, X and Y. This curve indicates that society could choose an output combination represented by point A with Xx units of X and units of Y produced per period of time, say, per week. Alternatively, it could choose output combination point B with more X and less Y. Any point on the frontier is attainable. Point C, although perhaps more desirable, lies outside the frontier and hence is not attainable by this economy. Also, any point such as D lying inside the frontier is attainable. But if goods are valued by individuals, points such as D would not be preferred because it would be possible to have more of good X or good Y or both by moving from D to the frontier. Our first task is to show what determines the position of the production possibilities frontier and under what circumstances economies might wind up inside the frontier at points such as D. To do this, we must examine the conditions governing production, that is, the relationship between inputs and outputs.

THE PRODUCTION FUNCTION Production is the process of transforming inputs into desired outputs. Production processes are governed by the underlying laws of physics, chemistry, and biology and by our understanding of technology. Definition: A production function is a quantitative expression that specifies the relationship between the level of inputs to the production process and the resulting

Output of X per period Figure 3.1

The Production Possibilities Frontier.

45

The Allocation of Resources in Production

output level. The relationship is based ultimately on technological data. It can be viewed as the engineer’s recipe for production. For purposes of this analysis we assume that the state of the art or existing technology is given and constant. An innovation or invention of a new and better way of producing a good would be represented as a change in the production function. Assume that there are only two types of inputs or factors of production, capital (K) and labor (L). In general, the production function for good X can be written as X = X(K, L) where K and L denote the rate of utilization of the services of homogeneous capital and labor, respectively. Production is treated here as a process that goes on at a given rate per unit of time. Thus X is the rate of output, for example, per week, and K and L represent the flows of inputs per unit of time. It may be convenient to think of X as a tangible commodity, for example, food. But X can also represent intangibles such as electricity or services such as medical care, legal advice, or teaching. In a more general model X could represent an intermediate good that itself is an input into further production processes. For example, wheat is an output of agricultural production but is an input in the production of various foods. However, in our simple model we will assume that all outputs are final goods that will be used or consumed by households. Although production might be described as a process of transforming inputs into outputs, we do not mean that workers are physically transformed during production. It is the services of workers that are the true inputs into production. The unit of labor input is the use of one worker for a specified period of time, say, one day. Thus if output is measured in units of X per week, the labor input is measured in units of “worker days” per week. Similarly, capital is not being directly consumed in the production process. It is only the services that capital provides that are being used up. The capital input to the production process is the services from one unit of capital for one day. And the input of capital is measured in “capital days” per week. Of course, capital (machines, etc.) is gradually worn out or depreciated by its use in production. If the capital stock is to be maintained at a given level over time, the owners of capital must undertake repairs and upkeep sufficient to counter the effects of physical depreciation.

Isoquants Production functions are specified for a given state of knowledge or level of technology. For any good the production function and its underlying technology can be portrayed graphically by a set of isoquants. Definition: An isoquant is a locus of all technically efficient combinations of inputs of labor and capital that will produce a given rate of output. For each rate of output it shows the minimum combinations of capital and labor that are necessary for produc¬ tion.

46

The Economic Problem: Allocating Scarce Resources

Figure 3.2 shows a typical isoquant for good X. One hundred units of X can be produced each period by combining 10 capital days of capital with 7 worker days of labor as shown by point A. Point B shows that the same output rate can be achieved by using less capital, say, 5 units, and more labor, 12 units. Any other combination of labor and capital on the isoquant is also capable of producing 100 units per period. At points such as C above and to the right of the isoquant, output should be at least 100 per period. But C represents more capital and labor than is necessary to produce 100 units per period. If production is technically efficient, then output should be above 100 units. Thus there is another isoquant through point C which stands for a higher level of X production. In fact, a production function consists of a whole family of isoquants each of which represents a different level of output. Isoquants and the production functions they portray represent a given technology. A technological improvement is an invention or innovation that reduces the amount of capital and/or labor required to produce a given output, or, what is the same thing, makes it possible to produce a greater output with a given input. Technological improvements shift the isoquants inward toward the origin. In Figure 3.2 a techno¬ logical improvement might make it possible to produce 100 units of X with, say, 9 units of capital combined with 6 units of labor, or 4 units of capital and 11 units of labor. The new X = 100 isoquant would have to pass below and to the left of points A and B.

On contour or relief maps contour lines show the height of the land above sea level. An isoquant diagram is a map of production where height measures the rate of output. Figure 3.3 is a three-dimensional diagram where the vertical dimension measures output levels. The horizontal axes measure the inputs of labor and capital as before. The surface labeled OABC is a production surface. For a point on the surface such as E, the height of the surface represents the maximum attainable level of output given the inputs of capital, OK , and labor, OL\. Lines such as DEF and GHI are contours of equal height or output. The isoquants of Figure 3.2 are simply the projections of these

Input of capital per period

X = 100 per period

Figure 3.2

An Isoquant.

47

The Allocation of Resources in Production

Figure 3.3

A Production Surface.

contour lines on to the two-dimensional surface represented by OAJC. These are shown as D'E'F' and G'HT. The isoquants of these two diagrams indicate that many possible combinations of capital and labor can be utilized to produce a given quantity of output. Starting from point D in Figure 3.3 one can reduce the capital input and increase the labor input, that is, to substitute labor for capital over quite a wide range while holding the output level constant at 100. Production functions with this characteristic are known as variable proportions production functions. Also, the production technology might be such that labor and capital can be com¬ bined only in fixed or constant proportions. For example, suppose that the only physi¬ cally possible way of producing X is to combine inputs in the ratio of two worker days to one capital day. This might be because production requires a machine of a particular design that utilizes two operators. Suppose further that 20 worker days plus 10 capital days produce 100 units of X and that doubling the inputs results in doubling the outputs. This production function is shown in Figure 3.4. The solid lines with the corners at points A and B are the isoquants for 100 and 200 units of X. If 20 worker days of labor are combined with 20 machine days of capital (point A'), output would not be increased and the extra capital would, in effect, be wasted. Now assume that there is also a second process for producing good X. Suppose that because of a different machine design, 10 units of labor can be combined with 20 units of capital to produce 100 units of X. The family of isoquants associated with this

48

The Economic Problem: Allocating Scarce Resources

K per period X= 100

30

20

X = 200

10

X= 100

i

20

10

30

40 L per period

Figure 3.4

A Fixed Proportion Isoquant.

process has corners such as at point C. The addition of the second process adds a surprising degree of flexibility in choosing combinations of inputs since the X = 100 isoquant now includes the line segment between points C and A. That is, it is possible to utilize the two processes simultaneously but at reduced levels. For example, the two processes might be operated at the following levels: First process: 10L + 5K = 50X Second process: 5L + 10K = 50X Total: 15L + 15 K = 100X

The total input requirements are indicated by point D in Figure 3.4. And since total output of the two processes combined is 100X point D must be on the X = 100 isoquant. With more than two separate fixed proportion processes the true isoquants would include the line segments drawn that connect the corners of each of the right angle isoquants. With more and more alternative fixed proportion processes the isoquants more closely resemble the smooth continuously curved isoquants of Figures 3.2 and 3.3. This demonstrates that even when production with a given process or machine design is characterized by fixed proportions, if production managers can choose among alternative processes and machines, their range of choice can be portrayed by a variable proportion production function and a family of smoothly curved iso¬ quants.

Long Run Versus Short Run In practice, changes in the level of output and substitution between inputs take time to plan and accomplish. For example, it takes time to acquire and install additional

49

The Allocation of Resources in Production

capital machines in order to expand output or to reduce the labor input required. In analyzing changes in inputs and output, one should consider the time period within which the adjustment must be accomplished. We can distinguish between short-run and long-run adjustments. Definition: The long run is a planning horizon or time period that is sufficiently long so that it is possible to vary the quantities of all inputs in production. Isoquants show the possibilities for altering inputs and outputs in the long run. Definition: The short run is a planning horizon or time period during which, for technological, institutional, or contractual reasons, at least one of the inputs cannot be varied; that is, it must be held fixed. For example, consider an automobile assembly plant. In the short run the rate of output from this plant can be varied only by increasing or decreasing the number of workers and the quantities of parts they utilize. A new night shift can be added or the assembly line can be shut down and left idle on weekends. In the long run output can be increased by adding to the assembly line equipment so that it can be run faster or by building a new duplicate line. Or if output is to be reduced in the long run, the assembly line can be dismantled and its equipment sold (perhaps for scrap).

Returns to Scale If in the long run all inputs are changed by the same proportion, for example, doubled, this is referred to as a change in the scale of production. What happens to output when all inputs are doubled? Are tripled? Are cut by 50 percent? The answer to these questions depends on the nature of returns to scale. For a given percentage or proportionate increase in all inputs there are three pos¬ sibilities: (1) Output can increase by the same percentage, in which case there are constant returns to scale. For example, a doubling of inputs results in a doubling of output. (2) Output can increase by more than the same percentage, in which case there are increasing returns to scale. A doubling of all inputs results in a more than doubling of output. (3) Output can increase by less than the given percentage, in which case there are decreasing returns to scale. A doubling of all inputs causes output to increase by less than a factor of two. Definition: Constant returns to scale describes a production function in which a change in all inputs by a given proportion leads to a change in output of the same proportion. Increasing (decreasing) returns to scale describes a production function in which when all inputs are increased by a given proportion, output increases by a larger (smaller) proportion. The nature of the returns to scale in production is reflected in the spacing of the isoquants. Figure 3.5 portrays the isoquants of a production function with constant returns to scale. Points A, B, and C show an initial level, a doubling, and a tripling of factor inputs. The isoquants through these points show an initial level, a doubling,

50

The Economic Problem: Allocating Scarce Resources

Figure 3.5

Isoquants with Constant Returns to Scale.

and a tripling of output. The isoquants are evenly spaced moving away from the origin. In contrast, in Figure 3.6(a) increasing returns to scale are revealed by isoquants that become closer together as inputs and outputs are increased in equal proportional increments. At point B inputs are twice the level of point A. But since the 2X, isoquant lines below and to the left of B, B represents a more than doubling of output. Figure 3.6(6) shows isoquants that become more widely spaced, revealing decreasing returns to scale. Between points A and B inputs double; but since the 2Xx isoquant lies outside point B, the doubling of inputs has not doubled output. As will be shown in later chapters, the nature of returns to scale has important implications for the shapes of cost curves of the firm, the viability of competitive market structures, and the ability of a market economy to achieve an efficient allocation of resources without government intervention.

Input Substitution in the Long Run In the long run the opportunities for input substitution are measured by the slope of the isoquants or the marginal rate of technical substitution. Definition: The marginal rate of technical substitution of capital for labor (MRTSLK) is the amount of capital that must be added to replace a one-unit reduction in labor in order to yield the same level of output. In symbolic notation1

'There are two aspects of this notation that may require explanation. (1) The identity symbol, = represents

51

The Allocation of Resources in Production

Increasing returns

Decreasing returns

Figure 3.6

Isoquants with Increasing or Decreasing Returns to Scale.

a definitional relationship rather than an equality relationship between different terms. (2) The symbol |*» means that the expression to its left is evaluated holding output, X, constant at some specified level, X .

52

The Economic Problem: Allocating Scarce Resources

AK

MRTSlk

AL

X*

Because output is constant in the definition, the marginal rate of technical substitu¬ tion describes what happens while moving along an isoquant. Because capital and labor are changing in opposite directions (one increasing and one decreasing), the minus sign is included in the definition so that the MR TS is always a positive number (see Figure 3.7).

The Short Run and the Law of Diminishing Marginal Productivity In the short run, by definition, only one factor input can be varied while the other must be held constant. For example, in Figure 3.3 capital might be held constant at OKt while labor is increased. The line K ^EH traces out the relationship between total output and inputs of labor, holding capital constant at OK This is reproduced in Figure 3.8(a). Although the total output of X (total product) increases as more labor is added to the fixed amount of capital, output increases at a decreasing rate. Definition: The marginal product of a factor input is the increase in output realized for each unit increase in that input, holding all other factor inputs constant. With capital held fixed the marginal product of labor is MPl

AT AL K*

The marginal product of labor for any given amount of capital is the slope of labor’s total product curve. The marginal product of labor is shown in Figure 3.8(h).

Figure 3.7

The Marginal Rate of Technical Substitution.

53

The Allocation of Resources in Production

L per period

L per period (b) Figure 3.8

Total and Marginal Product Curves.

Principle: The law of diminishing marginal productivity states that the marginal product of a variable factor input decreases with increases in that input at least beyond some point. This law is often called the law of diminishing returns. A numerical example of the relationship between total product and marginal product is given in Table 3.1 and portrayed in Figure 3.9. It shows, for example, that when 4 units of labor are being used, total output is 16. Adding one more unit of labor increases total output to 18. The marginal product of the fifth unit of labor is 2. There are several important facts to note about this law. First, it has not been proved by logic or deduction from basic scientific principles. Rather, it is an empirical generali¬ zation that has been verified by a number of observations and experiments. For exam¬ ple, a wide variety of agricultural experiments show the validity of the law as applied to the inputs of labor, fertilizer, seed, and pesticides when land is held fixed. Second, the law of diminishing marginal productivity need not apply over the whole

54

The Economic Problem: Allocating Scarce Resources

Table 3.1

The Total Product and Marginal Product of Labor*

% Labor input per period

Total output per period

0

0

1

4

2

9

3

13

4

16

5

18

6

19

7

19

8

18

Marginal product of labor (AX/ AL)

4 5 4 3 2 1 0 -1 *The input of capital is held fixed.

range of possible levels of the variable input. It applies only after some point. In other words, at very low levels of the variable input the total product curve could rise at an increasing rate, showing the increasing marginal product of the variable input (e.g., see Figure 3.9(a). Here the law of diminishing productivity does not apply until after the labor input has reached 2 units per period. Third, the marginal product of the variable input may but need not become negative after some point. A negative marginal product means that additions of the variable input actually reduce total output. This is shown in Figure 3.9(h). For example, additions of water to agricultural land will at first lead to increases in crop yields, although at a decreasing rate. There is some level of water input that maximizes output. Beyond that level additional water actually damages plants and reduces output; that is, it has a negative marginal product. In some other types of production processes, however, the marginal product curve might approach the horizontal axis but never cross it. In such cases the marginal product is always diminishing but never zero. Finally, the law applies solely to short-run situations in which only one input can be varied and the others are held fixed. What happens to the total product and marginal product curves of Figures 3.8 and 3.9 if there is an increase in the level of the fixed factor? Refer back to Figure 3.3. If capital is increased from OKx to OK2, the new total product curve is the line K2DGB. At all points except the origin this curve lies above the old total product curve (KXEH). At any level of labor input, for example, OL„ total output is higher with a greater

55

The Allocation of Resources in Production

Marginal product of labor

Figure 3.9

Total and Marginal Product Curves: A Numerical Example.

capital input. This indicates that the marginal product of capital is positive. Of course, capital must also obey the law of diminishing marginal productivity when labor is held constant. Because the new total product curve lies above the old one at every point, it must also be more steeply sloped throughout. Because its slope measures the marginal product of labor, the steeper slope of the total product curve means that the marginal product of labor is increased when more of the fixed factor is used. On the other hand, if so much capital were being used that its marginal product were negative, then the

56

The Economic Problem. Allocating Scarce Resources

opposite would be the case. A further increase in capital would reduce the total outputs possible with various levels of labor input; and the total and marginal products of labor would shift down.

Principle: As long as the marginal product of the fixed factor is positive, an increase in its use causes an upward shift of both the total product and marginal product curves of the variable factor input.

Diminishing Marginal Rate of Technical Substitution All variable proportion isoquants so far have been drawn convex to the origin. These isoquants become less steeply sloped as the production point is moving to the right with more labor and less capital. Since the slope of the isoquant represents the MRTS, the isoquants are characterized by diminishing MRTS. It seems plausible that isoquants should have this property. As we make equal successive reductions in the amount of capital being utilized, it is necessary each time to add more labor than before in order to maintain production at the designated level, that is, to stay on the same isoquant. It can now be shown that diminishing MRTS is implied by the law of diminishing marginal product of a variable input. In other words, these two features of production processes are results of the same underlying technological phenome¬ non. Start at point A in Figure 3.10 and move to point B by increasing the amount of labor, holding capital constant. For small changes in labor the increase in output can be computed as follows:

A.X = A LMPl

Figure 3.10

Marginal Products and the Marginal Rate of Technical Substitution.

57

The Allocation of Resources in Production

Now holding labor constant, decrease capital in an amount sufficient to return to the original isoquant at point C. The change in capital and output are given by — AX = — \KMPk

Because we have returned to the same isoquant, total output is not changed. Therefore, we must have AX -- — XX, and - A K MPk = M MPl

Rearranging gives AK

_ MPl

AL

MPk

Finally, recalling the definition of the marginal rate of technical substitution, we have:2

mrtslk

MPl MPk

_

AK_ AL

X*

This equation establishes that the marginal rate of technical substitution is equal to the ratio of the marginal products of the two inputs. Now to see that diminishing marginal productivity implies diminishing marginal rate of technical substitution, let us see what happens to the marginal products of labor and capital as we move from points A to B to C in Figure 3.10. Moving from A to B, holding capital constant, the marginal product of labor diminishes. Then with labor held constant, as capital is decreased in the move from B to C, the total and marginal product curves of labor shift down, thus reducing the marginal product of labor further. At the same time the increase in labor from A to B shifts the marginal product of capital upward, increasing its magnitude. And the reduction in capital from B to C increases the marginal product of capital even further (the law of diminishing marginal product in reverse). Thus in moving from A to C the numer¬ ator in equation (3.1) gets smaller, the denominator gets larger, and the ratio as a whole diminishes.

PRODUCTION WITH TWO GOODS Now assume that there are two goods, X and Y, each with different production functions. The total amount of X and Y that can be produced depends on the state of technology (the isoquants), the total amount of capital and labor available to the economy, and how these inputs are allocated to the production of the two goods.

2This derivation is correct only as a first approximation. The smaller the changes in labor and capital are, the better is the approximation. For a more rigorous derivation see the Mathematical Appendix to this chapter.

58

The Economic Problem: Allocating Scarce Resources

Assume that the total quantities of labor and capital available to the economy at any point in time are fixed. This means, for example, that in a market economy the total supply of labor would not change in response to a change in wage rates. This assump¬ tion of fixed factor supplies is necessary for the graphical model. More general models with variable factor supplies can be developed in mathematical forms. The fixed and limited supplies of factor inputs and their allocations to the production of the two goods can be portrayed in a box diagram such as Figure 3.11. The dimensions of the box are given by the total factor endowments, with labor being measured on the horizontal axis and capital on the vertical axis. The lower left-hand corner, Ox> is the origin from which X production will be measured; and the upper right-hand corner, Oy, is the origin from which Y production will be measured. Any point in the box indicates a division of capital and labor between X and Y production. For example, at point A, 0XKX] units of capital are allocated to X production while the remainder, OyKyu is allocated to production of good Y. Point A represents full employment of all labor and capital. The next step is to add the isoquants that represent the production functions for goods X and Y. These are shown in Figure 3.12. The X isoquants are solid lines and are oriented with respect to the lower left-hand corner of the production box. A con¬ ventional isoquant diagram for good Y has been turned upside down and placed with its origin in the upper right-hand corner of the box. The Y isoquants are dashed lines, with those lower and to the left (farther from O y) representing higher outputs of Y. Suppose that the economy initially allocates resources between X and Y as shown by point A in Figure 3.12. The output of X is X2 and the output of Y is Y3. Is this a desirable outcome from society’s point of view? Clearly not. The economy could, for example, obtain more Y without sacrificing any output of X by moving to point B. This would entail substituting labor for capital in X production while moving along the X2 isoquant and obtaining the extra labor by reducing the amount of labor used in 7 production and replacing it with capital taken from X. Alternatively, the economy

LY1

Oy

Ky\

Ky

Figure 3.11

Factor Endowments and the Production Box.

59

The Allocation of Resources in Production

Figure 3.12

The Production Box and Efficient Production.

could move to point C with a higher X production and no decrease in the production of Y. Or it could choose any other combination between points B and C with more of both X and Y. Points B and C represent tangencies between X and Y isoquants while these iso¬ quants cross each other at points like A. If production is at any point where X and Y isoquants cross, it is possible to reallocate resources so as to increase the production of either Y or X or both without decreasing the output of either good. But where the isoquants are tangent such as at point B, X production can be increased only at the expense of a decrease in Y production and vice versa. Principle: Efficiency in production occurs when it is not possible to increase the output of one good except by decreasing the output of the other good. Points of efficient production are characterized by the tangency of X and Y iso¬ quants; that is, X and Y isoquants have the same slope or the same MRTS. Definition: The efficiency locus is a locus of all points in the production box where an X isoquant is tangent to a Y isoquant. Condition for Efficient Production: Efficiency in production requires that the mar¬ ginal rate of technical substitution of capital for labor in X production be equal to the marginal rate of technical substitution of capital for labor in Y production. In other words,

60

The Economic Problem: Allocating Scarce Resources

x Y MRTS— = MRTS— LK

LK

where the superscripts refer to goods X and Y. It should be noted that although all points on the efficiency locus between Ox and Oy satisfy the conditions for efficient production and are preferred to points off the locus, as yet we have no basis for judging which of these points is better or preferred.

THE PRODUCTION POSSIBILITIES FRONTIER We are now in a position to describe how the production possibilities frontier of Figure 3.1 is derived from the underlying data on production technologies and factor endow¬ ments. Each point on the efficiency locus corresponds to a point on the production possibilities curve. At the lower left-hand corner of Figure 3.12, the X output is zero while the Y output is 7S, This establishes the point of intersection of the production possibilities frontier with the Y axis in Figure 3.13. At each point on the efficiency locus of Figure 3.12 there is one X and one Y isoquant. The pairs of values from these isoquants can be used to locate other points in Figure 3.13. Each such point represents an efficient output combination; and all such points make up the production possibili¬ ties frontier. Point A in Figure 3.13 is undesirable because it lies inside the production possibilities frontier. By looking at the production box, we can see why point A lies

Output of Y per period

Ye ^^X\ ,YS

^3

A

^2

h

!

0 Figure 3.13

>3

'V^4 ,

1

l\

1

|

x3

x4

Y'i

Wtj

\*6

Output of A per period The Production Possibilities Frontier.

61

The Allocation ol Resources in Production

inside the frontier. At point A the conditions for efficient production are not satisfied. Point A is not on the efficiency locus. As shown earlier, the slope of an isoquant defined the terms on which inputs could be substituted for one another. Similarly, the slope of the production possibilities curve indicates the terms on which one output can be substituted for another in production while moving along the efficiency locus. Definition: The marginal rate of transformation between X and Y (MRTXY) is the amount of Y production that must be given up in order to increase the production of X by one unit. It is measured by the negative of the slope of the production possibilities frontier. In other words, MRTxy

AT AT

The marginal rate of transformation can also be interpreted as the opportunity cost of X at the margin. Definition: The marginal opportunity cost of good X is the amount of Y production that must be given up or foregone in order to free the resources for increasing X output by one unit. For example, in Figure 3.13 when the output of X is increased from X3 to X*, the output of Y must be decreased from Y} to Y2. This reduction in the output of Y is the marginal cost of increasing X production measured in units of Y, rather than in monetary units. By the same reasoning, the reciprocal of the marginal rate of transfor¬ mation is the marginal cost of Y production measured in units of X.

The Shape of the Production Possibilities Curve Notice that in the cases of both X and Y the marginal opportunity cost of production rises as output of that good is increased. Why is this generally the case? The principal reason for increasing marginal cost is differences in the factor input ratios for the two goods. Returning to the production box of Figure 3.12, observe that at each combina¬ tion of outputs along the efficiency locus the ratio of capital to labor inputs is higher in X production than in Y production. This can be seen by drawing straight lines from each origin to points such as B and C and by comparing the slopes of these lines with respect to the labor axes of the box. The slope of each line is the ratio of capital to labor for that input combination.3 When X output is increased, Y output must be reduced simultaneously. This reduc¬ tion frees both capital and labor from Y production, but relatively more labor, because

’The capital-to-labor ratio is K/L. In Figure 3.12 the slope of the line from the origin to point B is the ratio of the distances Lxx - B and Ox - Lxx. The first distance measures the capital used in X production at point B, and the second distance is the quantity of labor used.

62

The Economic Problem: Allocating Scarce Resources

the capital-to-labor ratio is lower in Y. At the same time increases in X production would require relatively more capital, other things equal. This “conflict” could only be resolved by decreases in the ratio of capital to labor in the production of both X and Y. Because the technology is such that X production is relatively more capital intensive, that is, has a higher capital-to-labor ratio, this decrease in the K/L ratio is relatively more disadvantageous to X production. With successive increases in X production, successively larger increases in factor inputs are required to compensate for the declin¬ ing capital-to-labor ratio, which means successively larger reductions in Y production —increasing marginal opportunity costs. Another possible reason for increasing marginal costs is the presence of decreasing returns to scale in the production functions of one or both goods. In order to see the separate role of decreasing returns to scale in determining the shape of the production possibilities curve, assume that the production functions for the two goods are identical. This means that the isoquants for X have the same shape as, and can be directly superimposed on, the isoquants for Y. Given this assumption, the efficiency locus becomes a straight line diagonal between the two origins of the production box. And at every point on the efficiency locus the factor input ratios are the same for both goods. Then, as the output of one good is increased, it absorbs factors in the same proportions that they are being released by the other good. If at the same time production of both goods is characterized by constant returns to scale, then equal successive increases in the output of X require only equal successive increases in the inputs of capital and labor. These can be obtained by equal successive decreases in the output of Y. The marginal opportunity cost of X production is constant. If, however, X production is characterized by decreasing returns to scale, successive increases in X production require increasing increments of capital and labor and therefore larger and larger decreases in the output of Y. Of course, if Y production also was characterized by decreasing returns to scale, this would reinforce the effect on marginal opportunity costs. The production possibilities curve would be more sharply bowed. It is conceivable that a production possibilities curve could display decreasing mar¬ ginal opportunity costs over some range of output combinations (e.g., see Figure 3.14). But for this to occur, the production function for at least one of the goods would have to display increasing returns to scale over some range of output. Also, the increasing returns to scale would have to be strong enough to offset the tendencies toward increasing opportunity cost due to differences in factor input ratios and the possibility of decreasing returns to scale in the other good.

Shifting the Production Possibilities Curve Let us consider some of the things that might change the shape and position of the production possibilities frontier. One is obviously a change in the factor endowment of the economy. An increase in the quantity of either labor or capital available to the economy would result in a larger production box. The production possibilities curve

63

The Allocation of Resources in Production

Figure 3.14

A Production Possibilities Curve with Decreasing Marginal Cost.

would shift out at all points. If only labor increased, the production box would grow in length. The production possibilities curve would shift out, as before. But the shift would be greater along the axis of that good which uses relatively more labor in production, that is, has a higher ratio of labor to capital. The state of technology is the other major determinant of the position of the produc¬ tion possibilities frontier. Technological innovation in the production of X would shift all X isoquants in the production box toward the X origin so as to make possible greater outputs of X with an unchanged total factor supply and production of Y. This will also result in an outward movement of the production possibilities frontier at all points except its intersection with the Y axis.

The Production Possibilities Curve in Practice The assumption that there are only two goods in the economy is obviously unrealistic. But even in an economy with many goods it is clear that technology and limited factor supplies place limits on the attainable combinations of outputs. In a many-good world the production possibilities curve can still be used to portray the trade-offs between the outputs of any pair of goods, holding the outputs of all other goods constant by assumption. This assumption is equivalent to holding constant the quantities of inputs that are available for the production of the two goods in question. Many production managers face problems of production choice that can be de¬ scribed by a production possibilities curve. Petroleum refineries produce both gaso¬ line and heating fuels in variable proportions. For a given size of refinery and input of crude oil, more gasoline can be produced only if heating fuel output is reduced. The manager of a national forest is producing both lumber and recreation services for

64

The Economic Problem: Allocating Scarce Resources

visitors. The higher the timber output is, the less attractive is the forest for recreation and the fewer recreation visits “produced.” Can you think of other examples? Do you think these examples are likely to be characterized by increasing opportunity cost?

SUMMARY In this chapter we have developed a model for portraying the production opportunities that are open to a society. These opportunities are determined by the technology that is represented by the production functions and isoquants for each good and by the available factor supplies that determine the size and shape of the production box. We have defined the conditions for efficient production and have shown how the informa¬ tion on technology and resource endowments can be combined to derive the production possibilities frontier, a locus of efficient production points. But we have no way yet of knowing which point on the production possibilities frontier is preferred. To begin to approach that question we need to analyze consumer preferences. We turn to that topic in the next chapter.

KEY CONCEPTS Factors of production: Labor and capital Production function Isoquant Long run vs. short run Returns to scale Marginal rate of technical substitution Marginal product

Law of diminishing marginal productivity Production box Efficiency locus Production possibilities frontier Marginal rate of transformation Marginal opportunity cost

QUESTIONS AND PROBLEMS For Basic Review 1.

Define and explain the economic significance of each of the key concepts. 2* State the law of diminishing marginal productivity. Use an isoquant diagram to show how to derive the total product and marginal product curves of an input and the effect on these curves of a change in the quantity of the fixed factor. 3. Explain how the production possibilities curve is derived from the underlying assumptions about factor endowments, technology, and so on. 4. * Explain the difference between decreasing returns to scale and diminishing marginal productivity or returns. 5. Explain why isoquants are convex (show diminishing MRTS).

65

The Allocation of Resources in Production

6.

Explain why the production possibilities curve is usually drawn concave to the origin (showing increasing marginal opportunity cost). Under what conditions might a production possibilities curve be convex to the origin, at least over some range?

7. * How would the following changes in economic conditions affect the shape and position of the production possibilities curve? a. An increase in the endowment of labor. b. An equal percentage increase in the endowments of both labor and capital. c. An increase in the quantities of labor and capital allocated to X production offset by a decrease in the quantities of labor and capital allocated to Y production. d. A technological innovation affecting only X production. e. A technological improvement affecting production of both X and Y. f. The elimination of unemployment of labor.

Problems 1.

Suppose the production function for X is given by X = 2LVlKVl = 2 • vT • \Xk

Compute the output level for the following input combinations.

L 100

K

X

25

64

39.06

64

36

50

50

36

69.44

36

64

25

100

200

50

100

100

50

200

Plot the input combinations in a diagram with capital and labor on the axes. Sketch in and label the isoquants. Does this production function show constant returns to scale? 2.* Suppose that you are the plant manager of a large steel mill. The mill can produce either sheet steel or girders. Given the size of the mill (its capital

66

The Economic Problem: Allocating Scarce Resources

input) and the level of employment at the mill (its labor input), some of the possible combinations of output are: Girders (tons per week)

Sheet steel (tons per week)

100

0

92 75 50 15

100 200

0

300 380 400

a. Plot the production possibilities curve. b. If sheet steel output is 200, what is the marginal opportunity cost of increasing sheet steel output by 1 ton? c. Calculate the marginal opportunity cost of sheet steel at several output levels and plot the marginal opportunity cost curve as a function of its output. d. Do the same for girders. e. Your plant output last week was 60 tons of girders and 180 tons of sheet steel. What does this imply about efficiency in production and the kinds of steps that should be taken? f. What do you need to know in order to determine the best or optimum point on the production possibilities curve?

MATHEMATICAL APPENDIX TO CHAPTER 3 Diminishing Marginal Productivity and the MRTS The derivation in the text of the relationship between the MRTS and the marginal productivities is correct only as a first approximation. This is because the MPL and MPk are treated as constants over the range AB and BC when in fact they will change according to the law of diminishing marginal productivity. A precise derivation is based on the calculus by treating the changes in capital and labor as infinitesimally small. The production function is

X = X (K, L) Take the total differential of this function and in order to represent movement along an isoquant, set it equal to zero,

Rearranging gives: dK

_ dX/dL

dL

dX/dK

67

The Allocation of Resources in Production

The left-hand term is the MRTS of the isoquant. The numerator on the right-hand side shows the change in output for a small change in labor, holding other variables constant; thus it is the marginal product of labor. Similarly, the denominator is the marginal product of capital. Thus we have MRTSlk

mpl ~MPk

CHAPTER 4 Preferences and the Allocation of Goods to Individuals

I n this chapter we establish a basis for analyzing and evaluating the way societies answer the question “What to produce?” In some societies most of the production decisions are made by some central authority—a planning board, commissar, or chief¬ tain—in accordance with its own views of needs and priorities. These societies might allocate large quantities of resources and productive capacity to the raising and sup¬ porting of an army, to building pyramids, or to supporting the lavish life-styles of their leaders. In these societies, the preferences of individuals are of little concern to those in power. Economists wishing to understand the process of resource allocation in such societies must identify the locus of economic and political power and then examine the motivations and preferences of those who hold that power. The primary purpose of economic activity in such societies is to satisfy the preferences of those in power. In sharp contrast, it is assumed here that the primary purpose of economic activity is to increase the individual well-being or welfare of the members of society. Further¬ more, we assume that individuals are the best judges of their own degree of welfare or well-being. Individuals know what they want and when an economic change has made them better or worse off. In other words, economic welfare is defined in terms of the preferences of individuals. Thus the first task of this chapter is to develop a basis for describing and analyzing individual preferences and their implications for resource allocation.

PREFERENCE ORDERINGS There are basically two approaches to modeling household preferences and choice with respect to consumption of goods and services. The first approach is to assume the existence of something called utility which is created or produced by the act of 68

69

Preferences and the Allocation of Goods to Individuals

consuming goods and services. The existence of utility was taken for granted by economists in the nineteenth century on the basis of introspection or personal experi¬ ence. Utility is assumed to be a function of the level of consumption of goods and services; that is: U = U(X, Y)

where the U represents utility and X and Y are the levels of consumption of the two goods expressed in units per period of time, for example, per week. Other things equal, an increase in the level of consumption of a good is assumed to increase utility; that is, the marginal utility of consumption is positive. Also, successive increments to the consumption of a good, other things equal, yield successively smaller increments to total utility. In other words, marginal utility diminishes with increasing consumption of a good. On the basis of these assumptions about the nature of utility, and on the assumption that individuals seek to maximize their utility, it is possible to deduce several useful propositions about individual behavior. The alternative approach is to assume that individuals are guided by a set of rules or axioms in making their consumption choices. These axioms are plausible and taken together imply what is normally considered to be rational behavior. The axiomatic approach to consumer behavior involves working out all the implications of these axioms for individual behavior. For practical purposes the utilitarian and axiomatic approaches yield the same conclusions about observable individual behavior. The concept of utility is useful primarily as a hypothetical construct to enable the use of the simple mathematics of maximization from the calculus to deduce conclusions about individual behavior. The axiomatic approach has the advantage, from an intellectual perspective, of being based on observable phenomena, that is, the choices that people make, rather than the nonobservable and somewhat nebulous concept of utility. In this chapter the axiomatic approach is used to characterize individual preferences and to examine their role in the way society solves its economic problem. The relationship between the axiomatic approach and the utility approach will be explained in Chapter 7.

The Axioms of Preference Orderings We focus here on one individual who is faced with the problem of choosing one bundle of goods and services for consumption each period from among a range of alternatives. A bundle is analogous to a grocery bag, with each bag containing different quantities of the various goods. Assume that there are only two goods available, X and Y. This assumption is made so that consumption bundles and preferences can be described in a two-dimensional graph. The analysis can be extended to three or more goods through the use of appropriate mathematical concepts. All conclusions stated in this section have their counterpart in the equivalent three or “^’’-dimensional model. Four possible bundles might look like this: Bundles are described in the table on the top of the next page. These bundles are shown in Figure 4.1. It is assumed that in principle goods are divisible, so that, for example, there may be many additional possible bundles between points A and B. Each would contain 4 units of X and 5 and some fraction units of Y.

70

The Economic Problem: Allocating Scarce Resources

Bundle

Quantity of good X

Quantity of good Y

A B C D

4 4 5 6

5 6 6 3

If the individual were offered the opportunity to take one free bundle from among those shown in Figure 4.1, which one would she choose? It seems at least plausible that she more likely would choose bundle C than bundle A because bundle C contains more of both X and Y. But it certainly is possible that she would have a strong enough preference for good X so that she would choose bundle D even though it had only 3 units of Y. But rather than speculate on possible outcomes, it would be better to proceed in the following manner. First, three axioms are stated that are taken to characterize the preference orderings of all individuals. Then, these axioms are used to deduce several characteristics of preference orderings. A preference ordering is, in effect, a list of all possible bundles ranked in order of preference. Of course, there may be ties on this list. First Axiom of Preference Ordering: The individual has a complete ordering of all possible bundles. For any conceivable pair of bundles, for example, A and B, this ordering results in one of the three following statements: 1. The individual prefers bundle A to bundle B\ or 2. The individual prefers bundle B to bundle A; or 3. The individual is indifferent between bundle A and bundle B.

Y per bundle

B•

6

C •

A• 4 •D

2

0

2

4

6

X per bundle Figure 4.1

Alternative Consumption Bundles.

71

Preferences and the Allocation of Goods to Individuals

W

Note that these three statements are mutually exclusive; only one can apply to any pair of bundles. The indifference statement means that it does not matter to the individual which of the two bundles is consumed. The Second Axiom of Preference Ordering: Preference orderings display transitivity. This means that for any three bundles, A, B, and C, if the individual prefers B to A and prefers C to B, then she must prefer C to A. Also, if she is indifferent between B and A and is indifferent between C and B, then she must be indifferent between C and A. The transitivity axiom assures a basic kind of consistency in the preference ordering. The Third Axiom of Preference Ordering: If a bundle has more of one good and the same amount of the other good or more of both goods, it is preferred. This is sometimes referred to as the nonsatietion axiom. It means that more is always better and that an individual can never get too much of a good.

Indifference Curves Preference orderings can be portrayed graphically by what are known as indifference curves. If an individual is indifferent among bundles A, B, and C, and these three bundles are plotted in a figure such as Figure 4.1, then a line through these three points and through all other points that were also indifferent to these three bundles would be an indifference curve. Definition: An indifference curve is a locus of all bundles among which the individual is indifferent. Indifference curves are basic to the analysis of individual preferences and consumer behavior in a market economy. If an individual’s preference ordering is consistent with the three previously stated axioms, then that individual’s indifference curves have several important characteristics. 1. Bundles on higher indifference curves, that is, upward and to the right, are preferred to bundles on lower indifference curves. In Figure 4.2 bundle B on indiffer¬ ence curve 12 has more of both goods compared to bundle A. Therefore because of the nonsatiety axiom, B is preferred to A. By the definition of indifference curves the individual is indifferent between bundle B and all other bundles on I2 such as bundle C. Thus C is also preferred to A even though it has less of good Y than bundle A has. 2. Every possible bundle has an indifference curve through it. This means that the space of Figure 4.2 is literally filled with indifference curves, which follows from the assumption of perfect divisibility of both goods and from the axiom of complete ordering. Between any two bundles such as A and B in Figure 4.2 it is possible to locate a third bundle with slightly different amounts of one or both of the goods. Such a bundle would be on a higher indifference curve than bundle A because it would have more of either X or Y or both; but it would be on a lower indifference curve than bundle B.

72

The Economic Problem: Allocating Scarce Resources

Figure 4.2

Indifference Curves.

No matter how close together bundles A and B are, it is still possible to locate a third bundle between them, and hence to place another indifference curve through that bundle. 3. Indifference curves slope down to the right. This characteristic also follows from the axiom of nonsatiety. Consider bundle B in Figure 4.2 and the indifference curve that passes through it. First, points above and to the right of bundle B contain more of both goods and are preferred to bundle B. Thus the indifference curve through bundle B cannot pass into the shaded area above and to the right of bundle B in Figure 4.2. Similarly, bundles in the shaded area below and to the left of B contain less of both goods and therefore could not be on the same indifference curve as bundle B. Any bundle on the horizontal and vertical lines through B contains more of one good and the same amount of the other good. Thus it must be preferred to bundle B. The indifference curve through B cannot be a horizontal or vertical line. To find a bundle that has more of good Y but which is on the same indifference curve as bundle B, one must look to the left of the vertical line, that is, to bundles with less X. Hence the indifference curve through bundle B must go through the space above and to the left of B. Similarly, if a bundle has more X than bundle B, it must also contain less Y if it is to be on the indifference curve. It must lie below and to the right of B. Thus the indifference curve through B must also be a downward-sloping curve passing through the unshaded areas of Figure 4.2. 4. Indifference curves never intersect. This can be proved by showing that whenever a pair of intersecting indifference curves is drawn, a contradiction of one of the axioms of preference ordering is implied. Figure 4.3 portrays two indifference curves that intersect at point B. Since bundles A and B are both on indifference curve Ix, we know that the individual is indifferent between A and B. Similarly, the individual must be indifferent between bundles B and C. From the axiom of transitivity we know that because the individual is indifferent between A and B and also is indifferent between B and C, he must be indifferent between A and C. But this contradicts the nonsatiety

73

Preferences and the Allocation of Goods to Individuals

Figure 4.3

Indifference Curves Cannot Intersect.

axiom, he must prefer C to A since it contains more of both goods. Indifference curves that intersect cannot satisfy all of the axioms of preference ordering. 5. Indifference curves are convex to the origin. It is not possible to deduce this characteristic of indifference curves from the axioms of preference ordering. However, in the next section we will see that convexity is an intuitively plausible characteristic. It will also be shown in Chapter 7 that when individuals purchase goods in markets at fixed money prices, if indifference curves are not convex, then individuals would tend to choose bundles that contain only one good, that is, bundles that lie on one of the axes. Convexity of indifference curves is consistent with individuals who purchase and con¬ sume a variety of goods. The fact that individuals are commonly observed to consume bundles containing many goods supports the assumption that indifference curves are convex.

Goods Versus Bads The third axiom of preference ordering states that if a bundle contains more of one good, other things being equal, an individual would prefer that bundle. It is conceivable that some commodities, at least in some circumstances, could be viewed as bads. For example, water in small quantities is necessary to sustain life. In somewhat larger quantities it is useful for washing dishes and watering the lawn. But in very large quantities water can become a nuisance, causing some damage. Toxic chemicals in foods or in the atmosphere can cause ill health. A commodity is said to be a bad if any individual prefers bundles that contain less of that commodity, other things equal. The indifference curves between a good and a bad have some different characteristics compared to indifference curves between a pair of goods. Consider commodities X and Z, where X is a good, but Z is a bad. Bundle B in Figure 4.4 contains less Z but the same amount of X in comparison with bundle A. Therefore bundle B is preferred. As a consequence, indifference curves in this case will slope up to the right. And bundles lying on indifference curves below and to the right will be preferred.

74

The Economic Problem: Allocating Scarce Resources

Figure 4.4

Indifference Curves for a Good and a Bad.

If commodity Z is like water and is a good at low quantities but a bad at high quantities, indifference curves would start out sloping up to the left but would bend back to the right as shown in Figure 4.5.

Substitution in Consumption An indifference curve is a locus of all those alternative consumption bundles that in the individual’s eyes lead to the same level of satisfaction or welfare for the individual.

Z per bundle

h O Figure 4.5

X per bundle

Indifference Curves When Too Much Z Becomes a Bad.

75

Preferences and the Allocation of Goods to Individuals

The notion that different consumption bundles can yield the same level of satisfaction means that the individual can substitute one good for another in consumption. An indifference curve shows the rate on which one good can be substituted for another in consumption without changing the level of satisfaction or well-being provided by consumption. The terms on which this substitution can take place are measured by the slope of the indifference curve.

Definition: The marginal rate of substitution of Y for X {MRSXY) is the amount of Y that must be added to a consumption bundle to replace a one-unit reduction in the amount of X, holding the amount of satisfaction or welfare constant. In symbolic notation

MRSxy

AY

AX

U*

where U* represents the given level of preference or satisfaction. Because the level of satisfaction is held constant, the marginal rate of substitution describes what happens while moving along an indifference curve. Since Y and X are changing in opposite directions (one increasing and one decreasing), a minus sign is included in the definition so that the MRS is always a positive number. If indifference curves are convex to the origin as was previously assumed, the slope of the indifference curve is steep when the amount of X is relatively low and the MRS is high. This means that an individual starting at a position with a relatively large

Figure 4.6

The Marginal Rate of Substitution.

76

The Economic Problem: Allocating Scarce Resources

quantity of Y and not much X would be willing to give up a relatively large amount of Y in order to obtain a consumption bundle with one more unit of X (see Figure 4.6). But as he moves downward to the right along the indifference curve with the quantity of X increasing and the quantity of Y decreasing, the amount of Y the individual is willing to relinquish in order to obtain one more unit of X diminishes. In other words, the terms on which the individual is willing to give up Y in order to get more X diminishes as the amount of X increases relative to Y. Principle: The marginal rate of substitution between X and Y diminishes as the quantity of X increases along an indifference curve. Indifference curves with diminish¬ ing marginal rate of substitution are convex to the origin.

A SIMPLE TWO-PERSON ECONOMY Let us assume a very simple economy with only two people whom we will call for convenience Ann and Bob. Both have preference orderings that satisfy the axioms of choice and have the preceding characteristics. Their preference orderings need not be the same. That is, their indifference curve mappings could have different shapes and locations as long as they have the characteristics of being downward sloping, noninter¬ secting, and convex to the origin. In order to emphasize the problem of choice among consumption bundles, let us make some simplifying assumptions about production in this economy. Assume that each individual works independently and produces fixed quantities of two goods, X and Y. Ann produces 10 units of X and 2 units of Y per period. Bob produces 4 units of X and 6 units of Y per period. Each individual’s production and the total production of the economy is as follows: Output per period Produced by

X

Y

Ann Bob Total

10

2

_4 14

6

8

One question that might be asked of this simple model is, Given the total outputs of the two goods, how might they be distributed between Ann and Bob? This focuses on the “for whom?” task that any economic system must carry out. The output data can be used to construct a box diagram such as Figure 4.7. This is often called an Edgeworth box after F. Y. Edgeworth who first used this diagram to analyze two-person exchange in his book, Mathematical Psychics: An Essay on the Application of Mathematics to the Moral Sciences, in 1881.1

‘Reprinted by Augustus M. Kelley, Publishers, New York, New York.

77

Preferences and the Allocation of Goods to Individuals

Figure 4.7

Exchange Opportunities in a Two-Person Economy.

The horizontal and vertical dimensions of the Edgeworth box are given by the total outputs of X and Y, respectively. Any point in the box represents a division of X and Y between the two individuals, with the quantities going to Ann being measured with respect to the lower left-hand corner and the bottom and left-hand edges of the box. Similarly, the quantities assigned to Bob are measured with respect to the upper right-hand corner of the box. In principle, it is possible for a society to choose any distribution within the box, including points along any edge. The choice could be based on tradition, the whims of a dictator, or some ethical notion such as “to each according to his needs.” We cannot say much more about this issue without introducing some kind of criterion or specifying the social, political, and economic institutions of this society.

Exchange Let us suppose that this society grants to each individual the right to dispose of the fruits of his or her own labor as each person sees fit. If this is the case, since Ann produced 10 units of X and 2 units of Y per period, she could consume the bundle represented by point A in Figure 4.7. And of course, this point also represents Bob’s production and potential consumption bundle. If Ann and Bob are unable to meet with each other and communicate about their preferences, they must both consume what they produce. And there is no more to say about the matter. However, suppose that they are able to meet to discuss their economic situation and to exchange goods. What will happen depends on their preference orderings. In the absence of exchange they both consume the bundles represented by point A. Ann achieves indifference curve IAl, and Bob achieves indifference curve IBl. At this point

78

The Economic Problem: Allocating Scarce Resources

Ann has a low marginal rate of substitution of Y for X; she would be willing to give up a relatively large amount of X in order to get more Y. Bob, on the other hand, has a high marginal rate of substitution of Y for X, that is, he would be willing to give up a lot of Y for a relatively small amount of X. There is a potential for both of them to be better off. For example, suppose that Ann’s marginal rate of substitution is 5. Ann could relinquish one unit of X in return for one-fifth of the unit of Y and still be on her original indifference curve at point B'. But if she makes this trade with Bob, he will be much better off. He will be on a higher indifference curve. In fact, any exchange in which Ann gives up X to Bob in return for some Y that leads to a new point in the shaded area above and to the left of point A will be better for both Ann and Bob. Where will this process of exchange lead? We cannot be certain. But unless it leads to a point on the line segment BC, there will still be opportunities for further mutually beneficial exchange. For example, if the first exchange leads to point D, where the indifference curves of Ann and Bob intersect, they both can still attain higher indiffer¬ ence curves, now by having Bob give up some X in exchange for Y. In fact, only on the line segment BC will there be no further opportunities for mutually beneficial exchange. This segment is a locus of tangency points between Ann’s and Bob’s indiffer¬ ence curves. Once Ann and Bob have used exchange to achieve consumption bundles that he on BC, Ann can only achieve further gains in her welfare at Bob’s expense, that is, by moving upward to the right along BC, placing Bob on a lower indifference curve. Of course, there is no reason for Bob to enter into such an agreement voluntarily. Similarly, Bob can only increase his welfare by moves downward and to the left which necessarily make Ann worse off. Thus the line segment BC and its extension to the two origins is of considerable economic significance. It is called the exchange locus. Definition: The exchange locus is a locus of all points in the exchange box where an A indifference curve is tangent to a B indifference curve. Since where two curves are tangent, they have equal slopes, the exchange locus is also a locus of points that satisfy the following condition: MRSxy = MRSbxy where the superscript letters refer to Ann and Bob. The exchange locus is sometimes called a contract curve because it is a locus of all possible equilibrium contracts of exchange between the two parties. Starting from any allocation off the contract curve, both parties can make themselves better off by entering into a contract to exchange goods that places them on the contract curve. This curve is also sometimes referred to as a conflict curve because any effort on the part of, say, Ann to move along the curve up and to the right would engender conflict with Bob because it would make him worse off. This model has several interesting implications. First, the model shows that even in the most simple economy, there are elements of both cooperation and conflict. There is cooperation as people come together to communicate information and attempt to negotiate mutually beneficial exchanges. But there is also an element of conflict as each

79

Preferences and the Allocation of Goods to Individuals

individual tries to negotiate more favorable terms of exchange. Whereas Ann is better off at any point between B and C on the exchange locus, the closer she can get to C, the better off she is. We cannot say much about where on the exchange locus the two parties will wind up. This depends on factors such as bargaining skill and, perhaps, social and political power. However, if Ann tries to negotiate an exchange that leads to a point above and to the right of C, Bob would be better off by terminating negotiations and staying at point A. The second point is that the outcome of the exchange and bargaining process is influenced significantly by the initial allocation of goods between the two parties. If the initial allocation is close to the upper right-hand corner of the exchange box, then Bob can make himself better off by entering into an exchange. But the final outcome may still leave him in poverty and misery. The outcome of the exchange is an im¬ provement relative to the initial position. But it cannot be said to be good in any absolute sense. Third, the exchange processes we have been describing are bilateral, that is, involving only two people engaging in barter. Nothing has been said about prices, money, or markets. But it should be obvious that especially in an economy with many goods and many individuals, the existence of money and the availability of centralized markets should facilitate the exchange process and make it easier for people to reach the exchange locus and exhaust all possibilities for mutually beneficial trade. In fact, a major aspect of microeconomic theory is the positive analysis of the functioning of markets in various circumstances and the normative analysis of their implications for welfare. Finally, being on the exchange locus is better than being off the locus in the sense that moves toward the locus have the potential for making both parties better off. But we have not established in any rigorous way a basis for preferring one position on the locus over another. Clearly, positions upward and to the right favor Ann at Bob’s expense. But to say whether or not this is desirable requires some judgment about the relative deservingness of Ann and Bob. This involves judgments about equity. These will be discussed extensively in Chapter 18. Nothing more can be said here on this subject.

SUMMARY If individuals are given the opportunity to choose among alternative consumption bundles, and if they choose rationally (as defined by the axioms of choice), then their preference orderings of the alternative bundles can be described by a family of indiffer¬ ence curves. These curves slope downward and to the right, are nonintersecting, and are convex to the origin. An individual will choose the bundle that lies on the highest indifference curve. When two or more individuals, each with given bundles of goods, come together they are likely to discover opportunities to engage in exchanges that have the potential for making each of them better off in terms of their own preferences. Given the opportunity for exchange, we would expect people to engage in trade that alters

80

The Economic Problem: Allocating Scarce Resources

the composition of their bundles until they all reach the exchange locus, that is, until all their marginal rates of substitution are equal.

KEY CONCEPTS Preference ordering Indifference curves Goods versus bads

Marginal rate of substitution Exchange locus or contract curve

QUESTIONS AND PROBLEMS For Basic Review 1. Define and explain the economic significance of each of the key concepts. 2. State the assumptions and axioms of choice that are necessary to derive the modern theory of consumer preference. 3. Prove that a. Indifference curves between a pair of goods are downward sloping to the right; b. Indifference curves between a good and a bad are upward sloping to the right; c. Indifference curves do not intersect. 4. Use the Edgeworth box model to derive the contract curve. Show that exchange between the two people can be mutually beneficial.

Problem !•* a- Plot the locations of the five bundles described here.

Quantity of X

Quantity of Y

A

2

4

B C D

3 4 5 2

3 2 2 3

E

b. You are told that an individual is indifferent between A and B. What can you say about this individual’s ranking of the following pairs of bundles? A B A B C

and and and and and

E C C D D

CHAPTER 5_ Resource Allocation and Economic Efficiency

In the last two chapters we developed the components of a model for analyzing the way in which an economy carries out the three tasks of determining what to produce, how to produce it, and for whom. This is a model of a very simple economy in which there are only two people, two goods, and two factors of production. The production box with its isoquants shows the range of choice of alternative production techniques. The production box also portrays how the production technology and the availability of factor inputs limit the range of choice of outputs. This information can be used to derive the production possibilities curve that shows the range of choices of possible production bundles. And given the output levels of the two goods, the exchange box indicates how these goods could be distributed between two individuals. This chapter has three objectives. The first is to use these three components of the model to build a general model of a simple economy and to portray the full range of choices facing this economy. The second is to develop a criterion for evaluating the outcomes of the processes of production and distribution. As already shown, some choices of production technology are better than others in the sense of being efficient. Also, some distributions of the goods between two individuals are better than others in the sense that they make one or both the individuals better off. This idea can be developed systematically and applied to the whole range of economic choices. The third objective is to discuss some implications of this analysis for allocation processes in real-world economies with different institutional arrangements such as markets or command and planning systems.

81

82

The Economic Problem: Allocating Scarce Resources

THE CRITERION OF ECONOMIC EFFICIENCY Economic efficiency is a broader and in some ways a more subtle concept than engineer¬ ing or technical efficiency. The latter is conventionally defined as a ratio of actual output to some theoretically maximum attainable output, given technology and available inputs. This notion of technical efficiency is straightforward and easy to apply in the case of the production of one good. But it is more difficult to use an economy with two or more goods, because within some range, increases in the output of one good require decreases in the output of the other, making the net impact on the numerator of the efficiency ratio ambiguous. In Chapter 3 we offered a definition of economic efficiency in production with two or more goods. Production is efficient if it is not possible to increase the output of one good without decreasing the output of some other good. Production is inefficient if there exists some unexploited opportunity for increasing the output of any good while hold¬ ing inputs and the outputs of other goods constant. Efficiency in production is desirable, and in fact, is necessary for overall economic efficiency. But the concept deals only with production; and the purpose of economic activity is not production per se. Rather, it is the enhancement of human welfare. Overall economic efficiency is defined in terms of the welfares of the individual members of the society.

Definition: An allocation of resources is efficient in economic terms if it is not possible to increase the welfare of one individual without decreasing the welfare of at least one other individual. Efficiency in resource allocation requires that all possible opportunities for increasing the welfare of one individual without hurting someone else be identified and exploited. Allocations that are efficient are often referred to as Pareto efficient or Pareto optimal after the Italian economist Vilfredo Pareto. In his Manuel d'economie politique pub¬ lished in 1909, Pareto argued that the only economic changes that could be considered unambiguously good are those in which at least one individual is made better off while no other individual is made worse off. An economy in which there exist opportunities for making such changes is neither optimal according to Pareto nor is it efficient according to our definition of economic efficiency. Pareto optimality or efficiency requires that all such opportunities be exploited. The terms efficiency and Pareto optimality will be used interchangeably in what follows.

THE CONDITIONS FOR PARETO OPTIMALITY Pareto optimality can be analyzed in terms of what is produced (which point on the production possibilities curve), how it is produced (which point in the production box), and for whom (which point in the exchange box). This analysis reveals that there are three sets of conditions for efficiency in our simple economy with fixed factor supplies. Each condition is necessary. Together they are sufficient for Pareto optimality. They

83

Resource Allocation and Economic Efficiency

are the conditions for efficiency in production, exchange, and output. We discuss each condition in turn. This analysis is an extension of the models of production and exchange developed in the preceding two chapters. We assume that there are only two inputs, capital and labor, two outputs, goods X and Y, and two individuals, Ann and Bob.

Efficiency in Production Figure 5.1 shows a production box that represents the economy^ fixed supplies of labor and capital and the isoquants for production of goods X and Y. Consider point A which is not on the efficiency locus. The marginal rates capital and labor for goods X and Y are given by the slopes (with minus signs) of the X2 andT/Tsoquants at point A. ^The MRTS’s in production of the two goods are not equal. Suppose, for example, that the MRTS*K is equal to 10, while the MRTSlK is j. This means that if the capital input to X production were reduced by 10 units, only one additional unit of labor would be required in order to hold output constant at X2. This additional labor would have to come from the production of Y. In order to give up one unit of labor while holding Y production constant, one needs to substitute only \ unit of the capital obtained from X production. This reallocation would leave the production of both X and Y unchanged; but it also leaves 9) units of capital available to augment the production of either X or Y or both. The extra output of X and/or Y can be used to increase at least one person’s consumption, thus making someone yaAP

\x/ifVilaiit Vicirmincr qn\tnnp

*6

\ \ ^6

Figure 5.1

A Pareto Optimum in Production.

84

The Economic Problem: Allocating Scarce Resources

This numerical example demonstrates that whenever the marginal rates of technical substitution are not equal, it is possible to change the allocation of inputs to the production of two goods so as to increase the production of one or both goods while decreasing the output of neither good. Whenever marginal rates of technical substitu¬ tion are not equal (or what is the same thing, whenever the isoquants for two goods intersect), production is inefficient in the Pareto sense. Thus the condition for Pareto optimality in production is that the marginal rates of transformation be the same in the production of both goods. Condition I:

MRTSxlk = MRTSlx All points on the efficiency locus satisfy this Pareto optimality condition. All points off the locus are Pareto inefficient. The efficiency locus is a locus of Pareto optimal production points or input combinations.

Efficiency in Exchange Each point on the efficiency locus of Figure 5.1 corresponds to a point on the produc¬ tion possibilities curve shown in Figure 5.2. Suppose that the production combination represented by point C has been chosen. This determines the total quantities of X and Y that are available for consumption by the two individuals. The output combination determines the dimensions of an exchange box. As in Chapter 4, the indifference curves representing the preferences of the two individuals, Ann and Bob, have been included in the exchange box. Finally, in order to determine the initial allocation, suppose that Ann controls the production of X so that her initial bundle is made up of the total output ofX and no Y. Similarly, Bob controls the production of Y and his initial bundle includes no X. These initial bundles are shown by point D in Figure 5.2. Point D is not on the exchange locus. Ann and Bob’s indifference curves intersect at point D. Ann’s marginal rate of substitution of Y for X is different from Bob’s. Suppose that at point D Ann’s MRS is 1 while Bob’s MRS is 5. This means that Bob would be willing to give up as much as 5 units of Y in order to get one additional unit of X. This would leave him on the same indifference curve. If Ann were to relinquish one unit of X as part of this exchange, she would need to receive only one unit of Y to stay on her initial indifference curve. If Bob actually gives up 5 units of Y, Ann is obviously made better off while Bob is not harmed. Or if Ann receives only one unit of Y, she is not harmed while Bob is made better off. Or the exchange could take place at terms somewhere between the extremes, for example, 3 units of Y for 1 of X. Then both Ann and Bob would be made better off. This argument could be repeated whenever Ann and Bob’s indifference curves inter¬ sect and their marginal rates of substitution are unequal. Thus unequal marginal rates of substitution mean inefficiency and the potential for making one or both individuals

85

Resource Allocation and Economic Efficiency

Figure 5.2

A Pareto Optimum in Exchange.

better off while harming neither. Pareto optimality requires that the marginal rates of substitution of the two individuals be the same. Condition II:

MRSax y = MRSbxy All points on the exchange locus where indifference curves are tangent satisfy this condition. The exchange locus can be interpreted as a locus of Pareto optimal alloca¬ tions of X and Y to the two individuals, given the total quantities of X and Y available.

Efficiency in Output The first two conditions deal only with efficiency in producing a given output of X and Y and efficiency in allocating that output between the two individuals. Neither condi¬ tion provides a basis for judging whether that output is itself optimal or efficient. In order to judge that, we need to examine the relationship between the marginal opportu¬ nity cost of production as given by the marginal rate of transformation and individuals’ subjective evaluations of the two goods as given by their marginal rates of substitution. Suppose that the production of X and Y is efficient, so that the economy is on the production possibilities curve, for example, at point 0B in Figure 5.3. Further suppose that through exchange, Ann and Bob have reached the exchange locus at point D. Thus both the first and second conditions of Pareto optimality have been satisfied. The

86

The Economic Problem: Allocating Scarce Resources

Figure 5.3

A Pareto Optimum Output.

common marginal rate of substitution between Y and X is given by the slope (with a minus sign) of the line SS'. Suppose that this MRS is equal to The marginal rate of transformation is given by the slope of the production possibilities curve at point Ob and by the slope of the line TT' which is tangent to the production possibilities curve at that point. Suppose that the marginal rate of transformation is 2. Whenever the marginal rate of transformation differs from the (equal) marginal rates of substitution, it is possible to change the output combination and its distribution so as to make at least one person better off without harming the other. The relatively higher marginal rate of transformation indicates that the opportunity cost of X produc¬ tion (2 units of Y) is greater than Ann’s or Bob’s willingness to give up Y for more X Q unit of Y per A). Thus X production is excessive in relationship to the tastes and preferences of the two individuals. X production should be reduced. If X production were reduced by one unit, this would make possible the production of two more units of Y. By assumption, hold Bob’s consumption constant for the moment. Then, in order to permit the reduction of X production, Ann would have to reduce her consumption of X by one unit. She would be willing to do this provided that she received at least j- unit of Y. If this were done, then both Ann and Bob would be on the same indifference curves as before. But since the reduced X production makes it possible to increase the production of Y by 2 units and only \ unit was used to compensate Ann, there remain 1} units of Y to be used to make either Ann or Bob better off than before. In summary, whenever the marginal rate of transformation differs from the (equal) marginal rates of substitution of the two individuals, a disparity between the opportu¬ nity cost of production and the individuals’ subjective valuations is indicated. Thus there is the potential for changing output levels so as to make at least one person better

87

Resource Allocation and Economic Efficiency

off without hurting anyone. A Pareto optimal output is one for which the marginal rate of transformation is equal to the marginal rates of substitution of all individuals. Condition III:

MRSxy = MRTxy = MRSbxy

Conclusions There is an infinite number of possible resource allocations in even the simplest econ¬ omy with two people, two goods, and two factor inputs. But we have seen that many of these are clearly undesirable because they are inefficient. If at one of these allocations one or more of the Pareto optimum conditions are violated, it is possible to move to an alternative allocation and make someone better off without hurting anyone. But even after eliminating all inefficient allocations that are available to the economy, there is still an infinite number of efficient allocations that differ primarily in the relative degree of well-being of the two individuals. An allocation that conferred most of the benefits of production on Ann could be efficient, just as an alternative allocation that conferred most of the benefits on Bob could be. The efficiency criterion is blind to considerations of equity or relative deservingness. In order to make judgments about the merits of alternative efficient outcomes, we must have some basis for evaluating the fairness of the distribution of economic benefits between the two individuals. This is a problem that we leave for discussion (but not solution) in Chapter 18 on welfare economics.

EFFICIENCY AND PRICES This analysis of economic efficiency has been carried out without reference to any particular set of economic institutions. The conditions for achieving economic efficiency apply equally to (1) economies that are organized through private ownership of goods and resources with exchange taking place in markets, (2) economies with collective ownership of resources and central planning, or (3) primitive or traditional economies where resource allocations are determined as part of the whole process of social and cultural relationships. In a centrally planned economy, if efficiency is to be attained, it is necessary to make some arrangements for gathering data on marginal rates of substitution, marginal rates of transformation, and marginal rates of technical substitu¬ tion and for using this information to make decisions about the production and distribu¬ tion of goods. A remarkable characteristic of a market economy is that, under certain conditions, all of this is done more or less automatically. Basically, what is required is that all goods that enter into individuals’ preference orderings be capable of being bought and sold in a market and that all markets be competitive; that is, no buyer or seller has market or monopoly power.

88

The Economic Problem: Allocating Scarce Resources

As consumers come together in a market setting in an effort to make mutually beneficial exchanges, they communicate information about their marginal rates of substitution through their bids and offers. When this exchange process has reached an equilibrium with all individuals making exchanges that place them on the exchange locus, market prices will reflect marginal rates of substitution. And because all individu¬ als in the market face the same set of prices for each pair of goods, all individuals’ marginal rates of substitution will be equal. Thus the Pareto condition for exchange will be satisfied. Prices also convey information to producers. If production is carried out by firms that are part of perfectly competitive industries, firms will be induced to adjust their output levels to the point where the marginal rate of transformation will equal the marginal rate of substitution for all pairs of goods. Finally, competitive forces in input markets and the information provided by prices for factor inputs will combine to lead all producers to the efficiency locus in production. This argument, which is only sketched here and will be detailed in subsequent chapters, leads to the following conclusion: When all goods and all factors can be bought and sold in perfectly competitive markets, individuals in their several roles as suppliers of factors, as managers of production, and as consumers will act in such a way as to achieve an efficient allocation of resources, that is, Pareto optimality. The role of prices in achieving Pareto optimality in a competitive economy is crucial. As this role became better understood by economists, it also became clear that some¬ thing very much like prices existed and would play an important role in achieving efficiency in nonmarket economies. These came to be called “shadow prices” because although they were not directly observable, they played a pricelike role in resource allocation decisions in nonmarket settings. Definition: A shadow price is an indicator or measure of relative scarcity or value in a specific setting. Shadow prices exist for both goods and factors of produc¬ tion. In an economy with a monetary system shadow prices can be expressed in terms of money. But the essential features of shadow prices can best be seen in the context of the simple, nonmonetized or barter economy discussed in the last three chapters. There are four sets of shadow prices in this economy. 1. The marginal rate of substitution is a shadow price. It gives the value to an individual of one unit of X measured in terms of good Y. 2. The marginal products of factors are shadow prices. The marginal product of labor gives the value of an additional unit of labor in production measured in units of output. Similarly, the marginal product of capital gives the value of an additional unit of capital in production measured in units of output. 3. The marginal rate of technical substitution between labor and capital is the value of labor in production measured in units of the capital required to substitute for it, holding output constant. 4. The marginal rate of transformation is a shadow price. It indicates the relative

89

Resource Allocation and Economic Efficiency

scarcity of X measured in units of Y; that is, how much Y must be given up to increase the production of X by one unit. It should be clear now that the Pareto optimum conditions for economic efficiency are really statements about the relationships among different sets of shadow prices. For example, the first Pareto condition requires that the shadow prices of capital and labor be the same for all producers of all goods. And the third Pareto condition requires that the shadow prices of X to consumers (reflecting its value to them) should equal the shadow price of X to producers (representing its relative scarcity in production). Markets are useful economic institutions because they serve to convert shadow prices into market prices. Where markets do not exist or fail to function effectively, planners seeking economic efficiency must estimate shadow prices and use that information to redirect production and allocation decisions until the Pareto optimum conditions are satisfied. Of course, as resource allocations change, shadow prices will change. For example, if more X relative to Y is made available to individuals, their marginal rates of substitution will decrease. It is resource reallocations guided by shadow prices that cause the shadow prices to change in the desired direction, eventually satisfying the Pareto optimum conditions. Shadow prices often play an important role in planning for economic development in less-developed countries. Development planners are typically faced with the problem of choosing a limited number of investment projects from among a long list of alterna¬ tives such as building roads into rural areas, developing hydroelectric power plants on rivers, modernizing port facilities, and so forth. Planners should allocate their scarce resources to those projects that will produce the largest net economic benefits. But how are economic benefits to be measured? In an economy with a well-developed market system the prices of outputs can be used to calculate the benefits, and the prices of inputs will reflect their opportunity costs. But if markets are not well developed or do not exist for certain goods or inputs, then shadow prices must be estimated in order to determine which projects to undertake. For example, consider a proposal to build a road from a city to an isolated rural area. Suppose that the project is planned so as to utilize local labor. Suppose also that the local economy is based primarily on self-sufficient agriculture with limited production for local markets. If working for hire is not common, there will be no market wage with which to measure the opportunity cost of labor. Planners must estimate the marginal productivity of labor in agriculture and the value of its output in order to derive the shadow price of labor. The shadow price may vary with the season. It might be low during the dry season or between planting and harvesting. But the opportunity cost of labor could be quite high during periods of peak activity such as at planting or harvesting. Even in a highly developed market economy the price of labor may overstate its opportunity cost or shadow price. Suppose that there is a high rate of unemployment and a project would draw its labor primarily from the pool of unemployed workers. The shadow price of labor to this project is the output that is lost when labor is diverted

90

The Economic Problem: Allocating Scarce Resources

from other activities. If the other activity is the idleness of unemployment, nothing is lost, and the shadow price of labor would be zero.1 Even in a modern market economy such as the United States there are many things that are valued by people but which are not bought or sold in markets. Examples include the services of local streets and bridges, the recreation services of rivers and lakes, and air that is free from the health impairing and visibility reducing effects of pollution. The shadow prices of these goods are the amounts of money (or other goods) that individuals would be willing to give up in order to get more of them. Shadow prices must be compared with opportunity costs in order to determine whether it would be economically efficient to devote more resources to producing bridges, cleaner rivers, and cleaner air.

SUMMARY In the last three chapters we have provided an overview of the resource allocation functions of any economic system. We have seen how production technology and limits on factor supplies constrain choices. Also, we have introduced the concept of individual preferences in consumption to provide a means for assessing how well economic sys¬ tems perform in satisfying the wants and needs of individuals. The concept of economic efficiency was introduced and conditions for an efficient allocation of resources were established. It is now time to focus on one particular type of economic institution, a competitive market system. Part III begins with a discussion of the conditions for effective function¬ ing of markets. It then develops analyses of the several factors in the market system —first consumers, then firms as producers, and firms as demanders of inputs. Finally, we return to the scene introduced in this chapter, the overall equilibrium of the economy and evaluation of its performance.

KEY CONCEPTS Economic efficiency Shadow prices

Pareto optimality

QUESTIONS AND PROBLEMS For Basic Review 1. 2.

Define and explain the economic significance of each of the key concepts. Every economic system must answer three basic economic questions. What are these questions? Use the diagrammatic techniques developed here to illustrate

‘However, see discussion question 2 at the end of this chapter.

91

Resource Allocation and Economic Efficiency

these questions and examine the range of possible alternative answers. How might one distinguish between “good” and “bad” answers to these questions. 3. Define a Pareto optimum resource allocation. State the three marginal conditions for a Pareto optimum or efficient allocation of resources. Show that unless these conditions are satisfied, the resource allocation will be inefficient in the sense that you have defined the term. 4. * Is Pareto optimality a normative or a positive concept?

Problems 1. * An economy is on its production possibilities curve with MRTXY = 2. Output is allocated among individuals so that they are on the contract curve with MRSXY = 3. Assuming Pareto optimality is the objective, should output be changed? In what direction? Explain your answer and demonstrate that it is true. 2. In Problem 1, Chapter 2, what is the shadow price of spending the sixth available study hour watching TV?

FOR DISCUSSION 1,

Consider a centrally planned economy in a totalitarian state where the welfares of individuals as consumers are of no concern to economic decision makers. Rather, decision makers have their own preferences with respect to, for example, the production of military goods versus consumer goods versus perquisites and benefits for members of the regime. Does the concept of efficiency apply? What are the conditions for efficient resource allocation in this

economy? 2, * Can you think of any reasons that the shadow price of unemployed workers 3,

might be greater than zero? Give some examples of economic goods that are not bought or sold in markets. Discuss how one might estimate the shadow prices of these goods.

SUPPLEMENTARY READINGS Baden, John, Stroup, Richard, and Thurman, Walter. Myth, Admonitions, and Ration¬ ality: The American Indian as a Resource Manager. Economic Inquiry, January 1981, 19(1), 132-143. Koopmans, Tjalling C. Concepts of Optimality and Their Uses. American Economic

Review, June 1977, 67(3), 261-274.

FARTffl The Competitive Market System

CHAPTER 6 An Introduction to Markets and Exchange

actually all societies, whether primitive and simple or modern and complex, engage in some form of exchange.1 Exchange is a voluntary transaction that is entered into by two (or more) parties in which each gives up something and gains something in return. Typically, exchange is bilateral, that is, involving two parties. But more complicated, multilateral exchanges are sometimes observed, as for example, when three or more baseball teams engage in complex swaps of the rights to the services of several baseball players. The terms of exchange (what is sometimes referred to as the terms of trade) are defined by the ratio of what is received to what is given up. This ratio can be interpre¬ ted as a market price. This is clear if one party yields money in return for goods. Then the money given up divided by the quantity of goods received is the money price per unit of the good. Similarly, for the other party to the exchange, the ratio of goods yielded to dollars gives the price of money or the quantity of the good that must be relinquished in order to receive one dollar. More generally, for exchanges involving no money, the ratios of goods given up to goods received are relative prices or barter prices. Systematic and regular exchange implies the existence of a market. A market may not be a place, but rather, a group of individuals or firms that communicate regularly among themselves for the purposes of conducting exchange. They neither need to meet face to face to carry on exchange if other means of communication exist nor need to meet for the physical transfer of the goods exchanged, because what is exchanged is

‘See, for example, Frederick Pryor, The Origins of the Economy (New York: Academic Press, 1977) for a comparative study of exchange and other forms of economic transactions in primitive societies.

95

96

The Competitive Market System

only the right of ownership, not necessarily possession. This concept of rights will be discussed in a later section in this chapter. An economy in which the bulk of production and distribution activities is carried out through exchange is a market economy. A market economy is characterized by exchanges of goods between producers and consumers. Also, in a market economy producers obtain the services of their factors of production through exchange with factor owners. The next 11 chapters of this book entail a detailed analysis of market economies. We proceed by first analyzing the actions of individual actors in markets. These actors include individuals acting as consumers, individuals acting as suppliers of factor inputs, and firms acting as both buyers of inputs and sellers of outputs. This analysis is based on the assumption that actors in markets are motivated by self-interest. They face constraints imposed by technology, limited factor endowments, limited incomes, and so on. We will analyze how they respond to those constraints given the opportuni¬ ties for exchange presented by markets. The functioning of a market is studied as the interaction between two sets of actors, buyers and sellers, each with different motiva¬ tions and facing different constraints. The remainder of this chapter consists of a discussion of the conditions for the effective functioning of markets and a description of alternative market structures.

CONDITIONS FOR EFFECTIVE MARKETS Markets and exchange facilitate the movement of goods and factors into their highest value uses. In order to carry out this function effectively, markets and the societies of which they are a part must have certain characteristics. Unless these characteristics are present at least to some degree, markets will not develop or those that do will not properly perform their roles in achieving an efficient allocation of resources. These characteristics include a legal system that grants enforceable rights of ownership of factors and goods to individuals, that is, a system of property rights. It is also necessary that the costs of transacting business be low relative to the values of the goods ex¬ changed. Information on the prices at which exchanges take place should be readily available. Finally, buyers must have some means for obtaining information on the characteristics and quality of the goods being offered for sale. Each of these require¬ ments will be discussed in turn.

Property Rights A system of property rights is a set of socially sanctioned relationships among individu¬ als regarding their uses of things, where things can refer to either goods or factors. In order for a system of markets to emerge and function smoothly, the system of property rights must grant to individuals: (1) the right to use things, (2) the right to exclude others from using them, and (3) the right to transfer temporarily or permanently some or all of the rights to use and exclusion to someone else. A permanent transfer is a sale, whereas a temporary transfer is a form of rental.

97

An Introduction to Markets and Exchange

It is the right to use a thing and to deny its use to others that creates value to its owner. Property rights systems need not convey unlimited rights to use or exclusion. For example, many local governments utilize zoning ordinances to place restrictions on uses of land in certain areas. Some states place restrictions on the way small arms (rifles, pistols, etc.) can be employed and transported. In some states owners of land adjacent to certain types of water bodies may not prevent others from crossing their land in order to gain access to the water. To the extent that they are binding or meaningful, each of these limits to use or exclusion reduces the value of the thing in question to its owner. In some instances property rights systems effectively grant use of a resource to all members of the society, thus granting no one the right to exclude others. The classic example is the common grazing land of early England and the early days of the New England colonies, in which each member of the community had the right to graze livestock on the “commons.” Resources in which rights to common use are granted without power to exclude are called common property resources. Another modern example is the fishery resources of the oceans. This particular pattern of property rights tends to lead to overuse of the resource and economic inefficiencies. In deciding how many cows to turn into the common grazing land, each farmer weighs the benefits and the costs to him or herself of each extra cow. No farmer is required to consider the fact that his cow reduces the amount of grass available to all other farmers. Failure to take account of all the opportunity costs associated with his additional cow tends to lead each farmer to graze more cows on the common land than the land can effectively carry. This is one example that shows the importance of the nature of a property rights system in understanding how resources will be allocated in a particular situation. The right to transfer a thing is crucial to the role of property rights in permitting the processes of exchange to move resources into their best use. Restrictions on the right to transfer ownership impair resource values. For example, in the arid regions of the West owners of land adjacent to rivers and streams have been granted the legal right to withdraw certain quantities of water for their own purposes, usually irrigation and watering of livestock. However, some states have placed legal restrictions on the ability of owners of these so-called “water rights” to buy or sell them. As a consequence, water may be trapped in relatively low value uses even though other potential users would be willing to pay substantial sums to acquire these water rights. We have talked about property rights in things, either goods or factors of production. But it is also possible to establish property rights in intangibles such as ideas. A patent is a property right in a technical idea. Patents grant exclusive rights to the use of the idea to their owners. They can be bought and sold; or patent owners can grant limited rights to the use of the idea to others in return for a royalty payment. Copyrights on musical compositions, books, poems, and so on are another form of property right in an idea. The government can grant property rights in the form of licenses to carry out certain activities. A license to practice medicine is valuable to the doctor who holds it. There are limits on the activities of the doctor that are part of the terms of the license. And, of course, this license cannot be transferred to another. But a license to a trucking company that grants the right to offer freight services on a given route

98

The Competitive Market System

between two cities can, under certain circumstances, be sold to another firm. And the right to broadcast radio or television signals on a certain radio frequency is also transferable. This discussion of various examples of property rights suggests two conclusions: (1) As stated at the outset, some system of property rights is essential if markets are to emerge and play their role in facilitating exchange and resource reallocation. (2) The precise nature of property rights in a particular economy is an important influence on the nature and pattern of economic activity. The nature of the property rights system affects the economy in two ways. First, what things are included in the system of property rights is important. If certain things are omitted from coverage by a property right system, then markets for them cannot emerge and the normal incentives toward better resource use are absent. Would there be an air pollution problem if all individuals had an enforceable property right in clean and healthful air to breathe? What would happen to the rate of invention and technological improvement if people could not patent or copyright their ideas? As will be shown later, one major explanation for the failure of a market economy to achieve an efficient allocation of resources is gaps or imperfections in the system of property rights. Second, the way in which property rights are defined and allocated across individuals affects the distribution of economic well-being and economic power. For example, in the model of exchange the distribution of rights to ownership of the outputs of produc¬ tion determines what part of the exchange locus can be reached by mutually beneficial exchange. In fact, who owns what must be considered as a major determinant of the answer to the “For whom” question each economy must answer.

Transactions Costs In order for markets to be extensive throughout an economy and effective in carrying out their resource allocation role, the costs of carrying out exchanges must be low relative to the values of the goods being exchanged. These costs of transacting ex¬ changes include the costs of finding willing buyers and sellers, the gathering of informa¬ tion on offers to buy and sell, and the costs of negotiating and consummating exchanges. Transportation costs would not be considered a component of transactions costs, because the transaction involves only the exchange of the right of ownership of the good. If the buyer, having obtained the right of ownership, then wishes to obtain possession as well, she can enter into a separate exchange transaction with a provider of transportation services. The delivered good entails two exchanges, one for the right of ownership and one for the service of delivery. Transactions costs can take many forms. For example, searching for buyers and sellers and gaining better information on prices can take time. The cost is the opportu¬ nity cost of the time used. There can also be out-of-pocket expenses such as telephone charges, travel, and the legal expenses associated with executing contracts of sale. The activities of search and information gathering can be carried out by the buyer and/or the seller; or they may be provided by third parties who specialize in trying to make

99

An Introduction to Markets and Exchange

transactions easier and less costly for buyers and sellers. These individuals provide these services for a fee, thus acting as middlemen or brokers. Markets can work perfectly as in the simple textbook examples only when transac¬ tions costs are zero. In fact, this is usually the implicit or explicit assumption of the simple textbook exposition. In the absence of transactions costs the buyers’ demand curve Dx and suppliers’ supply curve Sx would lead to a market price of (see Figure 6.1). Suppose, however, that transactions costs are equal to tb per unit purchased for buyers and are ts per unit sold for suppliers. Transactions costs raise the cost of supplying any given quantity of the good and the market. The effective supply curve is shifted up by the amount of the transaction costs per unit incurred by sellers. The demand curve Dx represents buyers’ willingness to pay for a given quantity. With transactions costs, part of this willingness to pay is absorbed by the process of engaging in exchange. The part of willingness to pay that actually reaches the sellers is shown by the curve labeled Dx-tb. The effect of buyers’ transactions costs is to shift the effective market demand curve down by tb. As shown in Figure 6.1, the effect of transactions costs is to raise the effective price to buyers to P2 and lower it to sellers to P3. The presence of transactions costs also lowers the equilibrium quantity in the market, compared to what it would be in the absence of transactions costs. If transactions costs were to grow to be equal to or greater than the vertical distance DS, then the quantity exchanged in this market would drop to zero. High transactions costs can prevent markets from developing for goods. Conversely, a technological improvement that reduces transactions costs in a market can be expected to lead to a lower price to purchasers and to increase the quantity exchanged in that market. Although it may often be reasonable to assume costless transactions in constructing models of certain markets, some important economic phenomena can only be under-

Px, dollars

X per period Figure 6.1

Transactions Costs and Market Price and Quantity.

100

The Competitive Market System

stood when transactions costs are made an explicit part of the model. For example, transactions costs can explain why markets have not developed for some things. Most newspapers are read by only one or two persons before being discarded rather than being resold to other potential readers. But there are extensive and active markets for used cars, boats, airplanes, and houses. This is due at least partly to the fact that finding buyers for secondhand papers is costly relative to the value of a used paper, especially if the paper is a day or more old, whereas value is high relative to transactions costs for these other goods. Another implication of the concept of transactions costs is that it may be less costly to arrange some types of economic activity by means other than through markets. For example, this could explain why in most communities police and fire protection are provided by the government rather than arranged through private markets.

Information The speed with which information about price is disseminated to buyers in the market is an important influence on the performance of the market. For example, suppose that there are several sellers of a homogeneous product and that initially all sellers are charging the same price. Now suppose that one seller lowers the price. If there is no means of disseminating price information to potential buyers, the only people who will be aware of the lower price will be the existing customers of this firm. The firm’s quantity sold will increase somewhat as the existing buyers respond to the lower price by purchasing more. But the firm will gain no new customers and the two prices for this good will persist through time. If information on the lower price is disseminated gradually to other buyers, however, the firm will gradually gain customers and will continue to increase its quantity sold. But eventually the other firms will learn of the first firm’s lower price. To prevent further loss of customers they must lower the price, too. The speed with which informa¬ tion spreads determines how quickly the market is restored to an equilibrium with one price for all buyers. If price information spreads instantaneously and costlessly, then all transactions at a given point in time must take place at the same price. For markets to function well, potential buyers must also have good information on the characteristics and qualities of the goods or factors of production being offered for sale. Here, too, the conventional textbook expositions of markets and exchange usually assume perfect information on the part of all buyers and sellers. But in many instances the absence of perfect information has an important influence on the outcomes of market processes. First, in the absence of perfect information, it cannot be asserted that voluntary exchange is mutually beneficial. All that can be said is that at the time the exchange took place, on the basis of information available then, both parties thought they would be made better off by undertaking the exchange. But if the available information was incomplete, one (or both) of the parties might find out that she was mistaken about the quality of the goods she was purchasing and that she regrets entering into the exchange. In other words, the exchange actually made her worse off rather than better off.

101

An Introduction to Markets and Exchange

Because improved information on product quality may prevent costly mistakes or identify high quality goods at bargain prices, information on quality and price is valuable. Information may be costly to obtain; but it can be sold at a price. Hence markets may emerge for information on product quality. For example, engineering consulting firms find it advantageous to develop expertise on the characteristics and capabilities of pollution-control devices offered for sale by different manufacturers. They then sell this expertise along with design services to municipalities and companies being forced to meet pollution abatement requirements. Another example of the provi¬ sion of product quality information for a fee is the magazine Consumer Reports, published by an independent (and in this case nonprofit) testing organization. Because in some cases transactions costs for information may be high relative to the value of information, private markets for information may not emerge. If private markets for information do not emerge, governments might take action to compel the provision of information at no charge, for example, by requiring that product labels include information on ingredients, specifications, performance characteristics, and so on. The federal government now requires that many household appliances, including automobiles, carry labels providing information on their energy efficiency characteris¬ tics. Alternatively, governments may establish product quality standards and require that all units of the commodity that are sold meet these standards. The federal govern¬ ment has established limits on the residues of certain pesticides and toxic chemicals in foods that are sold in interstate commerce. And new automobiles must meet govern¬ ment-imposed safety standards. Potential buyers of these products are thus conveyed information about these aspects of the quality of the goods that they buy. The problem of information on quality is particularly acute where the good being exchanged is services of labor as a factor input. Potential employers seek information on labor quality through devices such as requiring that applicants take standardized tests or provide references from past employers or teachers. But this information may be unreliable where, as in the case of tests, it is poorly related to the worker characteris¬ tics of interest to the employer. This set of problems has led employers to adopt two modes of behavior in an effort to cope with poor information on worker quality. Both modes are sources of imperfection in the functioning of markets of labor services. The first mode of behavior is screening. Screening occurs when employers impose unnecessarily high requirements for job applicants, for example, in terms of education (high school graduate), or height as in the case of policemen. These requirements are imposed in the belief that the percentage of applicants possessing the desired worker characteristic will be higher in the pool of applicants who satisfy the screening require¬ ment than in the general pool of potential applicants. Screening is a rational response to imperfect information on the part of employers, provided that the benefits in the form of a higher probability of hiring workers with the desired characteristic outweigh the costs (if any) in the form of higher than necessary wages. But screening works to the disadvantage of persons who do possess the relevant worker characteristic but do not meet the essentially irrelevant screening requirements. The second mode of behavior is statistical discrimination. Statistical discrimination is similar to screening in that employers rely on the average characteristic of a group

102

The Competitive Market System

to draw some inference about the characteristic of an individual in that group. But it is more insidious in that the groups are defined in terms of characteristics such as race, sex, and age. For example, women on average and historically have had a weaker attachment to the labor force than men. They are more apt to leave the labor force when they marry or have children. When employers refuse to consider applications from women for positions requiring a long-term commitment on the part of the employee simply because they are women, this is statistical discrimination. Statistical discrimina¬ tion may be rational on the part of the employer if the inference drawn about members of the group is based on valid information, for example, that women are in fact more likely to leave the labor force. But it is irrational when the inference is based on an unrealistic stereotyped perception of the group in question. But whether it is rational or irrational from the employers’ point of view, statistical discrimination always works to the disadvantage of qualified applicants from the group in question.

MARKET STRUCTURES The term market structures refers primarily to the numbers of buyers and sellers on either side of the market. Structure is important, as will be shown in later chapters, because it is a major determinant of the market conduct of buyers and sellers. Conduct in turn is a major determinant of the economic performance of a market, that is, its ability to contribute to an efficient allocation of resources. In order to concentrate our analysis on the relationship between structure and performance, we will assume perfect functioning of markets in the following respects: (1) property rights in the goods in question are well defined; (2) transactions costs are zero; and (3) buyers have perfect information on prices and product characteristics. This last assumption guarantees that all transactions will take place at the same price in this market; that is, no buyer would willingly pay a higher price if he or she knew that some other seller was offering a lower price for the good.

Output Markets Typically, markets for outputs are characterized by large numbers of buyers. With large numbers no buyer is large enough so that his or her purchase can have any influence on the market price. All buyers, then, are price takers in these markets. There are four major categories of market structure in output markets of the sort described here. 1. Perfect competition. The output market is perfectly competitive if four conditions are met: a, A large number of sellers exist so that no one seller can influence the market price by increasing or decreasing the quantity supplied. In a perfectly competitive output market, sellers are price takers, too.

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An Introduction to Markets and Exchange

b. The product is homogeneous; that is, there must be no differences in the characteristics of goods sold by different producers. This makes buyers indifferent as to which producer’s output they purchase, provided that there are no differences in price across sellers. c. Mobility of producers/sellers exists. They must be free to enter or exit this market in response to the economic signals given by prices, costs, and profit or loss. Barriers to mobility can slow or halt the adjustment of the market to changing economic circumstances.

d. All participants in the model have full information concerning all the relevant economic variables. 2. Monopoly. A market in which there is only one seller who is free to set whatever price he or she chooses is a monopoly market. Barriers to entry, that is, to inward mobility, are frequently a factor in explaining the existence of monopoly. These first two categories, many sellers and one seller, represent polar extremes of market structure. The remaining two categories are intermediate cases. 3. Monopolistic competition. In a monopolistically competitive market each pro¬ ducer’s product is differentiated in some respect from those of all other producers in the market. Differentiation can arise because of differences in technical characteristics, because of allegiance to brand names, differences in the nature of the services provided with the product, or differences in the location of sellers relative to buyers. Although product differentiation distinguishes monopolistic competition from perfect competi¬ tion, both structures are characterized by many sellers. Product differentiation gives some degree of market power, that is, ability to influence the price of its product to each seller. If, when one seller raises its price somewhat, the quantity sold decreases but does not drop all the way to zero, the market is monopolisti¬ cally competitive. Sellers can raise their price somewhat without losing all sales because of differences in product quality. Some buyers are willing to continue some level of purchases even at the higher price. In other words, they are willing to pay the higher price for the perceived difference in quality. 4. Oligopoly. Oligopoly means few sellers. “Few” is an imprecise term. The term oligopoly covers markets with as few as two sellers and as many as a dozen, or perhaps a score of sellers. The major feature of oligopoly markets is that each seller must be aware of and take into account the pricing decisions of each, or at least some, of the other sellers in the market. The boundary between oligopoly and monopolistic competi¬ tion is reached when the numbers of sellers has grown to the point that each seller can ignore the pricing decisions of the other participants in the market.

Markets for Factor Inputs In general, markets for factor inputs such as the services of labor are characterized by many sellers. Of course, there are exceptions such as the markets for the services of individuals with unique capabilities and specialized talents, for example, professional

104

The Competitive Market System

athletes. But for the most part, it is reasonable to assume large groups of undifferen¬ tiated or homogeneous sellers of factor services, each with no power to influence the price of that factor. Economic theory distinguishes three categories of market struc¬ tures in markets with many sellers. Each category is differentiated by the numbers of buyers of factor services. 1. Perfect competition. Factor input markets are perfectly competitive if in addition to a large number of sellers of homogeneous factors, there is a large number of buyers, no one of which can influence the price in the market. 2. Monopsony. A market is monopsonistic if there is only one purchaser of the factor service. Thus that purchaser can influence the price in the market by its choice of quantity. 3. Oligopsony. A market is oligopsonistic if there are a few purchasers, each with the ability to influence the market price. In an oligopsonistic market each purchaser must be aware of and take into account the prices offered by the other buyers in the market.

Other Cases There may be cases in which neither the supply side nor the demand side is character¬ ized by large numbers of price takers. For example, cases may exist in which one monopoly seller faces a single monopsony buyer. This is called a bilateral monopoly. If a labor union organizes all workers in a labor market and attempts to negotiate a wage agreement on their behalf with a single monopsony buyer of labor, this would be a case of bilateral monopoly. There may also be cases of small numbers of buyers and sellers on each side of the market. But the economics literature has not coined a specific term for this case.

SUMMARY Systematic and regular exchanges of goods for goods or goods for money require the existence of markets. For markets to function effectively, there must be a well-defined system of property rights, transactions costs must be low relative to economic values, and there must be good information on product characteristics and the prices at which exchanges take place. Market structure (principally the number of buyers and sellers) is an important determinant of the conduct of market participants and the economic performance of a market. Output markets are typically characterized by many buyers. Output markets may be perfectly competitive, monopolistically competitive, oligopolistic, or monopo¬ listic depending on the number of sellers and the degree of market power conferred by such things as barriers to entry and product differentiation. Markets for inputs typically have many sellers and may be competitive, oligopsonistic, or monopsonistic depending on the numbers of buyers.

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An Introduction to Markets and Exchange

KEY CONCEPTS Market economy Property rights Transaction costs Information Market structure Perfect competition

Monopoly Monopsony Oligopoly Oligopsony Monopolistic competition

QUESTIONS AND PROBLEMS For Basic Review 1. Define and explain the economic significance of each of the key concepts.

For Discussion 1. * Can you think of some goods for which property rights are poorly defined, poorly enforced, or not defined at all? Describe the consequences of lack of effective property rights in each case. 2, It has been said that information is a good that can be bought and sold. Can you think of some examples of markets for information? Are there any barriers to the further development of markets for information?

SUPPLEMENTARY READINGS Demsetz, Harold. Toward a Theory of Property Rights. American Economic Review, May 1967, 57(2), 347-359. Demsetz, Harold. The Cost of Transacting. Quarterly Journal of Economics, February 1968, 82(1), 33-53. Stigler, George J. The Economics of Information. Journal of Political Economy, June 1961, 69(3), 213-225.

CHAPTER 7 Individual Preferences and the Theory of Demand

in this chapter we will analyze the behavior of individuals as purchasers of goods and services. Individuals are assumed to have preference orderings over all possible con¬ sumption bundles as described in Chapter 4. They have fixed money incomes and can purchase goods at fixed or constant prices up to the limit of their incomes. Individuals are assumed to strive to reach the most preferred bundle given the constraints imposed by fixed money incomes and prices. The objectives of this analysis of the behavior of consumers are twofold. First, at the positive level we wish to explain individuals’ actions in a market economy—specifically, to make predictions about how individuals respond to changes in prices and incomes. These predictions constitute the theory of consumer demand and provide the basis for the demand side of the supply-demand model of markets. The model developed in this chapter will also prove useful, with suitable modifications, in the analysis of several related areas of individual behavior and choice, for example, individual decisions about work and the supply of labor, the allocation of income between consumption and savings, and choices concerning goods that are not bought and sold in regular markets. Examples of such nonmarket goods are safety, clean air, and recreation. The second objective is normative—to provide a basis for evaluating the outcomes of market processes. We have already stated the value judgment that an economic system should be judged on the basis of its contribution to individuals’ welfare or well-being. And this well-being is defined in terms of individual preferences. One application of this value judgment is the concept of Pareto optimality that was devel¬ oped in Chapter 5. In broad terms, the normative objective of the analysis of consumer demand is to determine whether, or under what conditions, individuals acting in accordance with their own preferences and purchasing goods in markets will achieve Pareto optimality. 106

107

Individual Preferences and the Theory of Demand

Normative analysis also provides a basis for measuring in monetary terms the changes in well-being associated with changes in economic conditions such as prices or the availability of nonmarketed goods. Such changes are often caused by governmen¬ tal action in pursuit of some policy objective. Thus this analytical framework can be useful in the economic analysis of public policies such as pollution control, public housing, and food stamps. The economic evaluation of these policies is usually based on a comparison of benefits with costs. The model of consumer behavior developed here gives the basis for defining and measuring benefits. Before turning to the main part of the chapter, let us briefly discuss terminology. We have referred to the individual as the basic unit of analysis of consumer behavior. Many people live alone rather than in families or other groupings; for them, the concept of individual consumption choice is clearly relevant. But many individuals live as mem¬ bers of families or households. Households typically pool at least some portion of the incomes of their members. And many households include members with no income, for example, children or the elderly. A substantial part of the consumption of these households is collective in nature. Some goods provide benefits to all the members simultaneously rather than to each separately, for example, housing and major appli¬ ances. For this reason it may be more appropriate to speak of the household as the basic unit of the analysis of consumption. This terminology, however, tends to obscure two fundamental questions about household behavior: (1) How are collective decisions about consumption made? Is the authority to make consumption decisions vested in one individual? Are decisions made by majority vote? (2) By what rule or procedure are resources allocated within the household? To each according to his need? To each according to his contribution to household income? These are interesting areas of inquiry involving economics and other disciplines such as sociology. These questions also touch on some important issues that go beyond consumption choices, for example, decisions about having chil¬ dren, whether women members of the household will enter the labor force, and how responsibilities for household work are divided.

PREFERENCE FORMATION AND CONSUMER SOVEREIGNTY It has been assumed that individuals have preference orderings, but nothing has been said about where these orderings come from or what determines their characteristics. The usual approach is to ignore the question by taking preferences as given or deter¬ mined exogenously, that is, outside the economic system. Preferences are usually treated as objective data on which the analysis of consumer behavior and the evaluation of the outcomes rest. The doctrine of consumer sovereignty also rests on the assumption that preferences are exogenously determined. According to the consumer sovereignty doctrine, produc¬ ers respond to consumers’ preferences by adjusting output in keeping with the price signals sent by the market system. Outputs of goods in high demand by consumers are increased until an equilibrium is reached. Thus producers serve consumers. Because

108

The Competitive Market System

individuals are the best judges of their own welfare, all of this is good in terms of maximizing individual welfare. This doctrine and the assumptions on which it depends have been criticized on several levels. The easiest criticism is that advertising manipulates people and molds their preferences so as to induce them to make frivolous purchases. This criticism has been most closely associated with John Kenneth Galbraith.1 In an inversion of the consumer sovereignty doctrine he has argued that consumers respond passively to producers who decide what to produce and then manipulate consumers into buying it. In defense of consumer sovereignty it can be argued that advertising also serves to convey information about the availability and characteristics of products, especially new products. Also, when two or more companies advertise competing brands of the same products, their efforts may cancel out with a net effect of zero on consumer behavior. It is unsatisfactory to argue the issue at this level of generality. The question is essentially an empirical one. But it has proven extraordinarily difficult to separate the manipulative effect of advertising from all other influences on consumer behavior, including the purely informational aspects of advertising. The second level of criticism represents an attempt to get beyond the weaknesses and inconclusiveness of the advertising debate. Almost 50 years ago Frank Knight acknowl¬ edged that preferences cannot be taken as given entirely independently of the economic system. He said, In large part the individual wants themselves are created by social intercourse, and their character is also largely dependent upon the form of organization of the economic system upon which they are dependent for their gratification.2 An economic analysis that ignores or simply assumes away the influence of social and economic factors on preferences is potentially subject to serious error. But what can be said about this influence and its implications for consumer preferences and the doctrine of consumer sovereignty? Paul Baran has carried the criticism to a third and more fundamental level. He wrote, The truth is that wants of people are complex historical phenomena reflecting the dialectic interaction of their physiological requirements on the one hand, and the prevailing social and economic order on the other ... the issue is not whether the prevailing social and economic order plays a prominent part in molding people’s “values,” volitions, and preferences ... the issue is rather the kind of social and economic order that does the molding, the kinds of “values,” volitions, and preferences which it instills into the people under its sway.3 Baran went on to argue from a Marxist perspective that the effect of a market economy dominated by large corporations is to produce people who are overly materialistic,

'See John Kenneth Galbraith, The Affluent Society (Boston: Houghton Mifflin, 1958), especially Chapter 11. 'Frank H. Knight, On Economic Organization (New York: Harper & Row, 1933), p. 9. 'Paul Baran, The Political Economy of Growth (New York: Monthly Review Press, 1957), Forward to the Modern Reader edition, 1968, p. xvi.

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Individual Preferences and the Theory of Demand

dehumanized, competitive, gullible, and susceptible to manipulation by monopoly capitalists. Baran does not reject the principle of consumer sovereignty. He believes that individuals should not have their consumption patterns dictated to them, but rather, should be free to make their own consumption choices. As he put it, The real problem is . . . whether an economic and social order should be tolerated in which the individual, from the very cradle on, is so shaped, molded and “adjusted” as to become an easy prey of profit-greedy capitalist enterprise and a smoothly-functioning object of capitalist exploitation and degradation. ... a society can be developed in which the individual would be formed, influenced, and educated not by a profit- and market-determined economy, not by the “values” of corporate presidents and the outpourings of their hired scribes, but by a system of rationally planned production for use, by a universe of human relations determined by and oriented toward solidarity, cooperation, and freedom.4

The point of this is to show that at the bottom, the doctrine of consumer sovereignty rests on a somewhat circular argument rather than to endorse or reject Baran’s particu¬ lar critique of the preference patterns of American consumers or the economic system that helped to shape them. A market economy is said to be good, at least if markets are competitive, because it satisfies consumer preferences. But those preferences may be shaped in important ways by the nature of the market economy as a social institu¬ tion. Are these particular preferences good? Are they worth satisfying? Or would people be better off under an alternative economic system with the different preference patterns it would help to create? Clearly, Baran believes that the answer to the last question is “Yes.” Others may disagree with this conclusion. Where does this critique of the assumption of exogenous preferences and the doctrine of consumer sovereignty leave us? The assumption of exogenous preferences plays an important role in the positive analysis of consumer behavior. For the purpose of developing predictive models of consumer behavior the term “exogenous preferences” can be given a fairly narrow interpretation. We will take it to mean that individuals’ preference orderings are stable in the short run and not themselves dependent on prices, incomes, and the consumption choices made by individuals.5 Thus people repeatedly faced with the problem of choice will tend to react the same way if prices and income are unchanged. This may appear to be an overly restrictive interpretation. However, it is possible to

*Ibid, p. xvii. For a similar argument, see Herbert Gintis, “A Radical Analysis of Welfare Economics and Individual Development, Quarterly Journal of Economics, 86(4) (November 1972), 572-599. 5Leibenstein has argued that individual preferences may not be exogenous in this sense. Specifically, individu¬ als might prefer more of a good if they knew others were consuming it (a “bandwagon effect”) or prefer less of it if they knew it were popular with others (a “snob effect”) or prefer the conspicuous consumption of high-priced goods as a display of wealth and status. If preferences are influenced by price and the behavior of other consumers in these ways, some of the predictions of demand theory must be altered. See Harvey Leibenstein, Bandwagon, Snob, and Veblen Effects in the Theory of Consumers’ Demand, Quarterly Journal of Economics, 62(1) (February 1948), 165-201, reprinted in William Breit and Harold M. Hochman, Readings in Microeconomics, 2d ed. (New York: Holt, Rinehart and Winston, 1971).

110

The Competitive Market System

modify and extend the theoretical models developed in this chapter to accommodate dynamic phenomena such as new information, new products, and learning by doing. The result is more complex models. But there are no basic changes in the nature of the predictions these models make about how consumers respond to changes in prices and income. Clearly, it would be desirable to develop an economic theory of the formation of preferences that considered sociological, cultural, and historical influences on prefer¬ ences. Baran’s discussion of the impact of monopoly capitalism on preferences is a step in this direction. But it could hardly be called a theory. The development of such a theory is a task still waiting to be accomplished. Concerning the normative analysis of consumer behavior, the implications of this discussion are more disturbing. If it is accepted that cultural and social forces and the nature of the economic system are important influences in shaping consumers’ prefer¬ ences, then we must do one of two things in order to make normative statements about consumer behavior. One alternative is to state as a value judgment that individual freedom of choice in economic matters is a fundamental principle on which all norma¬ tive analyses must rest. This rules out any criticism of economic choices on any grounds. Given this principle, economic systems can be judged on the basis of the nature and degree of restrictions they impose on individual choice. The other alternative is to state explicitly a criterion for evaluating or judging preferences. This means that the analyst is placing him or herself in a superior position to the individual whose preferences are being judged. The analyst is saying, in effect, that she knows better than the individual what is good for him. That some economists are willing to judge the preferences of others is evident from the examples of Galbraith, Baran, and Gintis. But theirs is a minority position within the economics profession. In this book we will follow the conventional wisdom in taking consumers' preferences to the exogenous and to be a sound basis for making normative judgments.

THE INDIVIDUAL S EQUILIBRIUM Consider an individual who has a preference ordering over the two goods, X and Y, which is consistent with the axioms of preference given in Chapter 4. The assumption of only two goods is made primarily to permit graphical analysis of the problem. A comprehensive analysis with many goods is possible with other mathematical tech¬ niques. But the two-good model is perfectly capable of answering most of the questions we ask of demand theory; for example, How does the quantity demanded of a good vary with changes in its own price and in the individual’s income. The two-good model is adequate because the other good can be interpreted as an aggregation or index of all other goods combined. As long as there are no changes in the relative prices of any of the other goods, they can be treated as a single composite good in the analysis of individual preferences and demand. Assume that an individual has access to a set of markets in which she can purchase X and Y at fixed prices, Px and PY> and that her money income is fixed at M per period

Ill

Individual Preferences and the Theory of Demand

of time. She will choose to purchase that combination of X and Y that is most preferred —given that only certain combinations or bundles are attainable because of the con¬ straint imposed by prices and limited income.

The Budget Constraint The individual’s range of choice is limited to those bundles that can be purchased with her total income—that is, those bundles for which the total expenditure is equal to or less than money income. This is the income constraint or budget constraint. It can be stated algebraically, Px ■ X + PY ■ Y < M

(7.1)

If the inequality holds, then the individual does not spend all her income. But this is implausible given the assumptions. With unspent income she could increase her pur¬ chases of either X or Y or both, thus attaining a larger bundle. According to the axiom of nonsatiety, the larger bundle would be preferred. Thus the individual will spend all her income. This seems to rule out savings on the part of consumers. But savings can be accom¬ modated in a more complex version of the model with many goods by treating savings as a separate good. In Chapter 13 a simple version of a model with savings is presented. We have shown that Equation (7.1) can be treated as an equality. This budget constraint can now be rearranged algebraically to show the maximum amount of Y that can be purchased consistent with available income for each possible quantity of X. This relationship is

The first term on the right-hand side of this equation shows the maximum amount of Y that can be purchased if the amount of X being purchased is zero. If all income is spent on Y, the maximum amount of Y that can be purchased is M/PY. This is Ymax in Figure 7.1. Similarly, if the purchases of Y were zero, the maximum amount of X that could be purchased would be M/Px. This is shown as Amax in Figure 7.1. All other points on the straight line between the two intercepts, Yrnax and Xmax, can also be attained with the expenditure of M. This is the budget line. For example, suppose that income is $200 per period, the price of X is $10, and the price of Y is $5. Then the budget constraint is $200 = $10 -A + $5 Y. The budget line is Y = S200/S5 - ($ 10/$5) • X = 40 - 2X

If no X is purchased, 40 units of Y can be purchased. If purchases of Y are zero, then 20 units of X (2X = 40) can be purchased. How much Y could be purchased when purchases of X are at 10 units per period?

112

The Competitive Market System

X per period Figure 7.1

The Budget Constraint and Attainable Consumption Bundles.

As shown by Equation (7.2), the slope of the budget line is given by (with a minus sign) the ratio of the prices, PX/PY- The slope of the budget line shows how many units of Y must be given up in order to provide the money to purchase one more unit of X. From the previous example with Px = $10 and Px = $5, a reduction of 2 units in the purchase of Y makes it possible to purchase one more unit of X. Note that if Px were zero, the budget line would be horizontal (zero slope) and there would be no limit on the amount of X that could be obtained for consumption.

Shifting the Budget Line Because one of our main interests in this chapter is to be able to predict how individuals will respond to changes in money income and prices, it is important to see how these changes would affect the budget line. An increase in money income makes it possible to purchase either more X or more Y or more of both goods. This means the budget line is shifted out. And because only income has changed, the slope of the budget line does not change. Figure 7.2 shows the budget line M XM\ that is associated with an income of Mx. The effect of an increase in income from M, to M2 is a parallel outward shift of the budget line to M2M2. If income is decreased to M3, this is portrayed by a parallel inward shift of the budget line. An increase in the price of X, holding money income and the price of Y constant, reduces the amount of X that can be purchased but does not affect the maximum amount of Y that can be purchased when X is zero. As a result, the budget line rotates clockwise around its Y intercept. With an increase in the price of X, the slope of the budget line becomes steeper (as shown in Figure 7.3). A decrease in the price of X would result in a counterclockwise rotation of the budget line so that it becomes less steep and lies outside the old budget line at all points other than the Y intercept. A decrease in the price of Y, other things equal, makes it possible to purchase more

113

Individual Preferences and the Theory of Demand

Figure 7.2

The Budget Constraint with Changes in Money Income.

Y per period

Figure 7.3

The Budget Constraint with Changes in Prices.

Y but does not affect the maximum attainable quantity of X. The budget line rotates clockwise around the X intercept (as shown in Figure 7.3). On the other hand, an increase in the price of Y would make the budget line less steep. It would rotate counterclockwise around the X intercept.

The Optimum Consumption Bundle In order to determine which of the attainable bundles the individual will choose, we must examine her preference ordering. Figure 7.4 shows the individual’s budget con¬ straint for a given money income and prices and three indifference curves from her

114

The Competitive Market System

X per period Figure 7.4

The Optimum in Consumption.

preference ordering. It is apparent from visual inspection that the optimum consump¬ tion bundle is C. This bundle is on the highest attainable indifference curve, given the budget constraint. Other bundles such as A and B are on indifference curves that cross the budget line. All bundles on indifference curve I3 would be preferred to bundle C, but they are out of reach of the individual, given her limited income and the market prices for X and Y. The optimum bundle C is at a point of tangency between the highest attainable indifference curve and the budget line. Tangency is a necessary condition for the consumption bundle to be optimum for the individual. This tangency condition can be stated differently. We found from Chapter 4 that the negative of the slope of the indifference curve, — AY/AX, is termed the marginal rate of substitution or MRSXY. And we know that the negative of the slope of the budget line is PX/PY. Tangency between the indifference curve and the budget line means that their slopes are equal at that point. This in turn implies the equality of the marginal rate of substitution and the price ratio.

The Condition for Optimum Consumption: The optimum consumption bundle is the bundle that is on the highest attainable indifference curve, given market prices and a limited money income. To obtain the optimum consumption bundle the individual must spend all her money income and choose that bundle for which the marginal rate of substitution is equal to the price ratio; that is, MRSxy = Py

This condition can be explained in another way that more clearly expresses its economic content. Recall that the marginal rate of substitution reflects the maximum

115

Individual Preferences and the Theory of Demand

terms on which the individual is willing to give up some of one good in order to get one more unit of the other good by moving along an indifference curve. The ratio of prices reflects the terms at which the individual must relinquish one good through exchange at given market prices in order to get one more unit of the other good. Whenever there is a divergence between the individual’s marginal rate of substitution and the market price ratio, there is a potential for the individual to make himself better off by substituting at the given market price ratio. Referring back to Figure 7.4, suppose that at point D the individual’s MRS is 4 while the ratio of market prices, PX/PY, is 2. The individual is willing to give up as much as 4 units of Y in order to get one more unit of X. But the market requires that he only give up 2 units of Y to get more money to purchase an additional unit of X. Suppose Px is $10 and P Y is $5. Then reducing purchases of Y by 2 units saves the $10 required to purchase one more unit of X. This move along the budget line downward and to the right from point B clearly makes the individual better off, because by giving up only 2 units of Y he is on a higher indifference curve (see Figure 7.4). Suppose that at point A, MRSXY is equal to \ while the price ratio is 2. The individual is willing to give up j unit of Y to get one more unit of X while the market requires him to give up 2 units of Y to obtain one more unit of X. These undesirable terms of exchange relative to the marginal rate of substitution make it undesirable for the individual to move downward to the right from point A, increasing the consumption of X. Rather, the individual should consume less X and more Y. The assumed value for the MRSxy shows that the individual is willing to give up 2 units of X to get one more unit of Y. But the market prices show that if the individual reduces consumption of X by 2 units, he will have enough money to purchase 4 additional units of T. Clearly, this makes the individual better off; that is, it puts him on a higher indifference curve. Only when the marginal rate of substitution and the price ratio are exactly equal can there be no opportunities for attaining a higher indifference curve by some substitution of X for Y or vice versa.

Price and Marginal Willingness to Pay An examination of the condition for optimum consumption makes it possible to give a second interpretation to Px which is of considerable normative significance. Of course, Px represents the objective terms on which an individual can exchange money for X or vice versa. But it can also be interpreted as representing the subjective value of X to the individual at the margin. Recall that the marginal rate of substitution is AY

MRS x y

AX

u*

Substituting this expression into the condition for optimum consumption gives AT AX

and rearranging this gives

_

Px AP y

116

The Competitive Market System

pY • ay Px

=

AX

(7.3)

Since AX and A Y are of opposite sign, the right-hand side of this equation is positive. The right-hand side is a measure of the individual’s marginal willingness to pay for X. Definition: An individual’s marginal willingness to pay for X is the money value of the maximum amount of Y that the individual is willing to give up in order to obtain one more unit of X, holding well-being constant, that is, while staying on the same indifference curve. The condition for optimum consumption can be interpreted as requiring that the individual adjust his consumption to the point where his marginal willingness to pay for X is just equal to the market price of X. This in turn means that if the individual has chosen the optimum consumption bundle, the observed price of X can be taken as a measure of the marginal willingness to pay for X or the subjective value of X to the individual. Of course, by a different rearrangement of Equation (7.3) the same argument can be made for Y and its price.

Convexity of Indifference Curves In Chapter 4 it was assumed that indifference curves are convex to the origin. It can now be shown why this is a reasonable assumption and one that appears to be consistent with observations of individuals’ consumption behavior. The individual faced with a given budget constraint is observed to choose bundle A in Figure 7.5. From this we can infer that he prefers A to all other bundles such as B and C lying on or below the

Figure 7.5

Indifference Curves Are Convex.

117

Individual Preferences and the Theory of Demand

budget line.6 Because bundles such as D and E that lie on or above and to the right of the vertical and horizontal lines meeting at point A contain more of one or both goods, they must be preferred to A. Thus the indifference curve through A must pass to the right of points B and C but to the left of points D and E. Only a convex indifference curve can do that. The argument for convexity can also be made by examining what the model would predict about consumer behavior if indifference curves were not convex, but rather, were concave to the origin as shown in Figure 7.6. At point A indifference curve 7, is just tangent to the budget line and the marginal rate of substitution is equal to the price ratio. Because of the shape of the indifference curves, any other point on the budget line would be preferred to point A. Equating the MRSXY with the price ratio leads to the least preferred position attainable by spending the given money income, not the most preferred position. In Figure 7.6 the most preferred position is point B where all income is spent on good Y. Concave indifference curves imply that the optimum consumption bundle contains only one good; that is, it is always on either the X or Y axis rather than on the budget line between them. People are typically observed to spend their money on a diversity of goods rather than to concentrate their expenditures on only one good. The hypothesis that indifference curves are concave to the origin leads to a prediction about consumer behavior that is not con¬ sistent with the empirical evidence. Therefore the hypothesis should be rejected. The Y per period

Figure 7.6

Concave Indifference Curves.

6If the individual were indifferent between bundles A and B, the two goods would be perfect substitutes and the indifference curve through A would be a straight line that corresponds to the budget line. But then any small change in the price ratio would lead the individual to go to one or the other of the axes, purchasing only one good.

118

The Competitive Market System

hypothesis that indifference curves are convex is consistent with observed consumer behavior.

THE COMPARATIVE STATICS OF INDIVIDUAL DEMAND From our analysis of the model of individual preferences and demand we have found the conditions for optimum consumption. An individual is considered to be in an equilibrium of consumption when these conditions are satisfied. That is, whenever the conditions are satisfied, the individual has no incentive to alter consumption behavior or choices. It was argued in Chapter 1 that the appropriate test of an economic model is its consistency with the empirical evidence. Can this model be tested? Not in its present form. The model predicts that individuals’ marginal rates of substitution will be equal to the ratio of market prices. Although prices are observable, in general, there are no separate observations on individuals’ marginal rates of substitution. Thus there are no data to compare with the price ratios. And the prediction cannot be subjected to a direct empirical test. In order to make the model empirically relevant and testable, we must go through the exercise of comparative static analysis. This means the comparison of individuals’ static consumption equilibria before and after a change in one of the exogenous varia¬ bles, other things equal. In the case of the consumption model the exogenous variables are money income and the prices of the two goods, Px and PY. In this section we consider changes in each of these variables in turn under the assumption that all other conditions are unchanged. This analysis will lead to predictions about the changes in consumption choices expected to be associated with changes in the exogenous variables. These predictions can be checked against empirical observations as a means of testing the underlying model.

Changes in Income The Income-Consumption Curve. Figure 7.7 shows an individual’s preference map¬ ping and budget lines that represent alternative income levels. Given an income of M | and a budget line M1Ml, the individual’s optimum consumption bundle is A. An increase in income results in a parallel outward shift in the budget line. The budget lines labeled M2M'2 and M3Mj represent successive increases in income, holding all prices constant. If the indifference curves I2 and J3 are typical of this individual’s preference ordering, the optimum consumption bundles at these higher levels of income will be B and C, respectively. The line through points A, B, and C traces out optimum consumption bundles or consumption equilibria as income changes. This curve is the income-consumption curve. Definition: The income-consumption curve is a locus of optimum consumption bun¬ dles for different incomes.

119

Individual Preferences and the Theory of Demand

Figure 7.7

The Income-Consumption Curve.

The income-consumption curve in Figure 7.7 slopes up and to the right, showing that the consumption of both goods X and Y increases as income increases. This will be the typical situation. However, exceptions are possible. We will return to this point later.

Engel Curves. The information contained in Figure 7.7 can be used to establish the relationship between income and the consumption of X and between income and the consumption of Y. The relationship between income and X is shown in Figure 7.8. Points A', B', and C' correspond to points A, B, and C in Figure 7.7. Definition: An Engel curve shows the consumption of a good as a function of income,

holding all prices constant. An Engel curve can be drawn for each good consumed by the individual. The Engel curves for both goods X and Y for the individual whose preferences as shown in Figure 7.7 slope up and to the right, indicating that consumption increases as income increases.

Income Elasticity Of Demand. The relationship between money income and the consumption of a good can be characterized quantitatively by a measure known as the income elasticity of demand. Definition: The income elasticity of demand for a good is the percentage change in

120

The Competitive Market System

X per period Figure 7.8

The Engle Curve.

its consumption for a given percentage change in money income. The equation for income elasticity is: p

_ ax/x

-

=

A M/M AX M AM

X

where EM is the income elasticity of demand. According to this definition of income elasticity, if income and consumption of X move in the same direction, the income elasticity is positive. In principle, the income elasticity of demand for X can take any positive or negative value. The sign and magnitude of the income elasticity can be used to classify goods with respect to their income-consumption relationship. The three major categories are as follows: Superior good: The consumption of X rises (falls) more than proportionately to the increase (decrease) in income. Specifically, EM > 1. Normal good: Consumption of X rises (falls) proportionately or less than in proportion with the rise (decrease) in income. Specifically, 0 < EM < 1. Inferior good: The consumption of the good varies inversely with income Specifically, EM < 0. There is also the special case of a good the consumption of which does not vary as income changes. Its income elasticity is 0. Although one’s initial inclination is to think that all goods must be either normal or superior, the possibility of inferior goods cannot be ruled out. The fact of an income elasticity of demand less than zero does not mean that the good does not contribute

121

Individual Preferences and the Theory of Demand

to well-being. The negative relationship between income and consumption does not violate any of the axioms of preference orderings, as will be shown subsequently. The phenomenon of inferior goods arises out of a particular sort of substitution relationship between goods. A classic example of an inferior good might be a staple such as beans or potatoes in the diet of low-income families. If families with low incomes cannot afford to purchase meat, then the staple food will be a high proportion of total expendi¬ ture. As incomes rise, families may find meat is now within their reach. As they begin to purchase meat, they need to purchase fewer beans or potatoes, hence the negative relationship between income and the consumption of the staple good. Other examples can be drawn from categories of goods that are available at different quality levels and costs. At a low-income level an individual might purchase primarily inexpensive California “jug wines.” But as her income rises, she might purchase less of the jug wines and more of the better California wines. At even higher levels of income she might switch consumption entirely to high-priced French Chateau-bottled wines. In this example the jug wines are inferior goods; the better California wines are first superior and then inferior goods; and the French wines are superior goods at higher levels of income.

The Income-Consumption Curve and Income Elasticity. The income elasticities can be computed arithmetically from budget data giving consumption levels at different income levels. They also can be estimated graphically or geometrically from inspection of the income-consumption curve and the Engel curve. In order to infer the income elasticity of demand by inspection of the income-consumption curve, one should exam¬ ine the relationship between the income elasticity of demand and how the percentage of total income spent on a good (the expenditure share) varies with income. Relationship: For a superior good the expenditure share rises as income increases. For goods with a unitary income elasticity the expenditure share does not change as income changes. For normal goods with income elasticities less than 1 the expenditure

share falls as income increases and rises as income falls. For example, suppose that the expenditure on good X is equal to $10, income is $100, and thus the expenditure share is $10/$ 100 or 0.1. Suppose income rises 10 percent to $110. If the income elasticity of demand for A is equal to 1, the quantity of X consumed and the expenditure on it will rise by 10 percent to $11. The expenditure share will be unchanged ($11/$110 = 0.1). If the income elasticity of demand is greater than 1, the quantity of X and its expenditure will rise by more than 10 percent and the expenditure share must rise. Conversely, if the expenditure rises by less than 10 percent (normal good) or falls (inferior good), the expenditure share necessarily must fall. Suppose that at income Mx the optimum consumption bundle is point A in Figure 7.9. Construct a straight line from the origin through point A and extend it upward to the right. The slope of this line, YJXU gives the ratio of Y to X in consumption bundle A. Other points on the ray such as point B also have the same ratio of Y to X in consumption. Thus since the prices of X and Y are unchanged, all points on the ray represent the same expenditure share. Suppose point B represents the optimum

122

The Competitive Market System

X per period Figure 7.9

The Income-Consumption Curve with Elasticity of 1.

consumption bundle when income is increased to M2. Then since the expenditure share is unchanged over the range M ,M2, the income elasticity of demand for X must be equal to 1. And since the expenditure share of Y must also be unchanged, the income elasticity of demand for Y is also equal to 1. In Figure 7.10 the optimum consumption bundle with income of M2 (point C) is below and to the right of the straight line from the origin. This shows that the ratio of X to T and the expenditure share of X have both risen. The income elasticity of demand for X over this range is greater than 1. If the expenditure share of* has risen

123

Individual Preferences and the Theory of Demand

the expenditure share of Y must have fallen. Therefore the income elasticity of demand for Y must be less than 1 (it is greater than 0 because the quantity of Y has increased). Figure 7.11 portrays a case where the expenditure share of Y has risen with an increase in income. Therefore, the income elasticity of Y is greater than 1. Note also that the quantity demanded of X has fallen with the increase in income. X is an inferior good. There are two useful rules of thumb for characterizing the income elasticities of demand that can be inferred from the inspection of Figures 7.9 through 7.11. The rules involve constructing a line between the initial and new equilibrium consumption bun¬ dles and extending this line back toward the axes. The extension of this line will intersect the axis of the good whose income elasticity is less than 1. If the extension goes through the origin, then both goods have an income elasticity equal to 1. The second rule of thumb is that if the line is upward sloping to the right, both goods have income elasticities greater than 0. Otherwise one of the goods is an inferior good. Figures 7.9 through 7.11 make it clear that at least in the two-good case considered here the income elasticities of the two goods are somehow related. If the elasticity for one good is greater than 1, the other good must be less than 1. If the elasticity for good X is equal to 1, the elasticity for good Y must also be equal to 1. In fact, if one were to calculate a weighted average of the income elasticities of the two goods, where the weights were equal to the expenditure shares of each, this weighted average would always be exactly equal to l.7

Figure 7.11

The Income-Consumption Curve with Elasticity Less than Zero.

Tor a proof of this statement see the Mathematical Appendix to this chapter.

124

The Competitive Market System

Income Elasticity and the Engel Curve. The income elasticity of demand for a good can also be inferred from an examination of the Engel curve. The solid curved line in Figure 7.12 is the Engel curve for good X. Suppose that we wish to know the income elasticity of demand for X at point A. To measure the elasticity, construct a straight line tangent to the Engel curve at point A and extend it until it intersects the horizontal axis. The elasticity is determined by where this tangent line intersects the axis. Again, the elasticity is defined as „ AX M Em =AM X

The first term, AX/AM, is the reciprocal of the slope of the tangent line, or CX,/AX„ or (since AXl = OMx) CXx/OM^. The expressions for M and X are given by the corresponding distances on the two axes. Substituting these terms into the definitional equation gives CXt

OMx

CXt

Since the tangent line intersects the X axis to the right of the origin, this ratio is less than 1, as is the income elasticity of demand for X. Figure 7.13 shows the application of this geometric technique in a case where the income elasticity of demand is greater than 1. The tangent line intersects the vertical axis first. It intersects an extension of the horizontal axis to the left of the origin. The ratio CXx/OXx is greater than 1. In this case A is a superior good. Note that if the Engel curve itself is a straight line, there is no need to construct a separate tangent line. Equation (7.4) can be applied directly to the point where the Engel curve intersects the horizontal axis. Finally, if the tangent line goes through the

125

Individual Preferences and the Theory of Demand

Figure 7.13

An Engel Curve with Elasticity Greater than 1.

origin or if a straight line Engel curve goes through the origin, the income elasticity of demand is equal to 1.

Changes in the Price of X The Price-Consumption Curve. We will first consider the effect of a change in the price of X on the consumption of X. Assume that the price of Y and money income are given and do not change throughout this analysis. If the price of X is P xx, budget line is KK'. Consumption bundle A in Figure 7.14(a) is the optimum consumption bundle for the individual. If the price of X drops to PX2, the budget line rotates out counterclockwise about the Y intercept to K". There is a new optimum consumption bundle B. The experiment of lowering the price of X and finding the new optimum consumption bundle can be continued to find additional points such as C. The line connecting these points is the price-consumption curve. Definition: The

price-consumption curve is the locus of all optimum consumption

bundles when the price of one good changes, the price of the other good and money income being held constant.

The Demand Curve. The information contained in the price-consumption curve can be transferred to a new diagram to produce the familiar demand curve for X. This is also shown in Figure 7.14(h). Point A in Figure 7.14(a) corresponds to a price for X of Pxx and a quantity of Xt. Point A' in Figure 7.14(h) represents the same information plotted with respect to the price and quantity axes of the demand curve. Definition: The

demand curve is drawn in the price-quantity plane and shows the

126

The Competitive Market System

X per period (b) Figure 7.14

The Price-Consumption Curve and the Demand Curve for X.

quantity demanded of a good as a function of its own price, holding the price of the other good and money income constant.

Price Elasticity of Demand. The relationship between price and quantity can be characterized by an elasticity measure. Definition: The price elasticity of demand for X gives the percentage change in quantity demanded for a given percentage change in the price of the good. The equation for price elasticity is EP„

:

xx/x APx/Px

127

Individual Preferences and the Theory of Demand

AX

Px

A Px

X

Because with the usual demand curve the changes in price and quantity are in the opposite direction, the minus sign is inserted in the definition by convention to make the elasticity a positive number.8 If the price elasticity is greater than 1, demand is said to be elastic. A price elasticity less than 1 means that demand is inelastic. Whether demand is elastic or inelastic can be determined from the slope of the price-consumption curve. The key point is the relationship between the elasticity of demand and the behavior of total expenditure on X as the price of X changes. If demand is elastic (price elasticity is greater than 1), a price decrease leads to an increase in total expenditure and vice versa. But if demand is inelastic (price elasticity is less than 1), a decrease in the price of X leads to a decrease in total expenditure and vice versa.9 Returning to Figure 7.14, the upward-sloping price-consumption curve shows that as Px fell, the quantities demanded of both X and Y increased. If the quantity of Y increased, the expenditure on Y must have increased as well, because by assumption there was no change in PY• And since there had been no change in money income, an increase in the expenditure on Y implies a decrease in the expenditure on X. A falling price of X accompanied by a decrease in the expenditure on X implies an elasticity of demand less than 1. In Figure 7.15, as the price of X falls, the quantity of X increases but the quantity of Y decreases. This implies decreasing expenditure on Y and increasing expenditure on X. The price elasticity of demand for X is greater than 1. Relationship: If the price-consumption curve for X is upward sloping to the right,

the price elasticity of demand for X is less than 1. A horizontal price-consumption curve means the price elasticity of demand for X is equal to 1. And a downward-sloping price-consumption curve means that demand is elastic (price elasticity is greater than

1). Given the demand curve for X, it is possible to determine the price elasticity of demand by a geometric technique that is analogous to that previously outlined for income elasticity and the Engel curve. Figure 7.16 shows a demand curve. Suppose we wish to determine the price elasticity of demand at point A. The first step is to construct a straight line tangent to the demand curve at point A and extend it to both axes. The equation for the price elasticity of demand is

“Unfortunately not all writers in economics follow this convention. You may occasionally see price elasticities of demand written as negative numbers. Which convention is being followed is usually clear from the context. Tf the price elasticity of demand is greater than 1, the percentage increase in quantity following a price decrease is greater than the percentage decrease in price. Thus the expenditure-increasing effect of the quantity increase outweighs the expenditure-decreasing effect of the price decrease. The elasticity-expendi¬ ture relationship will be examined in greater detail in Chapter 8.

128

The Competitive Market System

Figure 7.15

X per period The Price-Consumption Curve for X When Price Elasticity Is Greater than 1.

The first term is the reciprocal of the slope of the tangent line, or BC/AB The quantity is OB and the price is OD = AB. Substituting gives „

BP

BC —

-

AB

AB •

-

OB

BC =

-

OB

129

Individual Preferences and the Theory of Demand

In this example the ratio and hence the elasticity are less than one. An alternative derivation is based on the fact that the reciprocal of the slope is also given by AD/DE. Thus —

EP A

AD DE

•

OD AD

—

OD DE

Changes in the Price of Y The indifference curve model can also be used to examine the effect of the change in the price of Y on the quantity demanded of X, other things equal. In Figure 7.17, as the price of Y falls from Pyi to PY2, the budget line shifts from KK' to K"K'. The quantities of both Y and X increase. Definition: Two goods are complements if the quantities demanded of X and Y change in the same direction in response to a change in one of their prices. Examples of complements include tennis balls and tennis rackets and beer and pretzels. In Figure 7.18, the quantity demanded of X falls as the quantity demanded of Y increases in response to a fall in PY.

Definition: Two goods are

substitutes if the quantities demanded of X and Y move

in opposite directions when one of their prices changes. Examples might include tea and coffee or butter and margarine. The relationship between the price of one good and the consumption of another can also be represented as an elasticity.

Y per period

X per period Figure 7.17

The Effect of the Price of Y on X When X and Y Are Complements.

130

The Competitive Market System

f

X per period Figure 7.18

The Effect of the Price of Y on X When X and Y Are Substitutes.

Definition. The cross elasticity of demand gives the percentage change in the quantity demanded of one good for a given percentage change in the price of the other good. The equation for the cross elasticity of demand for X is _

AX/X

h pY =-

APy/Py AX Py APy

X

The cross elasticity of demand for Y is defined in a similar manner. When the cross elasticity of demand is positive, the goods are substitutes. They are complements when it is negative.

The Demand Function The analysis of this section has shown that the quantity an individual demands of good X/s influenced by the individual’s money income, the price of X, and the price of Y. Given the individual’s preference ordering, the quantity of* demanded by the individ¬ ual is determined by these three variables together.

Relationship: The individual’s demand function for X is a functional relationship that determines the quantity demanded of X as a function of three exogenous variables, the price of X, the price of Y, and money income, XD = XD (Px, Py, M)

131

Individual Preferences and the Theory of Demand

where XD is the individual’s quantity demanded and the functional notation XD (•) embodies the individual’s preference ordering. Because this demand function has four variables, three independent variables, and one dependent variable, it cannot be shown graphically. However, the demand curve previously described that relates the quantity demanded of X to its own price is a two-dimensional representation of the demand function, holding PY and M constant. Specifically, the demand curve is a graphical representation of

XD = XD (Px, P$, M*) where the asterisks indicate the variables that are being held constant. Similarly, the Engel curve is a two-dimensional representation of the demand function, holding both prices constant. Specifically,

xd = *D (pi, Pi, m) If one of the variables held constant when the demand curve is drawn changes, the demand curve itself will shift. Understanding the nature of this shift is an important part of the comparative static analysis of individual demand. In Figure 7.19(a) the two budget lines labeled KK' and KL' show two different prices of X holding money income and the price of Y constant. Points A and B are optimum consumption bundles. They can be used to find points A' and B' on the demand curve L>, in Figure 7.19(h). Now assume that money income is substantially increased and price is held constant at PX1. This results in a new budget line parallel to but above the old budget line. It is labeled LL'. There is an optimum consumption bundle on this budget line, say, at point C. This corresponds to point C' in the lower part of the figure. Point C is at PXI but is not on the original demand curve. Rather, it is a point on the new demand curve corresponding to the new higher level of income M2. Now holding income constant at M2, let the price of X fall to PX2. The budget line shifts to LL". If the optimum consumption bundle is point E, then the corresponding point E' in the lower part of the diagram is also on the new demand curve D2. To summarize, this analysis shows that changes in money income will shift the demand curve that is drawn for a given money income and price of Y. As long as X is a normal or superior good, an increase in money income shifts the demand curve out and to the right. For an inferior good an increase in money income would shift the demand curve back and to the left. And for a normal or superior good, a decrease in income will shift the demand curve to the left. A similar analysis can be made of the effect of a change in the price of Y on the demand curve for X. Assume that X and Y are substitute goods. The solid budget lines labeled KK' and KK" are both drawn holding money income constant and the price of Y constant at PYl. As shown in Figure 7.20, the effect of the decrease in the price of X from Pxx to PX2 is to cause the individual to shift from consumption bundle A to bundle B and to increase the quantity demanded from X] to X2. This corresponds to points A' and B' on the demand curve Dx. Now assume an increase in the price of Y to PY2. The budget line corresponding

132

The Competitive Market System

L

N

"

Px, dollars

Figure 7.19

The Effect of Increasing Income on the Demand Curve for X.

to the initial price of X, Pxu is rotated counterclockwise to the line labeled LK'. The optimum consumption bundle is now point C. The quantity demanded of Y has decreased and the quantity of X has increased. Since the price of X is unchanged at Pxu the corresponding point C' in Figure 7.20(b) cannot be on the original demand curve, £>,. Rather, it is on a new demand curve, D2> which is outside and to the right of the original demand curve. Now when the price of X is again decreased, the budget line for PX2 rotates counterclockwise to LK" and the optimum consumption bundle changes from point C to point E. The quantity demanded of* increases to

133

Individual Preferences and the Theory of Demand

0

Xi X2 Z3Z4 X per period (b)

Figure 7.20

The Effect of a Change in the Price of Y on the Demand Curve for X When X

and Y Are Substitutes.

A4. This corresponds to point E' on the new demand curve D2 in the Figure 7.20(h). When X and Y are substitutes, an increase in the price of Y shifts the demand curve for X out to the right. The demand curve would be shifted in and to the left if the price for Y were to fall. Although this will not be shown graphically, if X and Y are complements, the shifts will be in the opposite direction. An increase in the price of Y will shift the demand curve for X in and to the left, whereas a decrease in the price of the complementary good Y will shift the demand curve for X out and to the right. Finally, What would happen to the quantity demanded of X if all prices and money

134

The Competitive Market System

income were to change by the same proportion? Suppose all prices and money income were to double. To determine the effect on the quantity demanded, first determine the impact of these changes on the budget line. Recall that the equation for the budget line is

Py

Py

A doubling of all prices and money income gives Y =2M_ IP y

2Px x 2Py

Since all the 2’s cancel out, the effect is to leave the budget line unchanged. Doubling all prices and money income has no affect on the quantity demanded of either X or

Y.

CHANGES IN PRICE: A CLOSER LOOK When a change in the price of a good leads to a change in the quantity demanded, this is the result of two different forces: a change in the price ratio as indicated by the slope of the budget line and a shift in the budget line reflecting a change in purchasing power or real income. These two forces result in a substitution effect and an income effect. An understanding of the nature of these two effects is important in explaining why and under what conditions the demand curve for a good is downward sloping. It will also prove useful in the analysis of other economic relationships such as that between the wage rate and the supply of labor and that between the interest rate and savings or deferred consumption. It is important to distinguish between moves along an indifference curve where the preference level is held constant and movements from one indifference curve to another that reflect a change in welfare. The substitution effect gives the change in the quantity of X resulting from a change in the price of X on the assumption that the individual is constrained to remain on the original indifference curve. Definition: The substitution effect of a price change is the change in quantity due

solely to the change in the price ratio, holding the preference level constant by assump¬ tion. A change in the price of X alters the ratio PX/PY and the slope of the budget line. In order to make the MRS equal to the price ratio, the individual must adjust his consumption bundle. For example, if the price of X decreases, the price ratio is lower and the individual must take action to reduce the MRS. Recall that the principle of diminishing marginal rate of substitution states that as the quantity of X is increased, the marginal rate of substitution between X and Y decreases. Therefore when the price of X is decreased, the individual must substitute X for Y in his consumption bundle in order to restore the equality of the MRS and the price ratio. If the price of A were

135

Individual Preferences and the Theory of Demand

to increase, the individual would have to substitute Y for X in order to increase the marginal rate of substitution to restore this equality. Thus price and quantity always move inversely. The substitution effect always leads to a quantity change in the opposite direction to the change in price. The substitution effect is always negative. The income effect abstracts from the change in the price ratio and focuses on the effect of changes in purchasing power or real income. Definition: The income effect of a price change is the quantity demanded due solely to the change in real income associated with a price change. A change in the price of X shifts the intercept of the budget line along the X axis. The set of attainable bundles changes. For a decrease in the price of X, the set of attainable bundles gets larger, reflecting an increase in the purchasing power of a given money income. If X is a normal or superior good, the quantity of X will increase. Similarly, a price increase reduces purchasing power and real income resulting in a decrease in quantity for a normal or superior good. For goods with a positive income elasticity of demand the income effect results in an inverse relationship between price and quantity demanded. If the good in question is an inferior good, decreases in real income result in increases in the quantity de¬ manded. And the income effect results in a direct relationship between the price and quantity demanded. For normal and superior goods the income effect is negative; that is, price and quantity vary inversely. For inferior goods the income effect is positive, indicating that price and quantity vary directly.

The Substitution and Income Effects and the Demand Curve The total effect of a change in the price of a good is the sum of the substitution effect and the income effect. The substitution effect is always negative; and for a normal or superior good the income effect is also negative. Thus these two effects are working in the same direction, one reinforcing the other, leading to an inverse relationship between the price and quantity demanded. However, for an inferior good the income effect is positive and works against the substitution effect. In principle, the income effect could be so large that it outweighed the substitution effect. If that were to happen, the quantity demanded would move in the same direction as the price, and the demand curve would be upward sloping. We will explore this possibility in more detail later. These relation¬ ships are summarized using algebraic notation in Table 7.1. They are discussed in greater depth in the next two sections.

Normal and Superior Goods. The income and substitution effects and their relation¬ ship to the demand curve can be shown graphically. Figure 7.21(a) shows the indiffer¬ ence curves for an individual for whom X is a normal good. If the price of X is initially Pxl and the budget line is KK', the individual’s optimum consumption bundle is point A on indifference curve The quantity demanded of X is Xx. This gives one point on the demand curve for X in Figure 7.21(b). Now let the price of X fall to PX2. The budget line shifts to KK", and the quantity

Table 7.1

The Income and Substitution Effects: A Summary

1. The total effect of a price change: AX

— substitution effect plus income effect

2. The substitution effect: AX A P,


as at point D, output can be increased by reducing the labor input and using more capital.

Some Comparative Statics As in the case of the individual consumer, we are more interested in the comparative static propositions that can be derived from the optimum conditions than the opti¬ mum conditions per se. Specifically, we would like to know how the optimum input

Figure 9.2

The Optimum Input Combination for Maximizing Output.

219

The Theory of the Firm and Production

combination changes with a change in factor prices. Because a complete answer to this question requires an analysis of the optimum output level and how it changes, a full treatment of this topic is deferred to Chapter 12 on the demand for factor inputs. However, a few useful conclusions can be drawn from the analysis undertaken up to this point. First, consider two different firms that operate in separate factor markets. Suppose that one firm faces a high price for labor and a low price for capital, whereas the opposite is true for the other firm. This means that the iso-cost lines of the first firm are relatively steep and its optimum input combinations will tend to be in the upper left-hand range of its isoquant map. Compared to the second firm, this firm will respond to the higher relative price of labor by economizing on labor and using relatively more of the low-cost factor capital. This helps to explain differences in the choice of production techniques across countries. A country with abundant labor and relatively scarce capital will tend to have low wages and high prices for capital. In comparison with a capital abundant country such as the United States, a labor abundant country would tend to use labor-intensive modes of production. For example, the more labor-intensive methods of agriculture in France compared with the United States reflect differences in the relative abundance of labor and land between the two countries. And the very labor-intensive methods of road and dam construction that are used in China and India represent rational re¬ sponses to labor abundance (and capital scarcity). A change in the factor prices faced by a firm will induce a change in production techniques and input combinations. In Figure 9.3 the slopes of the solid iso-cost lines

\

\

Figure 9.3

The Effect of Changes in Factor Prices.

220

The Competitive Market System

show a relatively low price of labor relative to capital. The firm would tend to choose input combinations that lie along the line OA. But if the price of labor were to rise or the price of capital to fall, the iso-cost lines would become more steeply sloped. The firm would respond by economizing on the relatively more expensive labor. It would choose input combinations along the line OB. This model could be used to analyze the responses of firms to higher energy prices, higher prices of labor, or subsidies to capital investment.

The Effects of a Subsidy on Capital. One form of subsidy to capital investment is the investment tax credit that allows firms to deduct a certain percentage of qualifying investments that are made in any given year from their tax liability. The effect of a 10 percent investment tax credit is to lower the effective cost of new capital to the firm by 10 percent.5 One justification sometimes offered for the investment tax credit is that by encouraging investment it leads to new job creation. But this justification is weak at best when it is examined through the use of the model of production. Specifically, we now ask two questions. Will an investment tax credit increase employment? And if stimulating employment is the primary objective, is an investment tax credit the most effective policy tool? Suppose that before the investment tax credit is allowed a firm is producing output X* at point A in Figure 9.4, It is using L{ of labor and K{ of capital. The investment

L per week Figure 9.4

The Effect of an Investment Tax Credit on the Utilization of Labor.

5Of course, this is only true if the firm has a sufficiently large tax liability in the absence of the credit. It does not help firms that are reporting losses or which have used other provisions of the tax code to reduce their tax liability to 0.

221

The Theory of the Firm and Production

tax credit lowers the cost of capital and rotates the iso-cost lines clockwise so that they become more steeply sloped. Assume for the moment that the firm holds output constant at X*. It responds to the investment tax credit by substituting capital for labor and moving to point B. Employment at this firm has decreased to L2 in response to the investment tax credit. The investment tax credit can only increase employment if increases in output require more labor than has been laid off because of the change in relative prices. Output increases for this firm because the lower capital price implies a lower cost and hence lower price of output. Also, there may be macroeconomic multiplier effects that are associated with the investment that increase the outputs and employment of labor of all firms in the economy. But the model suggests that a more effective way to stimulate employment would be a form of new job tax credit that subsidized new purchases of labor rather than capital.

Substitutes and Complements. In models with more than two factor inputs the relationships between changes in factor prices and the quantities of inputs can be more complex. This is because of the possibility of both substitute and complementarity relationships among pairs of inputs. Definition: Two inputs are said to be substitutes if when the price of one increases (decreases) the quantity of the other increases (decreases), other things, including the level of output, held constant. As this section has shown, if there are only two factors, they must be substitutes in production. However, with three or more inputs it is possible that any two of them may be complements. Definition: Two inputs are said to be complements if when the price of one increases (decreases), the quantity of the other decreases (increases) other things, including the level of output, held constant. When two inputs are complements, an increase in the use of one must be accom¬ panied by an increase in the use of the other. Thus when the price of one is decreased, this leads to an increase in the use of both inputs. Suppose that the aggregate production function for the U.S. economy could be represented by X = X (K, L, E), where E is energy. What will happen to the optimum input combinations as the price of energy increases, other things equal? Clearly, the quantity of energy used will decrease. But the direction of the changes in K and L will depend on whether they are substitutes or complements to energy. Although there is still some controversy over the interpretation of the data, the weight of the evidence suggests that capital and energy are complements and labor and energy are substitutes.6 If this is true, then the recent energy price increases can be expected to result in a

6See Ernst R. Berndt and David O. Wood, Engineering and Econometric Interpretations of Energy-Capital Complementarity, American Economic Review, June 1979, 69(3), 342-354.

222

The Competitive Market System

reduction in the demand for capital and an increase in the demand for labor to produce any given level of aggregate output.

SOME PRODUCTION FUNCTIONS AND THEIR PROPERTIES So far, production functions have been represented graphically by mappings of iso¬ quants and their associated total product and marginal product curves. In principle, any isoquant mapping and production function can be at least approximately repre¬ sented by some mathematical function that shows how output depends on the levels of inputs. The representation of production functions in mathematical or algebraic form is useful for analyzing some types of economic problems; and it is virtually essential for the analysis of production functions with three or more inputs (e.g., labor, capital, energy, and materials). In this section we present in nontechnical terms two classes of mathematical representations of production functions, examine some of their proper¬ ties, and discuss some problems in estimating these functions from empirical data on inputs and outputs. The only two properties of production functions that have been discussed up to this point are diminishing marginal productivity and diminishing marginal rate of technical substitution. All empirically relevant production functions are assumed to display these characteristics. We begin this section by introducing three additional properties of production functions and discussing their economic implications.

The Elasticity of Substitution The smoothly curving convex isoquants that are shown in this chapter reflect an important assumption about the nature of production functions, namely, the continu¬ ous substitutability of one input for another in production. The marginal rate of technical substitution measures the terms on which this substitution can occur while moving along an isoquant. The elasticity of substitution measures how these terms change as more of one input and less of the other is used. Definition: The elasticity of substitution relates the percentage change in the ratio of capital to labor to the percentage change in the marginal rate of technical substitution while moving along a given isoquant. Specifically, ES = A(K/L) K/L

^

AMRTSlk MRTSlk

Figures 9.5 and 9.6 show two extreme cases. The isoquant of Figure 9.5 is a straight line. If production is at point A, the ratio of K to L is shown by the slope of the line OA. If the production point is shifted down to the right, say, to point B, the ratio of capital to labor is decreased, but the marginal rate of technical substitution is un¬ changed. The formula shows that the elasticity of substitution is infinite in this case. No matter how far the substitution of labor for capital is carried out, the terms on which this substitution can take place do not deteriorate.

223

The Theory of the Firm and Production

Figure 9.5

An Isoquant with an Infinite Elasticity of Substitution.

L per period Figure 9.6

An Isoquant with a Zero Elasticity of Substitution.

At the other extreme, Figure 9.6 shows a right angle isoquant from a fixed-proportion production function. In the immediate vicinity of point A the marginal rate of technical substitution goes from infinity to zero. But there is no change in the capital to labor ratio. Thus the elasticity of substitution is zero at point A. If the mathematical equation that represents the production function is known, it is possible to compute the elasticity of substitution for any point on the isoquant mapping. Otherwise it is necessary to calculate an approximation by measuring the changes in the capital-labor ratio and marginal rate of technical substitution between two points on the same isoquant and by using an arc elasticity formula that is similar to those described in Chapter 8 for estimating the elasticity of demand. The closer together the

224

The Competitive Market System

two points are, the better will be the approximation to the true value of the elasticity of substitution. The elasticity of substitution may vary along any given isoquant or with moves from one isoquant to another. It can vary, that is, with the capital-labor ratio or output. However there is a class of production functions for which the elasticity of substitution is a constant. Figure 9.7 shows an isoquant from a production function where the elasticity of substitution is always equal to 1. Algebraically, the production function underlying this isoquant is X = L K \ The isoquant is for an output level of 5 units per period.

Substitutability and Essential inputs. Moving downward to the right, the isoquant of Figure 9.7 will approach but never touch the labor axis. Similarly, it asymptotically approaches the capital axis, which means that no matter how small the input of labor is, provided that it is not reduced to zero, production can be sustained at this level, provided that the input of capital is large enough. However, if either input is reduced to 0, output necessarily falls to 0. There is no quantity of either labor or capital that can make up for the absence of the other input. Both labor and capital are essential in this sense.

225

The Theory of the Firm and Production

Definition: A factor is essential if output is 0 when its input is 0, given positive amounts of the other factors. For the production function X = X(K, L), labor is essential if the following condition holds. X(K, 0) = 0

The isoquant represented by the heavy line in Figure 9.8 has an elasticity of substitu¬ tion which is constant and greater than 1. Isoquants with this characteristic intersect both axes, meaning that production is possible with only one input. Neither input is essential in this case. On the other hand, the isoquant drawn with a light line in Figure 9.8 has an elasticity of substitution that is constant but less than 1. It will not touch either axis. Rather, as capital is substituted for labor, the isoquant approaches asymptotically a minimum level of labor Lmin, which is essential for maintaining output at this level. Also at least Kmin of capital is required to produce this output level no matter how much labor is used. In this case both inputs are essential to production and there are limits to the extent to which one input can be substituted for the other. The minimum required levels of K and L depend on the level of output. Each isoquant has its own pair of asymptotes. The minimum inputs and asymptotes are higher for higher levels of output.

Substitutability and Growth of Output. The nature of the substitution possibilities in an economy as measured by the elasticity of substitution is important for a wide variety of economic questions, especially those dealing with the dynamic aspects of a growing economy and with the long-run prospects for the economy in the face of finite or limited natural resources.

Figure 9.8

Isoquants and Elasticities of Substitution.

226

The Competitive Market System

Consider the prospects for long-run growth in an economy with a stable population (zero population growth) and labor supply. Let X represent some measure of aggregate output such as GNP. In the absence of technological change growth can come only from increasing the stock of capital, that is, moving vertically in the isoquant diagram. Suppose that the fixed supply of labor is Lmin in Figure 9.8. If the elasticity of substitu¬ tion is equal to or greater than 1, output can grow without limit as long as some part of each period’s output is saved (not consumed) and added to the stock of capital. Each increase in the capital input leads to a production point further up the dashed vertical line Lmin. But if the elasticity of substitution is less than 1, there is an upper limit to output. As the production point moves up along the dashed line Lmin, output ap¬ proaches but can never reach the asymptotic isoquant for X*. In an economy in which capital and labor are growing at different rates, the ease with which the structure of production can be altered to accommodate the changing aggre¬ gate capital-labor ratio and the rate at which output will grow both depend on the elasticity of substitution. Again, let X represent GNP. Assume that at some point in time the economy has total supplies of capital and labor as indicated by point A in Figure 9.9. Assume that the rate of growth of capital is higher than the rate of growth of labor. At some later point in time, the total supplies of factors will be represented by a point such as B. Because the ratio of capital supply to labor supply has increased, there must be a corresponding change in the ratio of factor inputs in production. If the production technology is such that the elasticity of substitution is high, as shown by the heavy line isoquants, the increase in factor supplies results in an increase in aggre¬ gate output from Xt to X2. However, if the elasticity of substitution is low, as shown by the fine line isoquants X[ and X[, the growth in factor inputs leads to a smaller increase in aggregate output. The economy grows more slowly.

Figure 9.9

The Elasticity of Substitution and the Growth of Inputs and Output.

227

The Theory of the Firm and Production

Suppose for simplicity that capital and labor can be lumped together as one class of inputs and that natural resource materials constitute the other input in production. Assume that the material inputs are not renewable. That is, as quantities of the resource are dug out of the ground and used in production, the stock remaining to be dug decreases. Examples include iron, copper, and aluminum. The rate at which these materials are used in production must necessarily decrease in the long run. The pros¬ pects for the human race depend on the elasticity of substitution between the materials and the capital-labor aggregate. If the elasticity of substitution is greater than 1, materials are not essential and running out of materials is of no particular economic significance. If the elasticity of substitution is just equal to 1, materials constitute an essential factor input, but the economy need never run out. No matter how small the remaining stock of materials, the economy can sustain some level of production by using only a fraction of the remaining stock and substituting large quantities of labor and/or capital for the diminishing rate of input of materials. If the elasticity of substitu¬ tion is less than 1, however, eventually the rate of input of materials that are needed to sustain a given production level will exceed the remaining stock of material resources and production must necessarily fall, ultimately to 0.7

Isoclines and the Expansion Path The elasticity of substitution characterizes the shape of a particular isoquant at a given point. An isocline provides information on the way in which different isoquants are related to each other. Pick a point on a particular isoquant, say, point A in Figure 9.10. Measure the MRTS at that point and locate all other points such as A' and A " on other isoquants that have the same MRTS. Connect these points with a line. This line is an isocline. Definition: An isocline is a locus of all points in an isoquant mapping that have the same marginal rate of technical substitution. There is an isocline through every point on a given isoquant. As discussed previously, the optimum production choice requires an input combina¬ tion for which the marginal rate of technical substitution is equal to the ratio of given factor prices. Suppose that for output level Xl in Figure 9.10, point A is the optimum input combination. Then provided that there were no changes in factor prices, if the firm wished to increase or decrease the level of output, it would do so by choosing other input combinations on the isocline through point A. Given the factor prices that make A the optimum input combination for Xu this isocline is the expansion path. Definition: The expansion path is the locus of optimum input combinations for

7For a clear and nontechnical discussion of this aspect of the relationship between finite resources and economic growth, see Robert Solow, The Economics of Resources or the Resources of Economics, American Economic Review, May 1974, 64(2), 1-14.

228

The Competitive Market System

Figure 9.10

Isoclines.

different outputs, given constant factor prices. The expansion path is that unique isocline that connects all points for which the marginal rate of technical substitution is equal to the given ratio of factor prices. In any given economic situation there is only one expansion path. But the expansion path will change as factor prices change. Returning to Figure 9.10, if the price of labor were to decrease (or the price of capital were to increase), the optimum input combina¬ tion for producing X, would no longer be point A. Rather, it would be downward to the right along the isoquant, say, point B. At this new factor price ratio, expansion or contraction of output would take place along the isocline through point B. This would be the new expansion path. Principle: For any given level of production the position of the expansion path depends on the ratio of factor prices. As the ratio PL/PK decreases (as labor becomes relatively cheaper), the expansion path rotates toward the labor axis. An opposite shift of the expansion path occurs as labor becomes relatively more expensive (capital becomes relatively cheaper).

Homogeneous Production Functions Homogeneity is a mathematical property of some types of production functions. If a production function is homogeneous, its expansion path and isoclines are straight lines that emerge from the origin, and there is a direct and simple relationship between the degree of homogeneity and the nature of returns to scale. Definition: A production function is homogeneous if when all inputs are increased

229

The Theory of the Firm and Production

by a factor of t, the output increases by a factor of tk, where k is termed the degree of homogeneity. If a production function X = X(K, L) is homogeneous of degree k, the following must hold: X(tK, tL) = tk ■ X(K, L) The variable t is a measure of the change in the scale of inputs. The variable k determines how output changes with a change of scale. If k = 1, the production function is homogeneous of degree 1 or is linear homogeneous. With k = 1, doubling all inputs (f = 2) leads to a doubling of output. A linear homogeneous production function has constant returns to scale. If k is greater than 1, increasing all inputs by a factor of t leads to an increase in output by a factor of tk (greater than t); and the production function displays increasing returns to scale. If k is less than 1, returns to scale are decreasing. A second useful implication of the homogeneity property concerns the determinants of the marginal products of inputs and the marginal rate of technical substitution. Recall that homogeneity means that isoclines are straight lines that emerge from the origin. Thus for a homogeneous production function all points on a given isocline have the same capital to labor ratio; and by definition all isoquants have the same slope where they intersect any given isocline. This means that the MRTS depends only on the ratio of capital to labor and is independent of the level of output. If the production function is homogeneous, producers change output by making equal proportionate changes in all inputs—assuming other things equal, including factor prices. The behavior of producers is summarized by the variable t. But if the production function is not homogeneous, the expansion path is not a straight line from the origin. As producers change output, they will change the quantities of L and K in different proportions in their efforts to minimize the cost of a given output. In this situation the variable t loses its usefulness as a measure of changes in scale because it does not reflect the actual behavior of cost-minimizing producers. Scale can also be defined in terms of the total cost of inputs, given that there are no changes in factor prices. According to this alternative measure, scale is doubled if total cost is doubled. And if a doubling of cost is accompanied by a more than doubling of output, returns to scale are increasing by this measure of scale. The two measures of changes in scale (by cost of inputs or by quantities of inputs) are identical if the expansion path is a straight line from the origin. But if the expansion of output is accompanied by a change in the capital to labor ratio, then the two measures of changes in scale are different.

Measuring Production Functions In simple terms, estimating a production function involves obtaining a number of observations of inputs and output under different circumstances and using a statistical technique such as linear regression analysis to determine the mathematical expression that best fits or explains the data. There are several problems or questions that must be confronted in doing this type of empirical research.

230

The Competitive Market System

The first question is at what level of aggregation will production be measured? At one extreme we could estimate the relationship between GNP as a measure of aggregate output and the aggregate inputs of labor and capital. This production function for an economy would be of use in analyzing questions regarding long-term economic growth. At the other extreme there lies the production function for a specific good that utilizes data from individual firms that produce the good. Within these extremes there lie production functions for the aggregate output of a single firm that produces several products and for the industry output of a specific good or product category. Many firms produce more than one type of good. They employ many different types of labor. And capital is typically a heterogeneous mix of machines, tools, and buildings. Both inputs and outputs must be measured by some form of index number. Thus a problem of aggregation in the measurement of inputs and outputs almost always exists. This means that there are always questions of the choice of weights to apply to the components of the index. One source of data for estimating production functions is time-series data, that is, a series of observations of the same production unit at different points in time. The use of time-series data introduces a second problem. To be able to interpret the empirical estimate as a production function, one must either assume that all data reflect the same production technology or state of the art or attempt to control for technological change and innovation over time. Because the state of the art does change with time, the latter course must be chosen when using time-series data. Data can also be drawn from a cross section of production units at a point in time. But one must make sure that all production units have access to the same technological information. Otherwise the data will reflect more than one production function. After the data have been gathered, it is necessary to make some assumption about the mathematical form of the production function. The simplest and most commonly used production function in empirical work is the so-called Cobb-Douglas production function. It has the following mathematical form: X

=

aLbKc

This function is homogeneous. If both inputs are changed by a factor of t, then X = a(tL)\tK)c =

tb+caLbKc

The degree of homogeneity is found by summing the exponents b and c. If b + c = 1, the production function is linear homogeneous and displays constant returns to scale. Moroney used cross-section data from firms in the United States to estimate CobbDouglas production functions for 18 different categories of goods. The data were for 1957. The estimates of the coefficients and their sums (the degree of homogeneity) are shown in Table 9.1. One purpose of the study was to determine the nature of returns of scale in these industries. Because of statistical variation, small deviations in the degree of homogeneity from 1.0 may not be significant. Statistical tests show that the sums of the estimated values of b and c were significantly different from one in only

231

The Theory of the Firm and Production

Table 9.1

Estimates of Production Function Parameters and Returns to Scale in U.S. Industries (Cobb-Douglas production functions)

Industry

Estimate of labor coefficient (b)

Estimate of capital coefficient (c)

Degree of homogeneity (b + c)

Food and beverages Textiles Apparel Lumber Furniture Paper and pulp Printing Chemicals Petroleum Rubber and plastics Leather Stone, clay Primary metals Fabricated metals Nonelectrical machinery Electrical machinery Transportation equipment Instruments

0.51 0.88 0.91 0.65 0.91 0.56 0.62 0.89 0.64 0.58 0.96 0.40 0.59 0.88 0.62 0.66 0.79 0.83

0.56 0.12 0.13 0.39 0.20 0.42 0.46 0.20 0.31 0.48 0.08 0.63 0.37 0.15 0.40 0.37 0.23 0.21

1.07* 1.00 1.04 1.04 1.11* 0.98 1.08* 1.09* 0.95 1.06 1.04 1.03 0.96 1.03* 1.02 1.03 1.02 1.04

*Sigmficantly greater than one. Source: John R. Moroney, Cobb-Douglas Production Functions and Returns to Scale in U.S. Manufacturing Industries, Western Economic Journal, December 1967, 6(1), 39-51.

five cases. In these five cases the degree of homogeneity was greater than 1. Thus mild increasing returns to scale appear to be present in about one-third of the indus¬ tries. Other studies of industries have found essentially similar results. Estimates of the aggregate production function for the U.S. economy typically show constant returns to scale in the aggregate. It should be noted, however, that if the true under¬ lying technology had a different form from the assumed Cobb-Douglas relation¬ ship, the results of empirical studies such as Moroney’s will be biased and mis¬ leading.8 One limitation of the Cobb-Douglas production function for empirical work is that its elasticity of substitution is identically equal to 1. This means that this function cannot be used for research that has the purpose of estimating the degree of substituta¬ bility in production. The desire to investigate substitution conditions led to the develop-

8For example, the true production function could be nonhomogeneous, or the degree of homogeneity could itself depend on the output level.

232

The Competitive Market System

ment of the constant elasticity of substitution (CES) production function. It has the following mathematical form: X = a [bL~m +‘(1

-

b)K~m]~l,m

where the elasticity of substitution is equal to 1/(1 + m), and a, b, and m are parameters to be estimated from the data. This function is also homogeneous and displays constant returns to scale. When Kenneth Arrow and others estimated the constant elasticity of substitution production function for aggregate production in the United States, the data showed that the elasticity of substitution was less than 1. When the function was estimated for 24 different industries by using cross-sectional data from different countries, 14 of the industries had elasticities of substitutions that were significantly less than 1. None had elasticities greater than l.9 It appears that labor and capital are both essential factors of production in modern economies.

TECHNOLOGICAL CHANGE AND PRODUCTIVITY GROWTH Technological Change Technological change that increases the productivity of inputs acts to conserve inputs because the same output can be produced with fewer inputs. Also, technological change can be viewed as equivalent to an increase in total resource availability since, if the same output could be produced with fewer inputs, continuing to use the same level of inputs should result in higher outputs. Technological change can save mostly capital, or mostly labor, or both proportion¬ ately. Figure 9.11 shows an innovation that is biased toward saving mostly capital, that is, capital-saving technological change. The isoquant for a given level of output has shifted toward the origin. In addition, at unchanged factor prices the capital/labor ratio for the optimal input combination has decreased, indicating a proportionately greater reduction in utilization of capital to produce the same output level. If capital and labor are saved in the same proportions in which they are used, this is called neutral technological change. In terms of its impact on output, this is equivalent to an equal proportionate growth of inputs. And there is no change in the expansion path. Finally, if the capital to labor ratio is increased as the isoquants shift in, this is termed laborsaving technological change.

Measuring Productivity Broadly speaking, productivity is a ratio that reflects the relationship between inputs and outputs in production. Great interest attaches to measures of productivity because

9K. J. Arrow, H. B. Chenery, B. S. Minhas, and R. M. Solow, Capital Labor Substitution and Economic Efficiency, Review of Economics and Statistics, August 1961, 43 (3), 225-250.

233

The Theory of the Firm and Production

Figure 9.11

Neutral and Capital-Saving Technological Change.

of the implications of productivity change for human welfare. The more that can be produced from a given endowment of factor inputs, the greater will be economic welfare, other things equal. There are two classes of measures of productivity. One is termed single factor productivity. Definition: The single factor productivity of a factor is the ratio of total output to the input of the factor or simply the average product of that factor. The single factor productivity of labor is ProdL = X/L

The single factor productivity can be computed for any of the factor inputs. Single factor productivities can be computed for a single industry or productive activity or for the economy as a whole. In the latter case the numerator of the ratio must be some index of aggregate output. Most interest attaches to measures of labor productivity for the economy as a whole because of its implication for real wages, income, and economic welfare. The productivity of labor depends on the state of the art or technology and on the quantities of other factors that are being utilized. The second class of productivity measures is termed total factor productivity. Definition: Total factor productivity is the ratio of some measure of output to an aggregate or index measure of total factor inputs, or Prodf = X/F

where F is an index of inputs. Although the calculation of these measures of productivity is straightforward, given the availability of the data, the interpretation of changes in various productivity mea¬ sures can be tricky. In order to aid in understanding the meaning of various measures

234

The Competitive Market System

of productivity change, we first consider the effects of technological change and then the effects of changes in factor prices on the alternative measures of productivity, other things equal.

The Effects of Technological Change on Productivity Assume that there are no changes in factor prices. For purposes of this discussion, productivity will be measured by the quantity of inputs that are required to produce a given target level of output, Neutral technological change shifts the isoquant inward, say, to X[, but it does not shift the expansion path. With no change in the ratio of capital to labor, there is an equal percentage reduction in the inputs of both factors (see Figure 9.12). The single factor productivities of both labor and capital increase by the same percentage. And total factor productivity increases by this percentage as well. With capital-saving technological change, the ratio of capital to labor is decreased. The new isoquant for X[ would be tangent to the iso-cost line MM' at a point downward and to the right of B, say, at B1 or B". At B' the proportionate reduction in capital is greater than that for labor. This means that the productivity of capital has increased more than the productivity of labor. In fact, this provides another way of defining capital-saving technological change. Capital-saving technological change raises the productivity of capital proportionately more than the productivity of labor. If the new expansion path goes through point B ", the quantity of labor is actually increased and the productivity of labor is decreased by capital-saving technological change. A similar analysis applies to labor-saving technological change. The expansion path rotates up and to the left. Labor productivity increases more than capital productivity. And the measured change in total factor productivity will be somewhere between that for labor productivity and for capital productivity.

Figure 9.12

Neutral Technological Change and Measures of Productivity Change.

235

The Theory of the Firm and Production

The Effect of Changes in Factor Prices on Productivity Changes in factor prices lead to changes in the various measures of productivity. These changes, reflecting the rational responses of producers to changes in relative factor prices, do not indicate that there has been a change in the underlying technology. For example, if the price of capital increases or the price of labor decreases, producers respond by substituting labor for capital. The ratio of capital to labor declines, as does the measured productivity of labor. This is shown in Figure 9.13. The labor required to produce Xx increases from Lx to L[ when the relative price of labor decreases. In general, the measured productivity of any factor varies directly with its own relative price and varies inversely with the relative prices of inputs that are substitutes for it in production. Changes in factor prices also affect measures of total factor productivity. But because of the index number problem in constructing measures of total factor inputs, the direction of change in measured total factor productivity depends on which index of inputs is used.10 Thus measures of total factor productivity are essentially meaningless when all that is changing is relative factor prices.

Productivity in the U.S. Economy Throughout the 1950s and early 1960s the productivity of labor in the private sector increased at about 3.4 percent. Between 1966 and 1973 the rate of increase had dropped to 2.2 percent; and in the six years, 1973-1978, the rate of increase had dropped to only

Figure 9.13

The Effect of an Increase in the Relative Price of Labor on Measured Labor

Productivity.

,0See Chapter 8 for a discussion of the problems and biases in the use of index numbers.

236

The Competitive Market System

1.2 percent.11 This decline in the rate of increase of productivity has been a major topic of discussion and concern among economists and in the popular press. Two major influences on the productivity of labor are the amount of capital per worker and technology. It has been estimated that perhaps as much as one-half the postwar growth in output per worker has been due to innovation and technological change (inward shifts of isoquants), whereas another one-fifth to one-quarter can be attributed to increases in capital per worker (movements along isoquants).12 How much of the recent decline in productivity growth is due to a lag in innovation and technological change? Can the decline in productivity growth be attributed to a decline in the capital to labor ratio? And if so, is this a matter of concern? Space does not permit a complete treatment of these questions. Rather, what follows is meant only to illustrate the potential role that the microeconomics of production can play in the analysis of these problems. The decline in the rate of increase of labor productivity has in fact coincided with a decline in the rate of increase of capital per worker. The decline in the capital to labor ratio is not primarily due to a decrease in the rate of capital formation, but rather, to a significant increase in labor supply as measured by hours of work per year. This increase in labor supply is partly due to the coming of age of the post-World War II baby boom and partly due to the increase in the labor force participation rate for women. Also, it has had its influence on the relative prices of capital and labor. Specifically, the relative price of labor (PL/PK) was increasing in the earlier period at an annual rate of 2.7 percent, inducing a substitution of capital for labor. But since 1973 the increase in the supply of labor has held down the rate of increase of the relative price of labor to only 0.7 percent per year. This represents a significant reduction in the incentive to substitute capital for labor. And with less substitution of capital for labor the rate of growth of labor productivity will be lower. As Lester Thurow said, Looking at the relative prices of labor and capital, it is not at all clear that there is an “economic” productivity problem. A slowdown in [labor] productivity growth is exactly what the market is calling for and what is to be desired in a period when massive numbers of new workers need to be introduced into the labor force. These new workers lower wages and stop capital formation from rising, but that is what they are supposed to do in a supply and demand world.13

"These figures are from Gregory B. Christainsen, Frank Gollop, and Robert H. Haveman, Environmental and Health-Safety Regulations, Productivity Growth and Economic Performance: An Assessment, U.S. Con¬ gress Joint Economic Committee, 1980. Figures from other studies of productivity change may vary accord¬ ing to the choice of a measure of output (GNP, all private sector output, private sector nonfarm output, etc.), the time span over which changes in productivity are measured, and the technique used to eliminate the effect of the business cycle. For another study of the same problem see Edward F. Denison, Accounting for Slower Economic Growth: The United States in the 1970’s, Washington, D.C.: Brookings Institution, 1979. "See Edward F. Denison, Accounting for United States Economic Growth: 1929-1969, Washington, D.C.: Brookings Institution, 1974. "This quotation and the data in the preceding paragraph come from Lester C. Thurow, Discussion in The Decline Of Productivity Growth, Proceedings of a Conference, Federal Reserve Bank of Boston, June 1980.

237

The Theory of the Firm and Production

These trends are reinforced when one considers the fact that energy is also a factor input in production processes and the relative price of energy has been rising rapidly since 1973. As noted earlier, most studies of aggregate production show that energy and labor are substitutes in production in the U.S. economy while energy and capital are complements.14 An increase in the relative price of energy would therefore directly induce the substitution of labor for energy and indirectly cause a reduction in the amount of capital per worker through its effect on capital utilization. These forces would also tend to reduce the rate of growth of measured labor productivity. To summarize, in the earlier postwar years measured labor productivity increased due both to innovation as reflected in shifting isoquants and to the increase in capital per worker. The recent slowdown in the rate of productivity growth appears to be in part due to a slowdown in the rate of substitution of capital for labor in response to changes in relative factor prices. However, most authors conclude that changes in capital per worker can account for only a fraction of the total reduction in the growth of labor productivity. A full accounting of the slowdown must include such things as the possible effects of environmental and safety regulation, reduced innovation, changes in the age structure and education of the labor force, and changes in the composition of output.15

SOME ECONOMICS OF NATIONAL DEFENSE So far we have been discussing the theory of the behavior of producers who are assumed to be profit maximizers and who purchase inputs in markets at given factor prices. The theory has been essentially positive in that its purpose is to predict how producers will respond to changes in factor prices. The theory can also be applied to the analysis of production from a normative perspective. A potentially fruitful area for application is in the government production of services where the theory can be used to determine how to produce a given level of government output at minimum total cost. Where the government purchases its factor inputs at the going market price, the application of the theory is straightforward. But in some instances market prices do not reflect the opportunity costs of factor inputs that are being utilized by the government. A case in point is drafting soldiers to use in the production of national defense. The draft has been a controversial issue, involving questions of politics, ethics, the rights and responsibilities of citizens, international affairs, and military strategy. None of these questions will be discussed here, but we can use production theory to shed some light on one economic aspect of the draft—the effect of the draft on the cost of providing national security.

'“Ernst R. Berndt and David O. Wood, Engineering and Econometric Interpretations. 15Edward F. Denison, Accounting For Slower Economic Growth; Christiansen, Gollop, and Haveman, Envi¬ ronmental and Health-Safety Regulations and Gregory B. Christiansen and Robert H. Haveman, Public Regulation and the Slowdown in Productivity Growth, American Economic Review, May 1981, 71(2), 320-325.

238

The Competitive Market System

To do this we must make several simplifying assumptions. First, assume that national security is a measurable output that is produced by combining military personnel and capital and that, other things equal, increases in either labor or capital increase national security. The possibility that the addition of a new missile system may destabilize the relationship between the super powers, and thereby, our security, is ruled out by assumption. The second assumption is to treat inputs and outputs in broad aggregates without distinguishing between soldiers and sailors, or among submarines, missiles and bombers, and so on. The former are lumped together as labor and the latter represent various forms of capital. The problems of constructing indexes of capital and labor inputs for national defense are immense. But they are assumed away. The third assump¬ tion is that Congress has chosen S* as the target level of national security and directed the Pentagon to produce S* at minimum cost. First consider the situation with the draft. Labor is conscripted and paid a wage that is determined by Congress. Suppose that this wage along with the price of capital give the iso-cost line DD' in Figure 9.14. Given this iso-cost line, the least cost combination of inputs is point A. And the cost to the government of producing S* of national defense is given by the distance OD, multiplied by the price of capital. However, this does not give the true cost of producing national defense, because the wage paid to draftees is an underestimate of the true social cost or opportunity cost of providing labor to the military. This is clear because the coercion of the draft is required in order to induce people to give up their private jobs and other activities to become soldiers. The opportunity cost of labor used by the military is the wage that would have to be paid to induce the desired number of workers to enlist voluntarily in the military. This market-clearing wage is likely to be substantially higher than the wage actually paid to draftees for several reasons. First, available jobs in the private sector may pay higher wages than the government pays draftees. These jobs may offer less risk and more personal freedom, as well as have better working conditions and more opportunities for advancement.

Figure 9.14

The Cost of National Security with both the Draft and a Volunteer Army.

239

The Theory of the Firm and Production

Suppose that the opportunity cost of labor is known. If the military had to pay labor its opportunity cost, the true iso-cost line would be much steeper, for example, EE'. Since EE passes through point A, it shows the true cost to society of producing national security with this combination of capital and labor. The true cost is found by multiplying the distance OE by the price of capital. The difference between the true cost and the cost to the government (OE — OD) PK represents a tax on draftees. They, in effect, are subsidizing the provision of national defense by working for a wage less than their opportunity cost. Now suppose that the draft is eliminated. The wages of soldiers must be raised in order to induce sufficient numbers of them to work for the military. The cost of producing S* with the original quantities of capital and labor increases substantially. The iso-cost line through A has a steeper slope and is no longer tangent to the isoquant. The total cost of producing S* can be reduced by substituting capital for labor in production. This could result in a position such as point B in Figure 9.14. At point B the budgetary cost of national defense is greater than was the case with the draft. But since the Pentagon is now making production decisions on the basis of the true opportunity cost of labor rather than on the artificially low wage rate for draftees, the social cost of producing national defense has been reduced. The debate over the elimination of the draft was often confused. Budgetary planners were saying that the cost of a volunteer army would be higher, whereas economists were arguing that the cost would be lower. Actually, both arguments were correct because they referred to different concepts of cost. Since the involuntary tax on draftees has been eliminated, the budgetary cost is increased. But to the extent that the Pentagon has responded to the changes in its factor prices, social costs will have been reduced.

SUMMARY In a market economy, production is organized and carried out by firms that are hierarchical organizations directed by entrepreneurs. The conventional view is that this form of organization of productive activities evolved because it was efficient in minimiz¬ ing transactions costs and the cost of organizing and supervising the activities of supplies of factor services. For many purposes it is sufficient to view the firm as a black box that acts for the sole purpose of maximizing profit. But more sophisticated views of the behavior of firms emphasize things such as bounded rationality, satisficing, and the variety of incentives that motivate individuals who act within a hierarchical organization. Profit maximization requires that firms produce any given output at minimum total cost. Cost minimization in turn requires that inputs be combined in such pro¬ portions that the marginal rate of technical substitution between any pair of inputs is equal to the ratio of the input prices. As long as firms act to minimize production costs, an increase in the price of one factor will induce firms to substitute away from that factor. If there are only two factors of production, say, capital and labor, and if the price of, say, labor increases, this substitution always leads to a reduction in

240

The Competitive Market System

the ratio of labor to capital. But if there are three or more factors of production, there can be both substitute and complementary relationships between pairs of inputs. The elasticity of substitution is a measure of the degree of curvature of the isoquants of a production function. It relates the change in the marginal rate of technical substitu¬ tion to changes in the ratio of capital to labor. The expansion path is a locus of optimum input combinations for different outputs and for a given set of factor prices. Homogeneous production functions have straightline expansion paths that emerge from the origin. Production functions may be charac¬ terized by increasing, constant, or decreasing returns to scale. An isoquant mapping or production function reflects a given state of technological knowledge. Improvements in knowledge are called technological change. They result in an inward shift of the isoquants. Technological change can be neutral in its impact on the relative importance of factors. Or it can be either capital saving or labor saving. There are both single factor and total factor measures of productivity. Both measures of productivity can be influenced by changes in factor input ratios as well as by technological change. Changes in measured productivity must, therefore, be interpreted with care.

KEY CONCEPTS Entrepreneur Satisficing Isocost lines Elasticity of substitution Isocline Expansion path

Returns to scale Homogeneous production functions Capital-saving technological change Single factor productivity Total factor productivity

QUESTIONS AND PROBLEMS For Basic Review 1. 2.

Define and explain the economic significance of each of the key concepts. Outline and discuss the views of Coase, Alchian, and Demsetz on the nature and function of the firm as an economic organization. 3. Give a verbal proof of the proposition that to produce a given level of output at minimum cost the quantities of variable inputs must be such that the ratio of marginal physical product to price of input is the same for all inputs. Demonstrate the same proposition using an isoquant iso-cost diagram. 4. * If engineers prepare a table giving the amounts of product that can be obtained from combining all the necessary inputs in all possible proportions, can one find a point of “maximum efficiency” or “optimum proportion of inputs”? Explain. 5. * Use an isoquant diagram to show how much of an input will be used if it is

241

The Theory of the Firm and Production

free (has a zero price). What happens if a free input becomes a “priced” input? Can you think of some examples of once free inputs that now have positive prices?

Problems 1.

Suppose that the MRTSLK = 2, PL = $12, and PK = $3. Does this represent an optimum input combination? Show how the input levels could be changed so as to produce the same output at lower total cost. Also, show how output could be increased without increasing total cost. 2. * Suppose that MPL = 5, PL = $5, MPK = 5, and PK = $10. Does this represent an optimum input combination? Show how input levels could be changed so as to increase output without increasing total cost. 3. Suppose that the production function for X is X = 2K'ALVl, Does this represent constant, increasing, or decreasing returns to scale? (See your answer to problem 1, Chapter 3.) What if the production function is X = 5K0JL02 X = 2 K0SL03 4. * a. Verify that the isoquant in Figure 9.7 represents the production function X

5.

= L VlKVl when V = 5. b. How much labor will be required to produce 5 units of X if capital is reduced to Vi units per period? To Vio units per period? c. Is L an essential input in this production function? Suppose that you observe a 10 percent increase in the ratio PL/PK, and you also observe a 5 percent increase in the ratio K/L. Can you calculate the elasticity of substitution? What assumptions must you make?

FOR DISCUSSION 1.

If medical care is “hard to get,” “costs too much,” and we are having a “crisis in medical service,” does this mean we need more doctors? Discuss by considering medical service as an output and doctors as one kind of input. 2* “Antismoking ads or auto seat belt ads—which should we spend our money on?” (Is this a problem in production theory? What is the output?) 3. How would you expect farmers to respond to acreage limitations that are coupled with a price-support program? Can you show this with isoquant diagrams? 4. * An effluent charge is a price or tax charged for each unit of a polluting substance that is discharged to the environment by a firm. How would an effluent charge on pollution affect producers’ input combinations? 5. Recently an author stated that “historically farmers have tried to maximize

242

The Competitive Market System

agricultural output per acre of land, but now they should try to maximize output per unit of fertilizer.” Does this statement make sense from the perspective of production theory? Is it likely to be true either as a statement of historical fact or as a recommendation for present or future action? 6.* Assume that the production function for aggregate output is X — X(K, Ls, LN), where Ls = skilled labor and LN = nonskilled labor. Consider a policy that would subsidize the wages of nonskilled workers as an incentive to increase their employment. What will be the effect of this subsidy on the utilization rates of other factor inputs under the following assumptions about the production technology? a. Ls and LN are substitutes. b. Ls and LN are complements. c. Ln and K are substitutes.

SUPPLEMENTARY READINGS Alchian, Armen, and Demsetz, Harold. Production, Information Cost and Economic Organization. American Economic Review, December 1972, 62(5), 777-795. Coase, Ronald H. The Nature of the Firm. Economica, 1937, 4, 386—405. Dorfman, Robert. Mathematical or ‘Linear’ Programming: A Nonmathematical Expo¬ sition. American Economic Review, December 1953, 43(5), 797-825. Ferguson, Charles E. The Neoclassical Theory of Production and Distribution. London: Cambridge University Press, 1969, Chapters 1-6, 11, 14. Simon, Herbert A. Theories of Decision-Making in Economics and Behavioral Sciences. American Economic Review, June 1959, 49(3), 253-283. Simon, Herbert A. Rational Decision-Making in Business Organizations. American Economic Review, September 1979, 69(4), 493-513. Williamson, Oliver. Markets and Hierarchies: Analysis and Antitrust Implications. New York: Free Press, 1975.

MATHEMATICAL APPENDIX TO CHAPTER 9 Optimum Input Combinations As in the text, the condition for the optimum input combination can be derived in terms of either minimizing the cost of a given output or maximizing the output for a given cost. The condition can be derived from the calculus of constrained maximization. First, suppose the output target is X*. The objective is Minimize

C = PL ■ L + PK ■ K

subject to the constraint that output given by X(K, L) be equal to X*. Set up the Lagrangian expression:

The Theory of the Firm and Production

Min: Cx = PL ■ L + PK ■ K + X [X* - X(K, L)] and set the partial derivatives equal to 0. dX_

(a)

Pl

dL

-

X

0

dL

(b) ^ = PK-X— = o (c)

dK dC X

dK = X* - X(K, L) = 0

dX

Dividing (b) into (a) and rearranging gives (d)aXnL aX/aK

Pr

or , . dX/dL dX/dK (e)- = PL

Pk

The partial derivatives are the marginal products so the left-hand side of (d) is the MRTSlk, and (d) is equivalent to the condition given in the text. Equation (e) requires the equalization of the marginal net returns of expenditure on the two inputs. The solution of the set of three equations, (a) to (c), for the three unknowns, L, K, and X gives the optimum quantities of L and K. The solution for X gives the marginal value of the constraint that output equal X*, that is, how much cost could be reduced if X* were reduced by 1 unit. This is the marginal cost of X production. In the alternative formulation the objective is to maximize X = X(K, L) subject to the constraint that cost be C*. Set up the Lagrangian expression: Max: Xy = X(K, L) + X (C* - Pl L - Pk K)

(b) (c)

dX

dL dXx dK dXx

y

aXy

1

(a)

II o

and set the partial derivatives equal to 0: II

243

dL = « -,X.^ = 0 dK C* - PL ■ L - PK • K

dX

Dividing (b) into (a) and rearranging gives dX/dL

_

dX/dK

~ PK

dX/dL Pl

_ dX/dK ~

Pk

(

244

The Competitive Market System

These are equivalent statements of the condition for optimal production. The solution for A. gives the amount that output can be increased by relaxing the cost constraint by $1, that is, the marginal product of a dollar of expenditure.

CHAPTER 10 The Analysis of Costs

CONCEPTS OF COSTS

T

-M.he production possibilities curve introduced in Chapter 3 clarifies the fact that the cost of producing 1 unit of a good is what must be given up to make that production possible. Cost means opportunity cost. In the simple two-good economy with fixed factor supplies of Chapters 3 through 5 the opportunity cost of good X can be measured simply and accurately by the reduction in the output of Y which occurs when the production of X is increased. In a more complex economy with many goods and with factor supplies that may vary with factor prices, identification and measurement of opportunity cost may not be so easy. This is because the increase in production of one good may necessitate decreases in many other things. For example, production of one automobile absorbs steel, rubber, labor, plastics made from petrochemicals, and the services of capital equipment. Tracing out the consequences of withdrawing these resources and factor services from other productive activities can be quite difficult. There may be fewer refrigerators and air conditioners manufactured, less electricity produced because of the diversion of petroleum to plastics production, and less leisure available to the assembly line worker who must put in overtime. When measuring the opportunity cost of a good, all consequences of the increased production must be identified and incorporated in the measurement. It will be shown later in this section that the existence of markets and prices may under certain conditions greatly simplify this task of measurement of opportunity cost. It is important to note that opportunity cost is a concept that is independent of any particular set of economic and social institutions. Opportunity cost exists in all econo¬ mies. Different economic institutions affect primarily the form that opportunity costs take and who bears these costs. In particular, the nature of the system of property rights 245

246

The Competitive Market System

is a major determinant of the form and incidence of the opportunity costs of production. For example, military conscription is a form of limitation on an individual’s property right in his labor. And as seen in Chapter .9, the draft has a significant effect on the form of the opportunity cost of national security and on who bears the burden of this cost. In a modern market economy accountants record the costs of production for firms by adding up the payments to factors of production and suppliers of materials. Do these measures of cost correspond to opportunity cost? Or in more general terms, can the market prices of factor inputs be used to measure opportunity cost, and if so, under what conditions? There are three basic conditions that must be satisfied if factor prices are to be used to measure opportunity costs. They are: 1. The system of property rights must be well defined and complete. Property rights must have been established and be enforceable for all things that matter to individuals. 2. All goods that matter to individuals must be capable of being bought and sold in markets. 3. All markets must be perfectly competitive. The first and second conditions are clearly related in that the system of property rights is a prerequisite for the effective functioning of markets. Where property rights are not defined or enforceable some individuals may be forced to give up something as a consequence of a firm’s productive activity but may receive no compensating pay¬ ment. If this is the case, there is no monetary cost to the firm that corresponds to the opportunity cost borne by the individuals. As a result, money costs underestimate opportunity costs. Individuals’ property rights in clean, healthful air are not presently well defined. When a paper mill or coal-burning electric power plant discharges pollu¬ tants into the air, the pollutants may have adverse effects on the health of the people living downwind from the plant. The reduced health is an opportunity cost; but it does not show up on the accounting records of the firm. These are called external costs. Definition: External costs are those opportunity costs of production (or consump¬ tion) that fall on others and for which the firm (or individual) bears no responsibility. External costs are external to the accounting and decision-making framework of the producers whose actions cause them.

The fundamental importance of the requirement for perfect competition can best be seen in the following way. If all markets are perfectly competitive, producers will purchase additional units of each factor input as long as the monetary value of that factor to the producer is greater than its price. The value of the input is called the value of marginal product. Definition: The value of marginal product (VMP) of a factor is the money value of the additional output that is produced when one more unit of a factor is employed, holding everything else constant.

247

The Analysis of Cost

The VMP is found by multiplying the price of output and the marginal physical product of the input. And because the price of a product is a measure of consumers’ marginal willingness to pay tor the product, VMP is also a measure of the value to consumers of employing one more unit of the factor. In order to maximize profits, producers must adjust their purchases of inputs so that the price of each factor is just equal to the value of its marginal product.1 For example, if the price of a factor were $5 and the VMP of this last unit employed were $8, the firm could increase profits by using more of the factor. The next unit employed would add $3 (the excess of the VMP of the factor over its price) to the firm’s profits. As the firm increases its use of the factor, VMP declines because of the law of diminishing marginal productivity. Suppose the firm has increased its use of the factor to the point where its VMP is only $3. The last unit of the factor employed has actually reduced the profit of the firm because it added more to the firm’s cost ($5) than to the firm’s revenue. The optimum level of use for the factor is where its VMP just equals its price. If under perfect competition firms equate the value of marginal product of each factor to its price, then the price of a factor can be taken as an estimate of the value of the marginal product of that factor in any productive activity in which it is being used. If a producer in the X industry wishes to expand production by hiring one additional unit of labor, it can only do so by hiring that unit of labor away from the Y industry.2 Because the price of labor can be taken as a measure of the value of its marginal product in the Y industry, its price measures the value of the reduction in Y output that must occur, that is, the opportunity cost of shifting one unit of labor from Y to X. If the price of labor is $5 per unit, then the output of some good must be reduced by $5 if 1 unit of labor is to be shifted into employment in X production. In conclusion, if all markets are perfectly competitive and all factor inputs are purchased in markets, then the prices paid to factor inputs measure their values in other uses. And money payments for factor inputs measure the opportunity cost of production.

Accounting Costs and Profits We have seen that under conditions of perfect competition if accountants use market prices to record the values of all factor inputs used in production, their cost data can be taken as a measure of opportunity cost. But this is not how accountants do their job. Partly for historical reasons and partly because of certain features of the U.S. Inter¬ nal Revenue Code, accountants record primarily transactions between the firm and others. This means that they record data on only those inputs actually purchased from others. They do not record the costs of factors of production owned by the firm. This can lead to a substantial divergence between accounting measures of cost and opportu¬ nity cost. And it can also lead to some confusion over the meaning of the term “profit.”

'This analysis is more fully developed in Chapter 12. 2If factor supplies are not fixed but depend on factor prices, the extra unit of labor time could come from a worker’s leisure. But the factor price paid to the worker is equal to the value of the leisure time given up, that is, its opportunity cost. This will also be shown in Chapter 12.

248

The Competitive Market System

Consider the following example. Suppose in one year a firm purchases labor at a cost of $1000, materials for $400, and pays rent for a building equal to $100, as shown in Table 10.1. All these are transactions with others outside the firm. They are explicit costs and are recorded by the accountant. If the firm owns some of the factor inputs used in production or if the owner or entrepreneur provides his own labor services to the firm, there are no payments to others for the accountant to record. Yet the use of these inputs involves an opportunity cost to the firm. These unrecorded opportunity costs are implicit costs. Suppose, for example, that the owner of the firm provides 40 hours of labor to the firm but does not receive an explicit wage payment for this time. What is the opportu¬ nity cost? It is measured by the wage the owner could have received if he had sold his labor services on the market. If his potential wage was $5 per hour, the opportunity cost associated with the firm’s use of the owner’s time is $200. This is entered as an implicit cost in Table 10.1. Suppose also that the firm owns a machine (capital) that it uses in production. If the machine were purchased in the past, there would be no payment during this year to show up on the accounting records. There is no explicit cost associated with the use of the machine. Even if the machine were purchased during this accounting period, the expenditure on the machine would not be a valid measure of the cost of this period’s production, because the machine would still be able to contribute to the production of future periods. The implicit cost of the machine is its opportunity cost.

Table 10.1

Costs, Revenues, and Profits per Year: An Example

Explicit costs Labor Materials Rent Total explicit cost Implicit costs Owner labor User cost of capital machine Foregone interest 10 percent of $5000 Loss of value Total implicit cost Total private cost Total revenue

$1000 400 100 $1500 200 1500 $500 1000 $1700 $3200 $3200

Accounting profit: Total revenue less explicit costs $3200 - $1500 = $1700 Economic profit: Total revenue less total private costs $3200 - $3200 =

0

249

The Analysis of Cost

How is the opportunity cost of the machine to be measured? The answer lies in what has been foregone by the firm in order to use this machine. Suppose the machine has a current market value of $5000. The most obvious alternative for the firm is to sell it and lend the money at interest. Suppose the current market interest rate is 10 percent per year. The firm, by using the machine, has given up the opportunity to earn $500 in interest. This is one component of the opportunity cost of using the machine. In addition, we must take into account any expected change in the market value of the machine over the period of use. The market value of the machine might decline because of wear and tear and depreciation or because of general market conditions. For example, suppose the machine is expected to have a market value of only $4000 after one year of use. Then besides the foregone interest, there is an opportunity cost in the form of a loss of value of the machine. This more comprehensive measure is sometimes known as user cost.

Definition: User cost is the sum of the foregone interest on the market value of the machine at the beginning of the period and the loss of its market value over the period of its use. In this example the user cost of the machine is $1500 for the year. This cost is not in the form of payments made by the firm; rather, it is a loss of opportunities. Thus it is an implicit cost. When implicit costs are added to explicit cost, the total cost of production to the firm is $3200. Because the accountant and economist have different views of the nature of cost, they also have different views as to what constitutes profit. Suppose that this firm has revenues during the year of $3200. The accountant computes profit by subtracting explicit cost from total revenue.3 Accounting profit is $1700. But the true cost to the firm includes implicit costs of capital and labor. When implicit costs are taken into account in Table 10.1, economic profit becomes 0. Firms with positive accounting profits can nevertheless be losing money in an economic sense if their accounting profits are less than their implicit costs. Negative economic profit means that the firm would be better off using its capital and other owned inputs in some other activity. The returns in the alternative activities would be higher than the returns being earned in the present activity. A firm whose economic profits are 0 will be showing a positive accounting profit. But the accounting profit is just compensation for the opportunity cost of the firm’s and owner’s inputs. The lack of economic profit is in no sense a sign of economic distress. It simply means that returns in this activity are just as good as in the next best alternative. There is no incentive for the firm to move its capital and other resources to alternative activities. The condition of zero economic profit is viable in the long run for firms. In fact, it will be shown in the next chapter that zero economic profit is a condition for long-run equilibrium in a competitive economy.

'To be accurate, the accountant also deducts what he calls depreciation, a fraction of the historical purchase cost of the capital equipment. This unpaid “cost” could be considered to be a crude approximation of the second component of user cost, that is, the loss of market value.

250

The Competitive Market System

Private Cost Versus Social Cost When external costs are present, private cost is less than social cost. We have already presented one example of an external cost of production. Other examples include the loss of commercial fishing and recreation opportunities when a factory pollutes a waterway, the loss of quiet to home owners under the landing pattern at commercial airports, and the higher travel time and fuel costs that additional users of a highway impose on others during periods of traffic congestion. When external costs are present, economic profitability for a productive activity does not necessarily mean social desira¬ bility. It is possible that external costs exceed economic profit and that if the firm were required to take the external costs into account, it would curtail or cease the productive activity. The policy implications of external costs will be discussed in more detail in Chapter 17. There can be private costs to the firm that are not social costs or opportunity costs to the economy as a whole. For example, when a firm pays a fee to an inventor for the right to purchase a product on which the inventor holds a patent, that fee represents a private cost to the firm. But there is no corresponding social cost. No opportunities are foreclosed by the use of the patent information. There is no opportunity cost. Can you think of other examples of private costs that are not social costs? In this and subsequent chapters, unless otherwise specified, the term “cost” refers to private cost, both explicit and implicit. Furthermore, unless otherwise specified, it will be assumed that there are no external costs and that private costs are exactly equal to social costs. Summary of Cost and Profit Concepts Social cost = opportunity cost = external cost + private cost Private cost = explicit cost + implicit cost Economic profit = total revenue — private cost Accounting profit = total revenue — explicit cost = economic profit + implicit cost.

FROM THE PRODUCTION FUNCTION TO COST CURVES The cost curves of a firm show the total cost, average cost, and marginal cost of production as a function of the level of output. There are curves for both long-run and short-run conditions. In this section we discuss these curves and their relationships with one another and examine some of their properties. Because the total cost of producing a given level of output depends in part on the quantities of factors that are necessary for production, there must be a close relationship between the production function and the cost curves. In fact, the properties of cost curves derive essentially from the characteristics of the underlying production function. We begin the analysis of cost curves by analyzing this relationship between cost and the conditions of production.

251

The Analysis of Cost

The Cost Function Assume that there are only two factors of production, labor and capital, used in the production of one good X. Further assume that the firm purchases both factors in perfectly competitive markets at given factor prices, PK and PL. Total cost is then defined to be C = PK. K + PL. L

This is simply an accounting definition that states that total cost is the sum of the costs of all factors. It says nothing about the determinants of K and L, which in turn determine the magnitude of total cost. As this definition shows, cost depends on the prices paid for the factor inputs. Cost also depends on the level of output that determines the quantities of K and L that are required as inputs. The relationships among factor prices, factor quantities, output, and cost are expressed in the cost function.

Definition: The cost function is an expression that gives the minimum possible total cost of production as a function of the prices of factors and the level of output. It provides the total cost of producing a given output when the firm has chosen the cost-minimizing quantities of K and L as determined by the tangency of an isoquant with an iso-cost line. For a given level of output, say, X', the minimum cost of production can be written as C(X') = PK ■ K' + PL ■ L'

where K' and L' are the solutions to the cost minimization problem for producing X'. Because the cost-minimizing input combination depends on the shape of the isoquants or production function and on factor prices, the cost function can be written as C{X) = C [X(K, L), PK, PL]

As this expression makes clear, the production function for X and the given prices of labor and capital provide all the information that is needed to calculate the cost of producing any level of X. The cost curves to be derived in this chapter are simply two-dimensional representations of this cost function that are drawn, holding PK and PL constant. Any change in PL or PK will result in a change in the total cost of producing a given level of X. Thus when there is a change in one of the factor prices, the cost curves shift accordingly. The direction and magnitude of the shift can be determined through the cost function.

Long-Run Cost Curves In the long run all factors of production can be varied. There are no fixed factors. The long-run total cost curve for any production function can be derived graphically from the isoquant mapping that represents the production function and the iso-cost lines that reflect the given factor prices. This is the first step in our analysis. Once the total cost

252

The Competitive Market System

curve has been derived, the long-run marginal and average cost curves can be derived from it, as will be shown subsequently.

The Long-Run Total Cost Curve. One of the most important facts influencing the shape of the long-run total cost curve is the nature of returns to scale. Figure 10.1(a) shows two isoquants from a homogeneous production function with constant returns to scale. Suppose that the price of capital is $4 per unit and the price of labor is $2 per unit. These factor prices determine the slope of the iso-cost lines. The least cost combination for producing output of X = 10 is point A with 4 units of labor and 6 units of capital. The total cost of producing Xx can be found by multiplying each of the inputs by its respective factor price and adding the costs for all inputs. The total cost of X = 10 is $32 ($2 X 4 + $4 X 6). Because all other points on the iso-cost line have the same total cost, cost can also be measured by multiplying the price of capital by the vertical intercept of the iso-cost line ($4 X 8). Similarly, the product of the price of labor and the horizontal intercept of the iso-cost line also measures total cost ($2 X 16). The total cost for producing X = 10 is shown as point A' in Figure 10.1(h). In order to double the output of X to 20 units, we must double the inputs of both factors, thus doubling total cost. This is shown as point B in Figure 10.1(a) and point B' in Figure 10.1(h). The long-run total cost curve is the line emerging from the origin and passing through points A' and B'. Under conditions of constant returns to scale, the long-run total cost curve is a straight line. Figure 10.2(a) shows two isoquants with increasing returns to scale. In order to double output from Xu we need to increase the level of inputs by something less than

(fl) Figure 10.1

(b)

Isoquants and the Long-Run Total Cost Curve with Constant Returns to Scale.

253

The Analysis of Cost

00 Figure 10.2

O)

Isoquants and the Long Run Total Cost Curve with Increasing Returns to Scale.

double. This means that the cost of producing 2 A, (given by C2) is less than double the cost of producing Xx (given by C,). This is shown in Figure 10.2(h) in which the long-run total cost curve is upward sloping but concave from below; that is, it is increasing at a decreasing rate. Finally, Figure 10.3(a) shows two isoquants that reflect decreasing returns to scale. In order to double the output, factor inputs must be more than doubled and total cost rises by a factor greater than 2. The long-run total cost curve in Figure 10.3(h) is con¬ cave upward, showing that the total cost rises at an increasing rate with higher output. In textbook expositions of production and cost it is common to assume that produc¬ tion functions for typical firms are characterized by first increasing, then decreasing returns to scale. Some reasons for this assumption will be discussed in a later section. Following the analysis of Figures 10.2 and 10.3, it can be seen that the long-run total cost curve associated with such a production function will first be concave from below, and then will be concave from above.4 For an example, see Figure 10.4. Most of our re¬ maining analysis of costs will be based on a long-run total cost curve of this general form. Cost curves with continuously increasing, constant, or decreasing returns to scale can also be analyzed using the principles outlined subsequently. But many useful insights into the behavior of costs can be attained by analyzing the cost curves of Figure 10.4.

“As mentioned in Chapter 9, returns to scale can be defined in terms of either proportionate changes in all inputs or changes in total cost. The two definitions can lead to different conclusions about the slopes of cost curves if the production function is not homogeneous. If returns to scale are defined in terms of cost, the following statements are always true: A total cost curve that is concave from below (decreasing slope) means increasing returns to scale; and a total cost curve that is convex from below (increasing slope) means decreasing returns to scale. It is possible that a production function displaying constant returns to scale or slightly decreasing returns to scale when scale is defined in terms of inputs would display a concave total cost curve and increasing returns to scale by the cost measure. See problem 3 at the end of this chapter.

254

The Competitive Market System

(a) Figure 10.3

(b)

Isoquants and the Long-Run Total Cost Curve with Decreasing Returns to Scale.

O (b)

255

The Analysis of Cost

The Long-Run Marginal Cost Curve. Marginal cost is defined as the change in total cost with a small change in output. MC

AO AX

This definition applies to any cost curve, whether long run or short run. In graphical terms marginal cost is the slope of the total cost curve. When a long-run total cost curve is being analyzed, as is the case here, the resulting marginal cost is called long-run marginal cost (LMC). Figure 10.4 shows a total cost curve that is upward sloping throughout but is first becoming less steep (concave from below) up to output level Xx. Beyond this output the total cost curve becomes more steep (is concave from above). This means that the long-run marginal cost curve is downward sloping until it reaches a minimum at output level X, and then is upward sloping beyond that point. See the lower part of Figure 10.4.

The Long-Run Average Cost Curve. Average cost or unit cost is defined as total cost divided by output, or

X

The long-run average cost (LAC) for any level of output can be determined graphically from the long-run total cost curve in the following manner. Consider a point on the total cost curve such as point A in the upper part of Figure 10.4. Draw a straight line from the origin to point A. The slope of this line is the ratio AX1/OXl. The distance AXi is equal to the total cost at an output of Xx. The distance OXx gives output Xx. Therefore the ratio AXx/OXx measures average cost. Thus the slope of a line from the origin to a point on the total cost curve measures average cost. In the vicinity of point A in Figure 10.4, long-run average cost is decreasing as output increases. LAC decreases with output up to X2 at point B. At output level X3, LAC has increased to the same level associated with output Xt. Thus the long-run average cost curve associated with the total cost curve of Figure 10.4 is U shaped. At lower levels of output it is decreasing, implying increasing returns to scale. It reaches a minimum, and then increases, implying decreasing returns to scale. The graphical analysis of the marginal and average cost curves may also be used to establish the necessary relationships between the two curves. Notice that at point B and output X2 the long-run average cost curve is at a minimum. At this output the line from the origin to the long-run total cost curve, the slope of which measures long-run average cost, is tangent to the total cost curve rather than intersecting it. Because the slope of the line tangent to a curve also measures the slope of the curve itself, the slope of this line gives marginal cost as well as average cost. Thus marginal cost and average cost are equal at the output where average cost is at its minimum. Principle: When long-run average cost is at its minimum, it is equal to long-run

256

The Competitive Market System

marginal cost. The long-run marginal cost curve must intersect the long-run average cost curve at the latter’s minimum point. A corollary of this principle is that whenever the marginal cost curve is below the average cost curve, average cost will be decreasing. And whenever the marginal cost curve is above the average cost curve, average cost will be increasing. This corollary should be easy to grasp intuitively. It applies to the relationship between any average variable and its related marginal variable. For example, suppose that a student has taken three quizzes and has a quiz average of 80 percent. The grade on the fourth quiz is the marginal contribution to the total quiz score. If the grade on the fourth quiz is below the average, say, 70 percent, it will pull the average down. A marginal score above the average will pull the average up. The relationship between marginal and average cost can also be verified by inspection of the upper part of Figure 10.4. At points such as A where the long-run average cost curve is downward sloping, the slope of the line from the origin cuts the total cost curve from below, indicating that its slope is steeper than that of the total cost curve itself. Thus the long-run average cost is greater than long-run marginal cost. But at points beyond B where the average cost is increasing, the line from the origin cuts the total cost curve from above showing that its slope (LAC) is less than the slope of the total cost curve (LMC). Thus average cost is less than marginal cost when average cost is increasing.5

Changes in Factor Prices. The long-run total cost curve and the marginal and average cost curves derived from it were drawn under the assumption that factor prices were given. A change in the price of either factor will result in a shift in all the curves of Figure 10.4. Figure 10.5(a) shows the X, isoquant and the initial iso-cost line C,C',. The corresponding total cost curve is shown as the solid line in Figure 10.5(b). If the price of labor were to increase, the iso-cost line for C, would become more steep and shift inward to C,C x. This means it is no longer possible to produce output X{ at a cost of C,. In order to stay on the ATj isoquant, total expenditure on inputs must be increased to Ci, as shown by the C2C2' iso-cost line. If this is true for output Xu it must be true for all other output levels that are greater than 0. Thus the whole long-run total cost curve must shift upward for all positive output levels. This is shown by the dashed long-run total cost curve TC' in Figure 10.5(b). The same would be true if the price of capital were to increase holding the price of labor constant. And if either factor price fell, other things equal, the long-run total cost curve would shift downward. The shift in the long-run total cost curve also causes corresponding shifts in the marginal and average cost curves. If a factor price is increased, the new total cost curve must at all points lie above the old total cost curve, and the distance between the two curves must be greater at higher outputs. That is, at all output levels the new total cost

'The relationship between the average and marginal cost curves can also be derived mathematically. See the Mathematical Appendix to this chapter.

257

The Analysis of Cost

Figure 10.5

Total Cost Curves with Changes in Factor Prices.

curve is more steeply sloped. Thus the new marginal cost curve must be above the old marginal cost curve for all levels of output. Similarly, at any level of output, a line from the origin to the new total cost curve must be more steeply sloped. Thus for all levels of output, long-run average cost is higher with the higher factor price. In summary, an increase in a factor price, other things equal, leads to an upward shift in the long-run total cost curve at all points, except at the origin and to upward shifts in the long-run marginal cost curve and long-run average cost curve. Conversely, a decrease in either factor price, other things equal, causes corresponding downward shifts in each of the three cost curves. The magnitudes of the shifts depend on the size of the change in the factor price and the relative importance of that factor in produc¬ tion. For example, the higher the ratio of capital to labor in production is, the bigger will be the shift of the cost curves for any given change in the price of capital.

The Short-Run Cost Curves The Short-Run Total Cost Curve. By definition producers in the short run are not free to vary the inputs of both capital and labor in order to change the output level. Rather than move along the expansion path, producers are constrained to movements along the fixed factor line K* of Figure 10.6(a), varying labor but holding capital constant. Because in the short run the range of attainable input combinations for production is much more limited, the short-run total cost curve will be different from the long-run total cost curve. Specifically, it will lie above the long-run total cost curve, except for one point of tangency. If the producer whose isoquants are shown in Figure 10.6(a) were free to vary both capital and labor, his optimal input combinations would lie along the expansion path EiP. The total cost curve would be that labeled TCLR in Figure 10.6(6).

258

The Competitive Market System

Figure 10.6

Isoquants and the Long-Run and Short-Run Total Cost Curves.

Suppose the producer chooses output level X2 and produces at point F at a cost of C2. If the producer wishes to reduce output to X 1; in the short run he cannot move down along the expansion path to point E and cost C,. Rather, he must move along the horizontal fixed factor line K* to point E'. Since E' is not at a tangency point between an iso-cost line that reflects the given factor prices and the isoquant, it must represent a higher total cost of production than point E would. This is demonstrated graphically by the fact that the iso-cost line through point E' lies above the iso-cost line through point E. Thus total cost at point E' must be greater than C,, which is also shown in Figure 10.6(h). This indicates that in the short run for outputs less than X2, short-run total costs must be higher than long-run total costs. What will happen to total cost in the short run if output is reduced to zero? Because it is not possible to reduce the input of the fixed factor even though output is zero, total costs would still be positive. The total costs that remain when output is reduced to zero are called fixed costs. In this example fixed cost can be found by multiplying the quantity of the fixed factor, K*, by its factor price. This is shown as C0 in Figure 10.6(h). Suppose the producer wishes to expand output to X2. In the short run he is unable to increase the input of capital so he cannot move along the expansion path to point G. Rather, he must move to the right along the fixed factor line to point G'. Again, this is not a cost-minimizing input combination because the factor price ratio is not equal to the marginal rate of technical substitution. Hence the short-run total cost of producing at X2 must be above the long-run total cost of production at that level of output. Only at output X2 are long- and short-run total costs equal. The point where they are equal is the output level where the fixed factor line and the expansion path intersect. Only at that level of output is the fixed amount of capital just equal to the optimal

259

The Analysis of Cost

amount of capital. At all other output levels, short-run total costs are above long-run total costs, because the inability to vary the capital input prevents the attainment of the cost-minimizing input combination. Different quantities of the fixed factor lead to different short-run total cost curves. An increase in the availability of the fixed factor is represented by an upward shift in the line K*. This new line will intersect the expansion path above and to the right of point F and at a higher output. The new short-run total cost curve will be tangent to the long-run total cost curve at this higher level of output (see Figure 10.7). In fact, there is a short-run total cost curve for every possible level of the fixed input. And the long-run total cost curve can be interpreted as an envelope of the infinite number of possible short-run total cost curves (see Figure 10.7).

Short-Run Marginal Cost and Short-Run Average Cost. Short-run marginal cost (SMC) is the change in short-run total cost for a small change in output. Graphically, it is found by measuring the slope of the short-run total cost curve. Similarly, short-run average cost (5^1 C) is short-run total cost divided by output. Graphically, it can be found by measuring the slope of a straight line from the origin to any point on the short-run total cost curve. The S^C and SMC curves are related to each other in the same way as the corresponding long-run marginal and average curves. The SMC curve intersects the SAC curve at the latter’s minimum point. When the SAC curve is falling, the SMC must lie below it. And when the SAC curve is rising, the SMC curve lies above it. These relationships are shown in Figure 10.9.

a?

Figure 10.7

The Long-Run Total Cost Curve as an Envelope of Short-Run Cost Curves.

260

The Competitive Market System

Fixed Costs and Variable Costs. Total costs in the short run can be divided into fixed costs and variable costs (see Figure 10.8). Both fixed and variable costs can be divided by output to get average fixed and variable costs, respectively. Because fixed costs are invariant with output, dividing by an ever-larger output yields an everdiminishing average fixed cost. See Table 10.2 and Figure 10.9 for a hypothetical example. If the intercept (point A in Figure 10.8) of a short-run total cost curve is taken to be the origin, the curve shows total variable cost. Average variable cost (A VC) can be found graphically by measuring the slope of the line from the origin (point A) to the total variable cost curve. As with other average cost curves, the average variable cost curve is related to the short-run marginal cost curve in a specific way. The short-run marginal cost curve intersects the average variable cost curve at the latter’s minimum point. When the A VC curve is decreasing, short-run marginal cost is below it; and when the AVC curve is increasing, short-run marginal cost curve lies above it. The relationships among the various short-run cost curves can best be summarized through Table 10.2 and Figure 10.9. The first two columns of Table 10.2 show the total cost of production for output levels ranging from 0 to 10. The figures in all other columns can be derived directly from the information contained in the first two col¬ umns. The table illustrates the following points about short-run costs: 1. The total cost when output is zero is $50, since total fixed cost is $50. 2. Total cost is total variable cost plus total fixed cost. 3. Short-run marginal cost is determined by finding the difference between total costs as output changes by 1 unit. The short-run marginal cost data are entered in the table between the two lines at different output levels in order to indicate that they refer to changes in total cost and changes in output.

Figure 10.8

Short-Run Fixed and Variable Costs.

261

The Analysis of Cost

Table 10.2

Hypothetical Short-Run Cost Data

Output

Total cost

Total fixed cost

Total variable cost

0 1 2 3 4 5 6 7 8 9 10

50 76 98 122 154 200 266 358 482 644 850

50 50 50 50 50 50 50 50 50 50 50

0 26 48 72 104 150 216 308 432 594 800

Short-run marginal cost 26^22 24 32 46 66 92 124 162 206

Average fixed cost

Average variable cost

Short-run average cost

50 25 16.67 12.25 10 8.33 7.14 6.25 5.55 5

26 24 24 26 30 36 44 54 66 80

76 49 40.67 38.25 40 44.33 51.44 60.25 71.55 85

Note: Cost data computed from the following cost function: C = 50 + 30A - 5A2 + Xy

0

123456789

10

X per period Figure 10.9

Short-Run Cost Curves from Table 10.2.

262

The Competitive Market System

4. Short-run marginal cost can also be found by calculating the change in total

5.

6. 7. 8.

variable cost for a 1-unit change in output. Because fixed cost is independent of output levels, it plays no role in the determination of marginal cost. Changes in fixed cost leave total variable cost and short-run marginal cost unchanged. You should verify this by calculating total cost, total variable cost, and short-run marginal cost when fixed costs are changed, for example, to $100. Average fixed cost is found by dividing total fixed cost by output. Because fixed cost does not increase, average fixed cost decreases with increases in output. Fixed cost per unit decreases as fixed cost is spread over a larger output. Average variable cost is found by dividing total variable cost by output. Average variable cost is independent of the level of fixed cost. Short-run average cost is found by dividing total cost by output. It is also the sum of average fixed cost and average variable cost. Short-run average cost first declines with increases in output because of the large decrease in one of the components of the sum, average fixed cost. But eventually increasing average variable cost predominates, and short-run average cost rises with output beyond some point.

The average cost curves and short-run marginal cost curves are plotted in Figure 10.9. Because they refer to changes in output, the marginal cost figures are plotted at the midpoints of the ranges of the changes in output. For example, as output increases from 5 to 6, total cost increases by $66. And this figure is plotted at the midpoint between outputs 5 and 6.6 Note that the short-run marginal cost curve intersects both the AVC and SAC curves at their minimum points. As the table and figure show short-run marginal cost rises at least beyond some level of output. As with other characteristics of cost curves, this characteristic is a property of the underlying production function. In this case the property is the law of diminish¬ ing marginal productivity. This law has as a corrolary, rising marginal cost. This can be seen algebraically as follows. Marginal cost is defined as: AfCEE*£

AY

If labor is the variable factor, we have

AL

When there is only one variable input, the change in total cost is the change in expenditure on the variable input, AC = PL ■ AL

Substituting this in the definition of marginal cost gives

The first derivative of the cost function can be used to calculate the marginal costs at each output example, dC/dX = MC = 30 - 10Y + 3Y2. For X = 5, marginal cost = 55.

For

263

The Analysis of Cost

MC

The marginal product of the variable input and marginal cost are inversely related. If the marginal product is decreasing, the marginal cost must be increasing. This relationship can also be derived although less directly by using the total product curve for a variable input that was first introduced in Chapter 3. The upper right-hand quadrant of Figure 10.10 shows the total product curve for labor as a variable input. This curve shows first increasing and then decreasing marginal productivity for labor. Suppose the input of labor is Lx. Following the dashed lines up and counterclockwise

Output per period X

Total expenditure, dollars Figure 10.10

The Total Product and Total Variable Cost Curves.

264

The Competitive Market System

gives the total output Xx that is associated with Lx. Following the dashed lines down and clockwise through the lower right and lower left quadrants gives the total expendi¬ ture on labor and therefore the total variable cost. When total cost and output are related in the upper left-hand quadrant, this yields one point on the total variable cost curve. Repeating the procedure for other levels of labor input such as L2 will trace out other points on the total variable cost curve. Once the total variable cost curve has been traced out, standard procedures can be used to determine the short-run marginal and average variable cost curves. The total variable cost increases at low levels of output but at a decreasing rate. It is concave toward the axis that represents output. This reflects the range of increasing marginal productivity along the total product curve. But as diminishing marginal productivity sets in, the total variable cost curve rises at an increasing rate. It is concave upward. And diminishing marginal productivity has its counterpart in increasing shortrun marginal cost. In Chapter 3 it was shown that an increase in the level of the fixed factor results in an upward shift in the total product curve at every point except the origin. Thus at every point the slope of the new total product curve is greater than that of the old total product curve and the marginal product of labor is greater. From both the preceding algebraic analysis and this graphical model, it should be clear that the short-run marginal cost curve will shift down to the right. With an increase in the fixed factor average variable cost will also shift down. But the shift in the short-run average cost is more complex because one component of this curve is average fixed costs, which will have risen with the increase in the fixed factor.

The Short-Run and Long-Run Cost Curves Together It was shown earlier that the short-run and long-run total cost curves are related in a certain way. Specifically, the short-run total cost curve must lie above the long-run total cost curve at every output except the one where the short- and long-run curves are tangent. It follows that the short- and long-run marginal and average cost curves will also bear a necessary relationship with each other. This is brought out in Figure 10.11. The upper part of the figure shows the long-run total cost curve and one s ort-run total cost curve for a given level of capital. The lower part of the figure shows the long- and short-run average and marginal cost curves that were derived in the manner discussed earlier. features elatl°nShlPS betWeCn the long" and short-run cost curves have the following

' Tuhe slope of a line from the origin to point A gives both the long- and the short-run average cost at output level X, Thus the long- and short-run average cost curves must coincide at this output level. Short-run average cost must be above long-run average cost, since at every other output level the short-run total cost exceeds the long-run total cost. Thus the s ort-run average cost curve must be tangent to the long-run average cost curve at output a , and must he above it at all other output levels.

265

The Analysis of Cost

X per period (b) Figure 10.11

The Long-Run and Short-Run Cost Curves Together.

3. Since the long- and short-run total cost curves are tangent at point A, they have the same slope. This means that the long- and short-run marginal costs are the same at output Xx. 4. The short-run total cost curve lies above the long-run total cost curve to the left

of point A; but the distance between them decreases as output approaches Xx. This means that the short-run total cost curve is less deeply sloped. Thus to the left of output Xu short-run marginal cost is less than long-run marginal cost. But to the right of output Xu the short-run total cost curve is more steeply sloped than the long-run total cost curve. Short-run marginal costs are greater than long-run marginal costs. Thus the two marginal cost curves intersect at output Xu as shown in Figure 10.11.

266

The Competitive Market System

There is an economic reason for this relationship between short- and long-run marginal cost. Recall that at output X{ the conditions for the cost-minimizing input combination are satisfied in both the short and long run. But at all other outputs, the short-run input combination violates these conditions because of the inability to adjust the level of the fixed factor. Starting at an output level below Xx in the short run, an increase in output involves a move toward the optimal input combination. Thus the increase in cost associated with that move would be less than would be the case if the starting point had been a cost-minimizing point on the expansion path as in the case of the long run. Expansion of output beyond Xx in the long run involves movement along the expan¬ sion path from one cost-minimizing input combination to another. But in the short run the expansion of output can be realized only by increasing the variable factor input and moving farther away from the expansion path or locus of cost-minimizing input combi¬ nations. Thus in the short run costs must increase more rapidly than would be the case if long-run expansion were permitted. This is why the short-run marginal cost curve lies above the long-run marginal cost curve to the right of output Xx. Changes in the fixed factor lead to shifts in the short-run cost curves. There is a whole family of possible short-run cost curves, each associated with a different level of the fixed factor. The long-run average cost curve can be viewed as an envelope of the family of potential short-run average cost curves. This is shown in Figure 10.12. For each of the SAC curves, there is a SMC curve that intersects the LMC curve at the output associated with the tangency between the SAC and LAC curves. Each SMC curve must also intersect its STC curve at the latter’s minimum point. This is also shown in Figure 10.12. Cost, dollars

Figure 10.12

Curves.

The Long-Run Average Cost Curve as an Envelope of Short-Run Average Cost

267

The Analysis of Cost

The Cost Function and Shifting the Cost Curves At the beginning of this section it was stated that the cost of production is a function ot the level of output as determined by the production function and of the prices of capital and labor. The two-dimensional cost curves relate cost to output, holding factor prices constant. In the long-run cost function all factor inputs can vary in determining the output level. But in the short run one of the factors is held fixed. This leads to the following algebraic statement of the cost curves: CLr = C[X(K, L), P*K, P*]

and CSR = C[X(K*, L),

/>*,

P*]

where the asterisks indicate that variables are held constant as the cost curves are drawn. A change in any of the variables with asterisks will lead to a shift of one or more of the cost curves derived in this section. Consider first the long-run cost function. Increases in the prices of either capital or labor increase the cost of purchasing a given bundle of inputs. Thus the cost of any level of output is increased. Long-run cost curves shift up. Conversely, any decrease in a factor price causes long-run cost curves to shift down. Because in the short run the input of labor is variable while the input of capital is not, changes in the prices of labor and capital have different impacts on the short-run cost curves. A change in the price of labor affects total variable cost, and therefore average variable cost and short-run marginal cost. Short-run average cost is affected because one of its components is the average variable cost. An increase in the price of labor shifts these curves up, whereas a decrease in the labor price has the opposite effect. But a change in the price of labor has no effect on fixed cost. Because capital is the fixed factor, a change in its price changes fixed cost, average fixed cost, and short-run average cost. But because capital is not a variable input in the short run, average variable cost and marginal cost are unaffected by changes in the price of capital. A technological improvement reduces the quantities of inputs that are necessary to produce a given output. As a consequence, cost curves shift down. Because it may take time for information about an innovation to spread to all firms and for firms to adopt the new technologies, the downward shift of the long-run cost curves will not be instantaneous in practice. But our concept of the long-run cost function abstracts from time in this sense. It reflects the complete dissemination of information and adoption of new ideas. Short-run cost curves may also be shifted down by technological improvements. But if the adoption of the new technology requires the replacement of existing capital machines, then the innovation can have no effect on the firm’s costs in the short run. The new short-run cost curves reflect the short-run opportunities of a firm that has full information about its new technological options.

268

The Competitive Market System

MEASURING COST FUNCTIONS AND RETURNS TO SCALE In the preceding section long-run average cost curves were drawn to show first increas¬ ing and then decreasing returns to scale. In other words, these curves were U shaped. In this section we first discuss why the shape of the LAC curve is important. Then we examine some a priori reasons for believing that these cost curves are U shaped. Finally, we consider the mixed and inconclusive evidence from empirical research into the shape of LAC curves. The shape of the long-run average cost curve is a major determinant of the optimum size of the firm and the number of firms in an industry. If firms’ LAC curves are downward sloping throughout, there is no limit on the profitable expansion of the firm, other than that provided by the market demand curve. By expanding output, a firm can reduce average costs and lower price to expand its share of the market at the expense of its rivals. There is a tendency in this case toward monopoly or at least a very few large firms in coexistence. If the LAC curve has a minimum point, the output at which average cost is at a minimum represents the optimum size of the firm. If a firm is a monopoly in a market and this monopoly is protected by barriers to entry, the firm may find it profitable to produce at output levels beyond this optimum size. But if other firms can enter, the forces of competition will push this firm back toward (and perhaps to the left of) the point of minimum unit or average cost. (This conclusion will be established rigorously in Chapters 11 and 16.) If the optimum size of the firm is small relative to the market as a whole, a large number of firms can coexist in that market. This means a competitive market structure is viable. Thus whether the LAC curve has a minimum rather than being continuously downward sloping and at what output this minimum occurs are important in determining the market structure of an industry. There are several reasons for believing that the firm will experience increasing returns to scale at least at low levels of output. One such reason was first described by Adam Smith. It is the increasing opportunities for the specialization of tasks and the division of labor leading to greater labor productivity and lower unit cost. This is not just a matter of workers gaining proficiency by repeating simple tasks. Division and special¬ ization of labor make for more effective utilization of tools and capital as well. For example, suppose that at one level of output one worker divides her time between two tasks, using different machines for each task. This leaves each machine idle for half the time. If the output level were doubled and a second worker hired, then both machines could be utilized full time, and cost would have less than doubled. A second factor leading to economies of scale is the need in complex production processes to mesh properly machines and processes of different scales. Suppose that production requires both the molding and finishing of components. Suppose further that the molding machine has a capacity of 50 units per day and the finishing machine has a capacity of 75 units per day. Then to make optimum use of both machines, output must be 150 per day by utilizing three molding and two finishing machines. Average cost will be higher at smaller outputs because of the less than optimum utilization of one or both machines.

269

The Analysis of Cost

mally, where production involves the processing or transformation of materials, economies of scale, at least up to a point, may be a characteristic of the underlying technology. For example, the thermal efficiency with which fuel is converted to electric¬ ity can be increased, up to a point, by using more sophisticated boilers and heat exchangers. But these more sophisticated devices are larger and require a higher level ot output for efficient operation. Thus thermal efficiency can be increased and unit costs decreased, up to a point, by building bigger plants with larger capacities and output levels. ^ These arguments for increasing returns to scale at least over some range of output apply to plants as integrated production units under one roof. These arguments do not necessarily mean that there is no limit to increasing returns to scale at the plant level. In tact, in many cases, there may be clear limits to plant size imposed by the underlying technology and the ability of materials to withstand extremes in stress, temperature and so on. But our concern is with economies of scale to the firm. Suppose a firm has reached the limits of increasing returns to scale at the plant level. What is to stop it from further expansion by reproducing optimum size plants? If this were possible, the LAC curve for the firm would be downward sloping at low levels of output until increasing returns to scale at the plant level were exhausted. Then the LAC curve would become horizontal, representing the addition of optimum scale plants (see Figure 10.13). Does the LAC curve continue as a horizontal line without limit as shown by the solid line in Figure 10.13? Or does it eventually curve up, reflecting some limit to the size of the firm? The major limit to the size of the firm is probably the difficulty in coordination and management in large organizations. As the scale of the firm increases, the distance between the top level decision makers and the operating personnel will also increase. It becomes more difficult for top management to obtain information on what is happen¬ ing on the factory floor. It is also more difficult to communicate orders and instructions to production workers and to see that they are carried out effectively. There is also an increasing divergence of interests between top management (which presumably represents the interest of the owners and is motivated by profit maximiza-

Figure 10.13

Two Possible Shapes for the Long-Run Average Cost Curve.

270

The Competitive Market System

tion) and production workers who may want job security and opportunities for ad¬ vancement but who also want reasonable working conditions, coffee breaks, and so on. The larger the organization is, the more difficult it is for the entrepreneur or top management to assure that all actions taken by all members of the organization are fully consistent with cost minimization and profit maximization. Top management must rely on middle management and supervisors and foremen to monitor the activities of production workers. But these intermediaries are also likely to have motivations other than profit maximization. The more of these intermediaries there are, the more discrep¬ ancies there will be between the objectives of top management and the actions of the workers. And thus the higher unit production costs will be. The shape of the LAC curve and the optimum size of the firm are determined by the relative strengths of the division of labor, specialization, and technological factors that lead to increasing returns to scale versus the costs of control and management that lead to decreasing returns to scale. At what level of output (if any) do the latter forces outweigh the former? This is an empirical question and the answer is likely to vary according to the industry. What evidence can we bring to bear from econometric research? We have already cited in Chapter 9 some evidence on the nature of returns to scale from efforts to estimate Cobb-Douglas production functions for firms in several U.S. industries. Five of 18 industries showed mildly increasing returns to scale according to this study. However, these results are not particularly helpful concerning the ques¬ tion at hand; that is, does the LAC curve eventually turn up. This is because the assumed form of the production function used in that study allowed for only three possible shapes for the LAC curve: downward sloping throughout (b + c > 1), horizontal (b + c = 1), or upward sloping throughout (b + c < 1). It could not detect from the data a production function that generates a U-shaped LAC curve or one that eventually turns up at high outputs. Figure 10.14 shows the data points for an LAC curve that eventually turns up and shows the artificial LAC curve that would be Cost, dollars

LAC

O Figure 10.14 Cost Curve.

Output per period Observed Costs at Different Outputs and a Statistically Fitted Long-Run Average

271

The Analysis of Cost

perceived when a Cobb-Douglas function is fitted to these data by statistical tech¬ niques. What is required to settle this question is estimates of cost functions that are based on observations of costs, output levels, and other influences on cost for various firms in industry. The typical approach is to gather information on costs and output and other variables from a cross section of firms in an industry. There are several difficulties encountered m this type of empirical approach. The first is that the available cost data come primarily from accountants, and for reasons mentioned in the first section of this chapter, accounting costs may not accurately reflect economic costs. Implicit costs must be estimated and added to the accountant’s records of explicit costs. Second, when estimating the relationship between cost and output, one must control for the influence of other variables such as factor prices that may affect costs. For example, if labor prices are different in different parts of the country, then firms located in different labor markets will not be on the same cost curve. Finally, observed cost data may not always reflect the long-run equilibria of firms. Short-run cost data from firms that have not yet made the appropriate long-run adjustments of their scale of plant will give an overestimate of long-run costs. A number of researchers have attempted to estimate cost functions for different industries, considering the problems mentioned here. A. A. Walters carefully reviewed a number of these studies and concluded that increasing returns in the relevant range of output were clearly demonstrated only in the case of public utilities such as electric¬ ity. In other cases the difficulties in obtaining soundly based and accurate estimates of LAC curves prevented reaching any strong conclusions. One could not confidently assert that LAC curves were typically U shaped. Walters concluded that, “at least there is no large body of data which would convincingly contradict the hypothesis of a U shaped long-run [average] cost curve and the fruitful results which depend upon it.”7

APPLICATIONS Estimating Marginal Cost Most applications of the theory of cost make use of the concept of marginal or incre¬ mental cost. Sometimes casual students may be led into error by basing their analyses on average cost rather than on marginal cost. Average cost figures are relatively easy to compute, but they may be misleading. Marginal cost may be substantially greater than average cost. However, estimating marginal cost requires more detailed knowl¬ edge of the production process. Consider the following example.

Gasohol. Assume that gasoline made from imported crude oil costs $1.20 per gallon and that this is a valid measure of its marginal cost. Also, assume that because of

7A. A. Walters, Production and Cost Functions: An Econometric Survey, 1963, 31(1-2), 52.

Econometrica,

January-April

272

The Competitive Market System

government regulations that hold down the price of domestic crude oil, the marginal cost of a gallon of gasoline made from domestic crude oil is $1.00. Because of price controls, domestic gasoline is in limited supply. Now suppose that it is possible to use grain to make an alcohol fuel that is a perfect replacement for gasoline on a gallon for gallon basis. Suppose that growing the grain, harvesting and transporting it, and processing it into alcohol uses two gallons of domestically produced gasoline while producing three gallons of alcohol. Finally, suppose that the total cost of the alcohol, including the cost of fuel consumed in its production, is $3.30. Is it economical to produce the alcohol fuel? It might appear to be so, because its cost is $1.10 per gallon while gasoline from imported crude oil costs $1.20 per gallon. But this is misleading. The computed cost of the alcohol ($1.10) is an average cost. If the alcohol were not produced, two gallons of domestic fuel in the form of gasoline would be available at a total cost of $2.00. If the alcohol is produced, three gallons of domestic fuel in the form of alcohol are available for a total cost of $3.30. The marginal cost of the third gallon is $1.30, more than the cost of imported fuel. Making a policy decision on the basis of average cost rather than on marginal cost could be quite costly.8

The Marginal Cost of Water. Public utility commissions responsible for setting the prices charged by electric and water utilities, phone companies, and so forth have become increasingly concerned that the prices reflect the marginal cost of supplying the good or service to the customer.9 Some regulatory agencies have required that firms under their jurisdiction submit data on their marginal cost curves whenever they apply to the agency for an increase in rates or prices. Suppose a utility is considering an expansion of its annual production by 10 percent. The marginal cost of this addition to output consists of the marginal capital cost to build the new plant and the marginal operating cost—both expressed in dollars per unit of output. The cost of constructing and equipping the necessary addition to productive capacity can be estimated by engineers. This capital cost is incurred at the beginning of the plant’s useful life. Using an appropriate formula, one can convert this capital cost (amortized) to an annual equivalent cost spread over the lifetime of the plant.10 The annual equivalent cost of the added capacity is divided by the annual additional output to obtain the marginal capital cost per unit of additional output. The marginal operat¬ ing cost per unit is added to this to obtain the marginal cost of additional output, which is a measure of long-run marginal cost. This represents what society must give up in order to obtain the additional output. If a study of demand shows that individuals are willing to pay a price that is equal to this marginal cost for the additional output, the expansion is justified on economic grounds. The only way to be sure, however, that individuals are actually willing to pay that much is to charge a price that is equal to long-run marginal cost.

sIt should be noted that these figures are hypothetical and may not reflect the true economics of gasohol. However, this approach to determining the true marginal cost of increments to domestic fuel supply is valid. ’The theoretical basis for a “marginal cost pricing rule” will be developed in Chapters 11 and 17. l0See Chapter 13.

273

The Analysis of Cost

In some situations the relevant question is whether to build a new facility this year or to defer construction for one year. Of course, if the project is postponed, the same question should be asked a year from now. There is a savings if costs can be postponed by putting the resources required for construction to some other beneficial use in the meantime. The marginal cost of constructing the plant now is the foregone savings due to deferring construction for one year.11 Estimating this cost was the problem faced by the Spring Valley Water Company of New York when it was ordered by the New York Public Service Commission to study its long-run marginal cost of output.12 The company was considering initiating a construc¬ tion program at the beginning of 1980 that would increase its capacity to deliver water to homes by about 29 million cubic feet per year (ft3/yr). It was believed that this increase in capacity was needed to meet the needs of an expanding population. The company found that by postponing construction for one year it would reduce the present value of construction costs by about $1.5 million. Stated differently, starting the project in 1980 rather than waiting one year would add $1.5 million to the present value of costs. Di¬ viding the increase in cost by the increase in capacity gives the marginal capital cost per unit of capacity, of about $51.75 per 1000 ft3. Adding operating costs, the marginal cost of meeting 1980’s additional demand rather than waiting for one year was $53.75 per 1000 ft3. Water at that time was being sold for $20 per 1000 ft3. It was estimated that if consumers were charged a price equal to the long-run marginal cost of the additional water ($53.75), the quantity demanded would actually fall by 250 million ft3/yr. rather than rise by 29 million ft3/yr. In other words, consumers would not be willing to pay a price equal to the long-run marginal cost of expanding the output of water in 1980. The correct policy from an economic point of view would be to raise the price of water sufficiently to keep the quantity demanded within the capacity of the system to supply water. As long as the price is below the long-run marginal cost of expansion, expansion should be postponed. The new facilities should be built only when the price of water and therefore consumers marginal willingness to pay for water exceed the marginal cost of additional water.

Marginal Cost and Cost Minimization There are many instances in both private decision-making and public policy in which a given objective can be achieved by undertaking some combination of activities. For example, an electric utility company could meet a given electric energy production target with various combinations of nuclear, oil, coal, and hydropower generation. Or a government official might be faced with deciding on a set of regulations for different industries aimed at reducing deaths due to occupational accidents. Presumably decision makers in these situations would wish to choose that mix of energy sources or safety regulations that minimized the total cost of achieving any given target, other things

In technical terms, the cost is the increase in the discounted present value of the stream of construction costs (see Chapter 13). 12The analysis of marginal cost is described in Steve H. Hanke, On the Marginal Cost of Water Supply, Water /Engineering and Management, February 1981, 60-68.

274

The Competitive Market System

equal. Minimizing the costs of attaining the target requires attention to the marginal costs of the alternative means of attaining it. Principle: Whenever two or more activities contribute to the production of a good or achievement of an objective, and more of the good or objective is sought, additional units of the good should be obtained from the activity with the lowest marginal cost. The total cost of supplying the good cannot be at a minimum unless the marginal costs of each of the activities are equal to each other. Cost minimization requires equalizing

marginal costs across all activities. Suppose that the manager of a firm has two plants, A and B, each with different marginal cost curves as shown in Figure 10.15. Suppose also that he has established a target level of total output of the firm at X = 50. The firm manager’s task is to allocate the total output targets between the two firms so as to minimize the total cost of producing 50 units of X. Assume the manager uses a simple rule of thumb and requires each plant to produce 25 units. This cannot be cost minimizing because it is possible to reallocate production from one plant to the other in order to reduce total cost. At the initial allocation, plant B's marginal cost is $10 while plant T’s marginal cost is $16. Thus if production were reduced by 1 unit at plant A while plant B production was increased by 1 unit, total output would be unchanged but total cost would be reduced by $6 (the difference between the marginal costs at the two plants). Because after this reallocation of 1 unit from plant A to plant B the marginal costs are still different, further reallocation should take place until the marginal costs are brought into equality. Only then will the total cost of production be minimized. Their marginal costs are equal when plant A is producing 20 units and plant B is producing 30 units. When output is reduced to 20 units at plant A, total cost is reduced by the area under MCA between 25 and 20. When output is increased at plant B, total cost is increased by the area under MC B between 25 and 30. The net change in total

Plant A

Figure 10.15

The Multiplant Firm and Cost Minimization.

Kant B

275

The Analysis of Cost

cost is the difference between these two areas. The net reduction in total cost is equal to the two shaded areas in the figure. The principle of cost minimization is important, but it is often overlooked or ignored in the realm of public policy. As a result, the attainment of certain public policy goals is excessively costly and scarce resources are wasted. This is a particularly serious problem in the control of environmental pollution. In the 1960s a massive effort was undertaken to reduce polluting discharges into the lower Delaware River between Pennsylvania and New Jersey. The program was imple¬ mented by imposing strict limits on the pollution discharges of each of the factories and domestic sewage outlets along the river. Each outlet was required to cut back its pollution by the same percentage. It was estimated that the total cost of achieving the pollution control target by this uniform treatment approach would be $20 million per year in 1963 dollars. It was known that there were substantial differences in the marginal cost curves for pollution control at each of the outlets. If an effort had been made to adjust pollution control targets for each outlet so as to equalize their marginal cost of treatment while still attaining the desired overall reduction in discharges total pollution control, costs might have been reduced to as little as $7.0 million per year. Pollution control costs in this one river basin were higher than necessary by a factor of almost three.13 More recently, federal policy toward water pollution control has been based on establishing limits on the pollution discharge from each industrial activity or process. These limits are uniform for all similar activities across the nation. In a major industrial facility such as an integrated steel mill there may be several activities, each subject to a different control requirement. Many of these activities discharge the same substances. Yet the marginal costs of controlling these substances up to the established limits are often quite different from one activity to another.14 As a result, the total costs of controlling the aggregate discharge from the plant are often much higher than neces¬ sary. When marginal costs of treatment are different, plant managers could reduce their total pollution control costs without any increase in total discharges by reducing treatment levels where marginal costs are high and compensating by increasing control levels on discharges with low marginal treatment costs. From an economic perspective it would be desirable to alter the water pollution control laws so that cost-minimizing adjustments of control requirements would be permitted.

SUMMARY The cost of producing a good is what must be given up in the form of other goods and services, that is, the opportunities foregone. In a market economy, if all inputs to

"Allen V. Kneese and Blair Bower, Managing Water Quality: Economics, Technology, and Institutions, Baltimore: Johns Hopkins University Press, 1968. 14See Robert C. Greene, Water Pollution Controls for the Iron and Steel Industry, in James C. Miller, III, and Bruce Yandle, eds., Benefit Cost Analyses of Social Regulations, Washington, D.C.: American Enterprise Institute for Public Policy Research, 1979.

276

The Competitive Market System

production are purchased in competitive markets, opportunity cost can be measured in monetary terms by the total money value of factor inputs used. Costs to the firm include both explicit costs;—payments to others for the use of factor inputs owned by them—and implicit costs—the market value of inputs owned by the firm itself. Economic profit is the difference between total revenue and the sum of implicit and explicit costs. If the firm uses inputs that are, in effect, not owned by anyone, the social cost of production may exceed the private cost of production. The difference is the external cost, that is, the opportunity cost of using the unowned resource. The cost function relates the cost of production to the level of output. It is derived from the underlying technology as represented by the production function. The cost curves of a firm are graphical representations of the cost function drawn for a given production function and set of factor prices. The firm’s long-run cost curves show how costs vary, with output moving along its expansion path, altering all inputs so as to minimize total cost for any output. Short-run cost shows how costs vary with output, holding one factor fixed. All short-run total and average cost curves lie above the long-run cost curves, except for a point of tangency at the output for which the quantity of the fixed factor is also the optimum quantity for cost minimization. The shape of the LAC curve has important implications for the size and number of firms in an industry and the variability of competitive market structures. Division of labor, specialization of function, and technological factors are expected to lead to increasing returns to scale of the plant, at least up to some level of output. But increasing problems with information flow, coordination, and control are expected to lead eventually to decreasing returns to scale at the firm level. The hypothesis that these factors result in a U-shaped LAC curve cannot be rejected on the basis of available empirical evidence. But the minimum point of the LAC curve may come at relatively large outputs in some industries. The concept of marginal cost is important in making a variety of resource allocation decisions. In estimating marginal cost, one must take care to identify properly the true change in output and the true incremental costs.

KEY CONCEPTS Explicit costs Implicit costs User cost External cost Economic profit

Private cost versus social cost Long- and short-run cost curves Marginal cost Average cost Cost minimization

QUESTIONS AND PROBLEMS For Basic Review 1. 2.

Define and explain the economic significance of each of the key concepts. Draw an isoquant map that portrays a production function with first increasing

277

The Analysis of Cost

returns to scale, and then decreasing returns to scale. Verify that at given factor prices this isoquant map generates a long-run total cost curve with the shape shown in Figure 10.4. 3. * Use the production diagram (isoquants) to derive the relationship between a short-run cost curve and the long-run total cost curve. 4. Prove or demonstrate that a. The MC curve cuts the AC curve at the minimum point of the AC curve. b. When the AC curve is rising, the MC curve lies above the AC curve. 5. * Prove that when the short-run average cost curve is tangent to the LAC curve LMC = SMC. 6. If the LAC curve is horizontal, what does the LMC curve look like? 7. * Explain what happens to each of the following curves when fixed cost increases: average fixed cost; short-run total cost; total variable cost; short-run marginal cost; average variable cost; short-run average cost. 8. 9.

Explain the relationship between the marginal productivity of the variable factor and the short-run marginal cost curve. Discuss the factors affecting the shape of the LAC curve. What is the significance of the shape of the LAC curve for the analysis of a modern market economy?

PROBLEMS !•* a* Suppose you buy a new car for $8000. You anticipate that at the end of one year you will be able to sell the car for $5000. You insure the car against theft and collision for an annual premium of $500. In order to pay for the car you take the money from a one-year certificate of deposit with a 12 percent annual interest rate. What is the user cost of owning the car for one year? b. Suppose you anticipate driving the car 15,000 miles during the year. Gasoline, oil, repairs, and so on cost 20 cents per mile. Calculate the following: Total annual cost of owning and operating the car; Average cost per mile; Average variable cost per mile; Marginal cost per mile. 2* Based on the information contained in Figure 10.16, answer the following questions: a. At what output will long-run average cost equal the short-run average cost when K is fixed at 100 units? b. The price of labor is $1. The price of capital is $2. With K fixed at 100 units, what is the short-run average cost of production at X = 100, X = 150, X = 200, X = 250? c. What is the long-run average cost of production at X = 100, X = 200, X = 300?

278

The Competitive Market System

Figure 10.16

Production Data for Deriving Cost Curves for Problem 2.

d. At the least cost position for producing 100 units of X, what are the inputs of K and L? What is the capital to labor ratio? What is the MRTS? e. What will happen to SAC, LAC, and their tangency (i.e., at what cost and output levels) if the price of capital is increased? 3. Prove the statements made in the third and fourth sentences of footnote 4.

FOR DISCUSSION 1. What do you think the short-run cost curve for a college looks like? What are the economics of expanding the student body at your college? What about the long-run cost curve? 2. * An effluent charge is a charge leveled by the government for each unit of pollution dumped by a firm, for example, $10 per ton. How would an effluent charge affect producer’s cost curves? 3. You are a production manager with several plants. What rule would you follow to assign output quotas to the several plants?

279

The Analysis of Cost

SUPPLEMENTARY READINGS Ferguson, Charles E. The Neoclassical Theory of Production and Distribution, Cam¬ bridge: Cambridge University Press, 1969, Chapter 7. Gold, Bela. Changing Perspectives on Size, Scale, and Returns: An Interpretive Survey.

Journal of Economic Literature, March 1981, 19(1), 5-33. Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach (3rd ed.). New York: McGraw-Hill, 1980, Chapters 4-5. Samuelson, Paul A. The Foundations of Economic Analysis. Cambridge, Mass.: Har¬ vard University Press, 1947, Chapter 4. Stigler, George J. The Theory of Price (3rd ed.). New York: Macmillan, 1966, Chapters 6-9. Turvey, Ralph. Marginal Cost. Economic Journal, June 1969, 79(314), 282-299. Walter, A. A. Production and Cost Functions: An Econometric Survey. Econometrica, January-April 1963, 31(1-2), 1-66, especially Section 7.

MATHEMATICAL APPENDIX TO CHAPTER 10 The Relationship Between Average and Marginal Cost In the text it was stated that whenever marginal cost is greater than average cost, average cost is increasing. This principle can be proved for any form of cost function by the calculus. Let total cost, C, be an increasing function of X: C = f{X),

f (X) > 0

Average cost and marginal cost are: AC = f(X)/X MC = f (X) The slope of the average cost curve is dAC dX

= df(X)/X

_ X ■ f (.X) - f(X)

dX

X2

For the average cost curve to be upward sloping, the numerator of this expression must be positive, or X'f'(X) > f(X) f'(X) >

f(X) X

The left-hand side of the last expression is marginal cost and the right-hand side is average cost. Upward-sloping average cost requires that marginal cost be greater than average cost. Can you show that when MC is less than AC, AC must be decreasing?

CHAPTER 11 Price and Output in Competitive Markets

INTRODUCTION

analysis of price and output in competitive markets has two objectives: to explain and predict the outcomes of competitive market processes and to evaluate these out¬ comes in accordance with the criterion of economic efficiency. The primary objective of positive analysis is to be able to make comparative static predictions about the direction of change in price and quantity when the exogenous variables in the model change. The usefulness of the competitive market model is not limited to purely competitive market structures. The model also provides a starting point for the analysis of other market structures. In this chapter we will learn how the forces of profit and loss and the entry and exit of firms in response to price and profit signals shape the patterns of resource allocation in the economy. These forces operate to varying degrees in other market structures. Therefore it is not entirely accurate to say that because no industry is perfectly competitive the study of competitive markets is irrelevant. First, some industries do come reasonably close to approximating the competitive market model. Second, the forces and mechanisms that operate in competitive market structures are also prevalent although to a lesser degree in less competitive market structures. Our normative analysis of competitive markets provides a yardstick by which the outcomes of real-world market processes can be evaluated. In this chapter we will show that if the market for a good is perfectly competitive, the value of that good to consumers at the margin is just equal to the marginal opportunity cost of the good. If the marginal values of all goods are equal to their marginal costs, it is not possible to increase the aggregate value to consumers of the output of the economy by any change in the output of any good. This analysis represents a major step toward the principal normative conclusion of microeconomics, namely, if all markets are perfectly competi280

281

Price and Output in Competitive Markets

tive, the allocation of resources is Pareto optimal. This latter conclusion will be estab¬ lished in Chapter 17. The positive analysis of competitive markets proceeds in two stages. In the first stage we develop the theory of the single firm that operates in a competitive market. We analyze how the firm s output decisions are affected by changes in product price, factor prices, and so on. The product price is taken to be an exogenous variable. In the second stage we analyze the industry as an aggregate of individual firms. Here we show how the decisions made by them when taken together can influence the price of the product in the competitive market. Price is an endogenous variable that is determined as part of the market process. For a market to be perfectly competitive it must satisfy four conditions: 1. All buyers and sellers are price takers. They take the market price as given. Their actions must have no effect on market price, or at least they must believe that that is the case. As a practical matter this requires that there be many buyers and many sellers, each of whom is so small that his actions have an imperceptible effect on market price. 2. The product must be homogeneous, that is, there must be nothing that distinguishes the product of one seller from that of another. As a result, buyers are indifferent among alternative sellers of the product. 3. There must be perfect mobility of resources into and out of this industry. If firms wish to expand or contract their level of output, they must be able to hire additional labor (but not necessarily at an unchanged wage) or be free to release labor to seek employment elsewhere. Firms must be able to alter their purchases of material inputs and capital services. And most important, firms must be free in the long run to exit the industry if profits are negative, and new firms must be free to enter the industry if they see an opportunity to earn economic profits. This means there must be no barriers to entry such as patents or requirements for licenses and no restrictions on exit such as government-mandated requirements to provide service in the public interest.

4. All participants in the market must have perfect knowledge of all relevant economic variables. All buyers must know the prices charged by all sellers. Thus no buyer would make a purchase at a higher price if a lower price were available. Perfect knowledge of prices on the part of buyers forces a single price for the product at any point in time. For similar reasons producers must have perfect knowledge of factor prices. Also, producers must have perfect knowledge of the available technology. This means that they all face the same production function and have the same cost curves.

THE THEORY OF THE FIRM Profit Maximization Consider one firm of many producing X in a competitive industry. Assume that the firm strives to maximize profit and has perfect knowledge of market conditions and its

282

The Competitive Market System

production technology. Because this is a competitive industry, the firm takes product and factor prices as given. Prices are exogenous variables in this model of the single firm.

.

The economic profit, ^r, of the firm is given by 7t

= total revenue — total cost = PX

X - C [X(L, K), PL, PK]

where cost includes implicit as well as explicit costs. The only variables under the firm’s control are output and the inputs of labor and capital. Because we have already analyzed the problem of choosing optimum input combinations, we can focus here on the choice of the optimum or profit-maximizing output on the assumption that the firm produces this output at the minimum possible cost. In the upper part of Figure 11.1, the line TRX shows how total revenue varies with

s

X per period Figure 11.1

Profit Maximization for the Competitive Firm.

283

Price and Output in Competitive Markets

output. The firm takes the price of X to be given or a constant. It is unaffected by changes in the firm s output. Therefore, TRX is a straight line with a slope equal to px. The line TCX shows how total cost varies with output. The vertical distance between the total revenue and total cost curves gives the profit at that level of output. At low levels of output, say, in the neighborhood of X*, total cost exceeds total revenue, indicating that the firm is earning negative profits, that is, incurring losses. At output A the vertical distance between total revenue and total cost is greatest, thus showing a maximum of profits. At this output the jdopes of the total revenue and total cost curves are equal. At outputs to the left of X, the slope of the total revenue curve exceeds that of the total cost curve, indicating that the two curves are growing farther apart and profits are increasing with increases in output. But beyond X, the total cost curve is more steeply sloped than the total revenue curve and is narrowing the gap between the two as output increases. Thus profits are becoming smaller at output levels beyond X. The condition that the slopes of the two curves be equal in order that profits be maximized can be restated in economic terms. The slope of the total revenue curve is marginal revenue, that is, the change in total revenue with a change in output. The slope of the total cost curve is marginal cost. Relationship: In order to maximize profits, the firm must produce at that output where marginal revenue equals marginal cost: MRX = MCX

Rearranging gives MRX - MCX = 0

The difference between the extra revenue and the extra cost associated with an increase in output is the marginal profit or marginal net return of X. Thus this condition is an application of the first rule of maximization that was presented in Chapter 2. As already stated since Px is a constant to the firm, the slope of the total revenue curve is also equal to Px. Each additional unit of output sold by the firm brings an addition to total revenue just equal to its price. Thus under perfect competition, price and marginal revenue are equal. Relationship: Under perfect competition a firm maximizes its profits by choosing an output where price equals marginal cost: Px = MCX

All this is also shown in the lower part of Figure 11.1. The horizontal line labeled Px = MR x is, in effect, the firm’s demand curve. It shows that the firm can sell any quantity that it wishes at the going price of Px and that each unit sold adds the same amount to total revenue. That profits are maximized at an output of X, where price or marginal revenue equals marginal cost can be verified by the following mental experiment. Suppose that starting

284

The Competitive Market System

at output X, output is increased by AX The increase in total revenue is the area under the marginal revenue curve or price times the increment to output. Total costs are increased by the area under the marginal cost curve between X and X + AX. Because this latter area exceeds the increase in total revenue, profits must have been reduced by an amount equal to the area of the three-sided figure labeled A. On the other hand, suppose output were decreased from X to X — AX. The reduction in total revenue would again be given by the area under the marginal revenue curve between those two output levels. Marginal costs are decreased by the area under the marginal cost curve between X and X — AX. Because the decrease in total revenue exceeds the decrease in total cost, profits must have been reduced. Because profits are reduced by moves in either direction away from X, this must represent the profitmaximizing output.1 This condition for profit maximization is an application of the first rule of optimiza¬ tion, which states that the optimum level of an activity—in this case the optimum level of output—-is found where the marginal net return from the activity is zero. The marginal net return of an extra unit of output is the additional profit it brings in, or the additional revenue minus the additional cost: MNRX = Px - MCX

Marginal net return is 0 when Px = MCX.

The Behavior of the Firm in the Short Run In the short run when a firm changes its output thej;hanges in its total cost are given by the shorfijun marginal cost curve. Thus the firm maximizes profits in the short run by choosing the output that equates its short-run marginal cost with the price of output. The long-run marginal cost has no influence over short-run decisions. In Figure 11.2, if the price of output is PXI, the firm maximizes profit in the short run by choosing output X!< At this output profits are greater than 0 since price is above short-run average cost. If price falls to PX2, the firm will reduce output to X2, even though this results in negative profits. This is because losses would be even greater at any other output. In the short run, if price falls below short-run average cost, the firm has no choice but to incur losses. Even if the firm were to shut down, that is, reduce output to 0, it would still incur the unavoidable fixed costs with no revenue to offset them. There is a price below which the firm would be better off reducing output to 0 rather than continuing to produce at a loss. This minimum price at which shutting down becomes the preferred alternative is known as the shutdown price. Relationship: The firm will shut down production if price falls below average variable cost.

'The conditions for profit maximization are derived more rigorously in the Mathematical Appendix to this chapter.

285

Price and Output in Competitive Markets

X per period Figure 11.2

The Firm’s Short-Run Supply Curve.

When price just equals average variable cost at PX3 in Figure 11.2, total revenue just equals total variable cost. There is no revenue left over to cover any portion of the fixed cost. Therefore the firm incurs a loss equal to fixed cost. If price falls below average variable cost, total revenue is less than total variable cost. Then the firm incurs a loss greater than fixed cost. The firm can reduce its loss by shutting down production and avoiding all variable costs.2 We have now shown what determines the quantity produced by a firm in the short run as product price changes.

Definition: The firm’s short-run supply curve shows the relationship between the price of output and the quantity produced. The short-run supply curve consists of that portion of the short-run marginal cost curve that lies above its intersection with average variable cost. It is the heavy portion of the SMCX curve of Figure 11.2.

:In algebraic terms: 7r = total revenue — total variable cost — total fixed cost

= Px ■ X - A VCX ■ X - TFCX

= (Px

— A VCX) ■ X - TFCX

!f Px = AVCx> the term in the parentheses is 0 and n = - TFC x < 0. If Px < A VC x, the term in parentheses is negative and further reduces profits. Thus 7r < — TFCx. But if Px > AVCX, the term in parentheses is greater than 0 and is an addition to profit, partly offsetting the negative contribution of fixed costs.

286

The Competitive Market System

The firm’s short-run supply curve is drawn holding several factors constant. Because it is derived from the firm’s cost curves, it must be drawn holding the prices of variable inputs and the technology constant. Because it is a short-run relationship, it is drawn holding the quantity of the fixed factor constant. If any of these variables change, the firm’s short-run cost curves and short-run supply curve will change. By this point the student should be able to predict the direction of the shift of the short-run supply curve for a given change in one of these variables. For example, what happens to the short-run supply curve if the price of labor increases?3

The Behavior of the Firm in the Long Run Given the ability in the long run to adjust the quantities of all factor inputs, the firm chooses its output so as to equate its long-run marginal cost with the given price of the product. Suppose the price is Pxl in Figure 11.3. The profit-maximizing output is X{. In this example price is above long-run average cost, so the firm is making profits. This would be an equilibrium position if product price remained unchanged. But now we must begin to look at the whole market, not just at this one firm. If this firm and others like it are making profits, it is an incentive for other entrepreneurs to organize firms and enter this industry. As new firms enter, the total quantity supplied to the market increases. This in turn means that price must fall in order to accommodate the increased quantity supplied. Falling price reduces the profits of existing firms as well as inducing them to cut back their output. This process continues until price is pushed down to

PX2 where each firm is earning zero profits. The reverse process is set in motion if price is below long-run average cost. Firms

UACX Dollars

Px 1 Px 2

°l

h

x[

X per period Figure 11.3

Profit Maximization in the Long Run.

JThe cost curves and short-run supply curve shift up and to the left.

287

Price and Output in Competitive Markets

are experiencing losses. Some firms leave the industry. The reduced supply causes an increase in price. This process continues until price has risen to become equal to long-run average cost. Taking account of the processes of market adjustment, the only sustainable long-run equilibrium position of the firm is at output X2 where price is equal to long-run marginal cost and long-run average cost. At this output long-run average cost is at a minimum. The forces of competition push firms to produce at their point of minimum average cost in the long run.

THE INDUSTRY There is an important difference between the models of the firm and of the industry. The firm takes product and factor prices as given; they are exogenous variables in the model of firm behavior. But both product and factor prices can be influenced by the behavior of firms in aggregate. Prices are endogenous variables in the industry model; that is, prices are determined within the model by the interactions of supply and demand. We consider these interactions first in the short run and then allow for the long-run adjustment of the industry.

The Short Run In the short run no firm can alter its scale of output. In addition, no new firms can enter and no existing firms can exit the industry. Although each firm is a price taker in factor markets, when all firms in the industry change their use of a factor together, they can have an effect on the factor price. If the supply curve of the factor is upward sloping, an increase in utilization of the factor results in an increase in the price of the factor. This in turn causes firms cost curves to shift up. This shift must be taken into account in deriving the industry supply curves in the short and long run.

Th© Industry Short-Run Supply Curv©. Assume that there are n identical firms in the industry, each with short-run supply curves as shown in Figure 11.4(a). If the price is Pxl, the typical firm’s output is xu and the industry output, which is the sum of the outputs of all firms, is n • x, — X2. Now assume that product price increases to PX2. Each firm responds by attempting to expand output along its SMCX curve to x2. If the supply curves of all variable inputs to this industry are horizontal or infinitely elastic, then the industry can expand its use of these inputs without affecting factor prices. The firms’ cost curves do not shift. And the industry output is n ■ x2 = X2. This is point

B in Figure 11.4(h). Assume, however, that the supply curve of the variable input to this industry is upward sloping. As firms collectively try to expand output to X2, the increase in the demand for the variable input forces up the price of that input to the industry. The result is an upward shift in the cost curves of all firms. The new marginal cost curve of the typical firm is SMCX. Given the product price of PX2, each firm produces x'2, and the industry supply is n ■ x2 = X'2. This is shown as point B' in Figure 11.4(h). Taking

288

The Competitive Market System

Firm

Industry

O) Figure 11.4

(b)

Deriving the Industry Short-Run Supply Curve.

account of the effect of increasing output on factor prices, the short-run supply curve of the industry is the line connecting points A and B'. It is more steeply sloped than the horizontal summation of the individual firms’ short-run marginal cost curves. The quantity supplied by the industry in the short run is a function of product price; but it also depends on the number of firms, their scale of output, and the supply functions of the variable inputs. Assuming labor to be the only variable input, in algebraic notation this is: = XSR [Px, Ls(Pl)*, Kf, n*] where Ls(Pl) is the supply function of labor, K, is the amount of capital used by the z'th firm (a measure of scale), and where the underlying technology that determines the shapes of the firms’ cost curves is subsumed in the functional XSR(-). The asterisks indicate those variables held constant when the short-run supply curve is drawn. A change in the supply function of labor or a change in the number of firms will result in a shift in the short-run supply curve of the industry.

The Elasticity of Supply; A Digression. The responsiveness of quantity supplied to changes in price can be expressed in elasticity terms as follows: pS

Ppy

_ AXS/XS —

-

APX/PX ^Xs Px A Px

Xs

289

Price and Output in Competitive Markets

where Xs is the quantity supplied. If the supply curve is horizontal, the elasticity of supply is infinite. A zero elasticity of supply means a vertical supply curve. The elasticity of supply can be estimated graphically as follows. Suppose we wish to know the elasticity of the supply curve SS' at point A in Figure 11.5. Draw a straight line tangent to 55" at point A. The elasticity of SS' is

which is less than 1. This is derived as follows: By definition cS ^Py

— ^s

Px

A?x

Xs

-

If AX, is the change in price, then BX, is the change in quantity. So we can write BX, tP~

*

AX, •

AX, BX,

-

OX,

OX,

In Figure 11.5 the elasticity of supply is less than 1. If the tangent line goes through the origin, the elasticity is equal to 1. Any straight-line supply curve going through the origin has an elasticity equal to 1. If point B is to the left of the origin, the elasticity is greater than 1.

Short-Run Equilibrium. Figure 11.6(b) shows the short-run supply curve of an industry and the industry demand curve. The equilibrium of this industry is at a price of Pxl and a quantity of X,. As Figure 11.6(a) shows, at this price each firm is producing x,. Because in the short run the quantity of capital cannot be altered and

Figure 11.5

Estimating the Elasticity of Supply.

290

The Competitive Market System

Firm

Figure 11.6

Industry

The Short-Run Equilibrium of a Competitive Industry.

firms can neither enter nor exit this industry, this is an equilibrium for the firm and the industry. But notice that because price is above short-run average cost, firms are earning economic profits. This is an inducement for new firms to enter this industry. Thus the situation cannot be a long-run equilibrium in the industry.

The Long Run In the long run the scale of the firm and the number of firms are both variables. The industry is in long-run equilibrium only when there is no tendency for price to change, no tendency for changes in the scale of firms, and no entry or exit of firms. For firms to have no reason to change their scale of plant, price must equal long-run marginal cost. For there to be no entry or exit, profits must be zero, which means price is equal to long-run average cost. Combining these two conditions shows that each firm must be producing at the optimum scale of firm where long-run average costs are at their minimum. In other words, Px - LMCX = LACX

The Long-Run Supply Curve. The long-run supply curve of the industry is the locus of equilibrium industry outputs under different conditions of demand for the product. This long-run supply curve can be upward sloping, horizontal, or downward sloping, depending on the supply conditions in the markets for factor inputs to this industry. Definition: An industry is called a constant cost industry if its long-run supply curve is horizontal or infinitely elastic.

291

Price and Output in Competitive Markets

Definition: An industry is called an increasing (decreasing) cost industry if its longrun supply curve is upward (downward) sloping. If factor supply curves are upward sloping, as the industry expands output in the long run, factor prices increase and output can be increased only at increasing cost. Thus the long-run supply curve of the industry slopes up. If the supply curves of all factor inputs to this industry are perfectly elastic, factor utilization can be increased without any increase in factor prices and the firms’ cost curves. The industry long-run supply curve is horizontal. The case of a decreasing cost industry with a downward-sloping long-run supply curve requires that one of the factor inputs be produced under condi¬ tions of increasing returns to scale. Thus if the industry requires more of this input, the firm or firms producing this input can expand, realizing increasing returns to scale, and offer the input at a lower price. We now consider each of these cases in more detail.

The Constant Cost Industry. Figure 11.7(h) shows the industry demand DXI and the short-run supply curve SSR]. The short-run equilibrium price is Pxx. Industry supply is A,. Figure 11.7(a) shows the SMCX, LACX, and LMCX curves for a typical firm. Since our attention is to be focused on the long-run adjustment of this industry and these firms, the firm’s cost curves are omitted from the figure. The firm is in long-run equilibrium since Pxl is equal to LMCX and profits are 0. Now assume a shift in the demand curve to DX2. What might have caused this shift? Household incomes could have increased or the prices of substitute or complimentary goods could have changed. In the short run, with the number of firms fixed, the industry can respond only by moving up along its short-run supply curve SSR1 to output X2. The short-run equilibrium price is PX2. At this price firms are realizing economic profits. Thus there is an incentive for new

Firm

0) Figure 11.7

Industry

(b)

The Long-Run Equilibrium of a Competitive Industry with Constant Cost.

292

The Competitive Market System

firms to enter. Recall that the short-run supply curve is drawn for a given number of firms. As each new firm enters, the industry short-run supply curve is shifted slightly out to the right. The additional output from the new firms causes a reduction in price. This process continues with the short-run supply curve shifting out to the right, industry output expanding, and market price falling until profits are eliminated. Because this is a constant cost industry, as new firms enter and industry output expands, there are no changes in factor prices. Thus the cost curves of firms do not change. Price must fall all the way back to Pxl before profits are eliminated. The new industry long-run equilibrium output is at X3. The line through the initial and new long-run equilibria is the long-run supply curve of the industry. It is is horizontal.

The Increasing Cost Industry. Figure 11.8 also shows an initial equilibrium of the industry and the firm at Pxl and Xu given the demand curve DX1. As before, when the demand curve shifts out to DX2, price rises to PX2 and the industry responds in the short run by expanding output to X2. Again, the increase in price leads to profits for existing firms and entry of new firms. The short-run supply curve shifts out and to the right. But because this is an increasing cost industry, the initial expansion of output and the entry of new firms put upward pressure on factor prices. Cost curves shift up. The expansion of output continues until the falling price just meets the rising long-run average cost curves of firms. When this occurs, profits have been eliminated, and there is no incentive for further entry. This represents a new long-run equilibrium. This occurs at a price of PX3 and an output of X} in Figure 11.8. The line connecting the initial and new long-run equilibria is the long-run supply curve. In this case it is upward sloping. Firm

Industry

293

Price and Output in Competitive Markets

In the case of a constant cost industry the only force eliminating profits and restoring equilibrium is the falling product price as output expands. In the increasing cost industry there are two forces that eliminate profits: falling product price and rising cost curves of firms. These two forces choke off the expansion of output more rapidly. A given increase in demand brings out a smaller increase in quantity supplied. Thus the long-run supply curve with increasing cost is less elastic.4

^

The Decreasing Cost Industry. In a decreasing cost industry, as output expands m response to an increase in demand, the price of some input falls. This results in a downward shift in the firm’s cost curves. Output must expand further to drive price down sufficiently to eliminate profits and restore long-run equilibrium to the industry.

The Long-Run Supply Function. The long-run supply curve is a two-dimensional representation of the long-run supply function in which all influences on the quantity supplied other than price are held constant. In algebraic notation the long-run supply function is given by XLR=

XLR [Px, Ls(Pl)*, Ks(Pk)*]

where the asterisks indicate that variables are held constant when the supply curve is drawn. Changes in factor prices that result from movement along factor supply curves do not shift the long-run supply function of the good. The direction of factor price changes (determined by the slope of the factor supply curves) determines the slope of the supply curve of the good. A shift in the supply function of either factor input would shift the long-run supply function of the good.

COMPETITION AND ECONOMIC EFFICIENCY In order to maximize profit, each firm in a competitive industry must choose its output so as to equate its marginal cost with the given market price. This means that the equality of price and marginal cost is a characteristic of all competitive equilibria. This is a desirable characteristic. In an economy in which all other industries are perfectly competitive the equality of price and marginal cost in the market for good X indicates

This discussion has been based on the assumption that when firms initially increase output in the short run, the increase in their cost is less than the increase in product price. It has been shown that this need not be the case, however. It is possible that as the existing firms expand their output in the short run, the increase in the price of the factor input could shift the LACx curve and other cost curves up more than the increase in product price. If this happens, firms experience losses. Some firms exit. But the remaining ones expand their output. Thus the adjustment process is somewhat different, but the result is the same. In the new long-run equilibrium, output is higher, and product price is higher. The long-run supply curve is upward sloping. The one difference is that the number of firms decreases. For a mathematical treatment of this possibility, see Joseph T. Hughes, The Comparative Statics of the Competitive, Increasing Cost Industry, American Economic Review, June 1980, 70(3), 518-521.

294

The Competitive Market System

that the output of X is at the correct level according to the criterion of economic efficiency. To see this, we need to consider what price and marginal cost are measuring in a market economy. If consumers are free to choose their optimum consumption bun¬ dles with given market prices, product price is a measure of the subjective value of the good to the individual at the margin. In other words, price measures the marginal willingness to pay for the good (see Chapter 7). If all markets are competitive, the marginal cost of the good in dollars is a measure of the value at the margin of other goods that must be given up in order to produce one more unit of this good, that is, its opportunity cost. Figure 11.9 shows the market demand curve for good X and a marginal cost curve that is an aggregate of the marginal costs of individual firms. The MC curve represents the marginal opportunity cost to the economy of increasing the output of X. Suppose that there is some constraint on expanding output so that output is limited to X, where price exceeds marginal cost. Any individual consuming X is willing to pay an amount equal to the vertical distance AE to obtain one more unit of X. This distance is his marginal willingness to pay for X(MWTPx). At this level of output the marginal cost of X is BE. This means that to produce one more unit of X, the production of some other goods(s) valued by consumers at BE must be foregone in order to free the resources for expanding X production. If this realloca¬ tion takes place, consumers collectively gain a unit of X valued at AE while losing goods valued at BE. The net gain is AB. As long as price and marginal willingness to pay are greater than marginal cost, further marginal reallocations of resources toward the production of X increase aggregate welfare. The net gain of increasing output from Xx to X2 is the triangular area ABC in Figure 11.9. Expanding output beyond X2 where MCX exceeds MWTPx means that other goods are being given up that are valued more highly than the marginal willingness

X per period Figure 11.9

Efficiency Requires Price Equal to Marginal Cost.

295

Price and Output in Competitive Markets

to pay for the extra X. And this reduces the aggregate welfare of the economy. Thus ofe/01nt Where pnce equals marginal cost represents the optimum level of output This argument represents one step in the proof that a perfectly competitive economy will reach a Pareto optimum or efficient allocation of resources. Some important qualifications and assumptions have been ignored here. The full proof with all its necessary assumptions and qualifications will be presented in Chapter 17.

SOME COMPARATIVE STATIC ANALYSES The Effect of an Excise Tax on a Good An excise tax is a fixed tax per unit of the good produced or sold. The federal govern¬ ment and many states now levy substantial excise taxes on cigarettes and alcoholic beverages. We will consider the effect of an excise tax on a competitive industry, first under the assumption of constant costs, and then assuming increasing costs. Figure 11.10 shows a competitive industry in equilibrium before the tax is imposed. Price is equal to PXI> industry output is Xu and each firm is producing x,. If each firm must pay a tax equal to T per unit of output, the effective cost curves are shifted up by T. Also, the short-run supply curve of the industry is shifted up by the amount of the tax to SSR + T. The upward shift in the short-run supply curve causes an increase in market price to PX2. But market price does not increase by the full amount of the tax. If price were to increase by the full amount of the tax, all firms would wish to continue to produce Firm

Figure 11.10

Industry

The Effects of an Excise Tax on a Constant Cost Industry.

296

The Competitive Market System

at X3, and market supply would still be XBut at the higher price of PX1 + T, consumers would be unwilling to buy Xx. There would be an excess quantity supplied. And this would depress the price to PX2. At this short-run equilibrium of the industry, price is below each firm’s long-run average cost, including the tax. Firms are incurring losses. In the long run some firms will exit the industry. As firms exit, the short-run supply curve of the industry shifts up and to the left. This results in a gradual increase in the market price. As the price increases, the remaining firms increase their outputs. As firms exit and aggregate output decreases, the price continues to increase until it again equals LACX. Losses are reduced to 0. Long-run equilibrium has been restored at PX3 and aggregate output of X3. This model can also be used to determine the incidence of the excise tax. By inci¬ dence, we mean who bears the economic burden of the tax. As Figure 11.10 shows, in the short run price increases but by less than the full amount of the tax. The increase in price represents the burden of the tax on consumers. Because producers were experiencing losses, some of the burden of the tax fell on producers. In the long run, however, the price of the product rose by the full amount of the tax. The incidence of the tax in the long run lies fully on consumers. Figure 11.11 shows the long-run incidence. The tax shifts the long-run supply curve up. Because the long-run supply curve is horizontal, the price goes up by the full amount of the tax. Tax revenues are shown by the area ABCE and are paid entirely by the consumers of the good. Figure 11.11 also shows that the tax has created an inefficiency. Price is greater than the true marginal cost of production. In the new long-run equilibrium the difference between price and marginal cost is the vertical distance CE. This represents the potential social gain from expanding output by 1 unit. The triangular area CEF shows the total inefficiency loss in social welfare brought about by the tax. This is called excess burden.

X per period Figure 11.11

The Efficiency Cost of an Excise Tax in a Constant Cost Industry.

297

Price and Output in Competitive Markets

Definition: The excess burden of a tax is the loss in social welfare that results when a tax causes a divergence between price and marginal cost. Now assume that the industry is characterized by increasing costs. Figure 11 12 shows the situation. The short-run response ofthe industry to the tax is essentially the same as that illustrated in Figure 11.10 for % constant cost industry. The price rises by less than the amount of the tax. Firms experience losses. But with the reduction in output in the short run and the exit of firms and further reduction of output in the long run, another set of forces is brought into play. The reduced demand for factor inputs causes a decline in factor prices and a downward shift in the cost curves of firms. Thus while price is rising because of reduced output, cost curves are falling. This tends to eliminate the gap between long-run average cost and price more quickly. The new long-run equilibrium is achieved at the price of PX3, which is just equal to the average cost given by LACX -f- T. The new long-run equilibrium in the case of increasing cost is different from the case of constant cost because price _has not risen by the full amount of the tn This can also be shown in Figure 11.13. In an increasing cost industry the long-run supply curve is upward sloping. It is shifted up by the full amount of the tax, shown by the vertical distance ER: But mThe new long-run equilibrium, price has increased only by the amount GF. The total revenue from the tax is shown by the area AFEB Of this amount, however, consumers are only paying GFEH through the higher product price. Who is paying the remainder of the tax—the area AGHB1 In the long run it cannot be the firms because in the new long-run equilibrium profits have been re¬ turned to zero. The ultimate burden of this portion of the tax falls on those factor Firm

Industry

I

x per period

0) Figure 11.12

l

I

*3*2 *i

X per period

(b)

The Effects of an Excise Tax on an Increasing Cost Industry.

298

The Competitive Market System

Figure 11.13 Industry.

The Incidence and Efficiency Costs of an Excise Tax on an Increasing Cost

owners who have experienced a decline in the prices paid for their factor services. Suppose there is only one factor with an upward sloping supply curve. Figure 11.14 shows the supply and demand curves in this factor market. The upward-sloping supply curve in this figure is the cause of the increasing costs in the industry using this factor. The imposition of the tax causes a reduction in output and a leftward shift in the demand curve for this factor from DLlD^ to DL2D^2 This in turn causes a fall in the equilibrium factor price. Some units of this factor must seek employment elsewhere. Those that remain employed in this industry have experienced a decrease in their factor earnings that is equal to the area ECBA. This represents the incidence of the tax on factor owners and is equal to the area AGHB in Figure 11.13. What happens to the factors that are exiting this industry? By the assumptions of

Figure 11.14

Part of an Excise Tax Shifted to Factors of Production.

299

Price and Output in Competitive Markets

mobility of resources, perfect knowledge, and competitive markets, these factors are reemployed in other industries, perhaps at lower factor prices. Some other industries must be expanding their outputs because the government is assumed to spend the tax receipts somewhere. If the adjustment process is imperfect and factors remain unem¬ ployed for any significant period of time, this must be because of one or more of the following: a lack of knowledge on the part of factor owners of alternative opportunities; the inability or unwillingness of factor owners to move to locations where factor services are being demanded; or rigidity in factor prices that prevents factor prices from falling until quantity demanded equals quantity supplied.

Rent Controls Assume that the provision of rental apartments in a large city is essentially a competi¬ tive industry. Further, assume that the supply curves of all factor inputs in the produc¬ tion of rental apartments except land are horizontal but that the supply curve of land is upward sloping. This makes the rental apartment industry an increasing cost indus¬ try. If the industry is initially in long-run equilibrium, what would be the effects of a regulation limiting the rents (price) that can be charged to an amount below the long-run equilibrium rent? Figure 11.15 shows the initial equilibrium at price PAl and market quantity of T,. The rent control regulation limits the price to PA1. Firms experience losses. Thus some firms will exit the industry. Exit can take the form of converting apartment buildings to other uses such as shops and offices or to provision of forms of housing that are not subject to rent controls such as condominiums. As firms exit, the decreased demand for land for apartment buildings pushes down land prices. Thus the cost curves of firms shift down while the industry short-run supply curve is shifting to the left. The process

Figure 11.15 Industry.

The Effects of Rent Control If Housing Is an Increasing Cost Competitive

300

The Competitive Market System

continues until the firms’ cost curves have fallen sufficiently to eliminate the losses to firms. This is shown as LACA2 and SMCA2. The new equilibrium quantity in the industry is ^4 2. Who has benefited and who has been harmed by the rent control regulation? Cer¬ tainly those people still living in rental apartments are better off because they are now paying a lower rent. But some of the people initially living in apartments did not benefit because the supply of apartments contracted. Those people who were initially living in apartments A,A2 must be worse off. They were originally willing to pay rents of PA1 to live in them; but the apartments are no longer available at that price. Apartment owners experience temporary losses in the short run. But those who remain in the industry in the long run are no better or worse off than before. The other group of losers is landowners who experience a decrease in the demand for and the price of the factor input they own. Notice that if the maximum rent were set at PA3, the long-run equilib¬ rium quantity would be 0. This is a somewhat unrealistic example because actual rent control programs seldom force a reduction in rental rates from the rates being charged at the time the regulations are imposed. Rather, they place ceilings on rents so that rents do not increase over time. But if rents are initially controlled at PAl, and demand and/or costs increase, the long-run effect is essentially the same.

SUMMARY If a firm is to maximize its profit, it must set its output so that its marginal cost equals its marginal revenue. If the firm is operating in perfectly competitive markets, it faces a horizontal demand curve for its output and marginal revenue is equal to the given price. Thus the competitive firm maximizes profit by equating its marginal cost with price. The firm’s short-run supply curve is its short-run marginal cost curve. When all firms in the industry expand or contract in response to a change in demand, this may induce changes in the prices of factors of production. If factor prices change, the firms’ cost curves shift. This phenomenon must be taken into account in deriving the industry short-run supply curve. The industry short-run equilibrium is where the industry short-run supply curve intersects the market demand curve. In the long run, firms tend to operate at the minimum point of their long-run aver¬ age cost curves, that is, where LACX = LMCX. The long-run equilibrium of the in¬ dustry requires that profits be zero. If profits are positive (negative), new firms enter (exit), and their additional output drives price down (up) until profits (losses) are eliminated. The long-run supply curve of the industry is the locus of industry long-run equilib¬ rium positions for different demand curves. The long-run supply curve of the industry is upward sloping, horizontal, or downward sloping, depending on whether factor prices increase, remain constant, or decrease as industry output increases. Efficiency in resource allocation requires that price, which measures individuals’

301

Price and Output in Competitive Markets

marginal willingness to pay for a good, be equal to marginal cost. A perfectly competi¬ tive industry achieves the equality of price and marginal cost because of the profitmaximizing behavior of firms. Thus perfect competition in output markets contributes to the achievement of Pareto optimality or efficiency.

KEY CONCEPTS Condition for profit maximization: price equals marginal cost Conditions for economic efficiency: price equals marginal cost Shutdown price

Short-run supply curve of the industry Long-run supply curve of the industry Constant cost industry, increasing cost industry, decreasing cost industry Excess burden

Short-run supply curve of the firm

QUESTIONS AND PROBLEMS For Basic Review 1.

Define and explain the economic significance of each of the key concepts.

2.

Consider the case of a single firm in a competitive industry. Assume profit-maximizing behavior.

a. Prove through a verbal argument that in the short run this firm will maximize profits by producing at the output that equates price with short-run marginal cost.

b. Similarly, prove that in the long run the firm will choose the output that equates long-run marginal cost with price.

c. Derive the short-run supply curve for the firm and the industry. Derive the long-run supply curve for the industry. 3. * Define and explain these three terms: constant cost, increasing cost, decreasing cost. What conditions are likely to lead to increasing or decreasing costs in a competitive industry? What is the difference between increasing increasing returns to scale?

costs and

4. a. Assume a competitive industry in long-run equilibrium. Assume that all firms have identical cost curves, and that in the short run firms can change output without affecting the prices of factors. Draw the short-run and long-run cost curves for a typical firm. Show the short-run supply curve of the industry and the demand curve in a separate figure. Explain the derivation of the supply curve. Label the equilibrium price and quantities in both diagrams.

b. Assume a decrease in the demand for the product. Show the short-run adjustment of the industry to this change in demand. Explain the process of adjustment and the new values for price, industry output, output per firm, and profit.

c. Show the long-run adjustment of this industry to a new equilibrium under

302

The Competitive Market System

the assumption of constant costs. Explain the process of adjustment and the new values for price, industry output, output per firm, and profit,

d. Assume instead conditions of increasing cost in the long run. Show the long-run equilibrium and long-run supply curve of this industry.

PROBLEM 1.* An industry consisting of 1000 firms produces a standardized product. Each firm owns and operates one plant and no other size of plant can be built. The variable costs of each firm are identical and afe given in the adjoining table. The fixed costs of each firm are $200. Output

Total variable cost

1 2 5 10 11 12 13 14 15 20 25

5.50 12.00 37.50 100.00 115.50 132.00 149.50 168.00 187.50 300.00 437.50

Note: Although cost information has not been provided for all levels of output, the data given are adequate for plotting all the relevant cost curves.

The total cost function,

TC = f(X) is TC = 200 + 5X + >/2X2

The industry demand curve is X = 45,000 - 1000P

a. (1) Draw the marginal cost and average total cost and average variable cost curves for a typical firm.

Plot marginal values at the midpoints.

(2) Assume that the industry can expand or contract output without affecting factor prices. In a separate figure draw the industry short-run supply curve. Explain its derivation. (3) Also draw in the market demand curve and provide the following informa¬ tion: price, market quantity, firm quantity. Is this industry in long-run com¬ petitive equilibrium? Explain.

b. Congress now unexpectedly imposes a tax of $5 per unit on the manufacture of this commodity. The tax becomes effective immediately and remains in effect

303

Price and Output in Competitive Markets

indefinitely. Assume (a) no changes in the economic system other than those attributable to the tax and (b) none of the changes due to the tax has any effect on the prices of productive services used by this industry. (1) Show how cost curves, supply curves, and so on are changed by the imposi¬ tion of the tax. Explain. (2) After the industry makes its short-run adjustments, what are market price, industry output, output per firm, profit per firm? (3) Suppose all firms try to raise the price by the full amount of the tax. Explain what would happen. (4) If the market demand curves were more elastic at the original equilibrium, the short-run equilibrium would be at a higher/lower price and a higher/ lower quantity. c. (1) Is this industry in long-run equilibrium? What is the long-run equilibrium price and quantity for this industry? Will the number of firms increase, decrease, or remain the same? Explain. (2) We assume: (a) each plant has a life of 1000 weeks and (b) the plants in the industry are staggered in age so that at the time the tax was imposed, there was one plant one week old, one plant two weeks old, and so on. Describe what happens to the short-run supply curve of the industry as the number of plants diminishes. (3) When 100 weeks have passed (900 plants left), what will the price be? X4) Will the output per plant increase or decrease as the number of plants declines? Explain. (5) How many plants must be scrapped before the price rises to the new equilib¬ rium? (6) At the new equilibrium what are market price, market supply, output per firm? Show the new long-run equilibrium in the figures for the firm and the industry. (7) If the elasticity of demand were greater, the new equilibrium price would be higher/same/lower than that previously indicated. (8) If the elasticity of demand were less, the new equilibrium quantity for the industry would be higher/same/lower than that previously found. (9) What is the elasticity of the long-run supply curve? Explain your answer. d. (1) Incidence means who bears the burden of the tax. In the long run who actually pays the tax in this case, producer or consumer? Explain. (2) Is the incidence of the tax different in the short run? Explain. Who bears the burden of the tax in that case? (3) Would the long-run incidence of the tax be different if this were an increasing cost industry? Explain. Who bears the tax burden in this case? (4) Is the equilibrium with the tax a Pareto optimum (i.e., is it efficient in an economic sense)? Compute the social cost of the tax in the long run.

304

The Competitive Market System

For Discussion 1.

What is the likely effect of an effluent charge on pollution from firms in a competitive industry on product price, firm output, and industry output?

2* Assume that apples are produced and sold under conditions of perfect competition. The supply of land to this industry is upward sloping, but the supplies of all other factors are perfectly elastic. Assume that the industry is initially a long-run equilibrium. Evaluate the following policy: It has been

$S per bushel of apples in order to improve the economic welfare of laborers in the apple industry. (Hint. From the industry’s point of view the demand curve shifts up by $S.) Your answer

proposed to provide a government subsidy of

should consider both short-run and long-run impacts. Give explicit answers to the following: a. What are the effects on the price of apples, price of labor, price of land, profit, output, and employment of labor and land?

b. Who actually benefits? Who loses? c. Does the subsidy lead to an efficient allocation of resources? 3.

Assume that the fishing industry is perfectly competitive with each boat constituting a firm. Each boat/firm has the usual cost curves. There is perfect mobility of firms in the long run. This is a constant cost industry. The fishing industry faces a downward-sloping demand curve for fish.

a. Describe the long-run equilibrium of the industry and the firm in appropriate diagrams. Include long-run and short-run curves for this industry and describe their derivations. Are boats earning profits in this equilibrium?

b. Suppose that as part of a management plan, the government requires that boats/firms purchase licenses at

$F per period. What is the effect on firms

cost curves? Describe the new short-run equilibrium. Describe the new long-run equilibrium. What changes will occur in price, output, number of firms, and so on?

c. Suppose that as an alternative to the license, the government imposed a quota on the output or catch of each boat/firm. Let the quota be equal to 50 percent of the output per boat in the original long-run equilibrium. What will happen to market price in the short run and long run, total revenue to the industry, profits, and the number of boats in the long run?

(Note: You

may not have enough information to make firm predictions about some of these variables. In those cases, what additional information would you require? Describe all possible outcomes.) What additional information would you require to make firm predictions about the direction of change?

305

Price and Output in Competitive Markets

SUPPLEMENTARY READINGS Blaug, Mark. The Methodology Of Economics. Cambridge, England: Cambridge Uni¬ versity Press, 1980, Chapter 7. Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach. New York, McGraw-Hill, 1980, Chapter 6. Stigler, George J. Perfect Competition, Historically Contemplated. Journal of Political Economy, February 1957, 65(1), 1-17. Stigler, George J. The Theory of Price (3rd ed.). New York: Macmillan, 1966, Chapter 10.

MATHEMATICAL APPENDIX TO CHAPTER 11 Profit Maximization The conditions for profit maximization can be derived from the calculus. Profit is given by 7T = PxX - C(X) Taking the derivative and setting it equal to 0 gives the first-order condition for a maximum, d-n/dX = Px - C' (X) px = C' (X) where C'(X) is the derivative of the cost function with respect to X or marginal cost. The second-order condition for a maximum (rather than a minimum) is d2n/dX2 = d2Px/dX2 - C"(X) < 0 or d2Px/dX2 < C" (X) The left-hand term is the slope of the marginal revenue curve. This must be less than the right-hand side, which is the slope of the MCX curve. In other words, at the profit maximum the MCX curve must be more steeply sloped than the marginal revenue curve. In Figure 11.1 this condition is satisfied at X; but it is violated at X*, where it also happens that Px = MCX.

CHAPTER 12 Marginal Productivity and Factor Prices in Competition

MARGINAL PRODUCTIVITY AND INCOME DISTRIBUTION

T

.■.he principal objectives of this chapter are to' examine the role of factor prices in helping to determine the distribution of income among individuals and to explain how these factor prices are determined by the interaction of supply and demand in competi¬ tive markets. After discussing the relationship between factor prices and the distribu¬ tion of income, we then show how the demand for a factor input is related to the marginal contribution of that factor to output, that is, its marginal productivity. Next, we develop models of the supplies of labor and land and describe how factor supply conditions can generate certain forms of rents and surpluses. The chapter concludes with an evaluation of marginal productivity theory in both its positive and normative roles. In the late nineteenth and early twentieth centuries what is now known as microeco¬ nomic theory was then called the theory of value and distribution. This is because microeconomics was seen to have two major tasks: (1) the explanation of what deter¬ mines the values or prices of goods and (2) the explanation of the distribution of income. These are not separate independent problems, for, as will be seen, the value of what is produced by a factor service helps to determine the price of that factor service. And the prices that the owners of factors receive for the sale of their factor services play an important role in the determination of the distribution of income. Also, we have already shown that the distribution of income influences the pattern of demands for goods and through it their prices. The distribution of income can be examined from either the individual or a functional or class perspective. The individual perspective asks for each individual what deter¬ mines the total income from all sources, for example, from the sale of capital services,

306

307

Marginal Productivity and Factor Prices in Competition

from the sale ot labor services, and so on. The tunctional or class perspective seeks to determine how much of the total income of the economy is due to the services of capital, the services ot labor, and so on. Both perspectives share a common principle—the price of each factor service will be equal to the contribution that the factor service makes to the total revenue of the firm at the margin, that is, its marginal revenue product.

Definition: The marginal revenue product of a factor F, denoted as MRPF, is the increase in the total revenue of the firm employing that factor for a 1-unit increase in the quantity of that factor, other things equal. It is a money measure of the contribution of that factor to the output of the firm at the margin. For the factor input F being used in the production of X the marginal revenue product is MRPF

ATRX AF

When a firm adds 1 unit of the factor, other things equal, the contribution to physical output is given by the marginal physical product, MPF. When additional output is sold by the firm, its contribution to total revenue is given by the marginal revenue, MRX. Thus the marginal revenue product of the firm is the combination of these two factors, or mrpf

ATR x

AT

AT

AF

= MRX ■ MPf If the firm sells its output in a competitive market and takes product price as given, marginal revenue is equal to product price; and the marginal revenue product of a factor for a competitive firm is simply product price times marginal product. Recall from Chapter 11 that price times marginal product is the value of the marginal product of a factor (VMP F). The value of marginal product VMP measures the value to consumers of the additional output. We now have another basis for defining the value of the marginal product of a factor.

Definition: The value of the marginal product of a factor (VMP F) is the contribution to the total revenue of a competitive firm that is made by one additional unit of the factor, other things equal. Since for the competitive firm MRX = Px, we have VMPr = Px ■ MPf One of the advantages of perfect competition as an economic institution is that it makes the value to the firm of employing an additional unit of a factor just equal to the value to society of that factor’s output. The private interest of firms as reflected in profit-maximizing behavior corresponds to the interests of consumers. We now show why the price of a factor service will be equal to its marginal revenue product. Consider a firm that is one of many that has purchased a particular factor

308

The Competitive Market System

service. Because it is small relative to the factor market, the firm takes the factor price as given. Suppose first that for a firm the marginal revenue product of a factor is greater than its price PF. If the firm were to expand its use of this factor service by 1 unit, it would add more to total revenue than its cost to the firm (PF). The marginal net return of the factor (MRPF — PF) is positive. Therefore it would be profitable to purchase more of the factor service. On the other hand, if the marginal revenue product is less than the price of the factor service, the last unit of the factor purchased costs more than it is worth to the firm. Its marginal net return is negative, thus reducing profits of the firm. Therefore equating the marginal revenue product and the price of a factor service is equivalent to setting its marginal net return equal to 0—that is, to following the first rule of maximization. This is a condition for profit maximization. Relationship: When firms are price takers in factor markets, profit maximization requires that the utilization of each factor be carried out to the point where the marginal revenue product of the factor equals its price: PF = MRP F = MRX ■ MPF

Relationship: If firms are also price takers in output markets, then each factor will be utilized to the point where its value of marginal product equals its price: PF = VMPF = Px ■ MPF

Maximizing behavior on the part of competitive firms leads to factor prices being equal to factor productivities.

The Distribution of Income Among Individuals Each individual’s total income is the sum of the receipts from the sale of the services of each of the factors that she owns. In order to explain this total income, we must be able to explain both the prices at which factor services are bought and sold and the quantities of every factor owned and offered for sale by each individual. The explana¬ tion of factor prices can be carried out through the use of the usual supply and demand framework, which, with special attention to labor and to capital, is the subject of this and the next chapter. Explaining the distribution of factor ownership is more difficult. Take capital, for example. When an individual saves or sets aside a portion of her current income, she is accumulating capital, either directly or indirectly. This accumulation could take the form of direct ownership of tangible assets such as buildings or machines, or it could be indirect, through various financial instruments such as shares of corporations and other intermediaries. But the largest individual holdings of capital result from things such as the sale of rights to inventions and innovation, successful financial speculation, the ownership of unique and valuable resources, and inheritance, rather than from

309

Marginal Productivity and Factor Prices in Competition

savings. These processes cannot easily be explained as the result of normal market forces. Luck plays a major role here.1 Thus as far as microeconomic theory is con¬ cerned, we take the distribution of the ownership of capital as exogenous or determined outside of our economic model. The amount of labor income received by an individual depends on the number of hours of labor services supplied and on the price or wage received. Individuals’ deci¬ sions about the quantity of labor supplied to the market can be analyzed in a microeco¬ nomic framework. But the major source of variation across individuals in income from labor is largely due to differences in wage rates, rather than to differences in the quantity of labor supplied. These wage differentials reflect, at least in part, differences in skills and ability. To the extent that skills are acquired or learned through education and training, the creation of labor skills can be analyzed in an economic framework. Education can be viewed as a form of investment in which costs are incurred during the years of schooling and the returns come in the form of higher incomes in future years. Thus some part of labor income can be interpreted as a return to human capital, that is, capital embodied in the worker in the form of education and training. And some of the differences in wages and labor income must be due to differences in the extent of investment in human capital. Differences in education and training, however, cannot explain all the observed variation in marketable skills and wage rates. Some portion of the variation in skills and wages must be attributed to differences in the patterns of physical and mental capabilities. The distribution of abilities must be taken as exogenous to the economic system. The nature of the economic and social system may have a profound effect on the opportunities that individuals have for developing skills through education and training and for exploiting them in the labor market. This is especially true to the extent that family income or social status influence access to education and training. As this discussion shows, important influences on the size distribution of income from labor and capital are not amenable to analysis with the tools of conventional microeconomic theory. The result is that microeconomics is inherently incapable of providing a complete explanation of the personal distribution of income. Rather, we take the more limited objective of seeking an explanation for factor prices and for those aspects of factor supplies that are affected by economic decisions and processes.

The Functional Distribution of Income The functional distribution of income refers to the division of national income among the owners of labor, capital, and other factors such as land and natural resources. The nineteenth-century classical economists such as Ricardo and Marx made the functional distribution one of their major concerns as they analyzed how market economies would distribute income among labor, capital, and land. In the U.S. economy today about 75

'See, for example, Lester C. Thurow, Generating Inequality, New York: Basic Books, 1975, especially Chapter 6.

310

The Competitive Market System

percent of national income goes to labor in the form of wages and salaries, including the returns to human capital. The bulk of the remainder is income to physical capital, with the owners of land and natural resources receiving only a small percentage of the total. The aggregate production function for the economy is a useful tool in analyzing the functional distribution of income. Let X represent an index of aggregate output and K and L represent the total quantities of the two factors of production capital and labor. The total income of labor is the price of labor times the quantity of labor supplied or Pi ■ L. If the economy is perfectly competitive, then the price of labor is equal to its value of marginal product. Thus labor income is given by VMPL ■ L. Labor’s share is determined by its marginal productivity. Early research on labor income seemed to show that over time labor’s share was a constant fraction of national income. This evidence was consistent with the hypothesis that the aggregate production conditions of the economy can be characterized by a Cobb-Douglas production function. If the production function is X = a ■ Kb ■ Lc

where X is aggregate output, then the marginal product of labor is2 MP, = c • — L

The value of marginal product is X

VMPl

c

■

Px

L

If labor is paid its value of marginal product, labor earnings are VMPl ■ L = c ■ Px ■ X

This equation says that labor income is a constant proportion, c, of the total value of national output. But more recent work has cast doubt on the presumed tendency for labor’s share to remain unchanged over time. Thus the Cobb-Douglas production function may not be an entirely accurate representation of the aggregate production conditions of the U.S. economy.3

2The MPl is the partial derivative of the production function with respect to labor: dX

c- a- Kb ■ Lc~'

aL

caKbLc L

or by substitution: aT

X

aL

L

’See, for example, Robert Solow, A Skeptical Note on the Constancy of Relative Shares, American Economic Review, September 1958, 48(4), 618-631.

311

Marginal Productivity and Factor Prices in Competition

Conclusion As this discussion has shown, whether our primary concern is the functional distribu¬ tion of income or its personal distribution, the marginal productivities of factors are key variables. This entire analysis is sometimes referred to as the “marginal productiv¬ ity theory of income distribution.” But this is somewhat of a misnomer. As we will show, the marginal productivity relationships for factors are only one component in the determination of the demands for factors. And factor demands interact with factor supplies in determining factor prices and the distribution of income. Thus marginal productivity is only one component of a complete theory of income distribution.

THE DEMAND FOR A FACTOR We begin by examining the demand for a factor on the part of a single firm that is a price taker in both factor and product markets and which attempts to maximize profits. We then derive the industry demand curve as the aggregate of the demand curves of individual firms. We will see that this aggregation across firms is more complicated than that of aggregating individual demand curves for goods across households. Although the analysis that follows focuses on the determination of the optimum quantity of a factor input for the firm, this decision cannot be separated in principle from the determination of the optimum level of output. The two are related through the production function. Given a firm’s production function and its associated cost curves, and given the market price of the product, the profit-maximizing output can be determined, following the analysis of Chapter 11. Given the production function, the optimum inputs of all factors can be derived by solving the cost-minimization problem of Chapter 9. In this sense the demand for each factor is a derived demand. The optimum output level determines the optimum quantities of each input. The price of the output helps to determine the value of the marginal products of the inputs. And the values of marginal products are important determinants of the factor demands.

The Firm One Variable Input. When all factor inputs but one are fixed, the firm’s demand for that variable input is the factor’s value of marginal product curve. Suppose the variable input is labor. Its VMP curve is illustrated in Figure 12.1. If the price of labor is PL as shown, the firm maximizes its profits at point C by setting the marginal net return of labor equal to 0 and purchasing L x of labor. If the quantity of labor purchased is less than L„ the VMPL is greater than its price and purchasing an additional unit of labor adds more to total revenue than it adds to total cost. Thus profits can be increased by expanding labor purchases to point C. Point C is one point on the firm’s demand curve for labor. If the price of labor were to fall, the profit-maximizing firm would expand its purchases of labor until once again its VMPl has been brought into equality with the new price of labor. The points of

312

The Competitive Market System

Figure 12.1

The Firm’s Demand Curve for Labor When It Is the Only Variable Input.

equality of VMPL and PL all lie on the VMPL curve. Thus the VMPL curve gives the quantity of labor demanded at any price of labor. In Figure 12.1 the total expenditure of the firm on labor is the rectangle OACLx. Recall that the area under any marginal curve gives the total value of the variable. The area under the VMPL curve is the total revenue due to the use of labor. At PLX and L, the total revenue of the firm must be equal to the area OBCLx. The difference between total revenue and labor expenditure is equal to the area ABC. This amount is available to meet the fixed costs of production and possibly yield a profit. There are two things that can cause a shift in the firm’s demand curve for labor. First, a change in the price of X changes the VMPL directly. An increase in product price shifts the VMPL curve out and increases demand. Second, a change in the quantity of the fixed factor affects the marginal productivity of the variable factor. In the simple case of only two factor inputs an increase in the fixed factor increases the marginal productivity of the variable factor. This, in turn, shifts out the VMPL curve. With three or more inputs it is possible that an increase in one of the fixed factors could decrease the marginal productivity of the variable factor, thus leading to a leftward shift of its demand curve. This would be the case if the two factors were substitutes in produc¬ tion.

All Inputs Variable. In the long run, when all inputs are variable, a change in the price of labor induces changes in the quantities of other factors that, in turn, cause shifts in the VMP curve of labor. Also, factor price changes cause shifts in the firm’s cost curves. And these, in turn, induce changes in output and the inputs of all factors. These must all be taken into account in the derivation of the factor demand curve when factors are variable. Figure 12.2(a) shows the isoquant mapping for a firm. Let the initial price of labor be PL] and the profit-maximizing output be Xu The iso-cost line MM' in Figure 12.2

313

Marginal Productivity and Factor Prices in Competition

L per period (a)

(b)

L per period

(c) Figure 12.2

The Firm’s Demand Curve for Labor When All Inputs Are Variable.

(a) shows the total cost of producing Xx and its slope is P[A/PK. The firm will produce at point A with a labor input of Lx. Holding capital constant at Kx, a VMPX curve can be derived. It is shown as VMPU in Figure 12.2(c). Now assume that the price of labor falls to PL2. The iso-cost line associated with the initial level of total cost rotates out to MM". The firm’s response can be divided into a substitution effect and an output effect. The former shows the change in factor quantities, holding output constant at the original level, Xx. To find the substitution effect draw in a hypothetical iso-cost line parallel to MM" and tangent to the Xx isoquant. The tangency is at point B, indicating an increase in labor input to L2. This is also shown as point B' in Figure 12.2(c). Point B' is not on VMPL1 because the quantity of capital was reduced as labor was

314

The Competitive Market System

substituted for it. Given the new capital input of K2, there is a new curve VMPL2 through point B'. It lies below and to the left of the original VMPL curve.4 The output effect is the increase in labor that is associated with the firm’s adjustment to the new profit-maximizing output level. With the fall in the price of labor, the total cost of producing X ( is reduced. This is reflected in a downward shift in the LMC and LAC curves of Figure 12.2(h). Because the firm is too small to have any impact on market price, market price is held constant. With the new LMC' curve, marginal cost is equal to the price at a higher output level, requiring an increase in labor utilization beyond L2. Suppose that the new profit-maximizing output is X2. The optimum input com¬ bination is on the new expansion path through point B, which reflects the lower price of labor. The expansion path intersects the X2 isoquant at point C with a labor input of L3, which corresponds to point C' in Figure 12.2(c). The demand curve for labor is the heavy line through the initial and new equilibrium points A' and C'. It is downward sloping to the right because both the substitution and output effects lead to increases in the labor input when the price of labor is de¬ creased. Unlike the substitution effect, the output effect of a decrease in PL leads to an increase in the input of capital. This, in turn, causes the VMPL curve to shift out to the right, because labor has more capital with which to work. The new VMP curve through point C' is labeled VMPL3,5 Each equilibrium point, such as A' and C', showing quantities of labor demanded at different prices has a VMP curve going through it. The demand curve for labor (or for any factor) can be interpreted as a locus of intersections of price lines and equilibrium VMP curves after the optimum adjustment of the levels of capital and labor, and holding all other prices and technology constant. The firm’s long-run demand function for a factor shows how the quantity demanded of that factor varies with its price, the prices of other factors, and the price of output. The firm’s demand function for labor can be written as Ld =

Td(P L’

Pk*’ PX*)

where the asterisks indicate that variables are held constant in drawing the demand curve. An increase in PL reduces the quantity demanded of labor as the firm moves up to the left along its demand curve. An increase in the price of output increases the VMP of labor and shifts the demand curve for labor up and to the right. Finally, an increase in the price of capital affects the quantity demanded of labor through two channels working in opposite directions. First, the higher price of capital induces a substitution of labor for capital, that is, an increase in the quantity demanded of labor at a given labor price. Second, because costs are higher, there is a reduction

-This is strictly true only in the simple case of two factor inputs. With three or more factors it is possible that the reduction in the quantity of capital could shift out the VMP curve for labor. Note that if this new profit-maximizing output had been less than Xlt the equilibrium quantity of labor would have been less, say, at C" in Figure 12.2(c). In this case the VMPL3 through C" would have been to the left of VMPl j.

315

Marginal Productivity and Factor Prices in Competition

in output and in the quantities demanded of both inputs. The net effect of these two forces on the demand for labor cannot be determined without specific information on the production technology.

The Industry Demand Curve In analyzing the factor demand for a firm, we have held certain things constant, including the price of the output. That is, the firm was assumed to be so small that changes in its output level in response to factor price changes would have no perceptible effect on the market price for the good. The effect of output changes on product price cannot be ignored when we consider all firms in the industry responding to a change in the price of a factor. The following discussion applies both to the short run, one variable input case, and the long run, all inputs variable case. Suppose that the firm’s demand curve has been derived in the manner previously described. Suppose that the factor is labor, its price is PLl, and the aggregate quantity demanded at this price is Lx in Figure 12.3. The light line through point A shows the horizontal summation of the demand curves of all firms in the industry, given PLX and the market price of output. Now let the price of labor fall to PL2. If all firms were to expand along their individual demand curves, the aggregate quantity demanded of labor would be L'2. But this implies an increase in output that can only be sold if product price falls. The fall in product price causes a leftward shift in the VMPL curves for all firms. This tends to partially offset the initial increase in the quantities of labor de¬ manded. The new equilibrium, taking account of the effect of product price on the individual VMPL curves, will be a point such as B in Figure 12.3. The market demand

L per period Figure 12.3

The Industry Demand for a Factor.

316

The Competitive Market System

curve for labor is a line through points A and B. It is less elastic than the horizontal summation of the individual firms’ demand curves. The industry demand function for a factor, say, labor can be written as Lxd = Lxd [Pl, PI Xd(Px, . . .)*] where is the quantity of labor demanded by the X industry and XD (Px, . . .) is the market demand function for X. The asterisks indicate the variables that are held constant when the industry demand curve for L is drawn. The underlying production technology is reflected in the functional Lf[-].

The Elasticity of Industry Demand The preceding analysis does not allow us to be specific about the elasticity of the factor demand curves. More general reasoning, however, can identify four important influ¬ ences on the elasticities of the derived demands for inputs. 1. The elasticity of substitution in production. The greater this elasticity is, the greater will be the substitution effect of any price change and the greater will be the change in quantity demanded of the input for any given change in its price. 2. The elasticity of demand for output. When the price of a factor changes, it leads to a change in product price in the same direction. The more elastic the product demand curve is, the greater will be the change in output and the associated changes in inputs. 3. The share of total cost going to this input. The more important this input is in the production of the good, the bigger will be the change in the total cost associated with any change in the price of that input. Other things equal, the bigger the change in total cost is, the bigger will be the change in both output and the required levels of inputs. 4. The elasticity of supply of other factor inputs. In the simple two-factor case the greater the elasticity of supply of capital is, the greater is the elasticity of demand for labor. Suppose the price of labor falls. This induces a substitution of labor for capital and, holding output constant, a reduction in the quantity of capital. Unless the supply curve of capital is perfectly elastic, this will induce a decline in the price of capital, which tends to weaken the incentive to substitute labor for capital. The more elastic the supply of capital is, the smaller is the decline in its price and the larger is the increase in the quantity of labor in response to a decrease in its own price.

FACTOR SUPPLY Because of differences in the nature of factors and differences in the influences on their supply, the supply functions of the different types of factor inputs must be analyzed

317

Marginal Productivity and Factor Prices in Competition

separately. For example, in the short run the supply of services from capital machines is vertical or perfectly inelastic because the quantity of machines is taken as given. But in the long run new machines will be built if the expected stream of future returns (VMPK) is sufficiently high to make the machines appear profitable. Because the cost of producing the machine is incurred when the machine is built and the future returns are spread out over time, the question of profitability involves the time pattern of expected receipts and the interest rate. These matters will be considered in the next chapter. The supplies of land and certain other nonaugmentable natural resources can be taken to be fixed even in the long run. In other words, increases in price are not effective in bringing about an increase in the quantity supplied. Their supply curves are perfectly inelastic. There is no reason to believe that the supply of labor would be perfectly inelastic in either the short or long run. Individuals have alternative uses for their time and can choose between using time for work to earn income and for leisure activities. How people allocate their time is likely to be influenced by the relative values of time spent in work (the wage) and in leisure. We turn now to an analysis of the individual supply of labor.

Individual Supply of Labor Consider an individual who can allocate a fixed allotment of time between supplying labor to the market at a given wage rate to earn income and engaging in nonmarket activities.6 Such activities include what is normally thought of as leisure (recreation, reading, and so forth) as well as home production of goods and services as an alternative to purchasing them through the market, for example, tending a vegetable garden, repairing one’s automobile, or making one’s clothes. For simplicity, we will call all such activities “leisure.” In order to focus only on the work versus leisure trade-off, we can assume that this individual’s utility is a function of real income and hours of leisure, F. If all prices are assumed to be constant, money income, M, is an accurate measure of real income. The utility function can be portrayed by an indifference map with F and M measured on the horizontal and vertical axes, respectively. This is shown in Figure 12.4. The individ¬ ual is assumed to maximize utility subject to the constraint imposed by the scarcity of time and the terms on which time can be converted into money, that is, the wage rate of PL. If T* is the total amount of discretionary time available per period (after sleeping, eating, etc.), the time constraint is T* = F + L, where L is hours of labor supplied. Assume for now that work is the only source of income. Multiplying both sides of the time constraipt by PL gives

6As in the case of our analysis of preference theory and demand, this focus on the individual as the decision-making unit obscures some very interesting questions about labor supply decision making in mul¬ timember family units.

318

The Competitive Market System

Fper period Figure 12.4

An Individual’s Trade-off Between Labor and Leisure.

PL ' T* = PL ' F + PL ■ L = PL ■ F + M

Rearranging gives a budget line of the conventional form: M = PL ■ T*

—

PL ■ F

This is shown as the line KT* in Figure 12.4. The vertical intercept shows the maxi¬ mum amount of income that can be earned if leisure is 0. If income is 0, the total allotment of time can be allocated to leisure (T* = F). The slope of the budget line is — PL. This means that if leisure is reduced by 1 hour (a move to the left along KT*), income is increased by PL. The higher the wage rate is, the more steeply sloped is the budget line. A decrease in the wage rate rotates the budget line counterclockwise to the left. But its horizontal intercept remains at T*. The individual’s most preferred allocation of time between work and leisure is at point A where an indifference curve is just tangent to the budget line. The slope of the indifference curve is equal to the marginal rate of substitution between leisure and income, and the slope of the budget line is PL (ignoring the minus sign in both cases). Iherefoie the condition for an optimum allocation of time is that the marginal rate of substitution between leisure and income be equal to the money wage rate, or MRSFm = P i

In this case as in others our interest is less in the equilibrium conditions for the individual than in the comparative static predictions that the model permits. First, how will an individual respond to a change in the price of labor? Figure 12.5(a) shows the indifference map and budget lines of an individual who has experienced an increase in the price of labor. Figure 12.5(h) shows the supply curve of labor. At an initial price of PLi the budget line is KT* and the individual is in equilibrium at point A, taking Fj hours of leisure and supplying L1 (= T* ~ F{) hours of work.

319

Marginal Productivity and Factor Prices in Competition

Tper period

0)

L( = T* — F) per period

(b) Figure 12.5

An Individual’s Supply of Labor: The Upward-Sloping Supply Curve.

If the wage is increased to PL2, the budget line shifts up to K'T*, and the new equilibrium is at point C. This move can be separated into a substitution effect and an income effect: 1. To find the substitution effect, draw a new hypothetical budget line with a slope equal to -PL2 but tangent to the original indifference curve, Ix. The tangency is at point B. The substitution effect shows that as the price of labor goes up, the price or opportunity cost of leisure rises and the individual substitutes away from leisure toward more work and income. Leisure is decreased from Ft to F’2. 2. To find the income effect, move from point B on 7, to point C on I2. If leisure is a normal or superior good, an individual could be expected to allocate some portion of the increase in earnings potential to acquiring more leisure. This is shown by the increase in leisure taken from F'2 to F2.

x 320

The Competitive Market System

The substitution effect reduces leisure and increases labor supply while the income effect works in the opposite direction. In the case shown in Figure 12.5 the substitution effect is stronger and the net effect is that the increase in the price of labor leads to an increase in the labor supplied from Lx to L2. But this need not always be the case. Figure 12.6 shows an instance where the income effect is stronger than the substitution effect. The net effect is an increase in the amount of leisure taken when the wage rate increases. Thus the individual supply curve of labor slopes up to the left rather than to the right. Notice that although the quantity of labor supplied has decreased, the income received from labor has increased. The individual responds to the larger opportunity set created by the increase in the wage rate by taking more of both income and leisure.

Cb) Figure 12.6

An Individual’s Supply of Labor: Higher Wages Reduce Labor Supply.

321

Marginal Productivity and Factor Prices in Competition

The Shape of the Labor Supply Curve. What can be said about the likely shapes of the indifference curves and labor supply curve in practice? Will the labor supply curve slope up to the right or down to the right? Considering the question from a purely logical perspective, we see that it depends on things such as whether the individual receives income from sources other than labor supply and whether there are opportuni¬ ties for productive self-employment outside the market.7 Suppose that the individual can attain a subsistence livelihood outside the market by, say, hunting, gathering food, and so forth. If so, then there is some very low wage rate at which the individual will supply no labor to the market and will sustain himself by nonmarket work. Let this wage rate be PL0 in Figure 12.7(a). As the wage rate increases above this level, the substitution effect leads to an increase in the quantity of labor

(b) Figure 12.7

Different Possible Slopes for the Supply Curve of Labor.

’For a further exploration of some of these issues, see Yoram Barzel and Richard McDonald, Assets, Subsistence, and the Supply Curve of Labor, American Economic Review, September 1973, 63(4), 621-633.

322

The Competitive Market System

supplied to the market. But because the wage rate is low and the hours being worked are low, the income effect from an increase in the wage rate must be quite small. In this range it is too small to offset the substitution effect. Thus the net effect of the increase in wage is to increase the quantity of labor supplied. As income rises because of higher wage rates and more hours of work, the income effect of further increases in the wage rate becomes more substantial, eventually getting so large that it offsets the substitution effect. Beyond this point labor supply is reduced with further increases in the wage rate. Because income is also a normal good, an increase in the wage rate must always lead to an increase in money income. The decrease in labor supply can never be so large as to result in a decrease in money income. This means that the percentage decrease in labor supplied can never be greater than the percentage increase in the wage rate. In these circumstances the labor supply curve slopes up to the right and then bends back on itself at higher wages. Suppose instead that there were no nonmarket means of sustaining livelihood and that a minimum income of M0 were required for subsistence. Then at a wage of PL0 = M0 — T*, T* hours of work would be supplied. Life would not be possible at a wage below PL0. Unless the income elasticity of demand for leisure were 0, any increase in the wage rate above PL0 would result in at least a small increase in the demand for leisure and a reduction in the supply of work. The labor supply curve under these circumstances would have the shape shown in Figure 12.7(h). Other assumptions about initial conditions and alternatives lead to other deductions about the shape of the labor supply curve.

Empirical Evidence. The question of the shape of the labor supply curve can only be settled by examining the empirical evidence. The long-term secular decline in the average work week that has accompanied the rise in real wages over the past one hundred years or more suggests a negative elasticity of labor supply and a supply curve shaped like that in Figure 12.7(h). On the other hand, the rising labor force participa¬ tion rate of women is more consistent with the upward-sloping supply curve in the lower range of Figure 12.7(a). But it is dangerous to draw conclusions about the labor supply curve from this sort of casual historical evidence. Other things that influence labor supply (besides wage rates) could also have been changing over time; and these other things must be controlled for. Cross-section studies8 in which it is possible to control systematically for other factors that change over time provide a more reliable basis for drawing conclusions. Most recent studies confirm that the substitution effect on labor supply is positive. In other words, wage increases cause the labor supply to increase when income is held constant. These studies also confirm that the income effect of wage increases on labor supply is negative. It appears, however, that the income effect is stronger for men who are heads of households than for married women. The strong income effect apparently

“For reviews of the evidence see Glen G. Cain and Harold W. Watts, eds., Income Maintenance and Labor Supply, New York: Academic Press, 1973, especially Chapters 1 and 9, and Anthony Atkinson and Joseph Stiglitz, Lectures in Public Economics, New York: McGraw-Hill, 1980, Chapter 12.

323

Marginal Productivity and Factor Prices in Competition

results in a backward-bending labor supply curve for men. But the labor supply curve of married women slopes up to the right.

Labor Supply and Income Taxation. The model of individual choice can be used to analyze a number of problems in comparative statics. One example is the effect of a tax on earned income on the quantity of labor supplied. The individual will base her labor supply decision on the aftertax wage, that is, the wage net of tax payments. The effect of a tax on earned income is to lower the aftertax wage rate. The effect on labor supply depends on whether the individual is in the backward-bending portion or the upward-sloping portion of her labor supply curve. If the individual supply curve is backward bending over the relevant range, the tax increases labor supply and reduces leisure. This is because the negative effect of reduced income on the demand for leisure outweighs the substitution effect of the lower net wage. The effect of the tax can be examined with the indifference curve diagram. In Figure 12.8 the straight line budget line, KT*, shows the income-leisure trade-off for a given price of labor and no income tax. Point A represents the equilibrium of the individual. Suppose that the income tax is a fixed percentage t of labor income. If the individual receives PL per hour worked, his net wage is (1 — t)PL. The income tax shifts the budget line down to K T*. The slope of the new budget line is the aftertax wage, (1 — t)PL. The tax lowers the price of leisure. In the case shown in Figure 12.8 the substitution effect of the lower price of leisure outweighs the income effect. At the new equilibrium at point B leisure has increased from F, to F2 and labor supply has decreased. For another individual with different indifference curves, however, the opposite result could occur.

Nonlabor Income and Labor Supply. The analysis so far has been based on the assumption that the only source of income to the individual is supplying labor to the

Fper period Figure 12.8

The Effect of an Income Tax on an Individual’s Labor Supply.

324

The Competitive Market System

market. Suppose that the individual also has income from the ownership of land or capital machines. Denote this nonlabor income by M0. Then total income, M, is nonlabor income plus the earnings from woi*k. The budget constraint becomes M = Mb + PL (T* - F) = M0 + PL ■ T* — PL

F

In comparison with the previous model this budget line has the same slope but is shifted vertically by the amount of nonlabor income. This is shown in Figure 12.9. The budget line KT* shows the income leisure trade-off when nonlabor sources of income are 0. The kinked budget line K'M^T* is the budget line with nonlabor income of M0. Adding nonlabor income has an income effect. But because it does not change the slope of the budget line, there is no substitution effect, thus increases in nonlabor income lead to increases in the amount of leisure taken, that is, reductions in labor supply.

Welfare Programs and the Supply of Labor. The normative evaluation of alterna¬ tive welfare systems involves many considerations, including the fundamental one of what constitutes a just or equitable distribution of income and how can it be achieved. A discussion of this fundamental issue is deferred to Chapter 18. The objective of this section is simply to utilize one of the models developed in this chapter to predict the effects of alternative welfare systems on individuals’ supply of labor to the market. One form of welfare system establishes a minimum income M . For individuals with earnings E less than M a cash payment or grant is made. The grant G is equal to the difference between the target minimum income and earnings (G = M — E). Under this form of welfare system each $1 increase in earnings leads to a $1 decrease in the welfare grant. This is equivalent to a marginal tax of 100 percent on earned income. The economic incentives for work under such a system are weak indeed.

325

Marginal Productivity and Factor Prices in Competition

This system and its effect on individual choice can be analyzed by using the model of income-leisure trade-off developed earlier. Figure 12.10 shows the budget line M*T* for an individual with a given money wage. If that individual is also eligible for the welfare system with a minimum income of M, her effective budget line becomes the series of line segments M*ILT*. Suppose the individual has an indifference curve map as shown by indifference curves Ix and I2. With no welfare system she would choose point K and supply T* — F, of labor. With the welfare system she can increase both leisure and income by reducing labor supply to 0 and moving to point L. Even an individual with an indifference curve such as /; and earned income above M would be better off under the welfare system by reducing labor supply to 0. Only individuals with very strong preferences for income relative to leisure or who have opportunities for work at much higher wage rates would continue to work given the existence of this form of welfare system. One alternative form of the welfare system is the “negative income tax,” so called because for individuals with earned income below a specified breakeven level, the government makes negative tax payments to that individual to supplement his income rather than collecting positive tax payments. Such a system could be designed to guarantee a minimum income of M to individuals who supply no hours to the labor market. The budget line for this negative income tax program is shown as M*ILT* in Figure 12.11. Point / is the breakeven point below which individuals receive negative income tax payments equal to the vertical distance between the line segment IL and IT*. In contrast to the conventional welfare system, the line segment IL of the negative income tax system has a marginal tax rate which is less than 100 percent. Each additional dollar of income earned through work leads to a reduction of the negative income tax payment by less than $1. Thus there is an increase in money income for increases in hours worked.

Figure 12.10 Supply.

A Welfare System with a 100 Percent Tax on Earnings: The Effect on Labor

326

The Competitive Market System

Figure 12.11

A Negative Income Tax Increases the Supply of Labor in Comparison with a Conventional Welfare System.

Figure 12.11 shows how the negative income tax system can alter the work incentives of an individual who would supply no labor under a conventional welfare system. Suppose that an individual with indifference curves Ix and I2 would be at point L under the previously described welfare system with its 100 percent marginal tax rate. The budget line segment IL is not tangent to the indifference curve Ix at this point. Rather, the tangency occurs with I2 at point J, showing that the individual would be better off to work. This diagram indicates that at least for some people the negative income tax reduces the disincentive to work and increases labor supply. However, the increased work incentive does not apply to all people potentially affected by the welfare system. The budget line in Figure 12.12 shows the same mini-

Figure 12.12

A Negative Income Tax Can Decrease the Supply of Labor.

327

Marginal Productivity and Factor Prices in Competition

mum income level, marginal tax rate, and breakeven point. An individual whose equilibrium would be at point J under the other welfare system now finds it advanta¬ geous to reduce labor supply under the negative income tax system. Equilibrium with the negative income tax is at point K. Even some people whose initial equilibriums were above the breakeven point might find it advantageous to reduce labor supply somewhat under the negative income tax. The net effect of the negative income tax on labor supply in comparison with the other welfare system depends on the relative strengths of the negative influence of the income effect that decreases the supply of labor and the positive influence of the substitution effect induced by the lower marginal effective tax on income. These two forces arejn turn functions of the key design parameters of the system: the minimum income M, the marginal tax rate on income (the slope of IL), and the breakeven income level at I. The evidence taken from experiments with negative income tax systems on low income groups in several U.S. studies tends to support the following conclusions: 1. There is a small but significant net reduction in total labor supply among male heads of households; and 2. There is a larger reduction in labor supply on the part of female heads of households; but 3. There is little effect on labor supplied by married women.9

The Individual Labor Supply Function. We can summarize this discussion of the determinants of an individual s supply of labor by writing the labor supply function as follows: Ls = Ls [PL, M*, t(M)*]

where PL is the market price of labor, M0 is nonlabor income, and t(M) represents the schedule of effective taxes on income, that is, the combined effect of income and payroll taxes and welfare payments. The asterisks indicate that the tax rate schedule and nonlabor income are held constant when the labor supply curve is drawn as a function of the market price of labor. Changes in the tax rate schedule or nonlabor income will shift the labor supply curve.

The Market Supply of Labor The aggregate supply curve of labor is the horizontal summation of the individual labor supply curves. If individuals’ supply curves are backward bending, the aggregate supply curve will also be backward bending. This supply curve shows the supply of homoge-

9See, for example, Human Resources, man, and Richard Programs, Journal

Robert A. Moffett, The Labor Supply Response in the Gary Experiment, Journal of Fall 1979, 14(4), 477^187; and Michael C. Keeley, Phillip K. Robins, Robert G. SpiegelW. West, The Labor-Supply Effect and Costs of Alternative Negative Income Tax of Human Resources, Winter 1978, 13(1), 3-36.

328

The Competitive Market System

neous or undifferentiated labor to all potential purchasers of labor services. Even though the aggregate supply curve may be backward bending, the supply curve for any particular type of labor skill or occupation is likely to be upward sloping. The supply curve of labor to a single industry that is one of several industries purchasing labor from a common labor market will also be upward sloping. Suppose there are two occupations, painters and carpenters. An increase in the wage rate for painters may cause those who are currently employed in this occupation to reduce their labor supply. But at the same time, it will induce some people to stop working as carpenters and to offer their labor services as painters. When the possibility of shifts among occupations is taken into account, we see that the supply curve of labor to a particular occupation is likely to be upward sloping to the right. Suppose there are two industries, X and Y, that both purchase labor in the same labor market. Suppose the aggregate supply of labor to this market is backward bending. At any given wage rate the effective supply of labor to the X industry is the total supply of labor minus the labor demand on the part of the Y industry (see Figure 12.13). As Figure 12.13(a) shows, at a price of labor PLl, the Y industry’s demand for labor is just equal to the aggregate supply and the labor supply to the X industry is 0. At prices above PLi the aggregate supply of labor to the market decreases but the quantity demanded by the Y industry decreases more, leaving an increasing effective supply to the X industry. The effective supply of labor to X is an increasing function of the wage rate as long as the price of labor does not rise so high that it prices the Y industry out of the labor market. Thus the supply curve of labor to the X industry is upward sloping at least between the prices of PLX and PL2. Market

Figure 12.13 Factor.

Industry X

The Relationship Between the Industry and the Market Supply Curves for a

329

Marginal Productivity and Factor Prices in Competition

Rents to Factors in Fixed Supply Consider a factor such as land that is essentially in fixed supply. The total quantity of land available cannot be increased by economic activity. The ability of a piece of land to yield economically valuable services can be enhanced by dikes, drainage ditches, roads, buildings, and the like, but these improvements are forms of capital. The supply ot the services of land itself cannot be increased in response to a higher factor price. The income paid for the services of factors in fixed supply is called rent. Definition: Rent or pure rent is the income received by a factor owner for the services of a factor in perfectly inelastic supply.10 Suppose that there are only two inputs to the production of a good: the service of land that is in fixed supply and the service of labor that is in infinitely elastic supply. Figure 12.14 shows the factor demand curve for land. This demand curve depends on the value of marginal product of land and is derived in the previously described manner. The price or rent per unit of land is determined by the intersection of the demand curve with the vertical supply curve of land. Total rent is the area OABC. In the simple case of only two factors the rent to land can also be determined by examining the demand and supply curves for labor. Figure 12.15 shows the value of marginal product curve for labor. Because labor is the only variable input, this is also the demand curve for labor. The quantity of labor utilized is OC. Total revenue is the

Figure 12.14

Land Rent as Determined in the Market for Land.

‘“Some authors define economic rent as any payment to a factor in excess of the minimum amount required to induce that factor to be supplied to the market. This is analogous to consumer surplus, which was defined as the excess of willingness to pay over the minimum amount that must be paid to purchase a good. For this reason, this excess payment over the minimum required will be called “factor surplus.” This concept is discussed later.

330

The Competitive Market System

L per period Figure 12.15

Land Rent as Determined in the Market for Labor.

area under the VMPL curve out to this point, or OEBC. Part of the revenue, OABC, goes to pay for labor. The residual, AEB, is the return to the fixed factor, land. Because the triangle AEB in Figure 10.12 and the rectangle OABC of Figure 12.14 are alterna¬ tive measures of the same thing (rent), they must be equal to each other. The rent to a fixed factor such as land depends on several things. First, of course, is the supply of land. As Figure 12.14 shows, an increase in the supply of land leads to a decrease in the rent per unit of land. Thus rent per unit is a reflection of the scarcity of the fixed factor. The total rent paid to landowners can either increase or decrease with an increase in the supply of land, depending on whether the demand for land is elastic or inelastic. The prices of the variable inputs influence the unit rent and total rent to land. As can be seen from examining Figure 12.15, an increase in the price of labor leads to a decrease in rents. As both Figures 12.14 and 12.15 illustrate, the rent per unit also relies on the position of the value of marginal product curves of labor and land. An increase in the price of output will shift these curves upward, leading to an increase in rents. Rent also depends on the underlying technology that determines the marginal produc¬ tivity of the factors. A technological improvement that increased the single factor productivity of land would lead to an increase in rents, other things such as product price being held constant. In the case of agricultural land, noneconomic variables such as weather and soil fertility also affect productivity, and therefore rents.

Taxing Rents. One interesting feature of pure rents is that they provide a basis for nondistorting taxation; that is, they can be taxed without affecting resource allocation or creating economic inefficiencies and dead weight losses of the sort described in Chapter 11. The incidence of the tax falls entirely on the owners of the fixed resource. Figure 12.16 shows the demand and inelastic supply curves for land and the equilib¬ rium unit rent of R. Now suppose that a 50 percent tax on the rental receipts of

331

Marginal Productivity and Factor Prices in Competition

Figure 12.16

The Incidence of a Tax on Land.

landowners is imposed. If landowners attempt to raise rents in order to shift all or part of the tax forward to the users of land, there will be an excess supply of land. Competi¬ tion among landowners would force the unit rent back to R. The tax changes nothing except the net receipts of landowners. These are cut in half. In fact, any tax on rental receipts less than 100 percent leaves the resource allocation unaffected. Rather than tax the realized rental receipts of landowners, it is also possible to tax them on the basis of the market value of their land. As long as the tax is equal to or less than the maximum potential rental value of the land, the supply of land and resource allocation are unaffected. Landowners must allocate land to its highest valued use in order to obtain the rental receipts with which to pay the tax on the land. This analysis is the basis of Henry George’s proposal to tax land rents at 100 percent.11

Some Applications of Rent Theory. The theory of rents provides a basis for tracing out some of the impacts of economic changes. For example, for much of the twentieth century it has been federal policy to support the prices of certain agricultural products above the market equilibrium by purchasing the excess supply. Who benefits and who loses from this policy? It is clear that consumers of these products lose, because they face higher prices for food, and so on. The model of rents shows that the owners of farmland reap the benefits.12 Those farmers who do not own their own land but rent farmland from others do not benefit from the price support program. For another example, suppose that air pollution in one small agricultural region

"See Henry George, Progress and Poverty, New York: Robert Scholkenbach Foundation, 1955 (first pub¬ lished in 1879). I2Actually, the only beneficiaries are those who own farmland at the time that the price support policy is first instituted. Subsequent purchasers of farmland must pay the original owners for the right to receive the benefits of higher agricultural prices. This same point is made in a different context in Chapter 16.

332

The Competitive Market System

reduces the productivity of land and crop yields. If this region is so small that the reduced supply of agricultural output has no effect on the market price of farm output, then the only affected parties are landowners in that region, who experience a decrease in land rents. If air pollution or other negative factors such as drought or insect infestation affect agricultural yields over a large area, then the effects on the price of agricultural output must be taken into account. In Figure 12.17 the original supply curve for agricultural output (in the absence of pollution) intersects the demand curve at a price of PX1 and quantity of XBecause the supply curve 5 reflects the marginal cost of production, the area under this curve, OABX,, can be taken as a measure of the costs of labor, fuel, fertilizer, and so on used in producing the crop. The rent to agricultural land is the difference between total receipts (OP\BX^) and these costs. Thus the rent can be measured by the areas K + M. The pollution or drought shifts the agricultural supply curve up to S'. Price increases 1° PX2’ reducing the welfare of consumers. The welfare change of consumers is — N — L. In the new situation, rent is M + N. Thus farmland owners lose rent equal to K but gain rent equal to N. The net change in welfare, taking consumers and landown¬ ers together is A w = N- K- N- L = -K - L.

This is the area between the two supply curves and below the demand curve. Farmland owners’ losses are partly offset by the increased price of agricultural output. Part of the loss is shifted to consumers of agricultural products. The analysis of rents can be extended to cases where land is not homogeneous but

Agricultural output per period Figure 12.17 Affected.

Losses Due to Reduced Agricultural Productivity When Agricultural Prices are

333

Marginal Productivity and Factor Prices in Competition

varies in quality or economic productivity. Consider the case of farmland of different degrees of fertility. Assume for simplicity that there are three classes of productive land. Figure 12.18 shows demand and supply curves for each class of land. Class A is the most productive as reflected in its demand curve. Class B is less productive, because of possibly lower soil fertility or reduced rainfall or because of greater distance to the market and higher transportation costs for crops and inputs such as fertilizer. Class C land is least productive and also most abundant. The figure shows that the rent per unit of land declines as productivity decreases. In fact, Class C land has a zero rent. It is on the margin of economic usefulness or value. If the demand curve for Class C land were to shift to the left, some of the land would be abandoned. This model probably describes the situation in the West during the early days of settlement in the nineteenth century. As growing population increased the demand for agricultural products and as improvements in transportation brought some lands effectively closer to markets, the demand curves for those lands shifted to the right, eventually intersecting their vertical supply curve and leading to positive and increasing rents and land values. A similar analysis can be applied to land rents around urban centers. Urban cen¬ ters develop because of economies of scale in the provision of certain services such as communications and transportation and because of the benefits of proximity, for ex¬ ample, between banks and the commercial and industrial activities they serve. Land closer to the center of the city is more desirable because of the lower travel time between that land and the city center. Also, because of the smaller radius from the city center, there is less land close to the city than land at a greater distance. Thus as one moves out from the city center, the markets for land at each distance are characterized by demand curves that are closer in to the left and supply curves that are farther out to the right. The result is that land rents are lower at greater distances

Type A Rent

Type B Rent,

O

Land per period

(«) Figure 12.18

o

Type C Rent,

Land per period

o

Land per period

Cb)

Rent Differentials and Differences in the Productivity of Land.

(c)

334

The Competitive Market System

from the city center. A corollary of this inverse relationship between land rent and distance is that land closer to the city center will be more intensively utilized. Build¬ ings are a form of capital. As the ratio of land rent to the price of capital increases, the rational economic response is to substitute capital in the form of higher buildings for the relatively more costly land.

Quasi-rents to Factors Fixed in the Short Run The term quasi-rents refers to returns to factors that are fixed in quantity to the firm in the short run but variable in the long run. Definition: A

quasi-rent is the excess of total revenue over total variable cost for a

firm. Quasi-rents would be 0 if the firm has shut down or is exactly at the shut down point. Quasi-rents could never be negative, because the firm could eliminate negative quasi¬ rents by shutting down production. Positive quasi-rents do not necessarily imply profit¬ ability. For the firm to be earning profits in the short run, quasi-rents must exceed the opportunity cost of the fixed factors, that is, fixed cost. Quasi-rents are shown diagrammatically in Figure 12.19. A firm’s SMC, SAC, and A VC curves are shown, along with the given market price of Pxl. The firm maximizes profits or minimizes losses by producing an output Xt. The vertical distance CB is the excess of price over average variable cost. Quasi-rents are the area ABCD. Since the price is below short-run average cost here, quasi-rents are less than the fixed cost and the firm is receiving negative profits. At prices above PX2, quasi-rents are greater than the fixed cost and profits are positive.

Figure 12.19

Quasi-rent in the Short Run.

335

Marginal Productivity and Factor Prices in Competition

Factor Surplus When the supply curve for a factor is less than infinitely elastic, the price of the factor must increase in order to bring about an increase in the quantity supplied. This means that some factors will be receiving a price greater than the minimum price necessary to induce them to supply their factor services to the market.

Definition: Factor surplus is the excess of factor receipts over the minimum payment

necessary to bring forth that quantity supplied. Graphically, it is measured by the area above the factor supply curve and below the market price. Figure 12.20 shows an upward-sloping market supply curve for a factor F. At any price below OA, the quantity supplied is 0. OA is the minimum price necessary to induce any positive supply of this factor to this market. If the price rises to OB, the quantity supplied increases to OF,. The first unit of the factor would have been supplied at a price of OA, but it is receiving OB. The factor surplus for the first unit of the factor is the distance AB. At price OB all the units of the factors except the marginal unit would have been supplied at some price slightly below OB. Thus they are all receiving a factor surplus. The total factor surplus is equal to the area ABD. If the factor price increases to OC, even the marginal unit at F, experiences a factor surplus. The increase in factor surplus is the area BCED. When the supply curve of a factor is less than perfectly elastic, any shift in the factor demand curve can cause a change in factor surplus. One example of such a shift is the reduced demand for a factor caused by an excise tax on an increasing cost industry. In Figure 12.21 £>, is the factor demand curve in the absence of the excise tax. Quantity supplied is OF, and factor surplus is the area ACF. The excise tax on the product reduces the quantity demanded for that product. Industry output is re¬ duced and the demand for this factor is reduced to D2. Factor price and quantity

F per period Figure 12.20

Factor Surplus.

336

The Competitive Market System

Figure 12.21

Lost Factor Surplus and the Incidence of an Excise Tax.

both fall. At the new quantity of F2 factor surplus is the area ABE. Those units of the factor still employed in this industry have experienced a reduction in their factor surplus of BEGC. This is a measure of their part of the burden or incidence of this tax. In addition, FlF2 units of this factor are no longer employed in this industry. They are used in another industry, but at a lower price. As a consequence of the shift, they have lost factor surplus equal to the area EFG. This loss is a component of the dead weight or economic efficiency loss caused by the tax and described in Figure 11.11 in Chapter 11. The demand curve for a factor can be shifted by changes in the prices of other factor inputs that are complements or substitutes in production, and this can lead to changes in factor surplus. For example, assume that agricultural output is a function of the inputs of land, labor, and energy. Energy is required not only to operate farm equip¬ ment, but is a major ingredient in the production of pesticides and chemical fertilizers. There is evidence that labor and energy are substitutes in this production function.13 This means that an increase in the price of energy will lead to an increase in the quantity demanded of labor, other things equal. The sharp increases in the price of energy since 1972 have shifted out the demand curve for labor in the farm sector. If the supply curve of labor to a farming sector is less than perfectly elastic, farm workers will have benefited from the rising price of energy. This could be true even though consumers have lost welfare because of increases in food prices and landowners have lost because of reduced land rents.

'3See Michael Gisser and Keith Willett, Benefits of Resource Scarcity: A Case Study of the Farm Sector

Land Economics, May 1980, 56(2), 227-237.

337

Marginal Productivity and Factor Prices in Competition

Factor Surplus and the Economics of the Military Draft. At least in periods of peacetime, service in the military can be considered to be just another type of occupation subject to the same forces of supply and demand as other forms of work. In the 1950s and 1960s the U.S. government had to resort to conscrip¬ tion in order to obtain the desired number of workers for military service. This is evidence that the wage rate being paid to beginning military personnel was below the market equilibrium wage rate. Suppose that the military services decide that they need L2 entry level workers to staff the military service (see Figure 12.22). If the price of labor offered by the government is OA, then only L, workers will volunteer for military service.14 The remainder of the military service needs must be fulfilled by the draft.15 For a variety of reasons the government considered increasing the entry level pay for military service so that the military could be staffed with all volunteers. This step was actually taken in 1973. The major question was: How high would the price of military labor have to be in order to clear the market for military service? To answer this question, we need to know the shape of the supply curve of labor to the military. Empirical estimates of the supply curve of labor to the military suggested that the price of labor would have to be increased by approximately 25 percent in order to achieve the desired level of military manpower in peacetime. The position of the supply curve depends on the ratio of military pay to civilian earnings and the level of unem-

Figure 12.22

Factor Surplus and the Military Draft.

14The price of labor includes the monetary value of in-kind services such as housing, food, and training in specialized skills such as electronics. ‘'Actually, only a fraction of the L2L, short fall was drafted. The remainder enlisted in order to be assigned to the service of their choice rather than wind up in the army. These were termed “reluctant volunteers” and would not have volunteered in the absence of the threat of a draft.

338

The Competitive Market System

ployment in the civilian market. Higher unemployment and lower civilian earnings opportunities both tend to make military employment relatively more attractive at any given military pay rate. In 1970 dollars, military pay would have had to have been increased by approximately $700 per enlistee for a total additional budgetary cost of about $1.4 billion per year.16 This increase in the total wages of soldiers is the area ABCD in Figure 12.22. But as this figure makes clear, a very substantial portion, perhaps three-fourths of this amount, represents factor surpluses to inframarginal workers.

SOME APPLICATIONS Microeconomic Theory and Unemployment A major concern of microeconomics is the role of markets in allocating resources and in particular the role of price in bringing about the equality of the quantity demanded and the quantity supplied in a market. When markets are functioning properly, they will clear in the sense that there will be no excess demand or excess supply. Yet one of the most important markets in an economy, that for labor, seems often to be out of equilibrium, not to be clearing, and to have substantial excess supply. Why is this? The problem of unemployment is a major concern of macroeconomic theory. Macroeco¬ nomic models emphasize the role of the aggregate demand for output in determining the demand for labor. But there is a microeconomic dimension of the problem, too. Specifically, if the demand curve for labor shifts to the left, why does not the wage decrease in order to clear the market?17 Sustained disequilibrium in the labor market and excess supply or unemployment seem to require that wages be rigid; in other words, that there be some barrier that prevents wages from falling sufficiently to clear the market. What is it about labor markets that seems to prevent market clearing adjustments in wages when the demand for labor shifts to the left? Broadly speaking, there are two points of view. The first denies that this is an accurate description of the situation. The statistical measure of unemployment is based on a monthly survey of households. Those people in the survey who are not presently employed are asked if they have been actively seeking employment. If they answer yes,

16See Anthony C. Fisher, The Cost of the Draft and the Cost of Ending the Draft, American Economic Review June 1969, 59(3), 239-254; Benjamin P. Klotz, The Cost of Ending the Draft: Comment, American Economic Review, December 1970, 60(5), 970-978; and Anthony C. Fisher, The Cost of Ending the Draft- Reply American Economic Review, December 1970, 60(5), 979-983. ’ 1 "Actually, as macro models of the economy make clear, a decrease in the wage rate may not be sufficient to restore equilibrium in the labor market. A decrease in the wage rate means falling income and therefore falling demand for output. This means the demand for labor will shift farther to the left. However, if wages continue to fall, they may trigger another force that would halt the decrease in the demands for output and for labor. Falling wages also mean falling costs and prices. Falling prices increase the value of money balances and other financial assets that are denominated in dollars. The resulting increase in the real value of financial assets tends to increase the demand for consumption goods. This effect may eventually offset the impact of falling wages on consumption demands.

339

Marginal Productivity and Factor Prices in Competition

they are counted as unemployed. But this definition of unemployment need not be inconsistent with a situation of labor market equilibrium with no excess supply. The key question is whether those who are recorded in the survey as being unemployed would accept a job at the prevailing wage rate if it were offered, or have they, in effect, declined to work at the existing wage in the expectation or hope that they will sooner or later find a job at a higher wage. This latter situation is portrayed in Figure 12.23 where PLl is the going wage rate. L2L, additional individuals would work at a wage rate of PL2 if such jobs were offered. They may, in fact, be seeking jobs at that wage rate, thus satisfying the statistical definition of being unemployed. But they do not represent an excess supply of labor at the going wage rate. The second point of view takes for granted that those recorded as unemployed would accept work at the going wage rate. With the wage rate of Pu in Figure 12.24, L2 individuals wish to work but only L, are hired. And for some reason the wage does not fall to PL2 in order to clear the market. The existence of labor unions with long-term labor contracts explains sticky wages in the short run. But this does not explain why unions do not accept lower wages when new contracts are negotiated during periods of unemployment. The United Auto Workers’ agreement to forego an already negotiated wage increase from Chrysler Corporation in 1981 in order to stave off the bankruptcy of the firm is perhaps the exception that proves the point. What seems to be at work, according to this point of view, is a social convention against wage competition in slack labor markets. It is seen as just not fair for one individual to go to an employer and offer to take another worker’s place at a lower wage. But it is just this sort of behavior that is required if a market is to work competitively. Also, firms may implicitly agree to refrain from wage-cutting behavior as a means of attracting a higher quality labor force and maintaining worker morale. If this point of view is accepted, then it must be acknowledged that the competitive model is not completely applicable to labor markets. This conclusion has

Figure 12.23

The Labor Market in Equilibrium with Statistical Unemployment.

340

The Competitive Market System

implications for both micro and macro policy toward the functioning of labor mar¬ kets.18

Rents and Common Property Resources: The Fishery Natural resources such as forests and fisheries are like farmland in that they are productive. By that I mean that when labor and capital are applied to these natural resources, there is an output that can be sold. The receipts from the sale of output can exceed the expenditures on the variable inputs of labor and capital. Thus these natural resources are capable of producing a rent. But in some cases, such as fisheries, the institutional arrangements are such that no individual has a property right in that rent. And this has important implications for economic efficiency and the economic yield from the natural resource. A common property resource is a resource for which no private property rights have been established. As a consequence, anyone is free to use the resource without restric¬ tion or limit and without paying for that use. As will be seen, this feature of common property resources tends to lead to overuse and abuse, at least in an economic sense, if not in a physical sense. A classic example of a common property resource is an ocean fishery. In this section we examine the economic implications of open access to a common property resource such as a fishery. Consider a well-defined geographic and biological area such as a bay or fishing bank that supports a nonmigratory population of a commer¬ cially valuable fish species. The ocean bottom and its associated ecological system

'“For a more extensive discussion of these issues and a defense of the second or noncompetitive point of view, see Robert M. Solow, On Theories of Unemployment, American Economic Review, March 1980, 70(1),

341

Marginal Productivity and Factor Prices in Competition

constitute a fixed input into the production of caught fish. It is analogous to a fixed supply of farmland. For simplicity assume that this fishery resource is only one of a number of similarly situated resources so that changes in the quantity of fish caught from this resource are small relative to the total market for this fish species. Thus the price of fish can be taken as given in analyzing the economics of this resource. Finally, assume that capital in the form of boats and nets is combined in fixed proportions with labor in the activity of catching fish. This enables us to denote the variable input into the production of caught fish as “fishing effort.” One unit of fishing effort is one boat of a given size and capability combined with a specified number of fishermen. Given fixed prices of capital and labor, effort is supplied to the fishery at a fixed price of PE. Figure 12.25 shows the optimum level of effort in this fishery. The VMPE curve shows the value of marginal product for additional effort. The optimum level of effort is Ex where VMPE equals PE. The total value of fish caught is equal to the area OBCEx. If fishermen and boats are paid OACEx (which represents their opportunity cost), then the rent to the fishery resource would be the area ABC. Because this is a common property resource, there is no one with a property right in this rent. It accrues by default to the owners and operators of fishing boats. They receive a return over and above their opportunity cost. If the fishing industry is competitive with free entry, additional boats will enter in response to the return above opportunity cost. Entry will continue until the return per unit of effort is driven down to equal the opportunity cost of effort. In order to determine the open access equilib¬ rium, we need to introduce an additional variable. The return per unit of effort is also termed the value of average product (VAPE) and like the VMPE, it depends on the level of effort. The VAPE is the total revenue of the fishery divided by the units of effort applied. If the VMPE curve is linear, the VAPE curve is also linear with the same intercept and one half the slope (see Figure 12.26). The relationship between the value of average product and value of marginal product

Figure 12.25

The Value of Marginal Product of Effort and the Rent to a Fishery with the

Optimum Level of Effort.

342

The Competitive Market System

Effort per period Figure 12.26

The Equilibrium of an Open Access Fishery.

is the same as that between the average revenue and marginal revenue of output (see Chapter 8). In the new equilibrium, effort is increased to E2. At this point VAPE is equal to PE, and fishermen’s returns are just equal to opportunity cost. There is no incentive for further entry to the fishery. This equilibrium is inefficient. Too much effort is being applied. The additional effort (E2 — Ex) catches additional fish with a value equal to the area of E^CFE^ But the cost of this additional fish is the area E,CDE2. The area CDF is the excess of cost over additional revenue. It is also equal by construction to the area ABC, the potential rent under the optimal effort Elt19 The inefficiency takes the form of excess effort, which dissipates the potential rent from the natural resource. There are three possible approaches to eliminating the inefficiency associated with an open access, common property resource: vesting property rights, using fees or taxes, and direct regulation such as quotas on effort or on catch. If property rights to the fishery resource are vested in some individual or firm, it has an incentive to manage the resource so as to maximize the rent it receives. It could act in a manner similar to the landowner-farmer by hiring additional units of effort until the price of effort equals its value of marginal product. Or it could rent the resource to a fishing firm, which, since it strives to maximize profit, would also equate VMPE with PE. From the point of view of optimum management it does not matter whether the government gives away the property rights to the resource or auctions them off to the highest bidder. The only difference is one of the distribution of wealth. In fact, the government could retain the property rights for itself, returning the rents it receives to taxpayers in the form of tax decreases or increased provision of public services. The second approach involves the use of fees or taxes in an effort to restrict effort

19See Chapter 8.

343

Marginal Productivity and Factor Prices in Competition

to the optimum level. For example, if the government required each unit of effort to hold a license and charged a fee equal to the vertical distance CG in Figure 12.26 for each license, this would increase the cost of effort to fishermen. Some fishermen would find that their returns were less than the cost of effort and would exit the industry. Effort would be reduced to £„ the optimum level, and the government would collect license fees equal to the maximum potential rent from the fishery (GC X 0£\). Alternatively, the government could make available OF, licenses and auction them to the highest bidders. Fishermen would be willing to pay an amount up to the maximum profit per boat given the effort level of Ex. Again, this is the vertical distance CG. The government would collect this amount in the form of rent. An appropriate tax per unit of fish caught would have the same effect. It would lower the net return to the fishing effort. Fishermen would exit the fishery until the net return were equal to the opportunity cost of effort. This tax would yield revenue equal to the amount of the potential rent from the fishery. Fishermen could not pass the tax forward to consumers of fish products. By assumption, this fishery is very small relative to the total market for fish. So as fishermen reduce effort and the catch from this fishery is reduced, there is no effect on the price of fish in the market. Finally, the government could use administrative or regulatory means to reduce effort to the optimum level. If £\ licenses were made available and allocated to fisher¬ men on some basis, entry would automatically be restricted to the optimum level. The main difference between this approach and auctioning permits is in who retains the rent to the resource. The practical difficulty with this approach is political. The permits have an economic value. There are not enough to go around to all fishermen who would wish to receive them. Some politically acceptable means for allocating the limited permits must be developed. An alternative regulatory approach is to allow the existing number of boats (equiva¬ lent to an effort of E2) but to restrict their activity by either imposing a quota on fish caught per period of time or restricting their activity, for example, to a maximum of, say, three days per week. This would reduce catch to the optimum level. It does not, however, do so by decreasing the quantity of resources devoted to the fishery. Rather, it does so by decreasing the efficiency with which they are used. Under this form of regulation the rent is dissipated into excess capacity and inefficient resource utilization in the fishery. This application attempts to illustrate two important points: (1) the key roles of rent and property rights in achieving an efficient allocation of resources where land and natural resources are concerned and (2) the variety of possible institutional arrange¬ ments that could be used to correct for the economic inefficiencies associated with the open access common property resource.

Rents and Nonrenewable Resources The productive services of a natural resource such as land or a fishery can at least as a first approximation be represented as a flow per unit of time. But this is not the case with nonrenewable resources such as a deposit of coal or iron. In these cases the total

344

The Competitive Market System

quantity of the resource in the ground is not augmentable. Each unit of the resource harvested or extracted diminishes the remaining stock of the resource. There is no flow of output from the resource that can be maintained for an indefinite time period. This leads to some interesting questions about the determination of resource prices and optimum extraction over time. But these are beyond the scope of this chapter. Our purpose here is simply to show how the concept of rent is modified in the case of nonrenewable resources and how some of the conclusions about the incidence of taxes on rent must be altered. The rent per unit of a nonrenewable resource is equal to the price at which the resource is sold after extraction minus its extraction cost. This rent is not a flow of payments over time as in the case of the rent per period of use for land. Rather, it is a one-time payment that is realized at the time the unit of the resource is extracted from the ground. Unlike a tax on land rent, a tax on the rent of a nonrenewable resource can affect the supply and can be shifted forward to consumers in the form of higher prices. One form of tax on the rent of a nonrenewable resource is known as a severance tax. It is imposed at the time the resource is extracted or severed from the ground. If the severance tax is a fixed amount per unit of the resource, the tax can be avoided or at least postponed by delaying the date of extraction of the resource. If the market price of the resource is higher at a later date, but the severance tax per unit has not increased, the resource owner will receive a higher net rent (i.e., net of tax) by delaying extraction! Delay of extraction is profitable to the resource owner as long as the rent net of tax has increased by more than the rate of interest. If resource owners tend to delay extraction to postpone the payment of the severance tax, the reduced supply tends to push up today s price, thus shifting part of the burden of the severance tax on to consumers of the resource. One determinant of the extent to which the severance tax can be shifted forward is the elasticity of the derived demand curve for the resource that is faced by producers in the taxing jurisdiction. The elasticity of demand depends in part on the size of the taxing jurisdiction relative to the overall market for the resource. At one extreme, if the taxing jurisdiction has only a very few small producers, the demand curve faced by the producers would be infinitely elastic. Any reduction in current output by producers would have no effect on the price of the resource. The severance tax would come out of the rents to owners of the resource. Suppose that one small county in West Virginia imposed a severance tax on coal mined within its boundaries. Figure 12.27 shows the supply curve and infinitely elastic demand curve faced by local coal producers. The upward-sloping supply curve repre¬ sents the diminishing marginal productivity of capital and labor applied to the fixed stock of the resource in the ground. With no severance tax the quantity supplied is C, and rents to mine owners are equal to the area ABE. A severance tax of t per unit of coal shifts the supply curve up to Sct. Because the demand curve to the firm is horizontal, there is no change in price. The quantity supplied is reduced to C2 and rents fall to FBH. The severance tax revenue is paid entirely by resource owners. On the other hand, if a severance tax is imposed on all the producers in the market,

345

Marginal Productivity and Factor Prices in Competition

Figure 12.27

The Incidence of a Severance Tax with Infinitely Elastic Demand.

the relevant demand curve is the market demand curve for the resource. As shown in Figure 12.28, the tax shifts the supply curve up to the left. It intersects the demand curve at a higher price and lower quantity. Total tax revenue is equal to the area ABEF. Of this, consumers pay EFGH through the higher price for coal. But resource owners’ rents are reduced. Their portion of the tax revenue is equal to the area ABHG. This analysis of the incidence of a severance tax is helpful in explaining the motiva¬ tion behind two bills that were introduced in Congress in 1980. These bills would have placed ceilings on the amount of severance taxes that individual states could levy on coal mined within their boundaries. These bills were aimed primarily at the states of

Figure 12.28

The Incidence of a Severance Tax with Downward Sloping Demand.

346

The Competitive Market System

Montana and Wyoming, which between them control some two-thirds of the low sulphur coal in the United States. Being large suppliers of coal to the U.S. market, these two states face relatively inelastic demand curves for their product. Any severance taxes that they impose will tend to push up the price of coal. Because much of this coal is sold to utilities in other states, the severance tax is in part a mechanism to tax residents of other states. A limit on severance taxes would benefit the consumer of electricity in the populous midwestern states that rely on western coal as their source of fuel. It would also benefit the owners of coal deposits in Montana and Wyoming. The losers would be the citizens of these two states. The incidence of a severance tax can be affected by developments outside the state in question. Historically, Texas and Oklahoma have been major suppliers of crude oil to the U.S. economy. When those states imposed severance taxes on crude oil, part of the tax fell on resource owners within the state, but part of it was shifted forward to oil consumers in the rest of the nation. However, the development of the Organization of Petroleum Exporting Countries (OPEC) oil cartel altered the demand curves faced by the major oil-producing states in the United States. This is because OPEC was supplying more than one-third of all the oil consumed in this country. Figure 12.29 shows the domestic demand curve for oil in the United States, the domestic supply curve in the absence of a severance tax, and the OPEC price. Domestic producers cannot charge a price above POPEC because buyers would turn to OPEC. And it is not to their interest for producers to sell below POPEC. Thus domestic suppliers face a perfectly elastic demand curve in the U.S. market. This demand curve intersects the domestic supply curve at X,. Domestic production is at Xu whereas domestic demand is at X2. The difference is supplied by OPEC. The rents to domestic suppliers in the

Oil per period Figure 12.29

The Effect of a Severance Tax on the Price of Oil and Resource Rent.

347

Marginal Productivity and Factor Prices in Competition

absence of the severance tax are the area above the supply curve and below the OPEC price, ABE. If the severance tax is imposed, it shifts the domestic supply curve upward to Sus + T. The severance tax can have no etfect on the price of oil. But it lessens the incentives for domestic production and reduces the rents to resource owners to BCF20. The creation of OPEC has altered the incidence of the severance taxes imposed by in these two states. Whether this will lead to changes in the tax remains to be seen.

MARGINAL PRODUCTIVITY THEORY: AN EVALUATION As Positive Theory Marginal productivity theory is basically a theory of the demand for factor services. It is just one part of a demand/supply framework for analyzing the determination of factor prices. But we have seen that if markets are competitive, factors are mobile, and it is possible to make substitutions among factors in production, then each factor owner will receive prices for her factor services of labor, capital, and land, which are equal to the values of their marginal products in each activity. This conclusion can be evaluated in terms of both its positive and normative analytical implications. As for positive analysis, we have shown that marginal productivity theory is the basis for the hypothesis that factor demand curves are downward sloping.21 Also, it identifies other arguments in the demand function that can shift the factor demand curves. Marginal productivity theory is thus one component of the supply and demand model of factor price determination. This model has been shown to be useful for making comparative static predictions in a variety of situations, for example, on the effects of income taxes and severance taxes, on the effects of alternative welfare systems, and for explaining things such as the pattern of urban land rents and the effects of alternative property rights structures. To the extent that these comparative static predictions are not refuted by empirical observations, the theory finds support in the evidence. The principal conclusion that factor prices equal their values of marginal product is difficult to test directly. This is because a factor’s value of marginal product is typically not directly observable. In fact, some lines of empirical research proceed by assuming the validity of the theory and by using factor price (which is observable) as a proxy or indirect measure of the unobserved value of marginal productivity. For example, we observe the tendency for wages to be higher for individuals with higher educational attainment. We take this as evidence that education enhances productivity. But if wages do not in fact equal VMP’s, then the inference that education enhances productivity is not valid. The value of marginal product is in principle observable. What is required is an

20See Stephen L. McDonald, The Incidence of an American Oil Severance Tax Under World Pricing by OPEC: A Note, Natural Resources Journal, July 1980, 20(3), 547-550. 21Actually, marginal productivity theory is a sufficient but not necessary condition for downward-sloping demand curves. Other unspecified models might also lead to the same deduction.

348

The Competitive Market System

estimate of the production function, because the VMP is simply the marginal physical product multiplied by product price. At least two authors have attempted to compare estimates of values of marginal products derived from production functions with ob¬ served factor prices. Lester Thurow assumed that the aggregate production function for the United States was of the Cobb—Douglas form and estimated the parameters of this function from time-series data on inputs and output.22 He found that the estimated VMP of labor was greater than the average earnings of workers, whereas the estimated VMP of capital was less than the average return to capital. Peter Gottschalk compared computed values of marginal product and labor prices for eight categories of labor by estimating Cobb-Douglas production functions for various manufacturing industries. His source of data was observations of inputs and outputs by states in the United States in 1958. He used his estimates of the production functions to compute the VMP's for capital and for each occupational category of labor and compared these to earnings for each occupation. Like Thurow, he found that capital earnings were greater than the VMP of capital. And he found substantial deferences between the estimated VMP's and wages. For example, people in the occu¬ pations of managers and sales were paid prices that were more than twice their es¬ timated value of marginal product, whereas workers in the categories of craftsmen, operatives, and service were paid less than half their estimated VMP's.23 There are two possible explanations. Either marginal productivity theory is wrong or the observations are wrong, that is, the VMP's have been measured incorrectly. The theory finds the equality of VMP s and factor prices to be a logical conclusion of profit-maximizing behavior in competitive markets that are in equilibrium. If the theory is correct but the forces moving markets toward equilibrium are weak or moving slowly, observed VMP’s could be different from factor prices in a dynamic and chang¬ ing economy.24 If firm managers only satisficed, or if they pursued other objectives besides profit, we need not expect to find VMP’s equal to factor price. And as will be shown in Chapter 15, if markets are not competitive, VMP's will exceed factor prices reflecting monopoly and/or monopsony exploitation. Thurlow’s finding that labor’s wage was less its VMP might be explained by the existence of market power in the U.S. economy. And because economic profits and payments to capital were lumped together in the measure of returns to capital used by Thurow, the market power hypothesis is also consistent with his finding that capital is paid more than its VMP. In order to accept Thurow’s and Gottschalk’s estimated VMP’s as being accurate, one must assume that the Cobb-Douglas production function is an actual representa¬ tion of the underlying production technology. If the true production function is not of the Cobb-Douglas form, then efforts to fit the data to a Cobb-Douglas function will lead to biased and inaccurate estimates of the VMP’s. And the fact that the observed

22Lf*er Thur™’ Disequilibrium and the Marginal Productivity of Capital and Labor, Review of Economics and Statistics, February 1968, 50(1), 23-31. 23

Peter T. GomchaHc, A Comparison of Marginal Productivity and Earnings by Occupation, Industrial and Labor Relations Review, April 1978, 31(3), 368-378.

24Thurow, Disequilibrium.

349

Marginal Productivity and Factor Prices in Competition

VMP's do not equal factor prices cannot be taken as a refutation of marginal productiv¬ ity theory. In summary, efforts to test marginal productivity theory directly by comparing estimates of VMP's with factor prices have not supported the theory. But the existing studies do not permit us to say whether that is because the VMP's have not been correctly measured, or because the theory is wrong.

As Normative Analysis At the normative level the question is whether the factor prices that are determined according to marginal productivity theory lead to a just distribution of income. It is sometimes suggested that because workers and the owners of other factors of produc¬ tion are paid prices that reflect their contribution at the margin to output, the resulting income distribution is fair in some sense. But there are two reasons for rejecting this line of reasoning. First, the distribution of income is not determined by marginal productivity alone. The size distribution of income depends also on the size distribution of ownership of nonhuman productive resources such as land and capital and on the distribution of abilities and skills across people. Marginal productivity theory does not shed any light on the determinants of the distribution of skills and factor ownership. Thus, it cannot be used to justify the resulting distribution of income. Second, an assertion that factor prices are fair to factor owners because they reflect factor productivities seems to imply that factor productivities are intrinsic characteris¬ tics of factors. But this is not the case. A worker’s value of marginal product depends only to a limited extent on his own ability and training. Production theory tells us that the value of marginal product of labor also relies on the quantities of other factors used in the production process, the underlying technology, the demand and price of the output, and the number of other workers of similar skills who are being utilized in the production of that good. Because all these other influences on marginal productivity can change, an individual worker’s value of marginal product can be influenced by a number of forces that are beyond the control of the individual and which do not seem to be relevant to common notions of equity, fairness, or justice. Thus at the normative level, marginal productivity theory, if true, cannot be used to draw any conclusions about the fairness of the resulting distribution of income.

SUMMARY A profit-maximizing firm chooses the levels of factor inputs so that each factor s marginal revenue product is equal to the factor price. For firms operating in a competi¬ tive market for their product, price is given to the firm. Thus the firm’s marginal revenue product for a factor is equal to the value of marginal product for that factor. The firm’s demand curve for a factor shows the quantity demanded as a function of factor price. In the short run the firm’s demand curve for the variable input is the value

350

The Competitive Market System

of marginal product curve for that input. In the long run with all inputs variable the firm’s demand curve for an input reflects the effects of changes in all inputs and in output in response to a change in factor price. The industry demand curve for a factor input also reflects the effect of changes in industry output on product price. The industry demand curve is, therefore, less elastic than the firms’ demand curves. The prices of factors of production are determined by the intersection of factor demand curves and factor supply curves. An individual’s supply curve for labor can be derived from an analysis of the individual’s preferences for leisure and income. An individual may respond to an increase in the price of labor by either increasing or decreasing her supply of labor, depending on the relative strengths of the substitution and income effects on the amount of leisure taken. The model of individual labor supply can be used to analyze the effects of income taxes and alternative welfare systems on the incentives to work. The returns to factors in perfectly inelastic supply are called rents. Quasi-rents are returns to factors that are in inelastic supply in the short run. Factors whose market supply curves are less than perfectly elastic can earn factor surpluses, that is, payments in excess of the minimum amount necessary to induce factor supply. The marginal productivity theory is basically a theory of the demand for factors. Its value in positive analysis depends on the validity of the predictions of the model. The conclusion that in competition factors of production are paid prices equal to the value of their marginal product cannot be used as an ethical justification of the competitive market equilibrium. The equality of factor prices and values of marginal product is a necessary condition for the efficient allocation of resources. But there is no justification for claiming that factors are being paid what they deserve.

KEY CONCEPTS Marginal revenue product Value of marginal product Firm’s demand curve for an input Industry demand curve for an input

Individual’s supply curve of labor Pure rent Quasi-rent Factor surplus

QUESTIONS AND PROBLEMS For Basic Review 1. 2.

Define and explain the economic significance of each of the key concepts. Explain the derivation of the demand curve for a factor input for a competitive firm. Distinguish between the cases where this input is the only variable input and where it is one of several. How would the demand curve shift with a change in product price?

3.

Explain the derivation of the industry demand curve for a factor of production

351

Marginal Productivity and Factor Prices in Competition

when there are several variable inputs and the industry sells its output in a competitive market. Be specific about the relationship between the marginal physical product curve and the industry demand curve for the input. 4. * Use indifference curves to analyze the effect of a tax on wages on the supply of labor. What factors determine whether the effect will be positive or negative? 5. Consider the agricultural industry where land is the fixed factor and labor is a variable factor at a fixed wage. Graphically show the equilibrium and the returns to land and labor. Alternatively, consider a fishery where the ocean bottom and associated ecosystem is the fixed factor. Show the equilibrium and the returns to “land/ocean” and labor. 6* Draw the indifference curve map of an individual for whom work (as opposed to leisure) is a good rather than a bad, at least up to some point. Does this case lead to any different conclusions about the individual’s supply curve of labor? 7. Draw the indifference curve maps that correspond to the individual labor supply curves shown in Figures 12.7(a) and 12.7(h). 8. Draw the budget line for an individual who can sell labor at a fixed wage up to some maximum amount, say, 40 hours per week, and for whom the wage rate doubles for overtime worked beyond the maximum. How does double time for overtime affect the supply of labor? 9. * Draw the budget line for an individual who faces a progressive income tax, that is, one in which the percentage tax rate increases at higher money income levels. How does the institution of a progressive income tax affect labor supply?

Problem 1.* Suppose that there are 1000 of each of three types of farm. The farms produce wheat that is sold at a given price of $2 per bushel. The marginal product schedules of each type of farm are as follows: Marginal product of labor type of farm (in bushels)

Laborers per farm per year

1 2 3 4 5 6

A 19 17 15 13 11 9

B 15 13 11 9 7 5

C 10 6 2 — — —

(a) There are 5000 laborers who have no alternative employment; that is, the

supply of labor to these forms is completely inelastic. Show how market

352

The Competitive Market System

forces (assume competition) will allocate these laborers among the 3000 farms. Determine the wage rate per year for all workers and the rent per year for each type of farm. (b) Do the same when there are 8500 laborers. (c) Explain why rents per farm are higher and wages are lower in part b. (d) Explain why rents per farm are higher for type A farms.

For Discussion 1.

It has been observed that the hourly parking rate for outdoor parking in downtown center city parking lots varies widely among U.S. cities. Why? Outline a theory that will explain this variation among cities. This same theory should also be capable of explaining the parking rate differentials within urban areas. Does your theory do this?

2* If all farmers rent their land from landlords, who gets the benefits of agricultural price-support programs? Explain. 3.

Is it true that when all markets are competitive, factors of production are paid at a rate equal to their value of marginal product? Explain. What implication does your analysis have for the fairness or justness of the distribution of income resulting from perfect competition?

4. *

Between 1973 and 1979 OPEC engineered a ten-fold increase in the price of their oil sold to the United States. Other things equal, what do you think would be the effect of this exogeneous increase in the price of imported oil on: the rents received by owners of domestic oil deposits, of coal deposits, of agricultural farmland, of forest land; the relative prices of labor and capital; the functional distribution of income?

5.

Rents received by landowners are perceived by some people to be “unearned income. From an economic point of view, it does not matter who receives the rents (landowner, government through taxation, etc.); but the rents must be paid to someone to prevent economic inefficiency and misallocation of resources. Discuss.

SUPPLEMENTARY READINGS Blaug, Mark. The Methodology of Economics. Cambridge, England: Cambridge Uni¬ versity Press, 1980, Chapter 9. Ferguson, Charles E. The Neoclassical Theory of Production and Distribution. Cam¬ bridge, England: Cambridge University Press, 1969, Chapters 8, 12. Stigler, George J. The Theory of Price (3rd ed.). New York: Macmilkn, 1966, Chapters

CHAPTER 13 Capital Markets: Saving, Investment, and Allocation Over Time

In this chapter the main objective is to develop a model that explains the interest rate as a price that is determined in a market for loanable funds. The suppliers of funds to this market are households that are savers, that is, whose consumption is less than current income. By saving, these households are increasing their wealth and their future consumption possibilities. The demanders in this market are the builders of capital machines. They must borrow funds to finance the construction of capital equipment. They repay the loans from the proceeds of the sale of the services of the capital equipment over its useful life. In the course of building this model we will develop several analytical tools and concepts such as present value and discounting. These tools constitute a framework for dealing with questions of optimal resource allocation over time. The second objective of this chapter is to illustrate how these tools can be applied to questions such as the determination of asset prices, public investment decision making, and the optimal rate of extraction of a nonrenewable resource.

WHAT IS CAPITAL? There are three important defining characteristics of capital. 1. Capital is durable. It yields its services over a significant period of time. So time plays a key role in the economic analysis of capital. 2. Capital is an input in the production of goods and services. Or more accurately, it is the services or the use of capital that is absorbed in production. The value of capital lies in the productivity of its services over its lifetime. 353

354

The Competitive Market System

3. Capital is itself produced; that is, it is an output from a production process. Therefore the creation of a piece of capital has a cost. Its cost is the value of the other goods and services foregone to make available the labor, resources, and so on for the production of capital.

Examples of things that are capital include computers, steel mills, turret lathes, and airplanes. Refrigerators, stoves, and television sets are forms of capital because they are durable and are used in the household production of meals and entertainment. Land in its original, unimproved state is durable and provides services over time, but it is not capital because it is not itself an output of a production process. Land is not reproduci¬ ble by human productive activity. But improvements to land, such as roads, drainage ditches, and buildings, are forms of capital. As these examples suggest, capital is a heterogenous mixture of things. For purposes of simple analysis and discussion, however, it is useful to assume that capital is homoge¬ neous. Although this assumption is unrealistic and glosses over some important concep¬ tual and empirical problems, it will be used throughout this chapter.1 The boundary line between what is and what is not capital is not always clear. Some things have one or more of the defining characteristics of capital but do not fit the definition precisely. One example is the deposit of a mineral or fuel in the ground. These substances when extracted become inputs in production processes. Where deposits are durable, it typically is not practical to extract all the resource in one period of time. Thus the resource yields its services over time. The concepts of present value, discount¬ ing, and the interest rate play important roles in understanding how such natural resources will be used in a market economy and how they should be used in order to maximize economic welfare. But these deposits are not capital because they are not themselves the output of a production process. When people defer their entry into the labor force in order to continue their educa¬ tion and training, they are incurring costs in the form of foregone earnings and tuition, but they are also increasing their productivity. This greater productivity leads to higher earnings in future years as the individual supplies labor to production. Thus this activity has the characteristics of capital-it has durability, it is an input into production, it provides services over time, and it is produced by economic activity. In fact, this activity has come to be called investment in human capital. The characteristics that distinguish human capital from nonhuman or physical capital are the fact that it is not tangible and cannot be separated from the labor service in which it is embodied. Thus human capital cannot be bought or sold in a market; and it is not always easy to separate that part of an individual’s wages that represents returns to human capital from the payment for labor services. For these reasons the economic analysis of human capital must often proceed along different lines from the analysis of physical capital. This chapter is primarily about the economics of physical capital. But many of the concepts such as discounting, and investment criteria apply equally well to human capital

'Recall the discussion of Chapter 3.

355

Capital Markets: Saving, Investment, and Allocation Over Time

THE ARITHMETIC OF CAPITAL AND TIME Perhaps the single most important concept in the analysis of capital is present value.

Definition: The present value of an asset is the maximum amount a rational person would pay to obtain the right to the stream of future monetary returns from that asset. The present value depends on the magnitude and time pattern of the stream of mone¬ tary returns. It also depends on the interest rate, r, since r represents the alternative returns to investing money. Suppose a person offers to sell you an IOU, a certificate that promises to pay you $110 one year from this date. How much would you be willing to pay for this IOU? In order to answer this question, you need to know the market rate of interest that reflects alternative investment opportunities for you. Suppose the interest rate is 10 percent per year. Then the maximum amount that you should be willing to pay for the IOU is $100. If you paid this sum, you would be just as well off as if you had invested the $100 at the market rate of interest and received $110 one year from now (the $100 principal plus $10 in interest). If you could purchase the IOU for $90, this would be a good deal, because if you invested that $90 at 10 percent, you would get back only $99 instead of the $110 the IOU would produce after one year. You should not be willing to pay a sum higher than $100, say, $105, because if you invested that sum at 10 percent, you would get back $115.50 after one year, which is more than you would get from the IOU. In this simple case the formula for calculating the present value is

1 + r

where PV is present value, Rx is the future sum, the subscript indicates the year in which the sum is received, and r is the market interest rate. To verify the formula, rearrange it to obtain PV( 1 + r) = PV + rPV = R,

This shows that the present value is the sum that when invested at r returns principal plus interest equal to R u If the future sum is not to be returned until two years from the present date, the present value formula is

(1 + ry

Rearranging gives PV( 1 + r) (1 + r) = R2

This says that if the present value is invested for one year and the principal plus interest

356

The Competitive Market System

is reinvested for a second year, the result is just equal to the sum to be received two years from now. If the IOU specifies two payments at two different dates, the present value of the IOU is the sum of the present values of its individual components. For example, if the IOU specifies the payment of R, after one year and R 2 after two years, the present value is PV =

R'

+ — (1 +

r)

(1 +

ry

Generalizing the present value of any stream of payments to be received over the next n years is given by n

R,

2

PV

i—I

(13.1)

(1 + ry

In the special case where all the R ’s are equal and the stream of receipts goes on forever oo), this reduces to2

(n =

The present value of any stream is sensitive to the interest rate used in its calculation. Because the interest rate enters into the formula in exponential form, this sensitivity is more pronounced for time streams that extend farther into the future. The higher the interest iate is, other things equal, the lower is the present value of any given stream of payments. To see this, suppose there were a stream of equal annual payments of SI 000 lasting for fifty years. The second column of Table 13.1 shows the present value of that stream for each of six alternative interest rates. The third column of the table shows the present value of the single payment to be received in the 50th year, that is, R so/(1 + r)50. The last column of Table 13.1 indicates the present values of an infinite stream of $1000 per year at six alternative discount rates.

2This is the sum of an infinite series of the following form: OO

PV =

R

2 =1(i +

— where

k

=

1 i+ -L- +^_ + . . . + 1 + r (1 + r)2 (1 + ry R [1 + k + k2 + • • • + k' + . . .] — R

= R ry

- R

< 1 1 + r

As any algebra text will show, the infinite series in the brackets is equal to 1/(1 -

1

PV = R

=

- R

R

- R 1 +

R r

r

k).

By substitution:

357

Capital Markets: Saving, Investment, and Allocation Over Time

Table 13.1. Present Values of Streams of $ 1000/Year Payments Under Different Interest Rates and Lengths of Streams

%

Present value of 50-yr. stream

Present value of $1000 in 50 years

Present value of infinite stream

0 2 5 10 15 20

$50,000 31,424 18,256 9,915 6,661 4,999

$1000.00 371.53 87.20 8.52 .92 .11

Infinite $50,000 20,000 10,000 6,667 5,000

The present value of a stream can sometimes be more easily interpreted and com¬ pared with other magnitudes if it is expressed as an annual equivalent flow. Definition: For any stream of uneven payments over a given time period n, the annual equivalent is that equal annual payment over the same number of years that has the same present value. Specifically, for a stream of Rt the annual equivalent, R , is found by solving the following definitional expression for R : n

R

1 1 = 1 (1 + r)1

-

=

n R; 1 i = 1 (1 + ry

If the present value has been computed, the annual equivalent is given by R = PV-

r(1 + r)n

(1 + ry - 1

(13.2)

If n is infinite, this reduces to R = r ■ PV

The annual equivalent is often used to express the cost of an initial investment in annual terms for comparison with revenues. The annual equivalent of a cost C can be calculated by substituting C for PV in Equation 13.2. The annual equivalent of a cost is also sensitive to the interest rate. For any given cost the higher the interest rate is, the larger is the annual equivalent. For example, if the cost is one million dollars, the 50-year annual equivalent flow at alternative interest rates are: Interest rate 0 2 5 10 15 20

Annual equivalent flow $ 20,000 31,823 54,777 100,859 150,139 200,022

358

The Competitive Market System

An investment project typically is characterized by a large initial payment, which we will denote C0, followed by a stream of returns, RThe net present value of such an investment project is the present value of the total stream of payments and receipts where payments are entered into the formula with a minus sign. Another way to characterize an investment project of this sort is by its internal rate of return. Definition: The internal rate of return of an investment project is the discount rate r*, which would make the computed net present value of the project equal to 0. It is computed by solving the following expression for r*: n R - C„ + 2 -- = 0 '■ = ' (1 + r*y

For example, if C0 is

$200, Ri = $110, and R2 = $121, the internal rate of return

R1

-C0 +

1 -

200

+

1

+

r* 110

+

r*

+

=

0

(1 + r*)2 121

+ - = 0 (1

+

r*)2

r * _ 10% Another way to interpret the internal rate of return is as follows. If the initial cost were borrowed at a rate of interest equal to the internal rate of return, the stream of receipts over the life of the project would be just sufficient to make the interest payments and retire the principal of the loan by the end of the project life.

THE PRESENT VALUE CRITERION FOR INVESTMENT Suppose that an individual is considering the simplest sort of investment question, whether or not to undertake an investment in a single project. Suppose that the individual can borrow or lend money freely at the market interest rate, r. The answer to the investment question is straightforward. The individual will make a profit by undertaking this investment if its net present value calculated at the market rate of interest is greater than 0. The rule gives the correct answer either when the individual has the funds and is considering whether to invest in this project or to lend at the market rate of interest or when she must borrow at the market rate of interest to undertake this project. Assume that the cost of the project is $100. Further, assume that it is known with certainty that the project will have a return in year 1 of $115.5 and returns of 0 thereafter. If the interest rate is 10 percent, the net^ present value is

359

Capital Markets: Saving, Investment, and Allocation Over Time

1.1 = $5

The project should be undertaken. If the individual has the funds and lends them at the market rate of interest, she will have $110 at the end of one year but this project returns $115.5 at the end of a year, making it more attractive. The present value of the extra return in this project is $5, as the preceding calculation shows. If the individual must borrow the funds, she would have to pay back $110 at the end of one year. But the project return of $115.5 enables her to repay the loan in full, including interest and still retain a profit for her trouble. An alternative formulation of the net present value criterion commonly used by economists who analyze government investment projects is to compute separately the present values of the benefits and the costs and form the ratio, PVB/PVC. If this benefit-cost ratio is greater than 1, this implies that the net present value is greater than 0 and the project should be undertaken according to the net present value criterion. If there are two alternative but mutually exclusive investment projects, the rational individual will choose the one with the higher net present value. The two projects might be mutually exclusive if there were alternative ways of developing the same physical site or alternative ways of providing some service. For example, suppose that a parcel of land can be developed for either a low-density residential use or a commercial use such as a shopping center. Suppose that the present values of the costs and benefits of the two alternatives are as follows: Residential

Commercial

PVB = $3 million PVC = $1 million

PVR = $15 million PVc = $10 million

The commercial development alternative has the higher net present value, five million dollars compared to the two million dollars for the residential development. But its benefit-cost ratio ($15/$ 10 = 1.5) is less than that of the residential alternative ($3/$l = 3). As long as the funds are available or can be borrowed to undertake the larger commercial development, it is to be preferred. This example shows that the benefit-cost ratio can be misleading because it does not take into account differences in the overall size or scale of the alternative, mutually exclusive projects. For another example, consider an individual who must choose between purchasing a standard car and a car that is twice as durable but is alike in all other respects and costs twice as much. Should the more durable car be purchased? Assume that the utility from the car, maintenance costs, operating cost, and so on are identical for both cars. Further, assume that if the less durable car is purchased, it can be replaced after its useful life with another identical car at the same price. Because both types of cars provide the same utility, and so on, the present values of the benefits for both types of car are equal. Thus we can focus only on costs. The

360

The Competitive Market System

question is which alternative minimizes the present value of the cost of automobile ownership. For simplicity assume that the less durable car lasts one year and the more dur¬ able car lasts two years. If C is the cost of the less durable car, the present value of the costs is C (1 + r)

The present value of the cost of the durable alternative is

Since the term, 1/(1 -f r), is less than 1, the more durable car has a higher present value of its cost stream. Thus it is a more expensive way of purchasing the specified stream of services. The individual would be better off by purchasing the less durable car now for C while investing C at the market rate of interest (total initial expenditure is 2C). After one year the individual receives (1 + r)C from her investment and spends C on a second new car. She is better off by the interest earned on the investment during the first year. In general, rational investors strive to maximize the aggregate net present value of their stream of investment returns. If there are no limits on borrowing or lending at the market interest rate, investors should undertake all investment alternatives that have net present values greater than 0. If there are limits on the amount that can be borrowed and the sum of the available investment alternatives exceeds the available funds including what can be borrowed, this simple rule breaks down and more complex rules and forms of analysis must be undertaken. But these problems are beyond the scope of this text.3 The internal rate of return can sometimes be used as an alternative investment criterion. According to this criterion, an investment project should be undertaken if its internal rate of return is greater than the market rate of interest at which funds can be borrowed or lent. In most instances where there is no limit on the borrowing of funds, the internal rate of return and net present value criteria will give the same answer for any project or any comparison among projects. However, there are instances where these two criteria will give different answers to any particular investment question. In such cases the net present value rule is superior. The internal rate of return rule may be convenient, but it is not totally reliable.4

’See, for example, William J. Baumol, Economic Theory and Operations Analysis (4th ed.), Englewood Cliffs: Prentice-Hall, 1977, Chapter 25.

“Ibid.

361

Capital Markets: Saving, Investment, and Allocation Over Time

The Present Value Criterion and Resource Extraction: An Application The present value criterion is used by owners of stocks of nonrenewable resources such as minerals or fuels as they decide how much of the stock to extract and sell in any given period. If 1 unit of the resource is extracted and sold now, its owner receives a net rent equal to the market price of the resource minus its extraction costs. Let the net rent be denoted by N. If the resource owner decides not to extract that unit of the resource now, this decision is analogous to an investment decision. The resource owner should hold the resource in the ground for future sale only if she expects the present value of the future net rent to be greater than the present net rent received from immediate extraction. Assuming extraction costs are constant, this means that resource owners will hold some of their resource in the ground for future extraction and sale only if they expect the future price of the resource to rise. In fact, if leaving some of the resource in the ground is to be a profitable decision, the future price must rise sufficiently to make the net rent in succeeding periods grow at the rate of at least r percent per year, where r is the market rate of interest. Holding some of the resource in the ground for one year is profitable only if the present value of the future net rent is expected to be equal to or greater than the present net rent; that is,

1 + r Actually, if the inequality prevailed, it would not be profitable to extract any of the resource in the present; so we write

1 + r or N t + \ — (1 + r)N t If the net rent is not expected to grow at this rate, resource owners would find it more profitable to extract all their resources now and invest the proceeds at the going market rate of interest. But this would tend to depress present resource prices and net rents while increasing expected future resource prices and net rents. Similarly, if none of the resource were extracted now, this would raise present resource prices and potential rents while decreasing future prices and net rents. This would encourage some resource owners to extract some of their resource in the present period.

THE MARKET FOR LOANABLE FUNDS So far we have taken the stock of capital machines as essentially given. The services of these machines contribute to production and have a value of marginal product. Their owners are paid a price equal to the value of the marginal product of these services. The total stock of the machines in existence may change in the long run. But we have

362

The Competitive Market System

not examined how or why changes in the capital stock take place. We are now in a position to do so. Let us assume now that there are firms in existence whose sole purpose is to build and rent capital machines. In real life many firms both build capital machines and use them in producing other goods and services. But this assumption allows us to distinguish clearly between the separate economic functions of capital formation and the production of goods and services consumed by individuals. If a firm that is in the business of building capital wishes to build a new machine, it must borrow the funds now to pay for the labor and other factor inputs used to build the machine. The firm hopes to repay the loan including interest out of the receipts from selling the services of the machine. These firms constitute a source of demand in the market for loanable funds. We will analyze the determinants of this demand in greater detail later. The major source of supply of loanable funds is households that are consuming less than their current income. We will analyze households’ role in the market for loanable funds under two alternative assumptions. First, we will assume that there are no firms building capital machines. According to this assumption, the only participants in the market for loanable funds are households, some of which are supplying funds while others are demanding funds to finance consumption in excess of income. We will call this the pure consumption loan model because all loans serve the purpose of financing consumption. We will then introduce investment possibilities in two steps. First, we will allow households to make their own productive investments, then we will introduce the capital building firm and its demand for loanable funds. This will complete our model of the borrowing and lending of funds, the determination of the interest rate as the price of loanable-funds, and the role of the interest rate in determining the rate at which new capital machines are built.

The Pure Consumption Loan Model of Households Let us consider one individual who knows with certainty that he will live only two periods. He also knows with certainty the incomes to be received in each of the two periods. These incomes are M, and M2. The individual is free to borrow or lend in the first period at a given market rate of interest r subject only to the constraint that any borrowing in the first period must be repaid with interest out of income received in the second period. The individual is assumed to choose the levels of consumption in the first and second periods, Cl and C2 so as to maximize his utility subject to the con¬ straints imposed by the fixed incomes and the market rate of interest. The first step in the analysis is to formalize this budget constraint and represent it graphically in a two-dimensional diagram. The present value of the individual’s income stream is

1 + r This can also be interpreted as the individual’s present wealth or net worth in period one. The present value of the individual’s consumption stream is

363

Capital Markets: Saving, Investment, and Allocation Over Time

Vc = C, + I + r

The individual’s present value of consumption cannot exceed his present wealth. As¬ suming that no income is left unspent at the end of the second period, we must have Vc = V r m

By substitution, we get C,

+

C2 1 + r

or

C2 = C1 + r)Vm - (1 + r)Cj

(13.3)

This linear equation can be plotted in a diagram that has Cl and iff, on the horizontal axis and C2 and M2 on the vertical axis (see Figure 13.1). Point A shows the given incomes in the first and second period. It also indicates the consumption in the first and second periods if the individual neither borrows nor lends. The budget line show¬ ing alternative combinations of first and second period consumption must go through this point. As the budget equation shows, the slope of this budget line is — (1 + r). This means that for each dollar that current consumption is reduced, future consump¬ tion can be increased by $(1 + r) by lending that dollar at r percent for one year. The horizontal intercept of the budget line indicates the maximum amount of consumption possible in year 1 if the individual consumes all his current income and borrows the

consumption in year 1 Figure 13.1 Lending.

The Individual’s Budget Constraint for Consumption with Borrowing and

364

The Competitive Market System

maximum amount possible against his second-year income. This is found by setting C2 equal to 0 in Equation (13.3) and solving for C,:

1 + r If the market rate of interest changes, other things equal, the budget line rotates around point A, the initial income endowment. An increase in the interest rate rotates the budget line clockwise; that is, it becomes more steeply sloped. A decrease in the interest rates rotates the budget line counterclockwise about point A. The individual has preferences between first- and second-year consumption that can be represented by the utility function U = U(CU C2). This utility function can be represented by a set of convex indifference curves that show a diminishing marginal rate of substitution between C{ and C2. In order to reach the highest attainable indifference curve, the individual will choose that pattern of consumption where an indifference curve is just tangent to the budget line (see Figure 13.2). At this tangency point the following condition holds: MRS c c = 1 + r 1

2

This is shown in Figure 13.2 as point B. In year 1 the individual receives an income of M! and consumes C,. The excess of consumption over income is financed by borrow¬ ing C2 — Mi. In year 2 the individual receives income of M2 and devotes M2 — C2 [ = (Ci — Mi) (1 + r)] to repaying the loan. This leaves C2 for consumption in year 2. If the interest rate were to increase, this individual would borrow less in year 1. The

Income and consumption in year 1 Figure 13.2

The Equilibrium of an Individual Who Is a Borrower in Year 1.

365

Capital Markets: Saving, Investment, and Allocation Over Time

budget line would rotate clockwise around point A, becoming more steeply sloped. See the dashed line in Figure 13.2. This would induce a substitution effect that would reduce year 1 consumption and, therefore, borrowing. Also, because the new budget line would pass below and to the left of point B, this indicates that consumption opportunities have been reduced. Thus an income effect exists that also tends to reduce consumption and, therefore, borrowing in year 1. There is some interest rate at which borrowing is reduced to 0. There is an indiffer¬ ence curve through point A. The marginal rate of substitution of this indifference curve at point A determines the interest rate at which borrowing will be 0. The interest rate must be such that the slope of the budget line is just tangent to the curve at point A. The line of reasoning in the last two paragraphs shows that for those who borrow in the first year, the amount borrowed and the interest rate vary inversely. Borrowers have a demand curve for loanable funds where the interest rate is the price of borrow¬ ing. This demand curve is downward sloping (see Figure 13.3). As the interest rate increases, borrowing must decrease. At some interest rate borrowing is reduced to 0. Let this interest rate be r'. At interest rates above r', the individual will become a lender or supplier of funds. Figure 13.4 shows the budget line and indifference curves of an individual who is a lender at the going market rate of interest. Income in the first year is OM„ whereas consumption is only OCThe difference is lent at the interest rate r. When the loan is repaid with interest, this supplements the income of OM2 and permits consumption to be OC2. If the interest rate increases, the budget line rotates clockwise around point A. See the dashed line in Figure 13.4. This induces a substitution effect, which tends to reduce consumption in year 1. But it also expands the consumption opportunities of the lender. An increase in interest rates is always good for lenders. The income effect tends to increase consumption in years 1 and 2. In Figure 13.4 the substitution effect on C i is stronger than the income effect and consumption in year 1 is decreased to C\. The supply of loanable funds increases with an increase in the interest rate.

Loanable funds per period, dollars

Figure 13.3

An Individual’s Demand Curve for Loanable Funds.

366

The Competitive Market System

Income and consumption in year 1 Figure 13.4

The Effect of an Increase in the Interest Rate on a Lender: Lending Increases.

Figure 13.5 shows another possibility. Here the income effect on stemming from the increased potential interest income for the lender outweighs the substitution effect. Consumption in year 1 is increased to C[ and lending is decreased. The argument here is very much analogous to the argument supporting a backward-

consumption in year 1 Figure 13.5

The Effect of an Increase in the Interest Rate on a Lender: Lending Decreases.

367

Capital Markets: Saving, Investment, and Allocation Over Time

bending supply curve of labor in the preceding chapter. For individuals who are lending small sums, the income effect is likely to be small and not sufficient to outweigh the substitution effect. For them, increases in the interest rate lead to increases in the supply of loanable funds. But as loans become larger relative to first-year income, the income effect on Cj becomes more substantial, and eventually is strong enough to outweigh the substitution effect. At this point the supply curve of loanable funds bends backward, as shown in Figure 13.6. The consumption loan model can now be completed by aggregating the supply curves of lenders and the demand curves of borrowers across all individuals. This is done by horizontal summation of quantities demanded or quantities supplied by each individual at various interest rates. This is illustrated in Figure 13.7. The intersection of the demand and supply curves determines the equilibrium rate of interest in the loanable funds market. This diagram indicates an equilibrium interest rate that is greater than 0. But there is nothing in the logic of the model that assures this outcome. Suppose that the supply and demand curves were as shown in Figure 13.8. At a zero rate of interest there would be an excess supply of loanable funds. If income were received in the form of money and money could be stored from one year to the next at a zero cost, then the equilibrium interest rate would be 0. Those potential suppliers of loanable funds who could find no willing borrowers at a zero interest rate could store their excess of money income over desired consumption at zero cost until the following year. But if there were no storable money and income were paid in the form of a perishable commodity, then lenders would be willing to make loans at a negative interest rate, ru as long as this rate were less than the rate at which the perishable commodity spoiled. The existence of a commodity that can serve the role of money and which is storable at zero cost is

Loanable funds per period, dollars Figure 13.6

A Backward Bending Supply Curve of Loanable Funds.

368

The Competitive Market System

Loanable funds per period, dollars Figure 13.7

The Supply and Demand Curves for Consumption Loans.

Figure 13.8 The Supply and Demand Curves for Consumption Loans: A Zero or Negative Equilibrium Rate of Interest.

sufficient to assure that the interest rate is never negative. Money, including demand deposits, plays this role in a modern economy. It is interesting to examine the relationship between this model of individual saving and lending behavior and the Keynesian macro model of consumption behavior. The Keynesian model emphasizes the role of income in determining consumption; this

369

Capital Markets: Saving, Investment, and Allocation Over Time

model emphasizes the role of the interest rate in determining the quantity of saving. In the Keynesian model consumption and savings are functions of the level of in¬ come. And at least the naive Keynesian models assume that the level of savings is insensitive to the interest rate. Empirical studies of consumption and savings behavior have tended to support this assumption. The micro model presented here sheds some light on why this might be the case. In most years the household sector in aggregate is a lender of lunds or a net saver. If roughly as many individuals are in the backward-bending range of their supply curves as there are in the upward-sloping range, a change in the interest rate could have a negligible aggregate effect on the total supply of savings. This model can also be used to support the Keynesian hypothesis that savings increases with an increase in current year income. In Figure 13.9 the budget line is shifted to show an increase in income in year 1 from M, to M[, other things equal. At the original income level the consumer equilibrium is at B with consumption at OCj. As long as consumption in year 2 is a normal good, the individual will respond to the increase in income in year 1 by increasing consumption in year 2. This is shown by the shift to consumption point B' with consumption in year 2 at OC'2. The only way that consumption in year 2 can be increased is by increasing savings in year 1. Consumption in year 1 increases to OC[. But this is less than the increase in income in year 1. The difference goes to increased savings. Only if the income elasticity of demand for consumption in year 2 were 0 could an increase in income not increase savings in year 1. The result would be point B" in Figure 13.9.

consumption in year 1 Figure 13.9

An Increase in Year 1 Income Increases Saving.

370

The Competitive Market System

The Consumption Loan Model with Investment Opportunities Point A in Figure 13.10 is the income endowment of an individual, assumed to be known with certainty. The slope of the budget line KK' through point A is the market rate of interest at which funds can be lent or borrowed. The line PP' through point A shows this individual’s opportunities for direct productive investments. For example, she might devote (M, — MJ) of her year 1 income to an investment in a training program to enhance her labor skills. The investment opportunity curve PP' shows that this would increase her income in year 2 from M2 to M'2. Or alternatively, the invest¬ ment opportunities curve could represent potentials for adding to her ownership of productive capital machines, thereby increasing her income from the sale of capital services in year 2. Note that the investment opportunities curve in the range A to B is more steeply sloped than the budget line representing market opportunities for borrowing and lending. This means that over some range, reductions in current consumption are more profitable if they are invested in her own investment opportunities rather than at the market rate of interest. Another way of looking at this is that the internal rate of return on her own investments is greater than the market rate of interest. It must also be true, then, that the net present values of the investment opportunities portrayed along the

Figure 13.10

consumption in year 1 The Individual’s Equilibrium with Personal Investment Opportunities.

371

Capital Markets: Saving, Investment, and Allocation Over Time

range A to B are greater than 0. If the individual exploits all opportunities for personal investment with positive net present values or internal rates of return greater than the market rate of interest, she will move to point B on her investment opportunities curve. Starting from point B, the individual can further alter her consumption possibilities in years 1 and 2 by either borrowing or lending at the market rate of interest. If Ix is one of her indifference curves, the optimum consumption point is at C where that indifference curve is tangent to the budget line LL '. In order to reach this consumption point, she must borrow Cx — M[ and repay this amount plus interest out of her augmented year 2 income of M'2. The principal implication of this model is that the addition of investment opportuni¬ ties tends to reduce the lending of individuals and/or increase their borrowing. In terms of the market for loanable funds, the individuals’ aggregate supply curve of loanable funds is shifted to the left and the demand curve for loanable funds is shifted to the right.

Producers’ Demand for Funds At any point in time the stock of capital machines in the hands of machine owners is fixed. There is a demand curve for the services of these machines that is based on their value of marginal productivity. This is shown in Figure 13.11. The intersection of the demand curve with the vertical supply curve of capital services determines the shortrun equilibrium rental price for machines. The aggregate rent is the area OABKx. This shows the determination of the annual payment to the stock of capital, R. The value of this stock of capital machines is the present value of the stream of future R’s discounted at the market rate of interest. With knowledge of both the stream of future R’s and the cost of building a new capital machine, the net present value of a new machine can be computed. It is

K per period Figure 13.11

The Annual Return to the Stock of Capital Machines.

372

The Competitive Market System

PVK

n =

2

R —-!-C

,=1 (1 + r)‘ If the net present value of a machine is greater than 0, it is potentially profitable for machine owners to build or have built for them new capital machines. For this they need to borrow funds on the loanable funds market. In any period of time there will be a certain number of potential investment projects of this sort for which the net present value is positive and a demand for loanable funds to finance these profitable projects. If the interest rate decreases, the net present values of all potential investment projects increase. Some projects whose net present values were previously negative will now have positive net present values. This means that more loanable funds will be required to finance the construction of the newly profitable investments. Thus a decrease in the interest rate increases the demand for loanable funds on the part of capital machine builders. This demand curve is shown in Figure 13.12.

The Market for Loans The last step in the construction of the model of the loanable funds market is to add the machine builders’ demand for loanable funds (I)K) to the demand (D,) and supply (S,) of loanable funds on the part of individuals.5 This is shown in Figure 13.13. The two demand curves are aggregated by horizontal summation. The intersection of the

r

DK%

o Loans for capital machines, dollars Figure 13.12 Machine Builders’ Demand for Loanable Funds. To be complete, the net borrowing of the government should be added to the demand and supply curves of Figure 13.13. J

373

Capital Markets: Saving, Investment, and Allocation Over Time

Figure 13.13

The Market for Loanable Funds and the Equilibrium Rate of Interest.

aggreSate demand curve for loanable funds with the supply curve gives the equilibrium market rate of interest rx. The interest rate determines the volume of investment projects that have positive net present values, as well as the supply and demand for loanable funds on the part of individuals. What comparative static propositions can be deduced from this model? An in¬ crease in the stock of capital machines will decrease the rental price of capital ma¬ chines and the net present value of new machines. This will decrease the demand for loanable funds to construct new machines and lead to a lower rate of interest, other things equal. A technological improvement or an increase in the supply of complementary factors of production will increase the value of the marginal product of capital machines and the net present values of new investment opportunities. This will shift the demand curve for loanable funds to the right and lead to an increase in the interest rate. Because the future cannot really be known with certainty, what matters in the model of investment decision making is the expectations of machine builders about future rents and profitability. An economic change that leads to greater optimism on the part of machine builders will lead them to revise upward their expectations about the net present values of potential investments. This, in turn, will lead to an increase in the demand for loanable funds to finance the construction of more machines. Investment and the interest rate will increase. This is the link between our microeconomic model and the Keynesian macro model. The Keynesian model de-emphasizes the role of the interest rate in determining aggregate investment levels and treats investors’ expecta¬ tions and attitudes as the major shifters of the aggregate investment function. Finally, an increase in individuals’ income, other things equal, will tend to reduce the interest rate through its effect on the supply of loanable funds.

374

The Competitive Market System

SOME APPLICATIONS AND EXTENSIONS Efficient Asset Markets The concept of present value can be used to explain the market prices of durable assets such as farmland, buildings, oil wells, or coal mines. The concept also applies to the valuation of intangible assets such as shares in the ownership of corporations, patents, or copyrights. In a market economy the price of a productive asset will be equal to the present value of its stream of future returns. This is a natural consequence of competi¬ tion among buyers and sellers who operate in a market system with full information on the future returns of alternative investments. If for some reason the market price of an asset were to fall below the present value of its returns, investors would notice the opportunity for potential profit. And as they tried to take advantage of that opportunity by purchasing the asset, they would bid up its price. And no well-informed investor would be willing to pay a price greater than the present value of the asset. Given knowledge of the stream of future returns from the asset, asset prices can change only if there is a change in the interest rate used to calculate present values. A decrease in the market rate of interest will cause an increase in present values and an increase in all asset prices. In this way a decrease in the interest rate benefits owners of assets with known and fixed streams of future returns. Conversely, an increase in the interest rate lowers present values and asset prices. In a world where the future is not known with certainty, the price of an asset is determined by the expectations of the participants in the market concerning future returns for the asset. If all participants in the market have access to all presently known information that conceivably bears on the future returns of this asset, the market price of the asset can be interpreted as the best possible current estimate of the present value of the unknown future stream of returns. This is another way in which markets and prices convey information. They convey information about present demand, costs, value, and so on, and where assets are concerned, about the most expert evaluations of future prospects. If all current informa¬ tion is available to all market participants and if the market is competitive, it is said to be efficient in conveying information. It may be somewhat surprising to the reader that when asset markets are efficient, it is not possible consistently to make speculative or above normal profits through the purchase or sale of assets such as shares of common stocks. At any point in time the price of an asset is equal to the present value of the expected stream of returns to that asset. If a person purchases the asset at that price and subsequent experience proves those expectations to have been correct, the individual will earn a rate of return on his investment equal to the interest rate on which the present value calculation was based. And this same rate of return would be available on other assets of a similar form and similar degrees of risk. Suppose that the expectations on which the price of the asset are based turn out to be unduly pessimistic. Once the future has revealed itself sufficiently to make this known to the market, the market price will be immediately bid up to reflect the new

375

Capital Markets: Saving, Investment, and Allocation Over Time

expectations of future returns. The original owner of the asset can either continue to hold the asset and realize the unanticipated increase in returns, or he can sell the asset to take advantage of the unexpected higher price. In either case, however, the gain is fortuitous or unexpected. An individual learning of the new information cannot expect to take advantage of it because when he goes to the market to purchase the asset he will find that its price has already been bid up to reflect the new information. A similar story can be told if expectations turn out to be unduly optimistic. Thus holders of assets in efficient markets can only expect to earn the normal market rate of return plus or minus the random increases and decreases in market asset prices caused by the availability of new information. By definition, however, these price changes cannot be anticipated. The only way an individual can beat the market in this sense on a regular or systematic basis is to have access to new information before it becomes generally available so that he can make purchases or sales of assets before the market reacts to the new information. In the parlance of the stock market this is referred to as “insider information.” Buying and selling securities on organized securi¬ ties markets with the intention to profit on the basis of insider information is not legal in the United States.

Optimum Forestry Management Consider a parcel of land that is devoted to the sole purpose of raising trees for timber or paper making. Assume that all the trees were planted at the same date. Let V(t) represent the net value of the forest if it is harvested at the age of t. The net value is the market value minus the cost of harvesting. Finally, assume that there are no costs of maintenance or management for the forest other than those associated with the harvest itself. The growth of the net value of the forest typically follows a pattern such as that shown in Figure 13.14. For very young trees the growth in value is very slow. But value grows at an increasing rate. Then diminishing returns to time set in. Total value reaches a maximum at the age of t*, after which age, disease, and rot reduce the net value of the forest. What is the optimum age for harvesting this forest? Many people would guess that the forest should be left until it has achieved its maximum growth. Harvest should occur at the age of t*, they would say. But they would be wrong. That answer reflects a failure to look at the problem from a marginal perspective, and more importantly, a failure to take account of the opportunity cost of time. The opportunity cost of time arises because at any date the decision to postpone the harvest by one year means the foreclosure of the opportunity to invest the proceeds of the harvest, V, at the market rate of interest, r, and to earn a return of rV per year. Basically, the problem is to choose an age of harvest so as to maximize the present value of the stream of net returns from the forest over time. This maximization prob¬ lem can be solved mathematically. But the main elements of the problem can be described verbally and graphically. At any time t, if the forest is left to grow another year, it will increase in value by the amount of AF. Alternatively, if the forest is

376

The Competitive Market System

harvested and the proceeds are invested at the market rate of interest, the forest owner will receive rV in one year.6 If A V is greater than rV, leaving the forest standing one more year is a better alternative than harvesting the forest and investing the proceeds. Figure 13.15 shows the change in net value of the forest as a function of time. This curve, AV, can be interpreted as the value of marginal product of time for the forest. In geometric terms, AV is the slope of the V(t) curve of Figure 13.14. This marginal value first increases, then decreases, reaching 0 at time t * when the value of the forest has reached a maximum. This figure also shows rV, the interest cost or opportunity cost of postponing harvesting. rV is simply a constant proportion (r) of the V(t) curve of Figure 13.14. At ages below t the growth in value of the forest exceeds the potential interest return from investing the proceeds of the harvest. The forest is a better investment than the market alternatives. At ages beyond t, the potential returns from investing the proceeds of the harvest exceed the growth in value that can be realized if harvest is postponed for one year. Beyond t, continued investment in the standing forest is a poor alternative to the market. The optimum date of harvest is therefore t. The optimum condition is

Vo*' W,“ 9F"pa ™si2C37P'ete d,SCUSSi°n' “ Char'“ W-

377

Capital Markets: Saving, Investment, and Allocation Over Time

Figure 13.15 The Marginal Yield and Opportunity Cost of Time in Determining the Optimum Date of Harvest. AF = rV or when AF F This states that the optimum date of harvest is when the percentage rate of growth of the net value of the forest is just equal to the market rate of interest. At least for some commercial forest species, the difference between t and t* can be substantial. For example, research has shown that t* for a Douglas fir forest in the Pacific Northwest may be around 140 years. But the optimum harvest age may be only a little over one-third of that, in the neighborhood of 50 years.7 This model can also be used to analyze other situations where economic value grows with time but time has diminishing returns. Examples include determining the opti¬ mum length of time for fattening cattle before slaughter and the optimum period of aging for fine wines and whiskeys.

SUMMARY Capital is durable and yields its services over perhaps a long period of time. Therefore time plays an important role in the economic analysis of capital. The price of a capital machine is the present value of its stream of future returns, that is, the willingness to pay now for the right to receive the stream of future rental returns earned by the machine.

7Ibid.

378

The Competitive Market System

If the present value of a capital machine is greater than the cost of producing it, investors will borrow funds to build more machines. The lenders of these funds are individuals who wish to rearrange the time pattern of their consumption so as to consume more in the future than their expected future income would permit. The market rate of interest is the price of loanable funds. The market for loanable funds is in equilibrium when the interest rate makes the quantity demanded of loanable funds just equal to the quantity supplied.

KEY CONCEPTS Present value Internal rate of return Discount rate

Demand for loanable funds Supply of loanable funds Efficient asset markets

QUESTIONS AND PROBLEMS For Basic Review 1. Define and explain the economic significance of each of the key concepts. 2. Use indifference curve analysis to derive the demand and supply curves for loanable funds in a model with no opportunities for productive investment (a pure consumption loan model). Discuss the factors that would determine whether the equilibrium interest rate would be greater than, equal to, or less than 0. Briefly discuss the way in which opportunities for productive investment would modify the preceding results.

Problems !•* te) What is the maximum amount you would be willing to pay for the goose that lays the golden eggs? (Note: You have not been given enough information to calculate the required numerical answer. List the information required; give assumed values to all the required parameters and coefficients; then proceed with the calculations.) (b) How would your answer be affected if the price of U.S. Treasury bonds fell by, for example, 20 percent? Would you pay more or less than in (a)? (Hint. Because the future returns of U.S. bonds are guaranteed, what would cause their price to decrease?) (c) Suppose that the price of Super-Lay goose feed were to double. Would you pay more or less than in (a)? 2. Suppose the interest rate is 5 percent per year. A machine produces a net return of $15 in this year, $12 next year, and can be sold for scrap at the end of that year for $120. The machine costs $120 to produce right now. Is it a profitable investment?

379

Capital Markets: Saving, Investment, and Allocation Over Time

3. * You are thinking of buying a car that has a purchase price of $2000. The immediate resale value of the car is $1800. If you kept the car for two years (without using it) the resale value at the end of two years would be $1400. If you used the car for, say, 10,000 miles per year, the resale value will be $1300 in two years. (Assume a 10 percent interest rate.) (a) What is the cost of acquiring the car? (Hint: The cost of something is the subsequent reduction in wealth, which is not the same as the price.) (b) Given that the car has been purchased what is the cost of continuing possession for two years? (c) Assume that gas, tires, repairs, and so on cost $300 at the end of the first year and $350 at the end of the second year. What is the present value of the cost of operating the vehicle during the two years? (Remember to include additional depreciation.) (d) Suppose that instead of buying the car you could rent it for the same period. What would be the maximum rate per mile that you would be willing to pay if you had to pay in advance? If you had to pay at the end of each year? (Figure on 10,000 miles per year.) 4. Two salesmen want to sell you a car with an official list price of $2000. Salesman A offers it for $1900. Salesman B sticks with the list price, but he will let you pay him the full amount one year hence. Which offer is cheaper? Make any assumptions you need in order to answer the question. 5. It is usually the case that individuals must pay a higher rate of interest on borrowing for consumption purposes than they can earn on loans made through deposits in, say, a savings account. How does this affect the budget constraint of a consumer? Does this alter any of the basic conclusions of this model? 6. * You are the director of the Municipal Sewage Treatment Department for a large city. You have plans to build a new treatment plant costing $100 million. Because of expected population growth, the capacity of this plant will be fully utilized in 15 years. At that time an expansion of the plant would cost $20 million and would provide additional capacity to handle expected population growth between the 15th and 20th year of the plant life. You have the alternative of altering the design of this new plant now so that it will be large enough to handle the population expected in 20 years. The larger plant would cost $110 million to build. Suppose that the interest rate at which your city can borrow is 6 percent. Which plan should you choose? Is your answer different if the interest rate is 3 percent?

For Discussion 1.

Suppose that a solar hot water heater costs $2000 to purchase and install and saves $100 per year in fuel costs. For simplicity assume it will never wear out or require repairs. Assume that the market rate of interest is 7 percent. (a) Is the heater a good investment?

380

The Competitive Market System

(b) What changes in the economic environment would have to occur to stimulate the widespread adoption of solar hot water heating? (c) Suppose that the government decides to promote the adoption of solar hot water heating. What steps might it take? Are there any justifications for government steps that encourage adoption of solar heating beyond what the market would provide? 2* When pollution control regulations are imposed on firms, they typically respond by installing treatment equipment, investing in modifications and improvements to existing equipment, and so forth. Calculating the present value of the cost of pollution control is straightforward, at least conceptually. It consists of the cost of the incremental capital plus the present value of incremental operating and maintenance costs. Suppose instead that the firm chooses to meet the pollution control requirement by shutting down the plant. What is the cost of pollution control then?

SUPPLEMENTARY READINGS Baumol, William J. The Discount Rate for Public Projects, U.S. Congress, Joint Economic Committee, The Analysis and Evaluation of Public Expenditures: The PPB System, vol. 1, 1969, reprinted in Robert H. Haveman and Julius Margolis, eds., Public Expenditure and Policy Analysis (2nd ed.). Chicago: Rand McNally, 1977. Blaug, Mark. The Methodology of Economics. Cambridge: Cambridge University Press 1980, Chapters 10, 13. Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach. New York: McGraw-Hill, Chapter 12. Stigler, George J. The Theory of Price (3rd ed.). New York: Macmillan, Chapter 17.

CHAPTER 14 The General Equilibrium of the Competitive Economy

INTRODUCTION

1An general equilibrium analysis all markets for all goods and factor services are analyzed simultaneously. This is in contrast to the partial equilibrium analysis of Chapters 7 through 13, and especially Chapter 11. There the focus was on one market or at most two closely linked markets such as those for a good and for a factor used in its production or for two goods that are close substitutes. Partial equilibrium analysis assumes, in effect, that all economic interactions, except those that are explicitly mod¬ eled, are too small to worry about. This may be a reasonable assumption for many types of questions, for example, the incidence of an excise tax on shoelaces. But it can be seriously misleading for other types of questions, such as the incidence of a general sales tax on all final products. Broadly speaking, there are two approaches to the general equilibrium analysis of a market economy. One is mathematical in nature. It was pioneered by the nineteenthcentury economist Leon Walras and has reached a highly developed form in recent years through the work of Nobel Prize winner Kenneth Arrow and Gerard Debreu, among others. This approach is disaggregated and perfectly general in that it can be applied to economies with any number of individuals, firms, factor services, and goods. Demand functions are specified for each good for each individual. Each individual’s quantity demanded of each good is a function of the prices of all goods and the individual’s income. Income is received from the sale of factor services according to each individual’s set of factor supply functions. Similarly, firms’ supply functions for goods and demand functions for factors are specified. All factors in the economy are linked by the require¬ ment that each market for a good or factor clear, that is, that the sums of the quantities demanded for each good or factor be equal to the sums of the quantities supplied.

381

382

The Competitive Market System

The major objectives of this form of analysis are to determine whether an equilibrium exists in the form of an economically meaningful solution to the system of equations, to determine what mathematical conditions are necessary and sufficient for an equilib¬ rium, and to examine the economic meaning of these conditions. General equilibrium models of this type are far too cumbersome to be applied to real-world situations or to be manipulated to produce meaningful comparative static propositions. This form of general equilibrium analysis will not be discussed further in this chapter.1 The second approach is to simplify the economy very substantially by assuming only two or three goods, two or three factors of production, and two or three individuals. The three-good, three-factor models can reflect the richness of a variety of substitution and complementarity relationships between goods in consumption or factors in produc¬ tion, but they must be formulated and analyzed in mathematical terms. The simpler two-good, two-factor, two-individual model is amenable to graphical analysis. This is the approach that will be taken in this chapter. Our purpose is to show that a simple economy of this sort with perfectly competitive markets has an equilibrium and to describe how market forces will move the economy toward that equilibrium position. We will also describe how this simple model can be employed in comparative static analysis.

THE MODEL The model of this chapter builds on the basic model of production and exchange that was developed in Chapters 3 through 5. Here we add a market system as a social institution and analyze how the market system determines the prices of both goods and factors and the quantities of goods produced. We make four basic assumptions: 1. There are only two goods, two factor inputs, and two individuals. 2. The quantities of factor services available are fixed and do not respond to changes in their prices. 3. All individuals and firms act as price takers in the relevant markets. Thus the markets can be taken to be effectively competitive. 4. All individuals and firms strive to maximize their utility or profit. In the course of developing this model we will describe how a competitive market system carries out the three functions of an economic system: determining what to produce, how to produce it, and who gets the products. We will also show that the answers to these three questions depend on four sets of exogenous conditions: (1) the size of the factor endowments of labor and capital—these determine the size of the production box; (2) the technology or production function—this in combination with the size of the factor endowments determines the position and shape of the production

‘For an introduction to this type of general equilibrium analysis, see James Henderson and Richard Quandt Microeconomic Theory: A Mathematical Approach (3rd ed.). New York: McGraw-Hill, 1979, Chapters 9,

383

The General Equilibrium of the Competitive Economy

possibilities curve; (3) the preference orderings of the two individuals; and (4) the distribution of ownership of factors—this determines the size of the claims on output for both individuals and influences whose preferences get greater weight in the market¬ place.

Equilibrium in Input Markets As in Chapter 3, the fixed endowments of labor and capital determine the dimensions of the production box. The isoquant mappings for the production of X and Y are placed inside the production box. Their points of tangency define the efficiency locus (see Figure 14.1). Suppose that the initial production point is at A. Suppose also that the market prices of capital and labor are such that the producer of Y is minimizing his production cost for Y3. An iso-cost line SS' reflecting these factor prices is tangent to Y3 at A. Since SS" intersects the X2 isoquant, the producer of X is not satisfying her cost¬ minimizing conditions. Because her marginal rate of technical substitution far exceeds the factor price ratio she faces in the market for factors, she should substantially reduce the employment of capital and increase the employment of labor. Doing this, she will create an excess demand for labor that will tend to bid up the price of labor. As she releases capital, this will create an excess supply of capital, depressing the price of capital. The changes in the prices of the two inputs will also induce the Y producer to alter his factor combinations, reducing the use of the now more expensive labor and increasing the use of the now cheaper capital.

■LY

ky

LxFigure 14.1

The Equilibrium in Production.

384

The Competitive Market System

These adjustments will continue until both producers have moved to a point on the efficiency locus such as point B. There, the isoquants of both producers are just tangent to the common iso-cost line TT'. Both producers have selected cost-minimizing input combinations. The input markets are in equilibrium. The equilibrium price ratio, P,/PK, is given by the slope of TT'. Actually, the two producers could have wound up at point C, with equilibrium factor prices given by the slope of UU'. Or they could have settled it at any other point on the efficiency locus. As will be shown subsequently, the final position depends on the relative demands for goods X and Y and forces operating in the product markets. Note that in moving from the lower left corner to the upper right corner along the efficiency locus, the equilibrium price ratios change, with capital becoming more expensive relative to labor. This shows that the prices of inputs depend in part on the combination of outputs that is chosen by the economy. We will return to this point later. The information from the production box can be used to derive the production possibilities curve. Because the cost-minimizing behavior of producers acting in com¬ petitive factor markets leads them to points on the efficiency locus, this means the economy will be on rather than inside the production possibilities curve.

Equilibrium in Exchange Assume that the economy has chosen point C on the production possibilities curve (see Figure 14.2). This determines the dimensions of the exchange box that depicts the possible distributions of goods between the two individuals, Ann and Bob. Suppose that

385

The General Equilibrium of the Competitive Economy

the distribution of ownership of factors is such that Ann and Bob receive the endow¬ ments of the two goods depicted by point A in Figure 14.2. They both face a budget line through point A, the slope of which is determined by the price at which X and Y can be bought and sold in the market. Suppose that the prices are such that the slope of this budget line is SS'. With these prices Ann is in equilibrium in consumption, but Bob finds that his marginal rate of substitution of X for Y is substantially less than the price ratio he faces. He would like to trade some X for Y at these terms. As he offers X for sale, however, he tends to depress its price. And as he seeks to purchase additional Y, he bids up its price. This rotates the price line counterclockwise through point A and also disturbs Ann’s equilib¬ rium. Ann responds to the higher price of Y by selling Y to Bob and purchasing X. Both individuals are moving to higher indifference curves. This process continues until they have reached a point on the contract curve where both their marginal rates of substitution are equal to the common price ratio they face. This is shown as point C where the budget line TT' has a slope of PX/PY. This represents an equilibrium in exchange. Notice that a different initial endowment, say, point D, would likely lead to a different equilibrium price ratio in the product markets. This shows the influence of the initial distribution of factor ownership on the final outcome of production and ex¬ change.

Equilibrium in Production Although the equilibrium position just determined may represent an exchange equilib¬ rium for the given quantities of X and Y, it may not represent the equilibrium outputs for the firms producing X and Y. Their equilibriums depend on the relationship between price and marginal cost in the production of the two goods. Figure 14.3 shows the exchange equilibrium with its price ratio of PX/PY given by the slope of TT'. The marginal rate of transformation between X and Y is shown by the slope of the line UU'. Notice that the price ratio is less than the MRTXY. This implies that the prices are not equal to the marginal costs in the two industries. This is because the marginal rate of transformation between X and Y is equal to the ratio of their marginal costs. Recall the definition of the MRTXY: AY

MRTyy =AX -1/AX 1/A Y

If X is decreased, the reduction in the money cost of production of X must be just equal to the increase in the money cost of producing Y. That is, — ACX = A CY

Thus by substitution we have

386

The Competitive Market System

Figure 14.3

Attaining Equilibrium in Product Markets.

-ACy/-AX

MCy

ACy/AT

MCy

--- = -- = MRTxy In Figure 14.3 the marginal rate of transformation is greater than the price ratio. This implies that the marginal cost of X is greater than its price, while the marginal cost of Y is less than its price. Because the industries for both goods are competitive, the Y industry will expand while the X industry contracts. The increase in Y production will lead to an increase in its marginal cost and will push the price of Y down. In the meantime, the contraction of X production will cause the marginal cost of X to decrease while its price increases. This will eventually restore the equality of price to marginal cost in both industries. At that point equilibrium in production will have been attained. While these changes in the outputs of the two goods are occurring, there will be corresponding changes in the equilibrium of exchange and equilibrium in the input markets. Ann and Bob will be readjusting their consumption bundles as PX/PY changes. And a contraction of output in the X industry is accompanied by a move down and to the left along the efficiency locus of Figure 14.1. If the production functions for X and Y are as shown in Figure 14.1, an increase in the price of labor and a decrease in the price of capital will occur. This demonstrates the crucial linkage between output markets and input markets in the general equilibrium model. In this model only the price ratios, PL/PK and PX/PK have been determined. We have not determined the absolute magnitude of any of these prices. This is because a monetary unit in which prices can be measured has not been specified. Although this is basically a problem for monetary theory, it is straightforward to see how money prices can be determined. Suppose that the ratio PX/PY = 2. Now define a monetary

387

The General Equilibrium of the Competitive Economy

unit, say, a px must be ship, PL = determined

dollar, such that $1 = of a unit of Y. This makes PY = $10. Thus $20. The price of labor can be determined from the productivity relation¬ Px • VMPlx. And since the ratio PL/PK is known, the price of capital is as well.

The conclusions of this model can be summarized in four statements: 1. The cost-minimizing behavior of producers leads them to the efficiency locus where their equal marginal rates of technical substitution determine the ratio of input prices. 2. The utility-maximizing behavior of individuals leads them to the contract curve where their equal marginal rates of substitution determine the ratio of product prices. 3. The profit-maximizing behavior of firms leads them to adjust their outputs until the ratio of product prices is just equal to the marginal rate of transformation. 4. The position of this equilibrium is determined by the factor endowments and technology that give the shape of the production possibilities curve and by individuals’ preferences and the distribution of rights to output between them that influence the equilibrium of exchange and the firms’ outputs.

A COMPARATIVE STATIC APPLICATION We have described how input markets are linked with output markets. We now derive a specific comparative static prediction based on this linkage. Figure 14.4 shows the production box and efficiency locus for X and Y. The isoquants are omitted to keep the diagram simple. It can be seen that at any point on the efficiency locus, for example,

Ly

Oy

Ky

LX

Figure 14.4

The Effect of a Change in Output on Factor Prices.

388

The Competitive Market System

point A, the ratio K/L is greater in the X industry than in the Y industry. Thus we can say that the X industry is capital intensive relative to the Y industry. Now suppose that the output of X increases and the output of Y decreases. This could be because of an exogenous change in tastes and preferences. Starting from the initial equilibrium position in production at point A, if there is no change in factor prices, the X industry wishes to expand along its expansion path through A toward point B. But other things equal, including factor prices, the Y industry wishes to contract along its expansion path from A toward point C. Because the capital released by Y would be less than the capital demanded by X, the relative price of capital must rise to induce both industries to alter their factor input ratios and to maintain produc¬ tion on the efficiency locus. Thus our prediction is: The expansion of the output of a good leads to an increase in the relative price of the factor used intensively in the production of that good. For example, the expansion of the output of a capital-intensive good will tend to raise the price of capital relative to the price of labor. Additional comparative static propositions can be deduced from the model. Some propositions concerning the effects of market power and market failure will be dis¬ cussed in Chapter 17.

SUMMARY The basic interconnections between markets for goods and between goods and factor markets can be shown in the simple two-good, two-factor, two-person general equilib¬ rium model. In this model, producers select input combinations so as to minimize their costs of production. If at any given set of factor prices the quantities demanded are not equal to the quantities supplied, factor prices will change. Then producers modify their demands for factors. This process tends to move the economy toward the efficiency locus in the production box. A condition for the economy to be in equilibrium is that producers be on the efficiency locus. Similarly, individuals maximize utility by choosing consumption bundles so that their marginal rates of substitution are equal to the given price ratio for goods. If this results in quantities demanded that are not equal to the quantities being supplied, goods prices change. Quantities demanded can equal quantities supplied only if the economy is on the contract curve of the exchange box. This is another condition for the equilib¬ rium of the competitive economy. The third condition for general equilibrium is that price equal marginal cost in all markets or that the ratio of goods prices be equal to the marginal rate of transformation. If this condition is not satisfied, one industry will contract while the other industry expands. The economy will move along the production possibilities curve until it reaches a point where this condition is satisfied. Movements along the production possibilities curve also lead to changes in both the exchange box and the production box. Although this simplified abstract general equilibrium model can be used in a formal way only on very simple problems, it provides a perspective on the more complex

389

The General Equilibrium of the Competitive Economy

interactions of a real-world economy. The general equilibrium model identifies the main channels of interaction among markets in an interdependent economy. And it provides a framework for reasoning about how some real-world policy or exogenous change will reverberate through the economy. The general equilibrium model teaches us that in principle everything depends on everything else. Trying to analyze all interconnections is an unreasonable task. The art of applied economic analysis consists of being able to judge which of the interactions among goods markets or between goods and factor markets are most important for the question at hand. To test your ability to do this kind of applied “informal” general equilibrium analysis, see the following questions for discussion.

QUESTIONS AND PROBLEMS For Basic Review 1. Use the appropriate box diagrams, and so on, to describe the general equilibrium of a two-person, two-good, two-factor economy. Show how all prices are determined in the equilibrium position. It has been said that the position of this equilibrium depends on only four sets of factors. What are they? Discuss the way in which each influences the equilibrium position.

For Discussion 1. * The American steel industry has claimed that imports of steel from Japan have depressed steel prices in the United States and brought harm to the steel industry and the American economy. The industry has asked for quotas that would substantially reduce steel imports. What would be the principal microeconomic effects of a steel import quota? (Hint: Start with the effect of the quota on the price of steel and the quantity produced by U.S. firms. Then trace these effects through the economy.) 2.

What are some of the likely microeconomic effects of a substantial increase in the rate of recovery and reuse of waste paper? What about wages and employment of wood cutters? Prices of 2 X 4 lumber?

SUPPLEMENTARY READINGS Blaug, Mark. The Methodology of Economics. Cambridge: Cambridge University Press, 1980, Chapter 8. Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach (3rd ed.). New York: McGraw-Hill, 1980, Chapters 9, 10. McClure, Charles E. Jr. A Diagrammatic Exposition of the Harberger Model with One Immobile Factor. Journal of Political Economy, January 1974, 80(1), 56-82.

L-

PART IV Market Power

CHAPTER 15 Prices and Quantities in Monopoly Markets

INTRODUCTION

A

1 JL firm has market power if it is large enough to influence the market price through its own buying or selling decisions. It can have market power either in its role as a purchaser of inputs or as a seller of output. Other things equal, a firm’s market power is greatest when it is the sole buyer or seller in that market. In this chapter we examine the case where a single seller or buyer has the power to establish the price at which he sells or buys the good in question. In the next chapter we analyze the oligopoly case where a small number of firms shares market power. The term monopoly refers to the case of a single seller who faces a demand curve that is the market demand, that is, the aggregate of all individual demand curves. Unlike the oligopoly seller, the monopoly seller has no rival sellers in his market whose actions he must take into account in making pricing decisions. The analysis of monop¬ oly behavior also applies to those cases where several sellers share market power and collude to establish pricing strategies to maximize their collective profits. The term monopsony refers to the case of a single buyer in a market. The monopsony buyer cannot take the market price to be given. Rather, as he increases or decreases his demand for the good or factor service, he finds himself bidding up or bidding down the price he must pay. The objective of this chapter is to explain the prices and quantities for goods and factors that are traded in markets where monopoly or monopsony power exists. We will show that monopoly and monopsony power lead to results that are quite different from the outcomes in competitive markets. Specifically, where there is a monopoly seller, price will exceed marginal cost in the output market and the value of marginal products of factor inputs will exceed factor prices in the input markets. This latter result holds

393

394

Market Power

even if the monopoly seller has no market power in the factor markets. Where monop¬ sony power exists in a factor market, the outcome is also characterized by the values of marginal products being greater than factor prices. The quantities of inputs being utilized are less than if input markets were competitive. And because of this the quantity of output is also less than under competition. In the next section we take up the case of monopoly in the market for output. Subsequent sections deal with how monopoly power in the output market affects the firm’s demands for inputs, the consequences of monopsony power in factor markets, and the special case where a monopoly seller faces a monopsony buyer in a market.

MONOPOLY IN THE PRODUCT MARKET For a monopoly to persist in the product market, two conditions must be met. First, of course, the monopoly must be profitable. Monopoly price must be above long-run average cost. Otherwise the monopoly firm would exit this market. The existence of profit leads to the second condition. If one firm is receiving profits by selling in this market, there is an incentive for other firms to enter this market to share in that profit. So the continued existence of a monopoly depends on barriers to further entry. These barriers to entry can take several forms. 1. Patent. If the product itself or the technology with which it is produced is protected by a patent, sole ownership of the patent can provide a means for preventing the entry of other firms. Rights to use a patented technology can be sold or licensed on a nonexclusive basis. But the patent owner who wishes to use the patent to erect barriers to entry can refuse to license the technology to other potential producers. 2. Government action. If the government requires a permit or license as a condition of doing business in a market, and if the government severely restricts the number of licenses or permits issued, it is conferring market power or in the extreme case monopoly power on those lucky enough to obtain government permits. 3. Specialized factor service or natural resource. If production requires some specialized factor service or natural resource, ownership of that input can also provide the means for establishing monopoly power. 4. Significant economies of scale in production. If an existing monopolist is producing in the range of increasing returns to scale, it will have a cost advantage over any potential entrants who must anticipate having to produce at lower levels of output and therefore at higher cost. This can make it difficult if not impossible for new firms to enter a profitable but monopolized market. Although a market may technically be monopolized,1 the existence of the monopoly 'If the term is taken literally, every firm is a monopolist for the product it sells. Its product may be distinguished from those of other producers by real or imagined quality differences or by the location at which the product is sold. Meaningful monopoly power exists only if the cross elasticities of demand for the firm’s products are low. See the discussion of monopolistic competition in Chapter 16.

395

Prices and Quantities in Monopoly Markets

need not be of major concern if the monopolized product has close substitutes. The availability of close substitutes makes the demand curve for the product relatively more elastic. If the demand curve is elastic, the power of the monopolist to raise the price significantly above cost is restricted. With an elastic demand, relatively small price increases can lead to significant decreases in quantity demanded and sales for the monopolist. Thus absence of close substitutes and less than perfectly elastic demand must be added to barriers to entry on the list of conditions that may lead to significant monopoly power.

Profit Maximization: A Simple Model The key to understanding the price and output decisions of a monopolist is recogniz¬ ing that the monopolist must lower its price in order to increase the quantity sold, and the lower price may lead to either an increase or decrease in total revenue de¬ pending on the elasticity of the demand curve. Thus price is not taken as given by the monopolist; and the marginal revenue for an increase in output is not equal to price. In fact, marginal revenue must be less than price to reflect the fact that when price is lowered in order to sell an additional unit, a lower price must be charged for all the units sold. In the analysis that follows we assume that the monopolist has no market power in input markets. Figure 15.1 shows a demand curve and its associated marginal revenue curve. It also shows the marginal and average cost curves of the monopolist. Starting at an output of 0, the marginal revenue is greater than the marginal cost. The first unit of output sold adds more to total revenue than it does to total cost, thus increasing profits. As long as marginal revenue is greater than marginal cost, increasing output further will increase profits; that is, the marginal net profit or marginal net return of additional output is positive. At output X1 marginal revenue just equals marginal cost.

Figure 15.1

X per period The Profit-Maximizing Price and Quantity for a Monopolist.

396

Market Power

The marginal net return of output is 0. For the next unit sold beyond Xi marginal cost exceeds marginal revenue and the unit adds more to total cost than it does to total revenue. Thus it must decrease profits. Since profits are increasing as output is increased to Xt and decreasing beyond that output, Xx must be the output with the highest possible profit. The demand curve shows that the output of X, can be sold at a price of Pi. In this case price is above average cost, so profits must be positive. Profits are shown by the area DCBPi. We have established the following relationship.2

Relationship: The profit-maximizing monopolist chooses that output where marginal revenue equals marginal cost and charges the maximum possible price for that output as shown by the demand curve. This condition can also be established by examining the relationship between total cost and total revenue. Figure 15.2 shows the total revenue curve that is associated with the demand curve of Figure 15.1. It also gives the total cost curve of the monopolist. Whenever total revenue is greater than total cost, the monopolist is making profits. The maximum profit is realized at that output where the vertical distance between total revenue and total cost is greatest. At outputs less than Xx the slope of the total revenue curve is greater than the slope of the total cost curve and the gap between them increases with increasing output. But beyond Xx the total cost curve is more steeply sloped than the total revenue curve. Thus increasing output decreases the gap between the two curves. Profits are maximized where the slopes of TRX and TCX are equal. The slope of the total revenue curve is marginal revenue, and the slope of the total cost curve

Figure 15.2

The Profit-Maximizing Output for a Monopolist.

;This relationship is derived using the calculus in the Mathematical Appendix to this chapter.

397

Prices and Quantities in Monopoly Markets

is marginal cost. Therefore profits are maximized where MRX = MCX. This condition for profit maximization holds in both the long and the short run. In the long run the monopolist equates marginal revenue with long-run marginal cost and selects a scale of plant that is appropriate for that output level. The resulting monopoly price must be equal to or greater than long-run average cost. Profits cannot be negative in the long run. In the short run the monopolist is not free to vary the scale of plant along the long-run marginal cost curve. She must respond to changes in demand by choosing the output that equates short-run marginal cost with marginal revenue. There is nothing that guarantees a monopolist profits in the short run. It is possible that monopoly price could be less than short-run average cost. If price is below SACX but above LACX, the monopolist can adjust to the optimum scale of plant in the long run and restore profitability. An example is shown in Figure 15.3. Given the short-run marginal cost curve, the short-run profit-maximizing output is Xx But at this output, price is below SACX and profits are negative. In the long run the firm can adjust the scale of plant by equating long-run marginal cost with marginal revenue at output X2. At this output, price is above long-run average cost and profitability has been restored. The monopolist must always operate within the elastic range of her demand curve. Or to put it differently, if at a given output, demand is inelastic, the monopolist cannot be maximizing profit. If the elasticity of demand is less than 1, the monopolist can always increase profit by reducing output. The reduced output increases profit in two ways: (1) It reduces total cost and (2) Lower output means a higher price, and with an inelastic demand the higher price increases total revenue. Recall that price, marginal revenue, and elasticity are related in the following way:

Figure 15.3 mum Scale.

Monopoly Losses in the Short Run Can be Eliminated by Adjusting to the Opti¬

398

Market Power

Because marginal cost will always be positive, profit maximization requires that mar¬ ginal revenue also be positive. But this expression shows that if the elasticity of demand is less than 1, marginal revenue is negative. A positive marginal revenue requires an elasticity of demand greater than 1.

Some Comparative Static Predictions The usual sorts of comparative static analyses can be carried out with the monopoly model. We will first consider the effects of changes in cost on monopoly price, output, and profit. Then we will turn to the effects of several forms of taxes. Finally, we will examine the effects of changes in demand. In some cases we will see that it is not possible to make predictions about even the direction of the changes in price and quantity in the absence of information on the specific form of the demand function.

Changes in Cost. Figure 15.4 shows a monopolist in long-run equilibrium with marginal revenue equal to LMCX\ at an output of Xx. Suppose that costs increase to LMCX2 and LACX2. This could be due to an increase in the price of one of the factor inputs. The new LMCX curve intersects the marginal revenue curve at a lower output. The firm responds by contracting output to X2 and increasing the price to PX2. When¬ ever the change in cost is such that the marginal cost curve shifts, price and marginal cost change in the same direction while output and cost (and price) change in opposite directions. The imposition of a tax on the monopolist can be treated as a form of increase in monopoly costs. For example, an excise tax of t per unit of output causes parallel upward shifts of the monopolists’ average and marginal cost curves as shown in Figure

Figure 15.4

A Monopolist’s Response to an Increase in Costs in the Long Run.

399

Prices and Quantities in Monopoly Markets

15.4. Output falls and price increases.3 At least with straight line demand curves such as that in Figure 15.4 the increase in price from PXI to PX2 is less than the amount of the tax.4 As a consequence, profits are reduced by the imposition of the tax. Profit per unit (price minus average cost) is reduced because price rises by less than the tax, and total output is reduced. Before the tax, profit is the area of the rectangle ABCPxx or AB times BC. With the tax, profit is equal to the area GEFPX2. This is smaller because GE < AB and EF < BC. The incidence of the tax is divided between consumers whose price has increased and the monopolist whose profit has decreased. Suppose that the monopolist must pay a lump sum tax each period, that is, a tax that is independent of output. Such a tax could take the form of a license fee or franchise tax for the right to do business. What effects does this tax have on price and output? Because the tax is independent of output, it is a fixed cost to the firm. It has no effect on marginal cost. Therefore the output at which MC = MR does not change. There is no change in price or quantity, at least in the short run. Of course, the average cost curve shifts up. Profit is reduced. If the long-run average cost curve shifts up so far that it lies above the demand curve, price is less than average cost; there are losses, and the firm must eventually go out of business. A tax on the pure profit of the monopolist also has no effect on price and output. The tax does not affect marginal cost. Suppose that the tax is t percent of profit. As long as MR is greater than MC, a 1-unit increase in output adds to pretax profit an amount equal to MR — MC. And aftertax profit is also increased by (1 — t) (MR — MC). Where MR is less than MC additions to output reduce pretax profit by MC — MR and reduce aftertax profit by (1 — t) (MC — MR). The output where MR = MC maximizes both pretax profit and the profit retained after paying the tax.

Changes in Demand. The effects of a change in market demand are less clear-cut. An increase in demand may lead to either an increase or decrease in price. And the effect on output cannot be predicted without detailed information on the properties of the demand function. We first show a case where an increase in demand leads to an increase in output in both the short and the long run. We then describe a case where an increase in demand raises price but leaves output unchanged. Finally, we consider the paradoxical case of an increase in demand leading to a lower price. In Figure 15.5 with demand given by D, the monopolist is in short- and long-run equilibrium with marginal revenue (MR i) equal to both LMCX and SMCX at an output of Xi. An increase in demand to D2 leads to an increase in output in the short run to X2 and a higher price of P2. This is no longer an optimum scale of plant, since at X2 marginal revenue is greater than long-run marginal cost. Thus in the long run the monopolist will expand the scale of plant and increase output to X3. The additional increase in output is accompanied by a fall in price from P2 to P3. In this case an

’These propositions about the effects of taxation are proved in the Mathematical Appendix to this chapter. JIf the demand curve is not linear but is convex to the origin, that is, becomes less steeply sloped as quantity increases, then the possibility that price will increase by more than the tax cannot be ruled out.

400

Market Power

X per period Figure 15.5

A Monopolist’s Response to Increasing Demand in the Short and the Long Run.

increase in demand and price has led to an increase in quantity supplied, both in the short and long run. Does this mean that there is an upward-sloping monopoly supply curve? The answer is no. There is no unique relationship between the market price and the quantity supplied by a monopolist. In the case of competition we used comparative static analysis to derive supply curves for competitive firms. This was done by hypothetically shifting the firm’s horizontal demand curve and tracing out the successive intersections with the firm’s marginal cost curve. But it is not appropriate to do this in the case of monopoly, because the firm’s output is determined not by the intersection of marginal cost and demand but by the intersection of marginal cost and marginal revenue. In Figure 15.6 the demand and marginal revenue curves labeled D, and MRX lead to a quantity Xx and price of Px. If a unique supply curve existed, this would have to be one point on the supply curve. But there are other demand curves and marginal revenue curves that lead to the same quantity supplied but result in a different equilib¬ rium price in the monopoly market. For example, suppose that the demand curve shifts up to D2. D2 is more steeply sloped than £>,. Its marginal revenue curve MR 2 intersects the marginal cost curve at the quantity Xx. But at this quantity D2 calls for a higher monopoly price. An increase in price has not brought forth an increase in the quantity supplied. The quantity supplied does not depend in any simple way on product price; rather, it depends on the demand function, specifically its elasticity. Whether or not quantity increases depends on the elasticity of the new demand curve at the original output. In Figure 15.6 at the output X, the elasticity of DX2 is less than that of £>,. Had

401

Prices and Quantities in Monopoly Markets

Figure 15.6

The Quantity Supplied at Two Different Prices.

the elasticity at Xx decreased less or actually increased as the demand curve shifted, output would have increased too. In fact if the shift in the demand curve is such that at any output the elasticity of the new demand curve is higher, not only will output increase but price will fall as well. Figure 15.7 shows such a case. At every quantity D2 is more elastic than D. This can be seen by comparing the ratios BC/OB for the two curves where C is the horizontal

Px, dollars

Xi X2 X per period Figure 15.7

An Increase in Demand Can Lead to a Decrease in Monopoly Price.

402

Market Power

intercept and B is quantity demanded. The higher elasticity of D2 means that the gap between price and marginal revenue (and marginal cost) is smaller. And so while the new marginal revenue curve MR2 intersects the MC curve farther to the right with a higher output, the new price PX2 is actually lower.5

The Capitalization of Monopoly Profits (or How Monopoly Profits Can Become Costs) There are many instances where government regulates entry into certain economic activities by requiring that firms or individuals hold a license or permit. Frequently the number of licenses or permits issued is limited. The effect is to erect barriers to entry into that industry or activity and to confer market power on those who hold permits. A classic example is the regulation of entry into the taxicab business in major cities such as Chicago and New York.6 In New York each taxicab in operation must have a medallion. A limited number of medallions were issued over 50 years ago. Because no new medallions can be issued now, anyone wishing to enter the taxicab industry in New York must purchase a medallion from an existing operator. Can someone who pur¬ chases a medallion earn monopoly profits on his investment? Assume that the number of medallions issued was sufficiently small so that owners of medallions had market power, that is, faced downward-sloping demand curves for their services and earned monopoly profits. Figure 15.8 shows the case. Market price is PM, and monopoly profits per period are equal to the area APMBC. Suppose for simplicity that current demand and cost conditions are expected to continue far into the future. The medallion becomes a form of asset that conveys to its owner the right to receive a stream of monopoly profits in perpetuity. Anyone who contemplates entering the taxicab industry would have to purchase a medallion. He would be willing to pay any amount up to the discounted present value of the stream of monopoly returns in order to purchase it. At the same time, a present owner of a medallion should be willing to sell if offered a price equal to or greater than the discounted present value of future monopoly profits. These conditions determine the market price of a medallion. We can interpret the market price of a medallion as a measure of people’s expecta¬ tions of future monopoly profits. Unexpected growth of the market should lead to increases in the market values of medallions; whereas unexpected increases in operating costs would reduce the values of medallions. A repeal of the law requiring medallions

That D2 be more elastic is a necessary condition for price to decrease. It is a sufficient condition in the case of a horizontal MC curve. The monopolist sets MC = MR = P (1 — 1 /£) where E is the elasticity of demand. Since MC is constant, we have MC = MR, = MR2 and

U( 1

— ) = P2( 1-) E, E2

Since E2 > E,, we must have P, > P2. "See Edmund W. Kitch, Marc Isaacson, and David Kasper, The Regulation of Taxicabs in Chicago, Journal of Law and Economics, October 1971, 14(2), 285-350.

403

Prices and Quantities in Monopoly Markets

X per period Figure 15.8

Monopoly Profits with Limited Entry.

for taxicab operators would eliminate barriers to entry. New entrants would drive the price of taxicab rides down to the competitive level, eliminating monopoly profits. Medallions would then become worthless. Now consider the position of a new taxicab operator who has purchased a medallion for, let us say, $100,000. From the operator’s perspective, this purchase price is a cost of doing business, which is every bit as real as the purchase of a cab, gasoline, and so forth. If the normal rate of return on capital is 10 percent, then the purchase of the medallion represents an annual fixed cost of $10,000 per year. The cost curves of the new operator are shown in Figure 15.9. The demand curve, marginal revenue curve, and marginal cost curves are the same as in Figure 15.8. The annualized cost of the purchase of the medallion is incorporated in the average cost curve. It shows that,

Figure 15.9

Costs Including the Cost of Acquiring Monopoly Power.

404

Market Power

taking account of the purchase price of the medallion, our erstwhile monopolist is earning zero monopoly profits. There are two important points to emerge from this analysis. First, the only benefici¬ aries of the creation of monopoly power are those who own the enterprise at the time the monopoly power is created. Their benefit consists of the discounted present value of all future expected monopoly profits, as well as the initial profit. Subsequent owners of the enterprise must pay the creators of monopoly profits. Thus they earn only normal rates of return on their own investment. Second, the accounting and financial records of firms that have acquired the rights to monopoly profits through the purchase of licenses, patent rights, and so forth will produce an inaccurate view of the true social cost of production. They will overestimate the social cost of production because they count as a cost the expenditures for the rights to monopoly profit, as well as the expenditures on factors of production. Only the latter represent opportunity costs to society.

Price Discrimination Under Monopoly Price discrimination refers to the act of charging different prices for different units of a good or service where the price differences are unrelated to the cost of producing the good and delivering it to the buyer. There are two forms of price discrimination: (1) where different prices are charged for different units of the goods purchased by each buyer and (2) where a buyer pays the same price regardless of the number of units purchased, but different buyers are charged different prices.

Price Discrimination by Units Purchased. Suppose that a monopolist faces the demand curve DXDX for its product as in Figure 15.10. According to this demand curve, the maximum willingness to pay for the first unit purchased is ODx. If the

Figure 15.10

Perfect Price Discrimination by Units Purchased.

405

Prices and Quantities in Monopoly Markets

monopolist knew the exact position of the demand curve, it could offer the first unit for sale at that price. The individual with the highest willingness to pay would purchase it at that price rather than do without. The monopolist could then offer successive units for sale at slightly lower prices for each unit extracting some individual’s marginal willingness to pay for each additional unit of the good. Given this system of pricing, the total revenue of the monopolist would be the area under the demand curve. Total costs are the area under the LMCX curve. Profits, the area BDXC, would be maximized at an output of OX,. This method of discriminatory pricing, charging the marginal willingness to pay for each unit sold, enables the monopolist to extract consumers’ total willingness to pay for the good. Consumers’ surplus is 0. Discriminatory pricing of this sort is only feasible for the monopolist for goods or services that are not easily storable from one period to another and are not easily transferable from one buyer to another. If the good were storable, individuals could buy twice their normal needs during the first period, paying low prices for the extra units purchased. Then they could store these units until the second period and avoid making any purchases at the higher prices that reflect the upper range of the demand curve. The form of price discrimination described here is sometimes known as perfect price discrimination. This is because the monopolist is able to extract all potential consumers’ surplus by charging a price equal to the marginal willingness to pay for each unit. Perfect price discrimination requires perfect knowledge of the demand curve for the good. Aside from the unrealistic requirements for information, perfect price discrimina¬ tion would be difficult to administer in practice. But a modified version of price discrimination by units that are purchased is not uncommon in industries such as the electric utility industry. For example, a utility could offer the first X, units for sale to each individual at a price of PX\. If consumers wished to purchase more than X, units, the additional units could be purchased at a lower price, say, PX2. This is shown in Figure 15.11 where the

Figure 15.11

Imperfect Price Discrimination by Units Purchased.

Market Power

demand curve DD1 represents the demand curve for one individual. Given the schedule of prices, the individual would purchase X2 units and pay an amount equal to the areas OPxlBXl plus X,ACX2. In comparison with nondiscriminatory pricing, the monopolist captures extra revenue equal to the area PXXBAPX2 from each individual and each individual’s consumer surplus is reduced by that amount. This less than perfect price discrimination is sometimes known as “block-rate pric¬ ing,” because different prices apply to different blocks or increments of the quantity purchased. For any given demand curve and total quantity purchased the revenue of the monopolist can be increased by increasing the number of blocks. As the number of blocks increases, more and more of the potential consumer surplus is captured by the monopolist as additional revenue and the price schedule approaches more closely the perfect price discrimination of Figure 15.10. A typical declining block rate structure for an electricity utility firm might look like the following:7 Quantity purchased per month (kWh) 0-

25

Price per kWh ($) ($3.40 - minimum charge)

26- 100

0.0434

101- 300

0.0248

301-1000 1001-

0.0202 0.0184

For a consumer purchasing 60 kWh the cost would be $3.40 + 35 X $.0434 = $4.92

Price Discrimination by Purchaser. Price discrimination by purchaser occurs when one seller with market power simultaneously sells his product to different sets of buyers at different prices. Suppose that the monopolist does not find it practical to vary the price charged to an individual buyer according to the quantity purchased but is able to charge different buyers different prices for the same good. It will be shown that the monopolist can increase his profits by engaging in price discrimination, if the opportu¬ nity presents itself. In order for this form of price discrimination to be practical for the monopolist, two conditions must be satisfied. First, there must be some barrier that prevents the resale or transfer of the good from one buyer to another. If resale were feasible, then a buyer being offered a low price could purchase more than her own needs and offer the remainder for sale at a price that undercuts the monopolist’s efforts to charge a higher discriminatory price to other purchasers. This form of price discrimination is feasible for services consumed by the buyer, such as health-care and legal services, and for forms

The source is rates charged to residential users by the Central Maine Power Company in 1978.

407

Prices and Quantities in Monopoly Markets

of energy delivered by a fixed distribution network, such as electricity or natural gas. Second, the two markets must have different demand conditions in the sense that at any price the demand curves in the two markets have different price elasticities. It will be shown that if the demand conditions are different in this sense, the profit-maximizing monopolist will charge different prices to the different classes of consumers. Suppose that the aggregate demand curves for two categories of consumers are D , and Du as shown in the first two panels of Figure 15.12. If the monopolist is unable to discriminate, he faces an aggregate demand curve that is the horizontal summation of D] and £>„. This is Dx in the third panel of Figure 15.12. Associated with that demand curve is the marginal revenue curve MR x. The monopolist sets a single price, Px, for all buyers where marginal cost equals marginal revenue. The total quantity produced is X. At this price category I consumers purchase Xx and category II custom¬ ers purchase Xn. Now suppose that the monopolist is free to establish different prices for the two categories of consumers. What should he do? Notice that at P x and its associated quantities, the marginal revenue from sales to category I customers is greater than the marginal revenue from sales to category II consumers. If 1 unit less were sold to category II customers, total revenue would decline by MR „. If this unit instead were sold to category I consumers, total revenue would increase by MR} > MRU. The net increase in total revenue is MR ( — MR n. Because total output and total cost are unchanged, this is a net increase to profit. Profits can be increased by reducing the quantity sold to category II consumers and increasing the quantity sold to category I consumers as long as the marginal revenue in market I exceeds that in market II. The only way consumers in category II can be induced to purchase less is by charging them a higher price. Similarly, the only way that consumers in category I can be induced to increase their purchases is by offering them a lower price. Thus the price-discriminating monopolist will lower the price to category I consumers and raise it to category II consumers until the marginal revenues in the two markets are equal. The condition for profit maximization when the monopo¬ list can charge different prices in different markets is MR] = MRU = MCX

In order to satisfy this condition, the monopolist of Figure 15.12 charges P{ to category I purchasers and P'u to category II purchasers. They purchase X[ and X'u, respec¬ tively.8 . Profitable price discrimination by purchasers requires that there be differences in the elasticity of demand in the two markets. At the nondiscriminatory price of P x in the preceding example the higher marginal revenue of category I consumers implies that the elasticity of that demand curve at Xx is greater than the elasticity of demand for

“When th lead to a curve, pr_ _

Class I Buyers

Class II Buyers Market Demand and Firm Cost Curves

408 Market Power

409

Prices and Quantities in Monopoly Markets

category II consumers at X„. The greater elasticity of demand of category I consumers means that a price decrease to them will increase total revenue more than the decline in total revenue that is associated with the increase in price to category II consumers. Profit maximization requires that a higher price be charged to consumers with the lower elasticity of demand. Recall that MR = P(1 - 1 /Ex). Profit maximization requires MR, = MR n = MCX

Rearranging gives

Pu

1 - MExl

P\

1 - l/E™

Thus Pn > Pi implies 2*i ~ 1

>

EX\

2*n ~ 1

Exu

or 2*i > Exu

Examples of Price Discrimination. One example of price discrimination across buyers is in the market for electricity. Buyers are typically grouped into three categories for purposes of demand analysis and for setting electricity prices. These categories are: residential users, commercial users (i.e., businesses, offices, etc.), and industrial users. One study of the demand for electricity has found the following price elasticities of demand for these three categories:9 Customer

Elasticity of demand

Residential Commercial Industrial

1.3 1.5 1.7

On the basis of this evidence we would expect that electric utilities would charge the highest rates to residential consumers and the lowest rates to industrial consumers and that the rate differences would be greater than those that could be justified by differ¬ ences in the cost of service. In fact, studies of electric utility rate structures have tended to confirm this prediction.

‘‘Duane Chapman, Timothy Tyrrell, and Timothy Mount, Electricity Demand Growth and the Energy Crisis, Science, November 17, 1972, 178(4062), 703-708.

410

Market Power

The price-discrimination model can also be used to clarify a controversial issue that involves the governments of Japan and the United States and the U.S. steel industry. U.S. steel producers have claimed that Japanese steel is being sold in the United States at a price less than the domestic price in Japan and in fact at a price less than the Japanese cost of production. According to U.S. law governing exports and imports, when a foreign firm sells its output in the United States at a price below its cost, this is termed “dumping.” When dumping occurs, U.S. law calls for the imposition of tariffs sufficient to make the price to U.S. buyers greater than the cost of production in the foreign country. The allegation that Japan is dumping steel in the United States raises two questions: (1) Is dumping rational behavior on the part of the Japanese steel industry? And (2) If it is occurring, what, if anything, should we do about it? As for the first question, the steel case fits the model of price discrimination. Trans¬ portation costs between the United States and Japan and Japanese import regulations impose a barrier that makes resale of imported steel back to Japanese consumers impractical. Thus the Japanese domestic market and the U.S. market are effectively separated. Also, the Japanese steel makers face a demand curve in the United States that is much more elastic than the demand in their domestic market. This is because Japanese producers must compete in the U.S. market against U.S. producers as well as against imports from Europe, Canada, and Mexico. Thus profit-maximizing behav¬ ior on the part of Japanese sellers would call for them to charge a lower price in the U.S. market than in their own. But would it be rational to charge a price below cost in the U.S. market? The answer is yes, if by cost we mean average cost rather than marginal cost. And this in fact is the definition of cost employed in the U.S. trade laws. Of course, in the short run if demand were to contract, all producers might be forced to sell at a price below short-run average cost. But in the long run revenues must cover costs. Even in the long run a price discriminating seller may find it profitable to charge a price below long-run average cost in one market, provided that the price charged in the market with a less elastic demand is sufficiently above long-run average cost. In fact, this is the case in the example shown in Figure 15.12. If price discrimination is not possible, the single price is Px, which is just equal to long-run average cost at the output of A. If price discrimination is possible, the monopolist lowers the price to market I. Thus that price is below long-run average cost. And if market / were a foreign market, this would constitute dumping according to the legal definition. Is dumping bad? From the point of view of consumers in the United States, the answer is clearly no. Dumping makes steel cheaper than would be the case if Japanese producers were forced to charge the same price in both markets. U.S. customers’ gains come at the expense of Japanese steel consumers. If the U.S. government were to impose a tariff on steel imports from Japan, the tariff would hurt all U.S. steel consumers. Those who had been purchasing Japanese steel would clearly be hurt as the price of the steel they purchased rose. And the reduced competition from Japanese producers would also allow U.S. steel producers to raise their prices. The price discrimination model can also be used to explain certain pricing practices of commercial airlines. For a number of years airlines have employed a variety of discounts and special fares in an effort to promote air travel. The most recent example

411

Prices and Quantities in Monopoly Markets

is the “super saver fare.” These special fares are accompanied by a variety of restrictions on the time of day that flights can be taken, the day of the week, the number of days layover between the travel and return, and advance booking of the reservation. These restrictions tend to make super saver fares unattractive to business people and commer¬ cial travelers who constitute a substantial portion of total air passengers. But they may be attractive to students, retirees, and to people planning vacations, that is, individuals who might not otherwise travel by air if they had to pay the full fare price. In economic terms, super saver fares are designed to be attractive to passengers whose demand curves for air travel are relatively elastic, especially in comparison with business and commercial travel. If this line of reasoning is correct, super saver fares represent an effort to engage in price discrimination on the part of airlines. This means that super saver fares lower the price to groups with relatively elastic demands and that full fare prices to buyers with inelastic demands are higher than they would be in the absence of price discrimination. Price discrimination conveys benefits to buyers with elastic demands. But this comes at the expense of buyers with inelastic demands who face a higher price and therefore a loss of consumer surplus. This observation is true for all forms of price discrimination, not only discrimination in airline pricing.

The Social Cost of Market Power One of the major issues concerning public policy toward monopoly and oligopoly firms is whether consumers could be made better off by vigorous enforcement of the antitrust laws. Microeconomic analysis predicts that firms with market power will be able to charge prices above marginal costs, thus reducing output. The higher price and lower output levels impose costs on consumers. The issue is the magnitude of these costs. In this section we outline the theoretical basis for measuring the costs of market power and present the results of a recent attempt to measure the magnitude of these costs for the American economy.

Defining the Social Cost of Monopoly. Consider a product, X, which can be produced under conditions of constant returns to scale. In other words, the marginal cost and average cost curves are horizontal. This is shown in Figure 15.13. If this good were produced by many firms in a competitive industry, the market price would be Pc, and the quantity produced and sold would be Xc. Now suppose that a single firm obtains monopoly power in the production and sale of A. If this firm sets price so as to maximize profits, it reduces output to the point where marginal revenue equals marginal cost. Thus output would be Xm and price would be raised to Pm. Consumers of product X are clearly worse off because of the monopoly. A monetary measure of this loss in welfare can easily be derived from Figure 15.13. In the competi¬ tive equilibrium consumers realized a consumer surplus equal to the triangular area p jc. With the monopoly consumer surplus has been reduced to the area PmAB. The loss in consumer surplus is the area PCPmBCD.

412

Market Power

X per period Figure 15.13

The Social Cost of Monopoly Power.

This loss to consumers has two components: (1) The rectangular area PcPmBD represents a transfer of welfare from consumers to the monopoly seller. This transfer is measured by the increase in price (Pm — Pc) multiplied by the quantity sold by the monopolist. (2) The triangle BCD is a loss to consumers for which there is no offsetting gain elsewhere in the economy. So it represents a loss to society as a whole. This is known as the inefficiency loss or social cost of monopoly power. The nature of this social cost can be made more clear by considering how consumers would benefit if production were increased from Xm. At the monopoly output level, consumers are willing to pay an amount equal to Pm to obtain one more unit of good X. This is the marginal willingness to pay or the marginal value of good X. Marginal cost is less than this marginal willingness to pay. Recall that cost is really a measure of what other things have to be given up in order to expand production of X. When we say that the marginal cost of producing X is equal to Pc, we mean that society has to relinquish other goods and services that are valued at Pc in order to free the resources to expand the production of X. When price is above marginal cost, consumers place a higher value on expanding the production of X than they do on the other goods that have to be given up in order to make greater X production possible. If society were to expand the output of X from the monopoly level, it would experience a net gain equal to the excess of its marginal willingness to pay for additional X over its marginal cost. One additional unit of A will add an amount equal to the vertical distance BD to social welfare. After expanding X by 1 unit, we find that the price will still be above marginal cost. Successive incre¬ ments to X production will add decreasing amounts to consumer welfare until the price has been brought into a quality with marginal cost. The total addition to social welfare would be the area BDC, the shaded triangle in Figure 15.13.

Measuring the Degree of Monopoly Power. The power of a monopoly to cause

413

Prices and Quantities in Monopoly Markets

welfare losses and to receive monopoly profits is related to its ability to raise the price above marginal cost. The excess of price over marginal cost in percentage terms has been used as a measure of monopoly power. Definition: The degree of monopoly power D is the excess of price over marginal cost —as a percentage of price.

P - MC D = P For any given output where MR = MC, the price will be higher the lower the elasticity of demand is at that point. In other words, price (and the degree of monopoly) and the elasticity of demand are inversely related. In fact,10 1

D = Ex

Measuring Social Cost. A number of economists have attempted to measure the magnitude of the social cost triangles for monopolized and oligopolized industries in the U.S. economy. One recent comprehensive study was published by Cowling and Mueller in 1978.11 What follows is a brief discussion of their method and results. Assuming that the demand curve is linear and that production is under conditions of constant returns to scale, then the welfare change due to monopoly power is mea¬ sured by AIT = 1 AP • AX 2

where AX = Xm — Xc and AP = Pm - Pc. This is the formula for the area of the triangle BCD in Figure 15.13. Since AX is negative, AIT is also negative; that is, it is a social cost. To compute this area directly for a monopoly firm, we must know the competitive price and quantity (point C in Figure 15.13), as well as the monopoly price and quantity (point B in Figure 15.13). But only the latter can be known by direct observation. The

‘“Recall that MR = P( 1 - 1 /Ex). In monopoly MR = MC. Substituting and rearranging gives

P P -- = MC Ex P P _ MC = Ex P - MC P

1

~ Ex

1

D = Ex "Keith Cowling and Dennis C. Mueller, The Social Costs of Monopoly Power, Economic Journal, December 1978, 88(4), 727-748.

414

Market Power

former must be inferred or estimated indirectly. Cowling and Mueller’s contribution was to develop a method for computing the welfare loss without having to estimate the shape of the demand curve that passes through point B. They were able to show that there is a simple and direct relationship between the social cost of monopoly and the monopolist’s profit. Specifically,12

2 where n = profit. Pure profits can be estimated for each firm from its published accounting data if the normal or competitive rate of return is known. Cowling and Mueller took as a measure of the normal rate of return the average returns (dividends plus capital gains) from ownership of a diversified portfolio of common stocks. This return was about 12 percent per year in the period 1963 to 1966. One might be tempted to ask whether this return would include the monopoly profits of firms in the portfolio and thus overestimate the competitive rate of return. But the answer is no. Competition in the market for shares of stock assures that the present value of any anticipated monopoly profits is capitalized into the initial prices of stocks. Recall the case of the taxicab medallion. This is also an application of the concept of efficient asset markets described in Chapter 13. Thus future buyers can realize only a normal rate of return from their purchase or sale of the shares of stocks of monopoly companies. Given an estimate of the normal rate of return, the implicit cost of capital owned by the firm can be calculated from balance sheet data. The pure economic profit is simply accounting profit less the implicit cost of capital. Cowling and Mueller used financial data for a sample of 734 large firms in the United States for the years 1963 to 1966 to compute each firm’s pure profit and the welfare cost of its market power as revealed by its economic profits. These firms together imposed welfare losses on the economy of just over $4.5 billion per year in 1963 dollars. This was about 1 percent of annual personal income for the U.S. economy and amounted to about $25 per person. In addition to this social cost, there was the transfer from consumers to producers that was represented by the rectangle PcPmBD of Figure 15.13. The transfer amounted to over $9 billion per year. The combined losses to consumers amounted to over $13.5 billion per year, over 3 percent of personal income, or about $75 per person per year. Cowling and Mueller13 also estimated the socially unnecessary expenditures as-

1!The derivation of this relationship is shown in the Mathematical Appendix to this chapter. 13The measurement of the economic consequences of monopoly power is a complex and controversial matter. This section is certainly not a complete treatment of the issues/ The intention is only to illustrate the role of microeconomic analysis and basic relationships in defining and measuring certain effects. For a fuller treatment of the issues representing different points of view, see, in addition to Cowling and Muellerm Frederick M. Scherer, Industrial Market Structure and Economic Performance (2nd ed.), Chicago: Rand McNally, 1980; Richard A Posner, The Social Costs of Monopoly and Regulation, Journal of Political Economy, August 1975, 83(4), 807-827; Dean A. Worcester, Jr. Welfare Gains from Advertising, Washing¬ ton: American Enterprise Institute for Public Policy Research, 1978, and references therein.

415

Prices and Quantities in Monopoly Markets

sociated with developing, achieving, and maintaining market power through advertis¬ ing and other activities. When these were taken into account, costs to consumers (including the transfer to monopolists) could have been as high as $24 billion per year or more than $125 per capita.

Natural Monopoly Earlier we said that one potential source of monopoly power was significant econ¬ omies of scale in production relative to the size of the market. If a firm’s production function is such that its optimum scale of production roughly corresponds to the demand for the good at a price that covers cost, this is said to be a natural mono¬ poly. Definition: A natural monopoly exists when economies of scale make it possible for one firm to supply the market without experiencing decreasing returns to scale. The term “natural” monopoly is appropriate because the barriers to entry arise not from political decisions (e.g., the requirement to hold a government license) or because of the structure of property rights (e.g., the ownership of a patent or ownership of essential natural resources). Rather, the source of barriers to entry lies in the technology of production, which reflects the nature of things. Figure 15.14 shows a typical case of natural monopoly. The demand curve Dx intersects the long-run average cost curve before its minimum point. The profit-maxi¬ mizing monopolist equates marginal revenue with marginal cost and produces an output of Xl while charging a price of Pv The natural monopoly, like all monopolies, leads to an outcome where price is greater than marginal cost, which imposes dead weight or efficiency losses on the society. Where the objective of public policy is to increase the efficiency of the economy, and

X per period Figure 15.14

The Equilibrium of a Natural Monopoly and the Efficient Level of Output Under

Price Regulation.

416

Market Power

where monopoly arises from other than natural or technological factors, a policy of promoting entry and competition in the market is appropriate. With entry there is at least the potential for price competition that would push the price down toward marginal cost (but see Chapter 16). This avenue is not open in the case of natural monopoly. Economies of scale create a natural barrier to entry. And if two firms were to divide the market, each would be forced to produce at less than the optimum scale; and costs would be uneconomically high. An alternative policy is to impose price regulation on the natural monopoly. Because efficiency requires that price equal marginal cost, the regulatory agency should set a price of P2. The quantity demanded would be X2', and at this quantity, price equals marginal cost. But notice that since X2 is still in the range of increasing returns to scale, long-run average cost is declining and long-run average cost is greater than long-run marginal cost and price. Regulation to achieve efficiency imposes economic losses on the natural monopoly. This is not a viable position in the long run. It should be noted that losses are not inevitable under efficient regulation. If the demand curve intersects the LACX curve at or to the right of its minimum point, efficient price regulation still leaves price at or above average cost. There are two possibilities open to the regulatory agency. One is to compromise on the efficiency objective and to set price equal to average cost. Price would be set at P3, and the quantity sold would be X2. The monopoly firm is earning a normal rate of return. Economic profit is 0. So this is a sustainable position in the long run. Also, the magnitude of the dead weight efficiency loss due to monopoly power has been substan¬ tially reduced. This in fact is the form that price regulation of natural monopolies has typically taken. Historically, regulatory agencies have been more concerned with limiting mo¬ nopoly profits than with achieving economic efficiency. It is only recently that regula¬ tory commissions have begun to adopt marginal cost pricing policies in regulatory decision making. The other possible approach is to retain the principle that price should equal mar¬ ginal cost at the efficient output level and to seek additional revenues in other ways. One source of revenues is a subsidy from taxpayers by the government. Subsidies are common for urban mass transit systems, passenger rail service, and the postal service, all examples of natural monopoly. The other source of increased revenues while holding output at the efficient level is block rate pricing of the inframarginal units being produced, that is, price discrimination by units purchased. As long as the last units purchased by each consumer have a price that is equal to the marginal cost of their production, economic efficiency is attained. This form of price discrimination can be used to increase revenues sufficiently to cover the excess of long-run average cost over price.14

'"Revenues could also be increased by price discrimination across buyers. But this form of price discrimina¬ tion leaves at least some buyers paying a price for the last unit purchased which is greater than marginal cost. And this is inefficient.

417

Prices and Quantities in Monopoly Markets

Figure 15.15 shows a natural monopoly for which the long-run average cost exceeds price at all possible outputs. There is no single price at which output can be sustained in the long run. This good would never be produced by a private, profit-maximizing monopolist since profits would be negative at all levels of output. Should this good be produced? The answer requires a comparison of the total cost of production with consumers’ total willingness to pay for the output. If output is set at Xx where price equals marginal cost, consumers’ total willingness to pay for this output is the area OCBXx. The total cost of producing this output is the area under the long-run marginal cost curve, OABXx. The way the curves have been drawn, total willingness to pay exceeds total cost, and the economy as a whole would be better off if this good were produced at the efficient output level of Xx. If Xx is produced and sold at Plt the loss is the area P,BGH. If this output is to be sustained, this natural monopoly must either be subsidized by taxpayers or discriminatory pricing must be used to increase revenue. If block rate pricing is feasible, a price of P2 for the first X2 units purchased in aggregate would generate additional revenue that is sufficient to cover total costs.15 Does this situation capture the realities of rail mass transit in our urban areas? These

Figure 15.15

A Natural Monopoly Requiring Price Discrimination for Financial Viability.

l'In Figure 15.14 OX2 is equal to V4 OX,- and OP2 - OP, is equal to 2 X BG. The additional revenue generated by price discrimination, P,P2EF, is just equal to the excess of cost over revenue when a single price of P, is charged (the area P,BGH).

418

Market Power

systems are typically experiencing chronic losses. As fares are increased, ridership declines; and if demand is elastic, so do total revenues. There may or may not be some fare at which losses are eliminated. But if such a fare can be found, it would be substantially above marginal cost. Should fares be set at marginal cost for these sys¬ tems? And if so, where are the additional revenues to be found?

THE MONOPOLIST’S DEMAND FOR FACTORS In this section we examine the case of a monopoly seller of a product, who, nevertheless, is a price taker in the markets for all factors of production. We have seen that a firm with monopoly power in the product market will restrict output in order to raise the price above the competitive level. It follows, then, that this firm will also restrict its demands for inputs. As a profit maximizer the monopoly firm will increase its purchase of factors as long as each additional unit purchased adds more to total revenue than it does to total cost. Thus the profit-maximizing level of factor purchases is where the addition to total revenue just equals the addition to total cost. The addition to total revenue is the marginal revenue product. And because the firm is a price taker in the factor market, the addition to total cost is the price paid for the factor. Thus profit maximization requires that MRPF = PF

for all factors. The marginal revenue product for a competitive firm is the product price times the marginal product of the factor input. But in the case of monopoly the firm is not a price taker in its output market. And MRPF is not equal to VMPF. Rather, marginal revenue product is marginal revenue times marginal product; that is, MRPp = MR x ■ MPf

Because at any given product price marginal revenue to the monopolist is less than the price, the marginal revenue product of a factor used by a monopolist is less than its value of marginal product. This is the major difference between the analysis of the competitive firm and the monopoly firm in factor markets. The former equates the factor price with the value of marginal product; the monopoly firm equates the factor price with its marginal revenue product, which is less than VMPF. In other respects the analysis parallels that of the competitive firm. Suppose that in the short run there is only one variable input, say, labor. The firm’s marginal revenue product curve for labor is shown in Figure 15.16. If the price of labor is at PLl, the firm equates its MRPL with the price of labor by purchasing L, units of labor. If the price of labor drops to PL2, MRPL is equated with PL at L2 units of labor. Thus the marginal revenue product curve for labor is the demand curve for labor for the monopo¬ list. When all factor inputs are variable, the marginal revenue product curve shifts

419

Prices and Quantities in Monopoly Markets

L per period Figure 15.16

A Monopolist’s Demand for a Single Variable Input.

because of changes in the quantities of the other inputs. The analysis is similar to that of Chapter 12. Suppose that in the initial situation the price of labor is PLX and the marginal revenue product curve of labor is MRPLl. As shown in Figure 15.17, Lx units of labor are being purchased. If the price of labor drops to PL2, the response of the monopoly firm can be divided into two components. First, there is a substitution effect as the firm substitutes the now cheaper labor for capital, holding output constant. With less capital and more labor, the marginal revenue product curve shifts in to the left. See point B in Figure 15.17. The lower price of labor causes a downward shift in the firm s cost curves and an increase in the profit-maximizing level of output. As output is increased, the inputs of both labor and capital are increased. The increase in capital causes an outward shift

0

LXL2 ^3 L per period

Figure 15.17

A Monopolist’s Demand for a Factor When All Factors Are Variable.

420

Market Power

in the firm’s marginal revenue product curve for labor. But whether the new MRPF lies to the left or to the right of MRPlA cannot be determined on a priori grounds. As depicted in Figure 15.16, the new MRPL2 chrve lies to the left of MRPL1. The equilib¬ rium quantity of labor is L3. The demand curve for labor reflecting both input substitu¬ tion and output effects is the heavy line connecting points A and C. It is downward sloping to the right, indicating that the monopolist will increase the quantity demanded of factors when their prices fall. We have shown that the monopolist equates marginal revenue product with factor price. Since the MRPF is less than VMPF, the factor price is less than VMPF. This situation is sometimes referred to as exploitation. Definition: A factor of production is said to be exploited if it is paid a price less than its value of marginal product in that activity. This is different from the concept of exploitation of labor in the writings of Karl Marx. In Marx, labor is exploited by the owners of capital. Here, all factors, including capital, are exploited under monopoly. We argued in Chapter 12 that it was difficult to find any ethical significance in the proposition that factors are paid their value of marginal product in perfect competition. For the same reasons it is difficult to attach ethical significance to the exploitation of factors under monopoly. Rather, as will be shown in Chapter 17, the major significance of factor exploitation lies in its implications for the efficient allocation of resources, that is, Pareto optimality.

MONOPSONY: THE SINGLE BUYER WITH MARKET POWER When a firm is the sole purchaser of an input in a factor market, the supply curve it faces is the supply curve of the market. If the market supply curve is upward sloping, the price that this firm will have to pay for the factor will depend on the quantity it purchases. The firm cannot take price as given. Rather, the firm can determine the price it pays, at least within some range, by its choice of a quantity to purchase. It can reduce the price it pays by cutting back on its quantity demanded; but if it wishes to purchase more, it will push the price up. Monopsony situations are not uncommon in labor markets. A paper mill or textile mill in a small town is likely to be the largest single employer of labor in that local labor market. If the mill wishes to increase the quantity of labor it is using, it will have to offer higher wages to induce people away from other employment in that town and/or to induce people from nearby towns to enter this labor market. If they want to maximize profits, all purchasers of inputs, whether monopsonists, monopolists, or competitors, must use each factor to the point where its contribution to total revenue is just equal to its contribution to total cost. What sets monopsony apart is the fact that the contribution of an additional unit of a factor to total cost is not equal to the price of that factor. Rather, because the supply curve of the factor is upward sloping, the additional unit of the factor contributes more to total cost than its price. To see this, examine Figure 15.18. If the quantity demanded of the factor is Fu its price will be PFl. If the quantity demanded is increased by 1 unit to F2, the price rises to

421

Prices and Quantities in Monopoly Markets

Figure 15.18

The Increase in Total Expenditure When the Factor Supply Curve is Upward

Sloping.

PF2. The increase in total cost is not simply the vertical shaded column up to PF2 that represents the price of the additional factor. Because all units of the factor being purchased must be paid the same higher price, the contribution to total cost includes the shaded horizontal area between PF1 and PF2. The total shaded area in Figure 15.15 is the marginal expenditure on the input. Definition: The marginal expenditure on the input is the increase in total expenditure on a factor associated with a 1-unit increase in the quantity purchased of that input. If the buyer faces an upward-sloping supply curve for the factor, the marginal expenditure on input is greater than the price. The marginal expenditure on input (MEIF) is itself an increasing function of the quantity purchased. The MEIF curve can be derived from a straight line supply curve in the following manner. If the quantity demanded is OF, in Figure 15.19, the price of the factor is Pn. Total expenditure on the factor is the area OTDF,. Recall that the area under any marginal curve is equal to the total magnitude for that variable. Thus the MEIF curve must be drawn so that at an output F, the area under the MEI curve is equal to the area OADF,. To find such a curve, draw in the horizontal line AD at PFl and bisect that line. This gives point B. Then extend a straight line upward from the intercept of the supply curve with the vertical axis through point B to C. The area under this curve OSCF, is equal to the area OADFx. This is because they share the common area OSFDF,; and they differ only in that the area under the MF/f curve includes the triangle BCD while omitting the triangle SAB. However, these two triangles are identical. The sides BD and AB are equal to each other, as are the right angles at points A and D and the angles formed by CBD and ABS,16

“By now the reader should have recognized that this construction employs the same logic as that which lies behind the construction of a marginal revenue curve from a linear demand curve (see Chapter 8). The construction of MEIF for a nonlinear supply curve uses techniques similar to those described in Chapter 8.

422

Market Power

F per period Figure 15.19

The Derivation of the Marginal Expenditure on Input Curve from a Linear Factor

Supply Curve.

We can now determine the profit-maximizing quantity of the factor for given factor demand and supply curves. Assume that although the firm is the sole purchaser of this input, it is one of many sellers in the market for its output. Competition in the output market and monopsony in input markets are not incompatible. The small town textile mill or shoe factory are cases in point. The factor demand curve is DF in Figure 15.20. If this is the only variable input, the demand curve is the value of marginal product curve. And with all inputs variable the demand curve reflects the value of marginal product of the factor after optimum adjustments to the other inputs and to output. The factor supply curve is SF. The MEIF curve is also shown. The marginal expenditure on input is equated with the value of marginal product where these two curves intersect at point A. This means that the profit-maximizing level for the input is Fx. When the firm attempts to purchase this quantity of the factor on the market, it drives the price of the factor up to PFl. One consequence of monopsony is that given the factor supply and demand curves, the factor price is lower and less of the factor is utilized than would be the case if the factor market were competitive. Another consequence is that the factor price is less than its value of marginal product. So the factor is exploited. When monopsony power exists, two conclusions that were reached in Chapters 9 and 10 must be modified. The first conclusion concerns the conditions for a profit-maximiz¬ ing optimum input combination in production with more than one factor input. As¬ sume that there are two factors, capital and labor. To maximize profit, one must use each factor to the point where its marginal revenue product is equal to its marginal expenditure on input. In other words,

423

Prices and Quantities in Monopoly Markets

Figure 15.20

The Quantity Demanded of an Input and Its Price Under Monopsony.

MEIl = MR x ■ MPl and MEIk = MR x

MPk

Rearranging each of these gives MEIl

mrx

=

mpl

PEE MPy

or MEIl

_ MP,

MEIk

~ MPk

Recall that the second term is equal to the marginal rate of technical substitution between labor and capital. Thus the profit-maximizing input combination is character¬ ized by MRTSlk

MEI, MEU

If there is a monopsony power in the labor market but not the capital market, then the ratio of the MEI's will be greater than the ratio of the factor prices.17 And the monopso-

nGraphically, the iso-cost lines are not the straight lines of Chapter 8. Rather, they are curves that are convex to the origin. The more inelastic the supply curves of the factors is, the more sharply bowed are the iso-cost lines.

424

Market Power

nist will choose input combinations with relatively less labor and relatively more capital. The second modification of our conclusions involves the cost function and cost curves. In Chapter 10 it was assumed that producers took factor prices as given. Thus factor prices were parameters in the cost function. A change in a factor price led to a shift in the relevant cost curve. With monopsony the cost function is written with input prices as functions of the quantities purchased rather than as parameters. In other words,

C(X) = C[X(K, L), Pk(K), Pl(L)] And if cost curves are drawn holding factor prices constant, any change in output necessarily leads to a change in the quantities of inputs and their factor prices. Thus cost curves shift as output shifts.

The Effects of a Labor Union in a Monopsony Market If there are many buyers of labor in a given labor market, a labor union can only increase the price of labor by artificially reducing the supply of labor, thereby creating unemployment. Figure 15.21 shows the effect of a union in a labor market with many buyers. In the absence of the union the equilibrium price and quantity would be PLl and Lx. If the union is to be successful in raising the price of labor, it must be able to control the supply of labor. If it negotiates a wage contract at PL2, the industry will employ only L2 workers. At this price there is an excess supply of labor equal to L3 — L2. If those workers were free to compete in the labor market by offering to work at a slightly lower wage, their competition would tend to push the price back to PLl.

Figure 15.21 of Labor.

The Effect of a Union in a Competitive Industry on the Price and Employment

425

Prices and Quantities in Monopoly Markets

If the labor market is characterized by monopsony power, the formation of a labor union can result in an increase in both the price of labor and in employment. In effect, the market power of the union tends to offset the market power of the monopsony firm. If the demand, supply, and marginal expenditure on input curves for labor are as shown in Figure 15.22, the equilibrium in the absence of a labor union would be at an employment of L, and a price of PLX. If a labor union were to negotiate a wage contract at any price above PLl, the effective supply curve to the industry would become a horizontal line at that price out to the true supply curve SL. With a horizontal effective supply curve the marginal expenditure on input and the price of labor coincide. If the negotiated price is PL2, the effective supply curve is PL2ASL and the MEIL curve is PL2ABM'. The demand curve intersects the MEIL curve at point A, leading to an increase in employment to L2. In fact, at any negotiated price between PLl and PL3 the higher wage results in an increase in employment. However, at prices above PL2 actual employment will be less than the quantity of labor that workers are willing to supply at that price. Thus the union will have to restrict the supply of labor to prevent wage competition only if it negotiates a wage above PL2.

The Marginal Expenditure on Oil It has been argued that the monopsony pricing model can be applied to the relationship between OPEC (The Organization of Petroleum Exporting Countries) and its major customers, the United States, the nations of Western Europe, and Japan. The argument hinges on the assumption that the price OPEC charges for its oil depends directly on the quantity demanded by the importing nations, especially the United States. Assume

Figure 15.22 of Labor.

The Effect of a Union in a Monopsony Industry on the Price and Employment

426

Market Power

that if our demand goes up, the OPEC price goes up; and if our demand goes down, the OPEC price goes down. If this is a reasonable description of OPEC pricing strategy, then the United States as a nation faces an upward-sloping supply curve for the oil it imports and the marginal expenditure on oil, or its marginal cost, is greater than the OPEC price. Some people have suggested that the marginal expenditure on oil may be three to five times higher than the posted price.18 Oil purchases in the United States are decentralized and undertaken by a number of refiners, and so forth. No single buyer of OPEC oil perceives that his action has any effect on the price of oil. All buyers view themselves as price takers in the oil market. Thus they act rationally by equating their marginal revenue product of oil with its price rather than with its MEI. This is an instance where individuals acting in their own self-interest in decentralized markets do not maximize aggregate welfare. The nation as a whole would be better off if the buyers of OPEC oil were to recognize their collective impact on the price of oil and cut back on oil purchases until their marginal revenue product of oil was equal to the marginal expenditure on oil. How can this be accomplished? One possibility is to place a tariff on the imports of oil, with the tariff being equal to the difference between the marginal expenditure on oil and the price of oil. Oil purchasers would then equate their marginal revenue products with the price of oil plus the tariff. With a sufficiently high tariff, oil purchases would be curtailed substantially; and if the assumption about OPEC pricing strategy is valid, this would result in a decrease in the price of imported oil. There are two possible arguments against the tariff on oil. First, it is not clear that the assumption concerning OPEC pricing strategy is valid. If they did not lower the price of oil in the face of declining demand, there would be no gain to the American economy as a whole. In fact, there would be a dead weight economic loss analogous to the inefficiency cost of an excise tax. And it is conceivable that OPEC would respond to the tariff by increasing the price of oil in an effort to recoup lost revenues. If that were the case, the tariff policy would backfire. The second argument concerns the impact on the domestic economy. For one, the higher price of oil to consumers would aggravate inflation. Also, the price of oil sold by domestic producers would increase to be equal to the OPEC price plus the tariff. Thus domestic oil producers would reap substantial windfall profits or factor surpluses. On the other hand, the government could use the tariff revenues to mitigate the impacts of higher oil prices on the most sensitive sectors of the economy. In any event, the purpose here is not to argue for or against a particular policy with respect to OPEC oil. Rather, it is simply to show how one of the microeconomic models outlined here can help to bring about a clearer understanding of the economic dimensions of certain policy issues.

l8See, for example, Peter Passell, The Real Price of Oil, on the Op-Ed page of the New York Times June 27,1979.

427

Prices and Quantities in Monopoly Markets

BILATERAL MONOPOLY In the monopoly models developed so far either a single seller faced many buyers or a single buyer faced many sellers. What would happen in a market if there were only one buyer and one seller? This situation is called bilateral monopoly. Suppose that the buyer’s demand curve is Dx in Figure 15.23 and that the seller’s marginal cost curve is MCX. Let us first look at matters from the point of view of the seller. The seller faces a downward-sloping demand curve and knows that marginal revenue is less than the price. She would wish to sell that quantity where the marginal revenue as shown by MRX is just equal to her marginal cost. The quantity would be Xs and the monopoly seller would wish to charge a price of Ps. Now looking at matters from the buyer’s perspective, he would wish to purchase that quantity where the marginal expenditure on X intersects his demand curve. This is XB in Figure 15.23. He would wish to pay a price equal to PB. The market cannot have two prices simultaneously. And the theory is not capable of predicting what the actual price will be. The equilibrium of this market is indetermi¬ nate. But it seems likely that the price will lie somewhere between Ps and PB. The actual outcome may depend on the relative bargaining skills of the buyer and seller. Shrewd bargainers know that they should reveal as little as possible about their own demand or supply curves to the person on the other side of the bargaining table. The buyer would like the seller to think that his demand curve is very low; and the seller would like the buyer to believe that her marginal costs are very high. So it may not be

MEX

Px, dollars

MCX Ps

Pb

O Figure 15.23

xBxs Bilateral Monopoly.

X per period

428

Market Power

reasonable to assume that either party knows the shapes of the curves they face. This simply reinforces the conclusion that the model cannot be used to predict the outcome of the bargaining process.

SUMMARY A firm with monopoly power in the product market reaches an equilibrium that is different from that of the competitive firm in two respects. First, the monopoly firm equates marginal cost with marginal revenue rather than with price. This results in the price being above marginal cost and the output being less than would be the case if the price equaled marginal cost. Second, the monopoly firm chooses inputs so that input prices are equated with their marginal revenue products rather than with the values of marginal product. The marginal revenue product is less than the value of marginal product for each input. The reduced output has its counterpart in a lower demand for inputs. Monopolists may find it to their advantage to charge different prices for different units of a good sold to a buyer or to charge different buyers different prices for the same good. These two forms of price discrimination can increase monopoly profits. If monopoly prices are regulated by law so as to eliminate the inefficiency or social cost of monopoly, the price should be set equal to the marginal cost. If there are economies of scale in production, marginal cost might be below average cost. Thus price regulation of natural monopolies may result in revenue being less than cost. Price discrimination in these circumstances can provide a means of increasing revenues to maintain the financial viability of the enterprise without incurring the social losses associated with prices set above marginal cost. If a firm is the sole purchaser of an input it has monopsony power. The monopsony firm must take account of the effect of its purchases on the price that it pays. The monopsony firm equates its marginal expenditures on inputs to their marginal revenue products. The result is a smaller quantity demanded and a lower input price than would be the case if the firm were a price taker in input markets.

KEY CONCEPTS Price discrimination Degree of monopoly power Social cost of monopoly Natural monopoly Marginal revenue product

Exploitation of factors Monopsony Marginal expenditure on inputs Bilateral monopoly

429

Prices and Quantities in Monopoly Markets

QUESTIONS AND PROBLEMS For Basic Review

.

1

Define and explain the economic significance of each of the key concepts.

2* Derive the conditions for the price and quantity that maximize profit for a monopoly firm. Explain the difference between these conditions and the conditions for a perfectly competitive firm. 3. Is it possible for an increase in demand to lead to a decrease in the quantity supplied by the monopolist? Explain. 4. (a) What are the conditions under which discriminating monopoly pricing by purchaser can occur? (b) Use graphical analysis to show that if these conditions are met, the monopolist can increase his profits by practicing price discrimination (i.e., selling at two different prices). State the conditions under which monopoly profits are maximized. Give a verbal proof of these conditions, and relate your verbal argument to your graph. (c) Why would a large manufacturer of brand name appliances (e.g., RCA, GE) also sell their products to retailing companies such as Sears for distribution under the Sears brand name (e.g., Silvertone)? 5. * In an economic system where all markets but one are competitive, and one market is monopolized, is it possible to reallocate resources in any way to increase aggregate welfare? Explain. 6. The profit-maximizing monopolist always produces and sells in the inelastic portion of his demand curve. True or false? Explain. 1* If you are charged with regulating the rate charged by a public utility, what rule would you follow? What would you do if this rule resulted in the utility losing money? 8. Assume that good X is produced by a monopoly firm. Analyze the incidence of an excise tax on good X. 9. Consider a two-person, two-good, two-factor fully competitive economy with fixed factor supplies. Describe the general equilibrium of this economy. Now assume that the production of one good becomes monopolized, for example, by merger or takeover of existing firms. Use the model to analyze the effects of the monopoly on product prices, outputs of the two goods, and factor prices. 10. * Suppose that an individual is purchasing good X from a monopolist who is practicing perfect price discrimination. What does the individual’s budget line

.

11

look like? Explain the derivation of the demand for a factor input for a firm with a monopoly in the product market but competing in the factor market under the assumption that this is the only variable factor input.

430

Market Power

Problems 1.

You are a rock concert producer planning a rock concert. The demand curve for tickets is P — 75 — 0.005Y, where P = ticket price and X is attendance. (a) The fixed cost of putting on the concert is $150,000. Marginal cost per person attending is 0. The capacity of the hall is 5000. What price should you charge to maximize profits? What would you expect to happen if you charged $10 per ticket? (b) Costs are as in (a). The capacity of the hall is 10,000. What price should you charge to maximize profits? If this price left you with unsold tickets, what would you do? What price should you charge to maximize attendance? (c) If you charged the profit-maximizing price of part (b), what would total

revenue be? What is the consumer surplus of the concert? What is the total social value of the concert? Suppose that instead of selling 7500 tickets you gave them away to individuals whose names were drawn by lot. What would be the consumer surplus and social value of the concert? (d) Capacity is 10,000. Fixed costs are $300,000 and marginal cost is 0. What price should you charge to maximize profits? (e) Marginal cost is constant at $5 per person attending. What price should you charge to maximize profits? (Do you need to know fixed costs?) 2* Port Clyde Cab Company has a local monopoly on providing radio dispatched taxi service. It has been determined that the relationship between total revenue and the price per ride charged by the company is TR = P ■ X = 4000P - 1000P2

The total cost is a function of the number of rides, X, as follows: C = 1500 + X

(a) Assuming that the company acts to maximize its profits, what price should it charge? What quantity will it sell? What will its total profit be? (b) Monopoly causes a social cost due to restricted output. What is the magnitude of the social cost of this monopoly? (c) Assume that the company has been taken over by the new socialist government

of Port Clyde. The government wishes to set prices for its socialist enterprises so as to achieve an efficient allocation of resources. What price should it set? If the price is set at this level, what will its total cost be? What will its total revenue be? What will its profit (loss) be?

(d) The government decides alternatively to set the price per ride so as to have a 3.

“breakeven” operation. What price should they set? Consider a labor union that is negotiating a wage contract with a monopsony buyer of labor. Show how to find the optimum wage bargain (PL) from the union’s perspective under each of the following assumptions:

431

Prices and Quantities in Monopoly Markets

(a) The union’s objective is to maximize employment or quantity of labor

purchased. (b) The union’s objective is to maximize the price of labor without decreasing employment. (c) The union’s objective is to maximize the dues revenue it collects from its members where dues are a fixed dollar amount per member employed. (d) If the purpose of the analysis is to make comparative static predictions about the direction of the change in PL when the demand for output changes, does it matter which assumption is made concerning the union’s objective?

For Discussion 1.

“That price increases usually follow wage [increases] shows, more than incidentally, that profit maximization is not a purpose of the technostructure [management of monopolies and oligopolies]. If revenues can be increased just after a wage increase, they could obviously have been increased well before.” John Kenneth Galbraith, Economics and the Public Purpose, page 118. Discuss. Specifically, is the behavior described by Galbraith inconsistent with profit

maximization? 2. * It is sometimes said that if a monopoly firm is forced to incur additional costs to control pollution, it will simply pass these costs on to consumers in the form 3.

of higher prices. Discuss. Suppose a tax of t per unit of labor employed is levied on a monopolist. What would be the effect of the tax on quantity of labor purchased, output and price? Suppose that the tax is on the utilization of capital. Suppose that the tax is t

percent of accounting profit. 4. * When a monopolist can discriminate by purchaser, the social cost of monopoly power is greater than in the case of an ordinary, nondiscriminating monopolist. Why is this?

SUPPLEMENTARY READINGS Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach (3rd ed.). New York: McGraw-Hill, 1980, Chapter 7. Kahn, Alfred E. The Economics of Regulation: Principles and Institutions. New York: Wiley, 1970, especially vol. I, Chapter 5. Kessel, Reuben. Price Discrimination in Medicine, Journal of Law and Economics. October 1958, 1, 20-53. Stigler, George J. The Theory of Price (3rd ed.). New York, Macmillan, 1966, Chapter

11.

432

Market Power

MATHEMATICAL APPENDIX TO CHAPTER 15 Profit Maximization for the Monopolist Profit 7r is total revenue minus total cost, or 77 = TR - TC = Px ■ X - C(X) The demand function, XD = XD(Px,. ..), can be inverted to express price as a function of the quantity to be sold: Px = Px(X> ■ ■ .)• The problem is to maximize profit; that is, Max 77 = Px(X) ' X — C(X) Taking the first derivative with respect to X and setting it equal to zero gives — = Px + ^ • X - dC/dX = 0 dX dX =

^ 1 _ J_ j _ dC/dX = 0

We have shown in Chapter 8 that the first term is equal to marginal revenue. The second term is the change in total cost for a small change in output. Therefore the first-order condition for profit maximization is MRX - MCX We must still find the second-order condition to assure a maximum rather than a minimum of profit. To simplify the notation, let TRX stand for total revenue (Px ■ X ). Then a27r

_ 32TRx

dX2

dX1

d2C(X) dX2

The second-order condition for a maximum requires that this expression be nega¬ tive. The first term is the slope of the MR curve, whereas the second term is the slope of the MC curve. The second-order condition requires that the slope of the MR curve be algebraically less than the slope of the MC curve. In other words, the MC curve must cut the MR curve from below. This condition is satisfied in Figure 15.1.

The Effects of Taxes on Monopoly Output and Price Suppose that a tax of t per unit is imposed on the monopolist. Letting TRX stand for total revenue, monopoly profit is then (i)

77

= TR y - C(X) - t ■ X

Profit maximization requires that

433

Prices and Quantities in Monopoly Markets

.... 37r

3TRX

dC

dX

dX

(n)- = ----1 = 0

dX or

MR x = MCX + t Take the total differential of (ii) to obtain s2TRx

dx _ d2C(X)

3X2

dX - dt = 0

dX2

Rearranging and solving for dX/dt gives

dt

32TRx/dX2 - d2C(X)/dX2

Because the denominator of the right-hand side must be negative to assure a profit maximum, dX/dt < 0 and the tax reduces output. With a reduction in output, price must increase as long as the demand curve is downward sloping. In order to investigate the size of the price change, we must first solve the profit maximization condition for price. dC 1 \ (iv P ( I— - + t dX V Ex ) , x „ 3C (v) P = t + - -X 3X dX Taking the total differential of (v) and solving for dP/dt gives (vi)

dP_ =

dt

1 +

32C

dX2 3 2P —X dX2

dX

3P

dX

dt dX

dX

dt

dt

The sign of the third term in (vi) is negative since dP/dX and dX/dt are both nega¬ tive. The signs of the second and fourth terms depend on the slope of the MC curve and the direction of curvature of the demand curve, respectively. It is possible for both terms to be positive and thus for dP/dt to be greater than 1. However, if the MC curve is horizontal or upward sloping and if the demand curve is a straight line or is concave to the origin, the last three terms in (vi) are negative and dP/dt must be less than 1. Because we have already established that it is greater than 0, we conclude that in those circumstances a per unit excise tax raises price by less than the amount of the tax. A franchise tax or license fee has no effect on price or output. If F is the amount of the tax, profit is 77 = TRX - C(X) - F

434

Market Power

The first-order condition for a profit maximum is — = MRX - MCX = 0 dX Because F is independent of output, it drops out when the profit equation is differen¬ tiated with respect to output. Suppose that there is a tax on profit of t percent. The net or aftertax profit is ttn =

77(1

- 0 = TRx - C(X) - t[TRx - C(X)] = (1 - 0 [TRX - C(X)\

Differentiating gives = (1 _ 0 (MRX - MCX) = 0 dX Since (1 — t) is positive unless t = 100 percent, the second parentheses must be 0. So MRX = MCX The profit-maximizing output is unchanged with the imposition of a tax on profit.

A Formula for the Social Cost of Monopoly As shown in Figure 15.12, if the monopolist has constant returns to scale, the welfare change is the area of the triangle representing social cost; that is, (i) AW = j ■ AX ■ AP Since monopoly causes a decrease in output, AX and AW are negative. Multiply (i) by Xm/Xm, obtaining . (ii) AW = -f 2

AX AP-■ Xm y

Marginal revenue, price, and elasticity are related as follows:

Since for the monopolist, MR = MC, we have (iii) MC = Pm and by rearrangement (iv) Ex =

Pm Pm - MC

With constant returns to scale the constant MCX is also an estimate of the competitive price, Pc. Therefore

435

Prices and Quantities in Monopoly Markets

(v) Pm- MC = Pm - Pc = AP Substituting (v) into (iv) gives (vi) Ex = AP From the definition of elasticity of demand, we have , ... a* (vn)

AP

7

“

T~ r m

=

m

Substituting (vi) into the right-hand side of (vii) gives (vi,,) M. _ _ ,

xm

Finally, substituting (viii) into (ii) gives (ix) AW = -j AP ■ X„ This still contains the unobserved AP. But as Figure 15.12 shows, APXm represents the profits due to market power. If monopoly profits can be measured, the social cost of monopoly is simply one-half of profits; that is, 2

CHAPTER 16 Oligopoly and Monopolistic Competition: The Economics of Interdependence INTRODUCTION

A

1oligopoly is an industry characterized by a small number of sellers. The fewness of sellers leads to the two key features of an oligopoly industry. The first is that each seller has the power to influence the market price through its own actions. Each seller is large enough relative to the market so that changes in its own quantity offered for sale lead to changes in the market price. The second key feature is the recognition by each of the members of the industry of a mutual interdependence. This interdependence stems from the fact that each seller has an influence on the market price and each seller’s success or failure depends on the actions of its rival oligopolists. For example, firm A’s profit-maximizing quantity supplied depends in part on the amount of the product offered to the market by firm B. But firm B’s optimum quantity depends on A s decision about supply. The nature of this interdependence and its implications for the behavior of oligopoly firms will be explored more fully in this chapter. This simple definition of oligopoly hides a number of ambiguities and problems, because, in fact, the term oligopoly covers several different kinds of cases, and each one has different implications for understanding the behavior of oligopoly firms. “Few” is an ambiguous word. It can refer to an industry with only two sellers, a situation known as duopoly. But the upper limit on the number of sellers that fits the definition is hard to pin down. In practical terms, an industry is an oligopoly as long as the number of firms is small enough so that each firm has some influence over price and each firm must take into account the actions of other firms in its own decision making. An industry is termed a pure oligopoly if firms are producing a homogeneous or undifferentiated product, so that buyers are indifferent as to the source of the product they purchase. Examples might include standardized industrial commodities such as 436

437

Oligopoly and Monopolistic Competition: The Economics of Interdependence

petroleum products or basic industrial chemicals. An industry is a differentiated oligopoly if there are perceived differences in the quality or characteristics of basically similar products across sellers. Automobiles, major household appliances, and break¬ fast cereals are examples of differentiated oligopolies. Even the concept of the industry is ambiguous when firms are selling differentiated products. Typically, the industry is defined as a collection of firms selling the same product. But with product differentiation, this must be interpreted to mean firms selling closely similar products. Some judgment must be used in determining which products are to be lumped together as similar. The concept of substitutability provides a more reliable basis for determining groups of similar products than does some approach based on the physical characteristics of a product. For example, the good air transporta¬ tion from New York City to Washington, D.C. is very similar to the good air transpor¬ tation from San Francisco to Los Angeles. But they are not close substitutes for one another. Rather, bus and train transportation from New York City to Washington, D.C. are much closer substitutes for air travel between these two cities. In principle, an industry can be defined as those firms selling a group of products that have high positive cross-elasticities of demand among themselves. Where cross¬ elasticities of demand are high, the mutual interdependence among firms is also high. But what numerical value constitutes a “high” cross-elasticity of demand? As a practi¬ cal matter this must be left to the judgment of the analyst and decided on a case-by-case basis. Most of the analyses of the large, oligopoly corporation have taken one of two directions. One set of research questions focuses on the interaction between the firm and its market environment, including its rival firms. These analyses typically assume purposeful behavior on the part of the firm as an entity, that is, the firm strives to maximize something. That “something” is usually but not always assumed to be profit. It has been suggested that other objectives might include maximizing sales or maximiz¬ ing the rate of growth of the firm, both subject to a constraint that profits exceed some minimum level to assure the long-run viability of the firm.1 The objective of these analyses is to produce comparative static predictions concerning changes in price and quantity under various circumstances. The other direction that analyses of the firm have taken is to examine the internal workings of the firm as an organization. Here the objective of the analysis is to explain how pricing and resource allocation decisions are made within the firm under various assumptions about organization, the structure of property rights, and the degree of knowledge and motivation of decision makers. The major emphasis in this chapter will be on making comparative static predictions about price and quantity on the basis of models that deal explicitly with oligopolistic

'For a good discussion of alternative objectives of the firm and references to the original literature, see Malcolm C. Sawyer, Theories of the Firm, London: Weidenfeld and Nicolson, 1979, especially Chapter 7. He shows that in most cases where comparative static predictions are possible there are no qualitative differences between the predictions yielded by profit-maximizing models and those yielded by models in which firms maximize other variables. In other words, the predicted direction of change is the same.

438

Market Power

interdependence. We will see that this interdependence makes it very difficult to derive comparative static predictions about price and quantity changes in many realistic situations. Those models that deal with interdependence in a realistic way often do not yield any predictions. And the models that simplify the problem of interdependence to make it tractable to conventional methods of analysis often yield predictions that are contradicted by the evidence. In this respect the microeconomic analysis of oligopoly behavior cannot be said to have been successful. The models presented in this chapter serve primarily to illustrate the nature of oligopolistic interdependence and the difficul¬ ties in modeling the complexities of oligopolistic behavior with conventional analytical tools.

MODELS OF INTERDEPENDENCE The essence of oligopolistic interdependence is that firm A’s profit depends on what A decides to do about its price and quantity, as well as on firm B’s decisions. But B’s decisions are likely to be influenced by what he thinks A will do. What should A assume about B’s behavior when making decisions? A good analogy is the childhood game of hiding a coin in one of your hands and having your opponent guess which hand the coin is in. You might reason as follows: 1. “Since I hid the coin in my left hand on the last play, he will think I will switch to the right hand this time. So I will fool him by placing it in the left hand again.” 2. “But he might anticipate this ploy. So perhaps I can fool him by putting the coin in my right hand.” 3. And so forth. This line of reasoning is fruitless. In order to make a decision about which hand to place the coin in, you must commit yourself to some assumption about how your opponent will guess on the next move. There are several types of assumptions you might make about your opponent: 1. Assume naive behavior on the part of your opponent—he always guesses the left hand. 2. Assume he has a simple decision rule—he believes you will always shift hands. 3. Assume he believes you will not shift hands. 4. Assume he realizes that no simple decision rule will work well for him and guesses randomly—for example, flip a coin and guess “right” if it is heads and “left ’ if it is tails. If you believe that is his decision rule, you might as well decide which hand to put the coin in on a random basis. In each case you can make an optimum decision given that your assumption about your opponent’s behavior is true. The outside observer could also predict your behavior if she knew what assumption you had made about your opponent’s behavior. (But so could your opponent.)

439

Oligopoly and Monopolistic Competition: The Economics of Interdependence

All the models discussed in the remainder of this section make some assumption about the beliefs oligopolists hold about their rivals’ behavior. The models differ pri¬ marily with respect to the nature of the assumption made about oligopolists’ expecta¬ tions concerning rival responses. The models with the simplest assumptions lead to determinate results; however, they imply that people never learn from their own experience or from their observations of others' behavior. The more sophisticated models capture the problems of decision making with interdependence in a more realistic manner, but they do not yield determinate conclusions. This is the unresolved problem in oligopoly theory. We start with a simple model.

A Primitive Model The primitive models of interdependence are characterized by very simple assumptions about how each oligopolist expects the other to behave. Furthermore, these expecta¬ tions are wrong in the sense that each oligopolist actually behaves in a manner different from that expected by his rival. Yet no one learns from his experience; no one alters his expectations. Because of this, these models might better be called “dumb oligopo¬ list” models. The first and perhaps the most primitive of this type of model was developed by Augustin Cournot, a nineteenth-century Frenchman who was the father of mathematical economics. In the simplest version of the Cournot model there are only two sellers and the product is produced at zero marginal and average cost. This latter assumption permits a simple graphical exposition of the model. A more general version of the model with positive production costs is presented in the Mathematical Appendix to this chapter. If there are no barriers to entry in an industry with zero marginal and average cost, the situation of duopoly cannot prevail. At any nonzero price established by the two sellers they will earn profits. These profits will be an incentive for entry of new firms. Entry will continue as long as price and profits are greater than 0. The equilibrium of the industry with no barriers to entry requires a zero price and zero profits. For purposes of comparison we will call this the competitive solution. Let the market demand curve for the good in question be DD' in Figure 16.1. If there is only one seller whose monopoly position is protected by effective barriers to entry, the monopolist will equate her marginal revenue with the zero marginal cost. She will sell OY, at a price of Pxl. This is the monopoly solution. Now assume that there are two firms that are protected against further competition by effective barriers to entry. The market price will be the price that just clears the market given the quantity supplied by the two firms together. In other words, price is a function of the sum of the outputs of the two firms.2 The basic assumption underlying the Cournot model is that each firm takes the output of the other firm as given and believes that it will not change. The equilibrium of the market in the Cournot model

2The demand function X = f(P) can be solved for P as a function of X, giving P = f + X2).

l(X) = f

(*,

440

Market Power

Figure 16.1

The Cournot Model of Duopoly.

is reached by a sequence of steps in which first one firm and then the other adjusts its output according to its belief about the behavior of its rival. Let firm I be the first firm to make a production decision. Initially, neither firm is producing, so firm I believes that firm II will continue to produce nothing. Thus firm I’s effective demand curve is the market demand curve DD'. Firm I chooses the monopoly solution with output OX, and price Pxl. Now firm II chooses its production level believing that firm I will hold its output constant. Firm II’s effective demand curve is the segment AD', with X, as its origin. It equates its marginal revenue with the zero marginal cost by producing an output of X2 — X,. This addition to output pushes the market price down to PX2. Now firm I has reason to change its output. Given firm II’s output, which is i OX, firm I’s effective demand curve hits the horizontal axis at | OX. Given the linear demand curve of this example, marginal revenue is 0 at an output of k • I OX = | OX. So firm I cuts its output from OXx = \ OX to | OX. Because firm I, contrary to expectation, has reduced output, it is to firm II’s advan¬ tage to increase output. This induces firm I to decrease output further. The process continues until each firm finds that it has no incentive to change its output, given the most recent output decision of the other firm. This will be when each firm’s output is j OX and price is Px3, as shown in Figure 16.2. This is an equilibrium since if firm I is producing } OX, firm II’s effective demand curve hits the horizontal axis at y OX; its marginal revenue is 0 at f jOX = }OX = OX,. By the same line of reasoning, given that firm II has selected its profit-maximizing output of } OX, firm I has no incentive to change its output. In equilibrium, the total output in this market is at OX4. This is less than the competitive solution but more than the monopoly solution of OX,. Price is PX3. This is greater than the competitive solution but less than the monopoly solution.

441

Oligopoly and Monopolistic Competition: The Economics of Interdependence

Figure 16.2

The Equilibrium of the Cournot Duopoly Model.

In this model each firm follows a simple fixed rule in determining its output. There¬ fore each firm’s behavior can be described by a reaction function that gives its profitmaximizing output as a function of the output chosen by the other firm. A reaction function is a formal expression of the decision rule each firm follows in choosing its output. Each firm’s reaction function can be plotted graphically. Continuing with the example of Figures 16.1 and 16.2, we have seen that if firm II chooses an output of 0, firm I will choose an output of OXY. This is shown as point I' in Figure 16.3, where

Figure 16.3

Reaction Functions for the Cournot Duopolists.

442

Market Power

firm I’s output is plotted on the horizontal axis and firm II’s output is plotted on the vertical axis. If firm II chooses to produce OX, the market price is 0 and firm I will choose an output of 0. This is point I. The straight line connecting these points gives the profit-maximizing output for firm I for all possible output choices of firm II. By similar reasoning, firm II’s reaction function can be derived. It is the line II II'. The process of reaching an equilibrium can be described with these reaction func¬ tions. If firm I goes first, it chooses to produce OXt as shown by point /' in Figure 16.3. Given this, firm IPs response is shown by point A on its reaction function IIII'. Now firm I has an incentive to move to B on its reaction function. The process continues until the equilibrium is reached at the intersection of the two reaction functions at point C. Here neither firm has an incentive to change its output, given the output choices of the other firm. In equilibrium the two firms share a total profit equal to the area OPx3BX, in Figure 16.2. Notice that if the two firms could agree to restrict their total output to OXu they could share a larger total profit equal to the area OP^X,. Thus the firms have an incentive to collude or form a cartel. We will return to this point later. The Cournot model has a determinate solution. An equilibrium price and quantity can be found. Comparative static hypotheses can be deduced from the model. For example, if costs increase, both firms will decrease their quantities and price will increase. But the model is based on a very unrealistic assumption about the expectations that a firm holds about its rival’s behavior. Each firm is assumed to believe that its rival will never adjust its output in response to their own output choices. Each firm takes account of the effects of its own output choice on market price but believes that other firms will ignore these price changes and hold their own outputs constant. Firms continually see that their rivals are behaving contrary to expectation; that is, rivals are changing their own outputs. What is most unrealistic about the model is that firms do not alter their expectations as they accumulate experience about their rivals’ behavior. Our purpose in this discussion is not to ridicule the Cournot model. It was an extraordinarily sophisticated modeling effort for its time. It was followed by other models that made different assumptions about expectations and oligopolists’ percep¬ tions of their interdependence. But in each case the modeling efforts involved fairly simple-minded rules and required each firm to hold the view that its rival would not behave as it itself would behave, that is, that its rivals would not make profit-maximiz¬ ing adjustments as conditions changed. Eventually, this approach to modeling oligopo¬ listic interdependence came to be viewed as a dead end. We now turn to some other approaches to developing a theory of oligopoly behavior.

The Kinked Demand Curve The kinked demand curve model is based on a pair of specific assumptions about the oligopolist’s expectations concerning rivals’ responses to changes in its own price. Suppose that the oligopolist has established price ?! and is selling quantity X 1} as shown at point A in Figure 16.4. Assume that this is a differentiated oligopoly so that rivals’ products are not perfect substitutes for this oligopolist’s output.

443

Oligopoly and Monopolistic Competition: The Economics of Interdependence

Quantity.

Suppose that this oligopoly firm contemplates changing its price. If the oligopolist believes that rivals will hold their prices constant in response to an increase in price, then he can anticipate a fairly substantial reduction in quantities sold as his customers shift to purchasing the rivals’ products. Thus the oligopolist will perceive that his demand curve above and to the left of point A is relatively elastic; and the greater the degree of substitutability between products is, the greater will be the elasticity of the perceived demand curve above point A. Further, suppose that the oligopolist believes that rivals will match any reduction in price that he makes. Then if he cuts price, he cannot expect to draw customers away from his rivals. Rather, his increase in quantity sold will reflect only his share of the larger quantity demanded in the market. Given this expectation, the oligopolist per¬ ceives that his demand curve for prices below P, is relatively less elastic. This is shown by the line segment at AD’ in Figure 16.4. The demand curve that reflects these expectations is the “kinked” demand curve DAD'. It must be emphasized that this is not the true market demand curve based on individual preferences that was derived in Chapter 8. Rather, it is a perceived demand curve. In fact, Paul Sweezy, the economist who developed the model, called it an “imaginary demand curve.”3 Using the standard technique for finding the marginal revenue for a given demand curve, it can be shown that the marginal revenue curve faced by the oligopolist with these expectations has an unusual feature. At prices above P, with quantities below

’Paul M. Sweezy, Demand Under Conditions of Oligopoly, Journal of Political Economy. August 1939, 47(4), 568-573.

444

Market Power

Xi, the marginal revenue curve is the line segment DB in Figure 16.4. But since the slope and elasticity of the demand curve change abruptly at point A, there is a gap in the marginal revenue curve at X{. The marginal revenue curve associated with the segment of the demand curve to the right of Xl is the line segment CE. Suppose that the oligopolist’s marginal cost curve is as shown in Figure 16.4. It passes through the gap in the marginal revenue curve. The oligopolist has no incentive to change its output (and price), because at any other output, MR and MC would not be equal. In fact, even if the marginal cost curve were to shift up or down somewhat, as long as it still passed through the gap in the marginal revenue curve, there would be no incentive to change price. This leads to the major prediction of the model of the kinked demand curve: The prices charged by oligopolists will remain unchanged in the face of moderate increases or decreases in costs. The model also predicts that price rigidity is likely in the face of moderate changes in demand. For example, if the demand curve shifts out, the kink will still occur at the same price but at a higher output. At least if the marginal cost curve is not rising rapidly, it still may pass through the gap in the marginal revenue curve at the higher output. Thus with an increase in demand, there is an increase in quantity sold by the oligopolist, but no incentive to change price. These predictions provide a basis for empirical testing of the model. Unfortunately, these predictions find almost no support in the empirical evidence on the behavior of prices in oligopoly industries. Stigler examined the pricing behavior of firms in seven industries to determine whether price cuts by one firm were more likely to be matched by rivals than price increases. The actual pricing behavior of oligopolists was not consistent with the expectations assumed to be held by oligopolists.4 This evidence does not establish that oligopolists do not hold the expectations assumed in the model. It only suggests that if they do hold these expectations, they will be fooled by experience. A more fundamental test of the model involves a comparison of the degree of price rigidity in oligopoly markets and other markets. Stigler performed these tests and summarized his results as follows: 1. Monopolies had no kink, so these prices should be more flexible than those of oligopolistic industries. . . . The reverse was the case. 2. The fewer the number of firms, the less probable the kink, because of the realization that price increases that were not followed would quickly be rescinded. The facts were the reverse: price changed more often and more widely, the larger the number of firms. 3. Price leaders who were dominant firms . . . should have no kinks and hence have more flexible prices. The reverse was true. 4. The kink is sharper, the more elastic the upper branch, so prices should be more

4George J. Stigler, The Kinky Oligopoly Demand Curve and Rigid Prices, Journal of Political Economy, October 1947, 55(5), 432-449. For further discussion, see George J. Stigler, The Literature of Economics: The Case of the Kinked Oligopoly Demand Curve, Economic Inquiry, April 1978, 16(2), 185-204.

445

Oligopoly and Monopolistic Competition: The Economics of Interdependence

flexible with oligopoly with differentiated products than those with homogeneous products. This prediction was also contradicted. 5. The kink disappears when firms collude. Prices proved to be more rigid in periods of known collusion.5 All in all, it appears that the kinked demand curve model is unsuccessful in reflecting the realities of oligopolistic interdependence. The assumption about oligopolist’s expec¬ tations of rival responses may be reasonable in the case of an oligopolist who wishes to experiment with its price, that is, to change price in an effort to find the profitmaximizing position. But the assumption seems inappropriate in the case of an oligopo¬ list considering how to respond to a change in demand or cost. Changes in demand or cost typically affect all firms in the industry. If, for example, labor costs increase and the oligopolist is considering an increase in price, he can reasonably expect that his rivals, being similarly affected, will also be contemplating price increases. Thus it would be unlikely that they would hold their prices constant if he were to raise his price. It would seem that in general the oligopolist should be willing to change the price in the indicated direction whenever there are industrywide changes in cost or demand, be¬ cause he could expect rivals to be taking similar actions.

Oligopoly and the Theory of Games The models described so far have assumed either explicitly or implicitly that the oligopolist desires to maximize profits and is able to determine the profitability of alternative price or quantity choices. They also have taken it for granted that the relationship between rival oligopolists is one of conflict. But the interdependence be¬ tween oligopolists may make it impossible to identify a unique profit-maximizing price. Also, one way of coping with interdependence is to cooperate in the achievement of a shared goal, for example, the maximization of collective profits. What is required is a mode of analysis that will illuminate the difficulties in identifying profit-maximizing courses of action and which includes cooperative behavior as a possible option. The theory of games based on the work of John von Neumann and Oskar Morgenstern provides such an analysis.6 Consider the following problem, known as “The Prisoners’ Dilemma”: The police have arrested you and a friend and charged you both with a serious crime. However, the evidence against you both is weak and circumstantial. If neither of you confesses, the district attorney will have to settle for a conviction on a lesser charge carrying only a small penalty, say, six months in jail for each of you. The district attorney places each of you in separate cells, making communication between you and your friend impossible. Then she offers you the following deal. If you confess and provide

‘George J. Stigler, The Literature of Economics, pp. 189-190. ‘John von Neumann and Oskar Morgenstern, Theory of Games and Economic Behavior, Princeton, N.J.. Princeton University Press, 1944.

446

Market Power

the evidence that will make it possible to convict your friend of the serious crime, he will be sentenced to the maximum penalty, say, 10 years; and you will be set free. You know she has offered the same deal to your friend. However, if you both confess, she cannot set you both free. Rather, you will both be sentenced to shorter terms, say, five years. What would you do?

Your choices and the possible outcomes are displayed in Table 16.1. As the table makes clear, you cannot determine the best course of action for you without knowing what your friend will do. You are better off collectively if neither of you confesses. And if you could communicate with your friend, no doubt you would both agree to this course of action. But in the absence of communication, you have to consider the possibility that your friend will confess in an effort to get free and to protect himself against having to serve a ten-year term in the event that you confess. The prisoners’ dilemma has all the elements of a formal game of the sort analyzed in game theory. Each player must choose a strategy, that is, a specification of the actions to be taken under all possible contingencies as the game unfolds. A strategy must be chosen in the absence of knowledge of the future moves of the opponent. And the outcome of the game depends on both what strategy you choose and the actions of your opponent.

The Maximin Solution. The simplest form of the game has only two players and involves the division of a fixed sum. This is called a constant-sum game because for all possible outcomes the sum of the winnings of the two players is a constant. If the constant is 0, this is a zero-sum game. Matching pennies is an example of a zero-sum game. Table 16.2 shows the possible outcomes for a two-person, zero-sum game where each player has three alternative strategies. The table is called a payoff matrix, because the numbers in the table show the payoff or gain to player A for each possible outcome. For example, if A chooses strategy II and player B chooses strategy III, A loses $1. And since the sum of the payoffs must equal 0, B therefore wins $1. Suppose that the game is played sequentially; that is, A plays first, and then B responds. Put yourself in the position of player A. What strategy will you choose? Strategy III has the highest payoff to you if B chooses her strategy I or III. But if you

Table 16.1

The Prisoners’ Dilemma Your friend

You

Confesses

Does not confess

Confess

You serve He serves

5 years 5 years

You serve He serves

0 years 10 years

Do not confess

You serve He serves

10 years 0 years

You serve He serves

Vz year Vz year

447

Oligopoly and Monopolistic Competition: The Economics of Interdependence

Table 16.2

A Payoff Matrix for a Zero-Sum Game (in dollars) Player B Strategy

Player A Strategy A ( Strategy Au Strategy A]U The maximum payoff for each column (minimum payoff for B) (f)

The minimum payoff of each row (*)

5, +5 -5*

+ 4*}

+6

+4

+3

-1

-5

+ 8tv

+i*

+ 7t

+1

+8

+4

+7

choose strategy III, it is in B's best interest to choose strategy II because this minimizes her loss. Thus your payoff would be only $1. If you expect that B will choose the best option open to her (and therefore the worst for you), you should look for the lowest possible outcome for each strategy; that is, identify the minimum payoff in each row and choose the strategy with the highest minimum. This is called a maximin strategy because it involves maximizing the minimum or worst possible outcome. The maximin strategy for A is I. Alternatively, if B goes first, and she expects A to choose his best strategy condition¬ ed on her choice, she would identify the maximum payoff to A (B’s minimum payoff) in each column and choose that strategy/column with the lowest maximum payoff to A. (Remember that this is a zero-sum game so that T’s gain is B’s loss.) This is a minimax strategy. B ’s minimax strategy is II, which assures her of a loss no worse than $4. If A and B follow maximin and minimax strategies, respectively, neither player has any reason to regret his or her choice after the fact. Given that B has chosen strategy II, A’s maximin strategy I is also optimal in that other strategies would have lower payoffs ($3 and $1, respectively). No other strategy has a higher payoff for A. If we knew the payoff matrix, and if we assumed maximin and minimax behavior on the part of the two players, we could predict the outcome of this particular game. Unfortunately, the determinateness of this game is a contrivance. Not all zero-sum games have stable equilibrium outcomes of this sort. And for some games maximin behavior can be shown to be counterproductive. For example, in the prisoners’ dilemma game maximin behav¬ ior would lead both players to choose to confess. Table 16.3 shows the payoff matrix for a zero-sum game for which maximin behavior does not lead to a determinate outcome. This payoff matrix differs from that of the previous game only in the payoff when A chooses I and B chooses II. But this small change has a big effect on the outcome. A’s maximin strategy is still I and B’s minimax strategy is still II. But if B chooses II, A would prefer to shift to strategy II. Maximin is no longer optimum for A. If A chooses II, B would prefer I; and so forth. The outcome of the game cannot be predicted.

448

Market Power

Table 16.3

A Payoff Matrix for a Nondeterminate Zero-Sum Game (in

dollars) Player B

Player A +5 -5*

Strategy A ^ Strategy A n Strategy Am The minimum payoff for each column (minimum payoff for B) (|)

The minimum payoff of each row (*)

Bw

£,„

+ 2*

+6 -1

+2 -5

+ 7t

+1

+ 8f

+ 3t +i*

+8

+3

+7

Game Theory and Cooperation. The zero-sum game is a special case in game theory. And its payoff matrix may not accurately reflect the realities of oligopoly. A game in which the sum of the payoffs to the two players depends on the combinations of strategies chosen is called a variable sum game. The example in Table 16.4 might be representative of the situation faced by two duopoly firms. Suppose that if the two duopolists adopt low-price strategies, they both incur losses of $5. If A adopts a low price and B adopts a high price, A captures a large share of the market and reaps profits of $15 while B experiences losses of $9. The sum of the payoffs is $6. If both adopt high prices, they have profits of $10 and the sum of the payoffs is $20. This is a determinate game in that if both players adopt a maximin strategy, they will both choose low prices and neither will wish to change its strategy, given the choice of the other player. But clearly both players would be better off if they could both agree to pursue high-price strategies, because with high prices the joint payoff is maximized

Table 16.4

A Payoff Matrix for a Positive Sum Game (in dollars) Firm B

Firm A

Set a low price

Set a high price

Set a low price

A - 5* 5- 5f

A + 15 5- 9

Set a high price

A— 9 5 + 15

A + 10 5 + 10

*Maximin for A. +Minimax for B.

449

Oligopoly and Monopolistic Competition: The Economics of Interdependence

at $20. This is an example of a cooperative game, that is, a game in which there are incentives to cooperate toward the achievement of joint objectives, in this case, joint profit maximization. Note that the structure of this game is identical to that of the prisoners’ dilemma game. Note also that explicit agreement to cooperate may not be necessary to achieve joint profit maximization. If both players recognize the structure of the game and its payoff matrix, and if they both have reason to believe that the other player also understands the nature of the game, they may tacitly cooperate to their mutual benefit. Does game theory provide us with a good positive theory of oligopoly behavior? Unfortunately, the answer is no. The analysis of games has not been able to identify equilibrium outcomes except in the special case of the determinate zero-sum game, and these models have not yielded any testable comparative static hypotheses about oligopoly pricing decisions. But game theory has made several contributions to our understanding of oligopolistic interdependence. The first contribution is the introduc¬ tion of the maximin strategy as an alternative behavioral postulate when outcomes depend not only on the choices of rival firms, as well as on your own choices. However, we have seen that the maximin strategy is not always the best strategy for a firm to follow. And economists are not in agreement as to whether corporation decision makers actually use something like a maximin approach to making decisions. Perhaps the most accurate representation of the nature of oligopolistic interdepen¬ dence is the variable sum cooperative game described in Table 16.4. This game shows that there are strong incentives for cooperative decision making about prices. This leads us naturally to the consideration of collusion and price fixing and of the formation of cartels as rational means of coping with oligopolistic interdependence.

Cartels and Price Fixing When two or more firms producing the same product enter into a formal, open agree¬ ment on the price to be charged, this is called a cartel. Private cartels are not legal in the United States. However, the U.S. government has on more than one occasion established an official cartel by assuming the power to regulate the price at which certain goods or services are sold. For example, until 1978 the Civil Aeronautics Board set the fares charged by competing airlines on domestic routes. There may also be informal and/or secret collusion to fix prices above the competitive level. Secret cartels and collusion to fix prices are also illegal in the United States. But the U.S. Justice Department has detected and successfully prosecuted the participants in a number of price-fixing agreements. The most notorious of these was the case of General Electric, Westinghouse, and other manufacturers of electrical equipment, which came to light in 1960. The cartel presumably wishes to maximize the sum of the profits of all member firms. Given that objective, the analysis of cartel pricing is straightforward. The cartel must act as a monopolist. It must determine its collective or aggregate marginal cost curve. As long as changes in cartel output have no impact on factor prices, the cartel’s marginal cost curve is simply the horizontal summation of the marginal cost curves of

450

Market Power

the member firms. If input prices are affected by changes in cartel output, then this must be taken into account in the manner described by the monopsony model of Chapter 15. The cartel must also determine its demand and marginal revenue curves. Provided that all firms producing the product are members of the cartel, the cartel s demand curve is the market demand curve for the product. Collective profits are maximized when two conditions are met. First, the cartel must set total output at the point where the cartel’s marginal revenue equals its marginal cost and charge the price shown by the demand curve. Second, it must produce that total output at the minimum possible total cost. This means that the cartel must establish production quotas for each firm such that the marginal cost of production is equal for all firms (see Chapter 10). This simple analysis of cartel price formation has ignored several important problems and issues. First, if there are firms that are not members, the cartel may have difficulty establishing and maintaining a price different from the noncartel equilibrium price in this industry. The outcome depends on whether nonmembers recognize a mutual interest in high prices and tacitly agree with the cartel pricing policy or they perceive their interests to lie in price cutting to enlarge their share of the total market. Second, if a cartel is successful in raising profits above the competitive level, this will tend to attract new firms into the industry. If entry occurs, the carteFs power to maintain a monopoly price can only be sustained if the new entrants are made members of the cartel. But this means they must be given a share of the profits, and everyone’s slice of the pie gets smaller. Thus effective cartels require barriers to entry. Third, because joint profit maximization requires that total production costs be minimized, the cartel must have the power to determine output quotas for its members so as to equate their marginal costs of production. This may pose a problem for the cartel, especially if the profits are divided among firms according to each firm’s share of total output. A high-cost firm would be allocated a small production quota and would therefore receive a small share of the cartel profits. Such a firm might feel that it would be better off leaving the cartel and pursuing its own price and output policies. It might be necessary for low-cost members of the cartel to make compensating pay¬ ments to high-cost members in order to induce them to remain in the cartel. Because of the difficulties in negotiating a division of profits and cost-minimizing allocation of production, a cartel might try to determine production quotas by some more or less arbitrary rule of thumb. For example, quotas might be assigned according to plant capacity; or firms might be assigned geographic areas in which to market their output at the cartel price. Because such rules are not likely to be consistent with cartel cost minimization, they will result in a sacrifice of cartel profits. But this may be a necessary price to pay in order to achieve agreement on cartel pricing. To the extent that the production quotas result in higher than necessary costs, the cartel is imposing a further social cost or welfare loss on society in addition to that caused by the excess of price over marginal cost. A cartel might choose not to assign production quotas on any basis and to allow members to produce and sell whatever they can at the cartel price. The official cartels created by government price regulation typically do not control output. The absence

451

Oligopoly and Monopolistic Competition: The Economics of Interdependence

of output controls is likely to lead to various forms of nonprice competition among members as firms attempt to increase their share of the market and total profits. Nonprice competition can take several forms. Firms may offer better delivery terms, better service, or even improvements in product quality. When the government was regulating airline fares, airlines competed for passengers by offering more frequent flights, dressing hostesses in fashion designer uniforms, and offering in-flight movies and other forms of entertainment. Perhaps the biggest problem for cartels is finding a way to prevent members from cheating by offering their product at a price below the cartel price. The incentive to cheat can be very strong. Suppose that the cartel has established a price of Pxc as shown in Figure 16.5. Assume that a member firm’s quota is Xc. The firm realizes that as long as other members of the cartel continue to sell at price Pc, it could substantially increase its quantity sold by a small reduction in price. Thus the firm would perceive that its demand curve for price cuts would be very elastic, for example, Dx. Because the associated marginal revenue curve intersects the firm’s marginal cost curve at output Xu the firm would maximize its profits by offering to sell at Pxl, somewhat below the cartel price. In order to prevent this type of cheating on price, the cartel must be able to gather information on the prices actually charged by all its members. And it must have some credible threat of disciplinary action against those who are caught cheating. Once one firm cheats on the cartel price, other firms will be under increasing pressure to offer similar price concessions. Soon price cutting becomes the norm rather than the exception, and the cartel loses its effectiveness. Cheating is more likely the larger is the number of members of the cartel. For this reason cartels with more than, say, three or four members are difficult to form and even harder to sustain for long periods of time. The exception is a cartel with government sanction and enforcement of its pricing policy.

X per period Figure 16.5

A Cartel Member’s Incentive to Cheat on the Fixed Price.

452

Market Power

Price Leadership An agreement to establish a common price above the competitive level need not be explicit. As suggested in the discussion of the variable sum game, firms may reach a common understanding of their interdependence and their mutual interest in high prices and the elimination of competitive price cutting. When oligopoly firms collec¬ tively follow high price, collective profit-maximization policies without formal agree¬ ment or communication, this is called tacit collusion. When firms are involved in tacit collusion, how do they determine when their mutual interests would be served by a change in price? . In this situation one firm may assume a leadership role and take responsibility for determining when changing market conditions justify a change in the common price. When the price leader determines that prices should be changed, it signals this by publicly announcing the new price. The other firms in the industry acknowledge the leadership of the first firm by altering their prices accordingly. The price leader might be the largest firm in the industry, or it might be a firm that has demonstrated a superior capacity to assess market conditions.7 One difficulty with this model of price leadership is that it is empirically empty; that is, it is not possible to test the theory with empirical evidence. How does one distinguish between an industry characterized by this form of price leadership and one in which firms respond in a competitive fashion to changes in price by one of its members? Another form of price leadership can arise where an industry is characterized by one large dominant firm that coexists with a number of much smaller firms. Particularly if the industry produces a homogeneous product, the small firms find that their demand curves are essentially horizontal at the price established by the dominant firm. In these circumstances, what price will the dominant firm set? Because the small firms can sell all they wish to at the going price, the dominant firm is reduced to a role of residual supplier. It sells the difference between market demand and the quantity supplied by the small firms. Figure 16.6 shows the market demand curve DD' and the aggregate supply curve of the small firms Sx. This is the horizontal summation of the individual firms' supply curves. If price is as high as Pxl, the small firms would be willing to meet the total market demand. At prices below Pxl, the small firms’ supply is less than the market demand. This excess demand gives the effective demand curve of the dominant firm. If price falls to PX3, the quantity supplied by small firms is 0 and the total market demand is supplied by the dominant firm. The dominant firm’s effective demand curve consists of the line segments PX]AD'. Given the dominant firm’s effective demand curve, it maximizes profit where its marginal revenue equals marginal cost. This is at an output of X2 in Figure 16.6. The associated price established by the dominant firm is PX2. The small firms make up the

The U.S. Steel Corporation was acknowledged to be the steel industry price leader during the period between World War 1 and World War II. For an interesting case study of the steel industry, see Leonard W. Weiss, Economics and American Industry, New York: Wiley, 1961.

453

Oligopoly and Monopolistic Competition. The Economics of Interdependence

i_l

O

x4

x2

l

X3 X per period

Figure 16.6

Price Determination with a Dominant Firm.

difference between the dominant firm’s production and the market demand of X3. This is the distance X2X}, which is equal to X^X^, by construction. There are a couple of loose ends to be tied down in this model of dominant firm price leadership. First, why does the dominant firm tolerate the existence of the small firms? If it were to cut the price to PXi or slightly below, the small firms would be driven out of business. As soon as they had all exited the industry, the dominant (now monopoly) firm’s demand curve would be DD'^and it could charge the monopoly price and reap monopoly profits. The dominant firm may not do this because of laws prohibiting such predatory price-cutting practices. But even in the absence of such laws, the practice could be ineffective unless there were barriers to the reentry of small firms. Once the dominant firm established a monopoly price, potential small firms would see the oppor¬ tunity to enter the industry and earn profits. They would continue to enter and force the dominant firm to reduce the price until small firms’ profits were 0. One potential barrier to entry could be the pricing practice of the dominant firm itself. It could establish a price low enough to discourage potential entrants. This is known as entry limit pricing. Entry limit pricing can also occur in other forms of oligopoly. Another loose end involves the dynamic properties of the model and how the number of small firms in the industry is determined. For the industry to be in long-run equilib¬ rium the price established by the dominant firm must yield zero profits to the small firms. Otherwise small firms would enter or exit the industry according to whether profits were positive or negative and the dominant firm’s demand curve and profitmaximizing price would be changing. Finally, what explains the continued existence of small firms? Presumably they have access to the same technology that is being used by the dominant firm. What prevents some of the small firms from growing to take advantage of the economies of

454

Market Power

scale being realized by the large firm? Presumably some small firms would drop by the wayside because the industry could not support a large number of large firms. But the continued existence of small firms indicates imperfections in the access either to technological knowledge or to the capital necessary to expand the scale of the firm.

Conclusions We have reviewed several approaches to modeling oligopoly behavior from the primi¬ tive models of Cournot to the sophisticated models of game theory to the ad hoc models of the kinked demand curve and price leader. Do these models constitute a valid theory of oligopoly behavior? A negative answer has been given by Martin Shubik who said, bluntly, “There is no oligopoly theory.”8 At the worst, we have models like the kinked demand curve whose predictions of price stability are contradicted by the available evidence on the behavior of prices in oligopolistic industries. At the best we have the models of game theory that yield no predictions but deepen our insights and under¬ standing of the nature of oligopolistic interdependence. One area for future theoretical work is the explanation of other dimensions of oligopoly behavior besides price. Studies of particular oligopoly industries often empha¬ size the importance of things such as product innovation and product differentiation, advertising, and the use and manipulation of the government to preserve and enhance the economic position of oligopoly firms. A fully developed oligopoly theory in addition to coming to grips with the explanation of pricing behavior, will have to explain the role of these other forms of competition in diverting the rivalrous tendencies of oligopoly firms away from unwanted price competition. Turning to the normative side, there is a presumption that oligopoly firms will charge prices above their marginal costs and thus impose a social cost or welfare loss on society. The kinked demand curve, cartel, and price leader models all predict prices above marginal costs. The variable sum game theory model also suggests that outcome, at least if oligopoly firms can escape the prisoners’ dilemma and recognize their mutual interest in higher prices. The estimate of the social cost of monopoly described in the last chapter included the inefficiency due to oligopoly because there was no effort to distinguish between oligopoly and monopoly firms. There is continuing controversy over the magnitude of this social cost. And the policy implications of oligopoly inefficiency are unclear. If oligopoly arises because economies of scale require firms that are large relative to the market, it is pointless to advocate a return to small firms and perfect competition. Policies can try, however, to assure that firms are not larger than necessary to reap economies of scale, that artificial barriers to entry are eliminated, and that anticompetitive practices such as price fixing are prevented.

“Martin Shubik, A Curmudgeon’s Guide to Microeconomics, Journal of Economic Literature, June 1970 8(2), 415.

455

Oligopoly and Monopolistic Competition: The Economics of Interdependence

MONOPOLISTIC COMPETITION The presence of product differentiation among firms in an industry alters somewhat the nature of the interdependence among firms. Product differentiation gives firms some freedom to charge prices different from those charged by other firms in the industry. For example, a firm can charge a slightly higher price than the other firms in the industry without fear of losing all its customers. The greater the degree of product differentiation is, the lower is the cross-elasticity of demand and the less elastic is a single firm’s demand curve, other things equal. Product differentiation has been incor¬ porated in some of the oligopoly models discussed in the previous section. But product differentiation has played a relatively small role as these models focused on the oligopo¬ listic interdependence arising from the small number of firms. In this section we discuss the model of monopolistic competition in which product differentiation plays a key role, whereas interdependence is relatively unimportant.9 Monopolistic competition is defined by two characteristics. First, a monopolisti¬ cally competitive industry consists of a large number of firms, a large enough number so that a firm does not have to consider the effect of a change in its price on any of the other members of the industry. The large number of firms in the monopolistically competitive industry minimizes the significance of oligopolistic interdependence among firms. Second, unlike the competitive industry that also has a large number of firms, each firm in a monopolistically competitive industry produces a differentiated product. This means that each firm faces a downward-sloping demand curve for its product. The various retail trades are often cited as examples of monopolistically competitive indus¬ tries. For example, each drug store or gas station in an urban area is differentiated from its competitors at least in terms of location and perhaps also in terms of other character¬ istics such as hours, quality of services offered, and so forth.

The Short-Run Equilibrium For simplicity, assume that all firms are identical with respect to the underlying technology, their cost curves, and demand. This enables us to pick any firm in the industry and call it a “typical” firm. Because all firms are identical, any conclusions reached about the typical firm will apply equally to all firms. Suppose that the typical firm has established price PXI and is selling a quantity X , as shown by point A in Figure 16.7. There are two different demand curves going through point A. The demand curve DD' shows quantities sold by the firm as a function of its price, assuming that all firms’ prices change together. The other de¬ mand curve dd' shows how the quantity sold by the firm varies with its price, holding the prices charged by all other firms constant. Demand curve dd' is more elastic

9This analysis is based on Edward Chamberlin, The Theory of Monopolistic Competition, Cambridge, Mass.: Harvard University Press, 1933.

456

Market Power

X per period Figure 16.7 Monopolistic Competition in the Short Run: The Adjustment of the Firm’s Price Toward Equilibrium.

because if the firm cuts price while other firms hold price constant, it will capture a larger share of the market and experience a bigger increase in the quantity sold. Assume that the firm believes that other firms will hold their prices constant no matter what price it charges. This means that the firm’s perceived demand curve is dd'. This firm will perceive that its profit-maximizing output is X2, where the marginal revenue curve for dd' intersects the firm’s marginal cost curve. Accordingly, the firm will set the price at PX2. If this firm is a typical firm, all firms will believe that their profit-maximizing prices and quantities are PX2 and X2. But when all firms lower their price to PX2, each firm moves along the demand curve DD' and the quantity sold per firm is only X2. The firm is not yet in short-run equilibrium. Now that the price is set at PX2, the typical firm perceives a new demand curve more elastic than DD' but intersecting it at point B in Figure 16.7. Again, it attempts to equate marginal cost with the marginal revenue curve associated with the new demand curve. All firms make similar adjust¬ ments. And the process continues until an equilibrium is reached such as is shown in Figure 16.8. Given a price of PX3, the firm’s perceived marginal revenue curve and marginal cost curve intersect at an output of X3. But according to the demand curve DD', this is just the quantity that will be sold at PX3. So the firm has no incentive to change its price. And because this is true for all firms, the industry is now in short-run equilibrium. Whether or not this is also a long-run equilibrium depends on whether firms are making positive, negative, or zero economic profits. Long-run equilibrium requires that profits be equal to 0 for all firms.

457

Oligopoly and Monopolistic Competition: The Economics of Interdependence

Px, dollars

D d

AC*

pX 3

MR

0 Figure 16.8

X3

X per period

The Short-Run Equilibrium of the Firm in Monopolistic Competition.

The Long-Run Equilibrium The typical firm in Figure 16.8 is receiving economic profit in the industry short-run equilibrium position. The opportunity to capture a share of these profits provides an incentive for new firms to enter this industry. As new firms enter, the market is divided into a larger number of smaller slices. Each firm’s effective demand curve DD’ and perceived demand curve dd' shift to the left. Also, the additional quantities supplied by the new firms force all firms to lower prices. This process continues until profits are eliminated. The no-profit, long-run equilibrium of a typical firm is shown in Figure 16.9. The price is just equal to long-run average cost at point A. And the firm’s perceived marginal revenue curve intersects its marginal cost curve at an output of Xu the output that can be sold given the price of Pxl. The long-run equilibrium position of the firm has two important features: (1) The price is greater than marginal cost. (2) The long-run average cost is greater than the minimum achievable unit cost if output were expanded to X2. One major conclusion of monopolistic competition theory is that firms do not fully utilize their capacity and exploit potential economies of scale. In other words, a monopolistically competitive industry tends to have excess capacity. Do the divergence of price and marginal cost and the excess capacity indicate a social cost or welfare loss? This is a controversial question. These two features of the outcome are direct consequences of the fact that the demand curve for the firm slopes down to the right. But the downward-sloping demand curve is not so much a sign of market power. Remember that there are no barriers to entry and profits are competed away

458

Market Power

X per period Figure 16.9

The Long-Run Equilibrium of the Firm in Monopolistic Competition.

in the long run. Rather, demand curves are downward sloping because of product differentiation. Each firm’s product is a less than perfect substitute for the products of other firms. Monopolistic competition exists because firms produce a set of products with a variety of characteristics. If variety is a good in itself, then consumers might be better off for being able to choose from among products with different characteristics. The excess capacity and the divergence of price from marginal cost may be interpreted as the cost of providing something desired by consumers, namely, increased variety. For example, if the firms in a retail trade are differentiated by location, each firm could be expected to have excess capacity as shown previously. If the government decreed that there should be no product differentiation in thisindusfrv^alLfirms would have to move to a single location and compete only in the price. The price would equal long-run marginal cost and eachfirm would produce at the minimum point on its long-run average cost curve. But now many customers would have to travel farther to make their purchases. Spatial differen¬ tiation of firms reduces the transportation costs of customers. And this is one form of benefit of variety. This benefit has to be compared with the cost of variety due to excess capacity when making a normative evaluation of monopolistic competition. Of course, one can acknowledge that variety has a value and still question whether monopolistic competition produces the optimum amount of variety. The optimum amount of variety occurs when the marginal cost of variety in the form of excess capacity, and so on is just equal to the marginal value of variety to consumers. Our theory of monopolistic competition is not sufficiently developed to determine whether the optimum degree of variety will be provided.

459

Oligopoly and Monopolistic Competition: The Economics of Interdependence

Conclusions We have judged the value of economic models on the basis of their ability to yield predictions and the empirical validity of these predictions. How does the monopolis¬ tic competition model come out by this test? One of the predictions of the model is that monopolistically competitive firms will have excess capacity. Although there have been no careful tests of this hypothesis based on statistically estimated cost curves, most economists agree that the retail trades and similar industries have excess capacity. Thus this prediction of the model appears to be consistent with the evi¬ dence. The model predicts that if costs increase for the firms in the industry, price will increase and the number of firms in the industry will decrease. In this respect the model is not much different from the models of other market structures such as perfect competition or monopoly. In all cases costs and price are predicted to move together, at least in the long run. And where there is easy entry and exit the number of firms varies inversely with price and cost, other things equal. Although the model shows how price is determined, it does not explain how firms determine which characteristics to embody in their product. The model does not explain the nature and extent of product differentiation. This means the model cannot generate predictions about how product differentiation changes with changes in de¬ mand or cost.10 The monopolistic competition model shares this deficiency with the oligopoly models discussed in the preceding section. Finally, it is sometimes said that the monopolistic competition model cannot make a general prediction about the direction of the change in price when demand changes. This is true, but it is not clear that this is a meaningful criticism of the model. The direction of the price change depends on the precise nature of the change in demand. If the exact form of the new demand curve is known, it can be drawn into a diagram such as Figure 16.9, and the new equilibrium price can be determined. In this respect the monopolistic competition model is like the monopoly model. There is no unique supply curve. Thus when the demand curve shifts, the new price cannot be found by looking for an intersection between the new demand curve and a supply curve. Rather, the new price depends on where the associated marginal revenue curve intersects the marginal cost curve. And this in turn depends on what happens to the elasticity of the demand curve as it shifts.

10New developments in the theory of individual preferences incorporating characteristics of goods, however, are providing a basis for analyzing the economics of product differentiation. See, for example, Sherwin Rosen, Hedonic Prices and Implicit Markets: Product Differentiation in Pure Competition, Journal of Political Economy, January/February 1978, 82(1), 34-55 and Kelvin Lancaster, Variety, Equity, and Efficiency: Product Variety in an Industrial Society, New York: Columbia University Press, 1979.

460

Market Power

SUMMARY Oligopolistic industries are characterized by interdependence of pricing decisions of member firms. One firm must be aware of and take account of how other firms will respond to any price change it contemplates. The main body of oligopoly theory consists of a series of models that make different assumptions about how each firm perceives its relationship to the other firms in the industry. Some models can be solved for equilibrium positions for the industry. But they tend to make very unrealistic assumptions about how oligopolists expect their rivals to behave. The predictions of these models have not been supported by the evidence. On the other hand, those models that have been most successful in capturing the essence of the oligopoly interdepen¬ dence in general do not have determinate solutions, nor do they generate comparative static predictions. In this respect the state of oligopoly theory is quite unsatisfactory. And this is disturbing because of the extent and importance of oligopolistic industries in the economies of the Western capitalist nations and Japan. The theory of monopolistic competition is usually treated as a topic separate from oligopoly theory. This is because a large number of firms in the monopolistically competitive industry makes oligopolistic interdependence and rivalrous behavior rela¬ tively unimportant. Yet monopolistic competition theory shares one important short¬ coming with oligopoly theory, that is, its inability to incorporate nonprice variables, especially the nature and degree of product differentiation, into a comprehensive model. But the monopolistic competition model does yield a determinate solution for the price and quantity. The industry will have a long-run equilibrium with zero profits because of freedom of entry and exit. The price will be above the marginal cost and the firms of the industry will have excess capacity. The extent to which this excess capacity is a justifiable cost of providing product variety to consumers is an unanswered but important economic question.

KEY CONCEPTS Reaction function Kinked demand curve Maximin strategies

Price leadership Joint profit maximization Product differentiation

QUESTIONS AND PROBLEMS For Basic Review 1. 2.

Define and explain the economic significance of each of the key concepts. For the market structures known as perfect competition, monopolistic competition, oligopolistic competition, and monopoly briefly describe the similarities and differences among them with respect to: the number of firms,

461

Oligopoly and Monopolistic Competition: The Economics of Interdependence

the freedom of entry and exit, the degree of product differentiation, the likely existence of profit in long-run equilibrium, the relationship between price and marginal cost, and the likelihood of excess capacity. 3. * In the text it was said that the prisoners’ dilemma and the variable sum game were essentially the same in structure. Do you agree? What do you think would be the outcome of the prisoners’ dilemma game if the prisoners could communicate? What would be the outcome of a variable sum duopoly game if no communication were possible between the firms? 4. Briefly compare the achievements of oligopoly models as positive economic theory with those of the models of monopoly and perfect competition. What is it about oligopolies that leads to the differences in the results of theoretical 5.

6.

analysis? Briefly describe the derivation of the effective demand curve faced by a dominant firm acting as a price leader. What is assumed about the price leader’s expectations concerning the behavior of other firms? In the model of monopolistic competition, what does the firm believe about the price behavior of other firms in the industry? Describe the movement of the monopolistically competitive firm toward its short-run equilibrium. Would the outcome of the model be different if each firm believed all other firms would exactly match its price increases and decreases? Is that a reasonable assumption?

For Discussion 1. * Suppose an oligopoly firm expected its rivals to match any price increase it made but not to match any price decreases. Draw the perceived demand curve and marginal revenue curve for this oligopolist. Discuss the implications of these expectations and the perceived demand curve for the determination of 2.

oligopoly price. It is often said that the Organization of Petroleum Exporting Countries (OPEC) is a cartel. In what respects has the OPEC conduct since 1973 been consistent with the textbook model of a pure cartel? In what respects has the OPEC behavior been different from the textbook model of a pure cartel? Can you make any predictions about the long-term stability and future behavior of OPEC? What would you expect to happen if there were discoveries of large oil deposits in non-OPEC areas such as Mexico, Southeast Asia, and so forth? If OPEC is acting as a joint profit-maximizing cartel, what is your estimate of the price elasticity of demand for OPEC oil? (Very inelastic? Inelastic? Substantially greater than 1?)

462

Market Power

SUPPLEMENTARY READINGS Chamberlin, Edward H. The Theory of Monopolistic Competition. Cambridge, Mass.: Harvard University Press, 1932. Fellner, William. Competition Among the Few: Oligopoly and Similar Market Struc¬ tures. New York: Knopf, 1949. Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach (3rd ed.). New York: McGraw-Hill, 1980, Chapter 8. Sawyer, Malcolm C. Theories of the Firm. London: Weidenfeld and Nicolson, 1979. Stigler, George J. The Kinky Oligopoly Demand Curve and Rigid Prices, Journal of Political Economy, October 1947, 55(4), 432-449. Stigler, George J. The Theory of Price (3rd ed.). New York: Macmillan, 1966, Chapters 12, 13. Stigler, George J. The Literature of Economics: The Case of the Kinked Oligopoly Demand Curve, Economic Inquiry, April 1978, 16(2), 185-204.

MATHEMATICAL APPENDIX TO CHAPTER 16 The Cournot Duopoly Model The generalized Cournot model with a nonlinear demand function and nonzero costs can be expressed as follows. Let Px = f~^(X} + Yn) be the inverse demand function. The firms’ cost functions are C^Yj) and Cn(Yn), respectively. Each firm’s profit is given by Firm I: 7Tj = Y] ■ Firm II: 7r„ =

f (Y] Xn ■ f~\xl

+ Y)]) — Cj(Yj) + Yu) - Cn(Yn)

Each firm takes the other firm’s output as constant and chooses its output so as to maximize its profit. The first-order conditions for profit maximization for the two firms are: Firm I: Firm II:

37r,

dX1 37rn

= f~\Xi

+ Y„) + Y, -

df~\xl

+ Y„)

dXj

= f~\Y, + Yn) + Yn

*r\ y, + y„)

dCj(Y;) 3Y, 3Cn(Yn)

3Y„

The first two terms in each equation represent the marginal revenue to the firm when the other firm’s output is held constant. The third term is marginal cost. Each firm must equate its marginal cost with what it believes to be its marginal revenue. The two first-order conditions are a system of two equations with two unknowns, X{ and Y„. The solution of the system gives the equilibrium quantities for each firm. Each firm’s

463

Oligopoly and Monopolistic Competition: The Economics of Interdependence

reaction function can be found by solving its first-order maximum condition for its output as a function of the output of the other firm.

PARTY_ Welfare Economics

.

'

CHAPTER 17_ Welfare Economics: Competition and Efficiency

In this chapter and the next we return to a more comprehensive discussion of the normative question raised in Chapter 1: Is the outcome of the process of economic interaction through a market system good in some sense? The norm or criterion to be applied in answering this question is the level of economic well-being or welfare of the individuals comprising the economy, hence the term “welfare economics.” The basic premises of welfare economics are individualistic in nature. Specifically, it is assumed that each individual is the best judge of his own welfare and that an individual’s welfare depends on the extent to which he has satisfied his desires as expressed by his preference ordering or utility function. An individual’s welfare has increased if he has reached a higher indifference curve. The concept of Pareto optimality was introduced in Chapter 5. An equilibrium of an economy is Pareto optimal or efficient if it is not possible to reallocate resources so as to improve the welfare of one individual except by decreasing the welfare of someone else. The first step in this chapter is to provide a proof that the general equilibrium of a perfectly competitive economy is Pareto optimal. We then identify the reasons that a market economy might fail to reach a Pareto optimum position. Finally, we show that the concept of Pareto optimality is somewhat limited as a welfare criterion because there is an infinite number of alternative Pareto optimum positions for an economy. They differ with respect to the distribution of income and well-being among the mem¬ bers of the economy. But the Pareto criterion does not provide a basis for ranking these alternatives or choosing from among them. In the following chapter we turn to a discussion of alternative ways in which some notion of equity or fairness can be employed to rank alternative equilibrium positions. Some concept of equity is required in order to identify a unique optimum position or social welfare maximum. We then take up a less ambitious question. How can we 467

5 ST 468

M

Welfare Economics

determine whether a change in the economy results in a social welfare improvement. Several alternative welfare criteria are discussed and evaluated. In the final section we consider what this discussion of welfare economics and alternative welfare criteria has to say about the desirability of a market system as a basis for organizing economic activity.

COMPETITION AND PARETO OPTIMALITY In Chapter 1 the question was posed: Does the uncoordinated maximizing behavior of individuals operating in a market system promote social welfare? The question is poorly stated in this form. Since social welfare is an ambiguous concept, the answer is ambigu¬ ous. But if social welfare is defined so as to remove its ambiguity, an unambiguous affirmative answer can be given to the question.

Competition Leads to a Pareto Optimum If social welfare is defined in terms of the efficiency with which the economy uses resources for satisfying preferences, and if an efficient allocation of resources is defined in terms of Pareto optimality, the following proposition can be proven. Proposition: If all markets are perfectly competitive, and if all economic goods that enter into individuals’ preference orderings or utility functions can be purchased in competitive markets, the resulting resource allocation will be a Pareto optimal or efficient one. Social welfare will be maximized in the sense that it will not be possible to increase any individual’s well-being except by reducing the well-being of some other individual. In Chapter 5 the three conditions for the Pareto optimum of a simple two-good, two-factor, two-person economy were derived. In Chapter 14 the general equilibrium of this economy was derived for the case of a perfectly competitive market system. The task now is to show that in this general equilibrium the Pareto optimum conditions are satisfied.

Efficiency in Production. Efficiency in production requires that all producers be on the efficiency locus of the production box, that is, the marginal rate of technical substitution of capital for labor be the same for all producers of the two goods. Specifically, Condition I: MRTSXLK = MRTSlK

Each producer is striving to maximize profits. Factor prices are given by the market. Therefore each producer must select a combination of factor inputs for which the marginal rate of technical substitution is equal to the ratio of factor prices. Because all producers are purchasing their factor inputs in the same market, they all face the same factor price ratio. Thus profit maximization and the opportunity to purchase factor inputs in competitive markets means that

469

Welfare Economics: Competition and Efficiency

MRTSxlk = PL/PK mrtsylk = PL/PK and therefore MRTSxlk = MR TS ylk

The condition for efficiency in production is satisfied by producers operating in perfectly competitive factor markets, because they all respond to a common ratio of factor prices. In a more complicated economy with many factors and many goods a variation of condition I must hold for each pair of inputs and each pair of goods. The forces of competition will assure that the condition is satisfied for every possible combination.

Efficiency in Exchange. Efficiency in exchange requires that the two individuals, Ann and Bob, be on the exchange locus with equal marginal rates of substitution between the two goods. In other words, Condition II: MRSXy = MRSby Each individual who wishes to make the best of a given money income must choose a consumption bundle such that his or her marginal rate of substitution between the two goods is equal to the ratio of the market prices. Because both individuals purchase their goods in the same market, they face the same price ratio. Thus the maximizing behavior of individuals who have an opportunity to purchase goods in competitive markets leads to the following situation: MRS axy = Px/Py MRS bxy = PX/PY

and therefore MRSaxy = MRSxy

A competitive market system leads to efficiency in exchange. In a more complicated economy with many goods and many individuals a variation of condition II must hold for every pair of goods and every pair of individuals. Competition will assure that the conditions are satisfied for all goods and individuals.

Efficiency in Output. The first two conditions give the efficient method of producing a given output and the efficient allocation of a given output between two individuals. The third condition determines whether a given combination of outputs is efficient. Efficiency in output requires that for each individual the marginal rate of substitu¬ tion between two goods be equal to the marginal rate of transformation. In other words, Condition III: MRSAxy = MRTXY = MRSBXY Recall from Chapter 14 that the marginal rate of transformation can be interpreted as the ratio of the marginal costs of production. Each profit-maximizing firm operating

470

Welfare Economics

in a perfectly competitive market chooses its output level so that its marginal cost is equal to the given price. Thus competition assures that P x ~ MCX Py = MCy

and Px_

MCX

Py

MCy

MRTXy

As already shown, self-interested individuals equate their marginal rates of substitu¬ tion with the ratio of given market prices. The competitive behavior of firms assures that that price ratio is equal to the marginal rate of transformation. Thus with competi¬ tion we have MRTXY = ^ = MRSXY = MRSXY PY

Perfect competition in output markets leads to efficiency in output. In an economy with many goods and many individuals a variation of condition III must hold for every combination of a pair of goods and pair of individuals.

Efficiency in Factor Supply. The three conditions given in Chapter 5 are sufficient to define a Pareto optimum for an economy in which factor supplies are given and do not respond to changes in factor prices. But as shown in Chapters 12 and 13, the supplies of labor and capital services are likely to be functions of factor prices. If the quantity of a factor service supplied to the market depends on its price, a fourth set of Pareto optimum conditions must be satisfied. Basically, these conditions require that the increment to output from an additional unit of the factor service valued in monetary terms according to individuals’ marginal willingness to pay be equal to the opportunity cost of supplying that factor service. Efficiency in the supply of labor requires that for each individual the value of the marginal product of labor be equal to that individual’s marginal rate of substitution between leisure and income. Condition IVa: VMPL = MRSfm

The VMPL gives the value of the additional output produced by increasing labor supply by 1 unit. The MRSfm shows how much additional income the individual would have to receive to compensate him for the loss of 1 hour of leisure. Consider the following example in which the VfylPL is greater than the MRSfm. Suppose that the VMPL is $4, whereas the MRSm is $2. Because the condition for efficient labor supply is not satisfied, it must be possible to increase some individual’s welfare without decreasing another’s welfare. How can this be done? If the individual worked an additional hour, he would produce goods valued at $4. If the individual is paid $2, this just compensates him for the loss of 1 hour of leisure, leaving him on his original indifference curve. He has not been made worse off. But this leaves $2 of goods

471

Welfare Economics: Competition and Efficiency

that can be used to make someone in the economy better off. If the worker is paid his value of marginal product, it is the worker who is made better off. Thus when the VMPL is greater than MRS FM, it is possible to make at least one person better off without making anyone worse off by increasing labor supply. Alternatively, suppose that VMPL is $5 and the MRSfm is $8. If the individual takes an additional hour of leisure, the production of goods is reduced by $5. But the individual would be willing to give up as much as $8 in order to get one more hour of leisure. If the reduction in production comes entirely at the expense of the consump¬ tion of the individual, the individual is still better off by having reduced output. And there is no one in the economy made worse off by this change. Thus when the VMPL is less than MRSfm, it is possible to increase one person’s well-being without hurting someone else by decreasing the quantity of labor supplied to the market. Only when VMPl is equal to MRSfm can the economy be in a Pareto optimum position. Perfect competition in all markets assures that this Pareto optimum condition for efficient labor supply will be satisfied. Recall that the individual will choose that quantity of labor to supply to the market where his MRSFM is just equal to the market price of labor. The profit-maximizing competitive firm will select a combination of factor inputs such that the VMPL is equal to the price of labor. So if both individuals and firms are in equilibrium with respect to their market conditions, we have VMPL = PL = MRSm

and the condition for efficient labor supply is satisfied. Efficiency in the supply of capital requires that the ability of the economy to trans¬ form present output into future output be equal to each individual’s willingness to give up present consumption in return for future consumption. The first term is called the margin¬ al rate of transformation of present consumption into future consumption (MRTC1C2). It is a function of the value of marginal product of capital services and the cost of producing capital machines. The condition for efficient capital supply can be written: Condition IVb: MRTC1C2 = MRSCIC2 Suppose that the cost and productivity of a capital machine is such that a machine with an opportunity cost of $10 has a useful life of one year and has a VMPK of $12. This means that the MRTC1C2 is 1.2 and the rate of return on this investment is 20 percent. Suppose that there is an individual whose MRSC1C2 is 1.1. Then if the individ¬ ual gives up $10 of consumption in year 1, she needs to receive $11 worth of additional consumption in year 2 to keep her on the same indifference curve or at the same level of well-being. If the investment in this machine is made and paid for by reducing her consumption in year 1, the individual can be paid $11 for consumption in year 2 and thus be no worse off. This leaves $1 available in year 2 to be used to make at least one person better off. This demonstrates that if the condition for efficient capital supply is not satisfied, it is possible to make at least one person better off while making no one else worse off. If all markets are perfectly competitive, the maximizing behavior of individuals and firms will assure that the condition for efficient capital supply is satisfied. Firms will

472

Welfare Economics

borrow additional funds to build capital machines as long as the rate of return on these investments is greater than the market rate of interest. Profit maximization for firms requires that the rate of return on investments be equal to the market rate of interest, or what is the same thing:

MRT C\c2 = 1 + r We saw in Chapter 13 that the equilibrium for individuals who could borrow and lend at the market rate interest (r) requires that MRSCIC2 — 1 + r

As long as savers and investors operate in the same market and face the same market determined interest rate, the following must hold: MR. T cid — 1 + r = MRSC1C2

for all individuals and for all producers of capital machines. In a competitive market economy, maximizing behavior assures efficiency in factor supply.

MARKET FAILURE Although a perfectly functioning competitive market system will achieve an efficient allocation of resources as defined here, in a complex modern economy there are several important reasons to believe that this degree of perfection might not be attained. In other words, market systems might fail in practice to achieve Pareto optimality. In this section we consider several important possible sources of market failure. Each source can be discussed in terms of the manner in which it results in a violation of one or more of the four Pareto optimum conditions.

Monopoly When a firm has monopoly or oligopoly power in the output market, it is a price maker rather than a price taker. The monopoly firm sets the quantity so that marginal revenue is equal to marginal cost. And since marginal revenue is less than price, price exceeds marginal cost. Although the profit-maximizing output for the oligopolist is not determi¬ nate, there is a presumption tha^ price exceeds niargmal cost in oligopoly markets as well. In the simple two-good model, if the production of one good, say, X, is monopo¬ lized, the equilibrium can be characterized as follows: MRTxy

MCX MCy

_

MRX

Px

Py

Py

MRSXy

MRT Xy < MRSXy for all individuals. Thus with monopoly the condition for efficient output is violated. If factor supplies are fixed, this equilibrium can also be shown in terms of the

473

Welfare Economics: Competition and Efficiency

production possibilities curve and exchange box. Point 0B in Figure 17.1 shows the equilibrium outputs of X and Y when the X industry is monopolized. The slope of the production possibilities curve at point 0B is given by TT'. The equal marginal rates of substitution for the two individuals consuming X and Y are given by the slope of the line PP' in the exchange box. This line is more steeply sloped, indicating that the marginal rates of substitution exceed the marginal rate of transformation. If the monopoly power in the X industry could be eliminated, the output of X would expand while the output of Y contracted. The MRTxy would increase. And as more X is produced relative to Y, the price of X would fall relative to the price of Y. This would induce both individuals to substitute X for Y in consumption, resulting in a decrease in their MRSxy s. Market forces would continue to push the economy in this direction until the following condition holds: MRTxy = —^ — MRSXY Py

and the condition for efficient output is satisfied. Because the Pareto optimum condi¬ tions were violated under monopoly, this means that there must be some way of distributing the additional output of X so as to assure that no one (not even the monopolist) loses by this move, while at least somejndividuals benefit. If factor supplies depend on factor prices, monopoly in the market for X also results in the violation of the conditions for efficient factor supply. Recall that the monopolist chooses combinations of inputs such that their marginal revenue products are equal to

Figure 17.1

The Effect of Monopoly in the X Industry on the General Equilibrium of Produc¬

tion and Exchange.

474

Welfare Economics

factor prices. The equilibrium under monopoly is characterized by the following condi¬ tion for labor: MRPl = PL = MRS FM

But since for a monopolist the marginal revenue product of a factor is less than its value of marginal product, the following holds: VMPl > MRSfm

and too little of the factor is utilized. Similarly, since VMPK > MRPK, capital is underutilized as well. This inefficiency in factor markets is the mirror image of the monopolist’s reduction of output in the product market.

Monopolies in Both Goods. Monopoly in the X industry results in the production of too little X and too much Y. Could it be that monopoly in the Y industry, having the opposite effect, could offset the adverse effects of X's monopoly on resource alloca¬ tion and efficiency? Suppose that both the X and Y industries are characterized by monopoly power. Recall that marginal revenue and price are related in the following way:

The general equilibrium of output will be characterized as MRTXy = MCx MCy

= MRx MR Y

= Px(l ~ X/Ex) PY( 1 - 1 /Ey)

Now suppose that at this equilibrium the degree of monopoly power is the same in both industries; that is, Ex = E Y. Then in the preceding expression the terms in parentheses cancel out, and the equilibrium is MRT XY = — = MRSxy Py

for all individuals. In other words, with equal elasticities of demand the ratio of price to marginal cost is the same in both markets and the equality of the marginal rate of transformation and marginal rate of substitution is preserved. This seems to say that although monopoly in one industry violates the Pareto optimum conditions, efficiency can be achieved when there are two equally powerful monopolies in the two indus¬ tries. Can it be that two monopolies are better than one? The answer is, “No,” at least not if factor supplies are functions of factor prices. With variable factor supplies both monopolies violate the conditions for efficient factor supply. Too little of both factors is supplied; and the outputs of both goods are smaller than is required for Pareto optimality.

475

Welfare Economics: Competition and Efficiency

Monopsony Monopsony power in an input market can also lead to a violation of the Pareto optimum conditions. Suppose that the output market for the X industry is competitive but that each firm in the industry has monopsony power in its market for labor. Suppose that all other markets in the economy are perfectly competitive. The monopsony firm chooses the level of labor input such that the value of marginal product of labor is equal to the marginal expenditure on labor (MEIL). The marginal expenditure on labor is greater than its price. Considering both inputs together, the profit-maximizing monopsonist chooses that input combination that satisfies the first equality in the following expression: MRTSxlk = MEIlx Pk

>

= MRTSylk Pk

The profit-maximizing firms in the Y industry where competition prevails in both factor markets and product markets satisfy the second equality in the preceding expression. Because the marginal expenditure on labor is greater than the price of labor, however, the two industries are equating their marginal rates of technical substitution to different ratios. The marginal rates of technical substitution of labor for capital will be different in the two industries, and the condition for efficient production will not be satisfied. The firms will be off the efficiency locus. This is shown in Figure 17.2, where the slope of the line MM' gives the ratio of the marginal expenditure on the input of labor to the price of capital. The slope of PP' is the market factor price ratio. The two industries settle on the input combination shown by point A. But since the slopes of the isoquants are different, point A is not on the

Ly Oy

Ky

Lx-*■ Figure 17.2

The Effect of the Monopsony Power of the X Industry of the General Equilibrium

of Production.

476

Welfare Economics

efficiency locus. If firms in the X industry were to respond to the price of labor rather than to its marginal expenditure, they would substitute labor for capital in X produc¬ tion. The resulting improvement in efficiency and expansion in output would make it possible to increase the welfare of some members of the economy while assuring that no members experienced a lower welfare. When factor supplies depend on factor prices, monopsony in an input market also leads to inefficiency in factor supply. In the case of labor monopsony firms equate their value of marginal product of labor to the marginal expenditure on labor. Individuals equate their marginal rate of substitution between leisure and income to the price of labor but this is less than the marginal expenditure on labor. So factor supply is characterized by the following: VMPlx = MEIlx > Pl = MRSfm

The condition for efficient factor supply is violated. If more labor were supplied and utilized in the production of good X, somebody could be made better off without reducing the welfare of anyone else.

Taxes Many forms of taxation in modern economies introduce distortions of the price signals from the market system and result in deviations from Pareto optimality. For example, we saw in Chapter 11 that an excise or sales tax on a good results in the price of the good being greater than its marginal cost. This violates the condition for efficient output. Also, at least when factor supplies depend on factor prices a tax on the income from the sale of labor or capital services drives a wedge between the cost of the factor to the producer and its value of marginal product on the one hand and the aftertax re¬ ward to the owner of the factor and the relevant marginal rate of substitution (MRS C1C2 or MRSfm) on the other. The inefficiency caused by the deviation from Pareto optimal¬ ity due to taxation is called the “excess burden” of taxation. A tax with no effect on the price signals of the economy and therefore no excess burden is called a “neutral tax.” Taxes on pure rents are neutral in this respect. Recall the discussion of taxation of land rents in Chapter 12.

Externalities One of the principal virtues of the perfectly competitive market system as an idealized means of organizing economic activity is that all economically relevant interactions among individuals take the form of exchange. Exchanges are reciprocal in that each party both gives up something and gains something. Because all exchanges are volun¬ tary, it is apparent that every exchange must result in at least one of the two parties being better off and neither party being hurt by the exchange. In the real world some economically relevant interactions take place outside the market system. They are not reciprocal exchanges; rather, they are one-way impacts

477

Welfare Economics: Competition and Efficiency

in which one economic agent’s actions cause a gain or loss to another agent without a corresponding quid pro quo. Such interactions are called externalities, because the channel through which the effect is transmitted is external to the market system. An externality is an uncompensated effect. Definition: An externality occurs when one economic agent’s action directly confers a benefit or imposes a cost on some other agent without that consequence being reflected in market prices and exchange transactions. Externalities can either be positive or negative. A positive externality or external benefit occurs when one agent creates a benefit for another without compensation. When one agent imposes a cost on another without having to make a compensating payment, that is a negative externality or external cost. Markets can fail to achieve Pareto optimality when externalities are present. As the example to follow will demonstrate, externalities arise typically because of some combi¬ nation of an incomplete specification of property rights and high transactions costs in defining property rights, enforcing them, and executing exchanges based on them.

External Costs. Pollution is a form of negative externality. Suppose that a factory emits sulfur compounds and soot that reduce crop yields on nearby farmlands and cause poor health for neighboring residents. The farmers and residents experience a cost or loss of economic well-being because of the pollutants. They would rather not “ac¬ cept” these substances. Their property rights do not include the right to prevent the delivery of these pollutants to their lands. As a consequence, the plant manager has no reason to pay the landowners any compensation for their losses. Nor does she have any economic incentive to reduce the plant’s discharges. If enforceable property rights in clean air had been vested in the adjacent landowners, the plant manager could not emit pollutants unless she had obtained the prior agreement of the landowners to accept them. And this would require that she compensate them by an amount at least equal to the monetary value of the losses to crops and to health. The effect of a negative externality on resource allocation can be seen with the aid of Figure 17.3. Suppose that good X is produced by a competitive industry. The supply curve that gives quantity supplied as a function of market price is SPS'P. It is based on the private costs of production to the firms. Because firms do not have to take any negative externalities associated with production into account in their supply decisions, these external costs do not affect the quantity supplied. These costs are external to the firm’s calculation of profit or loss. Given the demand curve, Dx, the market equilibrium of this industry is at X { with a price of Pxl. The existence of negative externalities means that third parties are experiencing uncompensated costs that are associated with the production of X. Sup¬ pose that at a production ofXlt negative externalities of an amount equal to the vertical distance AB are being imposed on third parties. This means that the true social cost of production, counting external costs, is the vertical distance CB. The dashed curve labeled S'P + E shows the social marginal cost of production at each level of output. It is the sum of private marginal costs and external costs.

478

Welfare Economics

Figure 17.3

The Effect of a Negative Externality Associated With the Production of X.

At an output of Xr social marginal cost exceeds the market price of Pxl. Because it is social costs that are relevant to Pareto optimality, this market outcome is not efficient. The marginal rate of transformation must be equal to the ratio of social marginal costs; that is, it must reflect both private and external costs. Thus in terms of the simple two-good, two-person general equilibrium model, the negative externality in the pro¬ duction of X results in the following: MRTxy

SMC x

Px

SMCy

> PY

MRSxy

Thus the divergence between private and social marginal cost results in the violation of the conditions for an efficient output. Too much X and too little Y are being produced. Efficiency or Pareto optimality requires that price equal social marginal cost. Return¬ ing to Figure 17.3, this requires that price be increased to PX2 and output be reduced to X2. This efficient outcome might be achieved by imposing a tax on the producers of X equal to the external cost of production. Alternatively, if property rights were specified so that producers were required to make compensating payments to all in¬ dividuals affected by the pollutants, these compensating payments would become a part of private cost. This is sometimes termed “internalizing” the external cost. Once producers of X are forced to bear the entire cost of production, their private supply curve is shifted up to coincide with S'P + E.

External Benefits. Suppose that an individual purchases a watchdog in order to decrease the probability that his house will be burglarized. If the watchdog barks at strangers in the neighborhood and deters criminals from burglarizing the neighbors’ houses as well, this is a positive externality. The neighbors receive a benefit due to the

479

Welfare Economics: Competition and Efficiency

economic action of the purchaser of the dog; but they are not making any payment to the dog owner for the benefits they receive. Specifically, they are not sharing in the cost of the dog. The effects of positive externalities on resource allocation are shown in Figure 17.4. Suppose that the consumption of good X creates a positive externality. The demand curve DD' shows the marginal willingness to pay of purchasers of X. It is based on the utility or benefits conferred on purchasers of X. This private demand curve intersects the supply curve at a quantity of Xx and a price of PX]. With this quantity of X being consumed, third parties, that is nonpurchasers of X, are also experiencing benefits. They have an aggregate marginal willingness to pay for these benefits equal to the vertical distance AB. The social marginal value or social marginal willingness to pay for X is the sum of the willingness to pay of purchasers plus the money value of the external economy to the neighbors. The curve DD’ + E shows the social marginal willingness to pay as a function of X. At an output of Xu social marginal willingness to pay exceeds marginal cost. It is social marginal willing¬ ness to pay that is relevant for resource allocation and Pareto optimality. Efficiency in output is achieved when the output of X is expanded to X2 with a price of PX2. This outcome could be achieved by a government subsidy to the purchasers of X equal to the positive externality per unit purchased. Alternatively, if property rights in X could be redefined so that third-party beneficiaries of the consumption of X are required to compensate the purchasers of X, then the market demand curve for X would shift up to DD' + E, and the market would achieve Pareto optimality. In the discussion of these examples of positive and negative externalities it was suggested that an appropriate specification of property rights might lead to transactions in which the monetary value of the externality was internalized in the decision making

Figure 17.4

The Effect of a Positive Externality Associated With the Consumption of X.

480

Welfare Economics

of the economic agent that creates the external effect. We now examine this possibility in more detail. There are two questions: (1) Under what circumstances is a market solution feasible? (2) If the market solution is feasible, does it make any difference to whom the property rights are assigned? In brief, the answer to the first question is that a market solution is feasible only when the number of agents is small so that the costs of negotiating and executing the necessary exchanges are small relative to the value of the external effects. The answer to the second question is that it does not matter to whom property rights are assigned as long as they are assigned to someone. Consider a river on which are located a paper mill and a brewery. The brewery draws its water from the river to make beer. The paper mill is upstream from the brewery and discharges waste into the river. When the paper mill is discharging waste, the brewery must filter the water to remove the contamination. This adds $100 per month to the total cost of production at the brewery. Finally, suppose that the paper mill could control its waste discharge and eliminate the external effect at a cost of $50 per month. The first thing to note about this example is that economic efficiency would be served by having the paper mill control its waste. Controlling wastes creates benefits to the brewery of $100 per month in the form of reduced treatment costs; yet the cost of control is only $50. The net benefits are $50. Will the correct or efficient outcome be achieved under alternative assignments of property rights in the river? Suppose first that the property rights in clean water are assigned to the brewery. Then the paper mill could dump its waste in the river only if it had reached an agreement with the brewery allowing it to do so. The brewery would permit the mill to use its river in this way only if the mill agreed to pay at least $100 per month for the right to dump its waste. This payment would compensate the brewery for its higher treat¬ ment costs. If the mill were to pay the brewery more than $100 per month, the brewery would be better off allowing the river to be used as a waste dump and treating the water that it used. But the paper mill would not be willing to pay as much as $100, because it can treat its wastes for only $50 per month. Thus with property rights assigned to the brewery, the outcome would be a clean river with the paper mill treating its waste. Suppose instead that the law assigned rights to the river to the paper mill. The mill would be free to use the river in any way desired, including employing it as a dump for its wastes. Because the mill owns the rights to the river, it has an incentive to allocate the river to its highest value use. The best use of the river as an economic resource turns out in this example to be as a source of clean water for the brewery. The brewery would be willing to pay as much as $100 per month to the paper mill for the right to withdraw clean water. Because the cost to the paper mill of providing clean water for the brewery is only $50 per month, the mill and the brewery should be able to reach a mutually advantageous exchange. The brewery will pay somewhere between $50 to 100 per month to the mill, and the mill will treat its wastes and provide clean water to the brewery. Even though in this instance the law assigns property rights to the paper mill, bargaining between the two parties will lead to an economically efficient outcome. The outcome is independent of the assignment of property rights. But it does depend on the feasibility of negotiating and carrying out the appropriate exchange.

481

Welfare Economics: Competition and Efficiency

To see the importance of having a small number of parties to the externality, suppose

in this example that instead of one brewery, there were 100 home owners, each incur¬ ring $1 per month of treatment costs because of the mill’s discharge. Economic effi¬ ciency still calls for the mill to control its waste at a cost of $50 per month. But it would be much more difficult for the 100 home owners to organize themselves and to negotiate effectively with the paper mill. Suppose now that the cost to the paper mill of controlling its waste is $150 per month. The economically efficient outcome is now different, because the costs of control exceed the benefits of control in the form of reduced treatment costs at the brewery. But bargaining, if feasible, will lead to the economically efficient outcome regardless of the assignment of property rights in the river. If property rights are assigned to the mill, the mill will have no reason to control its waste. The most that the brewery would be willing to pay to purchase a clean river is $100; but it would cost $150 per month for the paper mill to provide a clean river. If the property rights were assigned in the brewery, the brewery could prevent the paper mill from dis¬ charging wastes. But it would not be in its own economic interest to do so. The paper mill would be willing to pay up to $150 per month for the right to discharge waste in the river. And at any price above $100 per month the brewery should be willing to allow the waste discharge, because the payment would cover at least the cost of treating its intake water. Again, the river resource is allocated to its highest value use no matter which firm is assigned the property rights in it. The two alternative property right assignments differ only in their implications for who receives the economic value of the river.1

Public Goods Up to this point our analysis of production, demand, and markets has focused exclu¬ sively on what are called private goods. Private goods have two key characteristics. First, consumption of a private good is rivalrous in the sense that when one person consumes 1 unit of the good, the aggregate quantity available for consumption by others is reduced by 1 unit. Second, when one person purchases a unit of the private good for her own consumption, she can exclude others from any and all the benefits of consump¬ tion. In other words, the property rights assignment is specific and enforceable. A pure private good is at one end of a spectrum of types of goods with varying degrees of rivalry and excludability. If the consumption of a good conveys a positive externality, rivalry in consumption is not complete and it may be difficult if not impossible to exclude others from realizing the external benefit of consumption. The other end of the spectrum is occupied by pure public goods. Definition: A public good is a good that

'For a comprehensive treatment of this question, see Ronald Coase, The Problem of Social Cost, Journal of Law and Economics, October 1960, 3, 1-44. See also Thomas Crocker, Externalities, Property Rights, and Transaction Costs: An Empirical Study, Journal of Law and Economics, October 1971, 14(2), 451^164 and Steven Cheung, The Fable of the Bees: An Economic Investigation, Journal of Law and Economics, April 1973, 16(2), 11-34, for examples and further analyses of property rights and externalities.

482

Welfare Economics

once produced is available in equal quantity to all without restriction. Consumption of a pure public good is nonrivalrous, and exclusion is not possible. Examples of pure public goods include national defense, the aid of a lighthouse marking a hazard to navigation, and TV and radio broadcast signals. In each case the consumption of the good or service by one individual does not diminish the availability of the good to anyone else. Furthermore, once a producer has furnished 1 unit of one of these goods to an individual for consumption, he cannot exclude others from benefit¬ ing from the good. Once it is produced, it is freely available to all. Table 17.1 provides a comparison of private goods and public goods in terms of several important characteristics. Nonrivalry in consumption is defined in line 2 of Table 17.1. For a private good the aggregate consumption is equal to the sum of the quantities consumed by all individuals. But for a public good aggregate consumption is equal to the quantity consumed by individual I, which is equal to the quantity consumed by individual II, and so forth. The property of nonrivalry in consumption leads to several important differences in the microeconomic analysis of public goods. First, although the aggregate or market demand curve for a private good is found by adding individual demand curves hori¬ zontally, the aggregate demand curve for a public good is found by adding demand curves vertically. For a private good, for each possible price, the quantities demanded by each individual are summed to determine the market quantity demanded. But in the case of a public good the same quantity is available to all. Figure 17.5 shows the derivation of the aggregate demand curve when there are only two people in the economy. Individual I’s willingness to pay for the first unit ($6) must be added to individual II’s willingness to pay ($4) in order to determine the aggregate willingness to pay for 1 unit ($10). This vertical addition or summation of willingness to pay is

Table 17.1

Private Goods and Public Goods Compared A is a private good

1. Property rights

2. Aggregate consumption 3. Aggregate demand curve

Excludable Rival:

A = A, + A2 + - + A n Horizontal addition of individual demand curves

A is a public good Nonexcludable Nonrival: A = A 1 A 2 = ■■■ — Vertical addition of individual demand curves

Xn

4. Condition for optimum provision (partial equilibrium)

MWTPx = MCx

1 mwtpI = MCv /=i A x

5. Pareto optimum condition for efficient output

MRSjcy = MRTXy

iMRSlXY = MRT xy

483

Welfare Economics: Competition and Efficiency

Dollars

Individual I 6

l\ I \ 3 -t- 1 1 ' d\ i l 1 0] X\ *2

A

X per period

\

i i i i

Dollars

4 3

Oil

i i i

xl

i 1 1 1 1 ]

Individual II

^—^11

1

x2

X per period Figure 17.5

Individuals’ Demands and the Aggregate Demand Curve for a Public Good.

carried out for each alternative quantity to determine the aggregate demand curve for the public good. Also because of nonrivalry in consumption, the conditions for the optimum provision of a public good and the Pareto optimum condition for efficient output where public goods are involved are different from the corresponding conditions for private goods. Recall from Chapter 11 that the optimum quantity of a private good is supplied when its price (which measures the marginal willingnesses to pay of each of its consumers)

484

Welfare Economics

is just equal to the marginal cost of production. The marginal unit of the private good can only go to one individual, thus its marginal cost should just equal the marginal willingness to pay of that individual for the good. The marginal unit of a public good goes equally to all its consumers. Thus the optimal provision of the public good requires that its marginal cost be equal to the sums of the marginal willingnesses to pay of all those who benefit from its provision (see line 4 of Table 17.1). By similar reasoning the Pareto optimum condition for efficient output of a public good requires that the sum of the marginal rates of substitution equal the marginal rate of transformation. The marginal rate of transformation gives the amount of Y that must be given up to obtain one more unit of X in production. The marginal rate of substitu¬ tion gives the amount of Y an individual is willing to pay to obtain one more unit of X while staying on the same indifference curve. If X is a public good, the sum of the MRSXy s is the total amount of Y that can be taken away from all individuals together while leaving them all on their original indifference curves when one more unit of X is supplied to them all. The property of nonexcludability makes it very unlikely that the optimum quantity of a public good will be supplied by producers in a competitive market. Suppose that a firm enters into an agreement with an individual to provide, say, 3 units of a public good at a price per unit that just covers the firm’s average and marginal costs. Assume that given the price, this is the optimum quantity demanded for this individual. Thus the individual’s marginal willingness to pay is just equal to the marginal cost of production. But once the good is provided to this individual, everyone benefits from its availability. When their MWTP’s are taken into account, it is clear that the output of this public good should be expanded. But because the firm cannot exclude these others from benefiting from the amount of the public good already provided, the firm will not be able to capture additional revenues to cover the additional costs of expand¬ ing output beyond the level of 3 units. Thus nonexcludability severely weakens the economic incentive of suppliers to produce public goods and prevents the expansion of their output to the efficient or optimum level. There is an additional reason to believe that the market will fail to provide the optimum quantity of a public good. When the individual whose expenditure made possible the provision of 3 units of the public good sees that everyone else is benefiting from his expenditure without contributing to the cost of the public good, he might well reason as follows: “If other people can benefit from my expenditure on the public good without helping to pay for it, perhaps I should not spend any money on the public good in the hope that I can benefit from someone else’s expenditure. ’2 From the demand side of the market the desire to be a “free rider” weakens the incentive for consumers to offer to purchase the public good. Thus because of both weak supply incentives and incentives to refrain from expressing demand in the market, the market will fail to produce the optimum quantity of a public good. The public good, if produced at all, will be produced in less than optimal quantities.

2Does the free rider problem have anything in common with the prisoners’ dilemma game of Chapter 16?

485

Welfare Economics: Competition and Efficiency

THE MANY PARETO OPTIMUMS The finding that a perfectly competitive market system achieves an efficient equilibrium or Pareto optimum is one of the principal conclusions of normative microeconomic analysis. If social welfare is defined in terms of efficiency or Pareto optimality, then we have established that the maximizing behavior of individuals in a perfectly competitive market system leads to a maximum in social welfare. But there are some problems in defining social welfare in this way. Principally, such a definition of social welfare ignores a possible social concern with equity or the pattern of distribution of income and welfare among members of the society. In this section we show that there is an infinite number of alternative Pareto optimum equilibria for an economy. They differ in the way in which they distribute well-being or utility among the members of the society. The concepts of economic efficiency and Pareto optimality provide no basis for choosing among these alternative equilibria. We must resort to some notion of equity in order to define a unique social welfare maximum. We will turn to this problem in the following chapter. For simplicity assume that there are only two individuals in the economy and that there are only two goods and two factors of production that are available in fixed quantities. Assume that the economy is on the production possibilities curve of Figure 17.6 at point M. This means that the condition for efficient production is satisfied. The exchange box and exchange locus associated with point M are also shown. In what follows it will be useful to employ the terminology of utility theory. Assume that cardinal utility functions have been used to assign utility numbers or indexes to

Figure 17.6

The Utility Possibilities in the Exchange Box.

486

Welfare Economics

each indifference curve for each of the two individuals. The utility functions for the two individuals need not be the same. The utility information from the exchange locus of Figure 17.6 can be used to derive a utility possibilities curve. For example, at point M* on the exchange locus, Ann’s utility is 30 units, whereas Bob’s utility is 17 units. This information is plotted in Figure 17.7. The horizontal and vertical axes of this figure are the utility levels of Ann and Bob, respectively. For each point on the exchange locus there is a corresponding point in the utility diagram of Figure 17.7. The locus of all these points is a utility possibilities curve (UPC). Definition: A utility possibilities curve is a locus of all possible utility combinations for two individuals that can be attained from a given total output of goods. For any given utility level for one individual, say, UA = 40, the utility possibilities curve shows the maximum utility attainable by the other individual, given the total production of the two goods, X and Y. The UPC always slopes down to the right. This reflects the fact that for movements along the exchange locus, it is not possible to increase one individual’s utility except by decreasing the utility of the other individual. Suppose that at point M* on the exchange locus the marginal rates of substitution for both individuals equal the marginal rate of transformation between X and Y. Thus the third Pareto condition for efficient output is satisfied. This means that the output corresponding to point M and its allocation to the two individuals at M* is a Pareto optimum position. Now consider an alternative position on the production possibilities curve, say, point N in Figure 17.6. A new exchange box and exchange locus can be drawn. The utility

Figure 17.7

Ann’s utility per period The Utility Possibilities Curve.

487

Welfare Economics: Competition and Efficiency

information from the exchange locus can be used to derive a new utility possibilities curve. This is shown in Figure 17.8, where the utility possibilities curve from point M has also been reproduced. This new utility possibilities curve must pass below and to the left of point M*. This is because point M* is known to be a Pareto optimum position. And we know that starting from a Pareto optimum position there is no other position in the economy that can yield more utility for one individual without resulting in less utility for the other; that is, there are no other positions in the economy that can lead to utility combinations above and/or to the right of M*. Suppose that there is one point on the new exchange locus at which the third Pareto condition for efficient output is satisfied. The utilities for Ann and Bob that are as¬ sociated with this point are shown in Figure 17.8 as N*. This point must be on that part of the new utility possibilities curve that lies outside UMUM’. If this exercise is conducted for every point on the production possibility curve, a whole family of utility possibility curves will be generated. Assume that every possible UPC curve has one Pareto optimum position on it.3 Thus each UPC curve will have one point on it that corresponds to a Pareto optimum position. The bold line labeled GG' in Figure 17.8 is a locus of all such Pareto optimum utility combinations. It can

Ann’s utility per period Figure 17.8

The Grand Utility Possibilities Frontier.

3This need not be the case. If there is no point on the exchange locus that satisfies the third Pareto optimum condition, the associated UPC curve will lie entirely inside the grand utility possibility frontier described here. And if there is more than one point on the exchange locus that satisfies the Pareto optimum conditions, the associated UPC curve will have more than one point of tangency with the grand utility possibility frontier.

488

Welfare Economics

also be viewed as an envelope of the family of all UPC curves. This is called the grand utility possibilities frontier (GUPF). Definition: The grand utility possibilities frontier (GUPF) is the locus of the utility combinations generated by all possible Pareto optimum positions for an economy. It represents the maximum level of utility attainable by one individual for any given level of utility that is assigned to the other individual, given the factor endowments and production technology. The GUPF slopes downward to the right, reflecting the definition of a Pareto optimum position. For any Pareto optimum position represented on the GUPF it is not possible to increase the utility of one individual by any reorganization of the economy without decreasing the utility of the other individual. The GUPF shows that for any economy there is virtually an infinite number of alternative Pareto optimum positions. They differ from one another only in terms of the relative utility positions of the two individuals. A position up and to the left close to the UB axis indicates that Bob has received a relatively larger share of total out¬ put and is experiencing a high level of utility relative to Alice. From this perspec¬ tive it appears that some Pareto optimums are more equitable than others, at least in terms of the distribution of goods between the two individuals. Is it possible to say that some Pareto optimums are better than others? Is there one Pareto optimum that is better than all others? In order to rank Pareto optimum positions, some concept of equity or deservingness must be introduced. And this might involve making compar¬ isons of the utility levels of the two individuals. We turn to this issue in the next chapter.

SUMMARY A market system in which all goods and services and factor inputs are exchanged in perfectly competitive markets will reach an equilibrium that satisfies the Pareto opti¬ mum conditions for economic efficiency. In the simple model with fixed factor supplies these conditions define efficiency in production, in exchange, and in output. Where factor supplies are functions of factor prices, a fourth set of conditions defines efficiency in factor supply. These conditions are also satisfied under perfect competition. Perfect competition can be viewed as an ideal yardstick against which the structure and performance of real-world economies can be measured. In the real world there are several significant sources of market failure that can lead to violation of the Pareto optimum conditions and losses in economic efficiency. These include monopoly and monopsony power in product and factor markets, taxation of the production and/or sale of goods and services and of factor incomes, positive and negative externalities, and the existence of public goods that have the property of nonexcludability and nonrivalry in consumption. There is an indefinite number of Pareto optimum positions, each differing according to the distribution of utility among the members of the society. The range of alternative

489

Welfare Economics: Competition and Efficiency

distributions can be portrayed by the grand utility possibility frontier. Each point on this frontier is a Pareto optimum position.

KEY CONCEPTS The Pareto optimum conditions for efficiency in production, exchange, output, and factor supplies Market failure

Public goods Utility possibilities Grand utility possibilities frontier Externalities

QUESTIONS AND PROBLEMS For Basic Review 1. Define and explain the economic significance of each of the key concepts. 2. (a) Define and explain the concept of economic efficiency that underlies the Pareto optimum conditions. (b) State the conditions for Pareto optimality for the simple two-factor, two-good, two-person economy with variable factor supplies. Explain or demonstrate why these conditions are necessary for attaining economic efficiency. 3. Use the appropriate box diagrams, and so on, to explain the derivation of the grand utility possibilities frontier from the underlying data on factor endowments, technology, and preferences for a two-person, two-good, two-factor economy with fixed factor supplies. 4. This chapter discusses several sources of market failure. Describe each of these sources and show how they affect the ability of the economy to achieve a position in which the Pareto optimum conditions are satisfied. Can you think of examples of each of these types of market failure in addition to those mentioned in the text?

PROBLEM 1.* Jones raises his cattle on land suited only for that purpose. On adjoining land Smith grows wheat. Jones’s cattle freely roam across the property line causing damages to Smith’s wheat of $100 per year. A fence would cost $75 per year to build and maintain. (a) From the point of view of economic efficiency, should the fence be built? Explain. (b) If the fence should be built, can economic reasoning determine who should pay the cost? Explain. (c) Suppose the existing property rights law absolves Jones from any liability for damages caused by his cattle. Would the fence be built? If so, by whom?

490

Welfare Economics

(d)

If the fence cost $150 per year, should it be built? (e) Suppose the existing law makes Jones liable for damages caused by his cattle. If the fence cost $150 per year, what outcome would you expect? Is this outcome “good”? Discuss.

CHAPTER 18 Equity and Social Welfare

SOCIAL WELFARE FUNCTIONS

■e have shown that an efficient allocation of resources is one that places the economy on the GUPF and that the GUPF represents the locus of an infinite number of Pareto optimum positions for the economy. We have also shown that it is not possible to rank the many possible Pareto optimums to determine which one is best unless some notion of equity or deservingness is introduced. If some way of defining equity in the distribu¬ tion of well-being can be defined, it can be used to relate the welfare or utilities of individuals to the welfare of the society as a whole and to rank and compare alternative Pareto optimums. Definition: A

social welfare function is a rule for measuring the aggregate welfare

of society as a whole as a function of the welfares or utilities of the individual members of society. A social welfare maximum is that allocation of resources and distribution of output that leads to a maximum attainable value for the social welfare function, given the constraints of technology, factor endowments, and individual tastes and preferences. The first step in measuring aggregate welfare is to agree on a measure of the well¬ being of each member of society, that is, on how the variables in the social welfare function are to be measured. The traditional approach in welfare economics has been to assume that each individual’s utility can be measured on a cardinal scale and that it is meaningful to compare the utility measures of different individuals. This means, for example, that if Ann’s utility is 200 units while Bob’s is 100 units, it can be said that Ann is twice as well off. These are, in fact, implausible assumptions. In the modern view of utility and preference theory such comparisons cannot be made, nor can utility 491

492

Welfare Economics

be measured in cardinal units. Thus efforts to define social welfare in terms of utilities are not likely to provide any guidance in identifying a social welfare maximum in practice. But because of their role in the historical evolution of the theory of economic welfare, we will review several such efforts in this section. An alternative approach to defining social welfare is to assume that it is a function of the incomes of individuals. Money income is an objective measure of the consump¬ tion opportunities open to an individual, given money prices for goods. As long as prices do not change, money income and any ordinal index of utility always change in the same direction. After reviewing utility-based approaches to defining a social welfare maximum, we will consider the possibility of defining social welfare in terms of money income.

Social Welfare and Utilities Assume that each individual’s utility can be measured in cardinal units. Social welfare is a function of the welfares of the individuals. In our two-person economy welfare is given by

W = W(UA, UB) where the functional form of JT() embodies society’s value judgments about the social value of increments of utility to its members. A social welfare function can be used to derive a set of social welfare curves. Definition: A

social welfare curve is a locus of all combinations of utilities for the

two individuals that result in the same level of welfare for society as a whole. Social welfare is maximized when society attains the highest possible social welfare curve.

Utilitarianism The roots of the utilitarian social welfare function can be traced back almost two hundred years to the writings of Jeremy Bentham. The basic value judgment underlying the utilitarian social welfare function is that an additional unit of utility is of equal social value no matter to whom it accrues. Thus society’s welfare is maximized when the sum of the utilities of all individuals is maximized. This social welfare function can be written as

W =1

U:

1=1

where W is social welfare, 17, is the (cardinal) utility of individual i, and there are n individuals in the society. The utilitarian social welfare curves are straight lines that slope downward to the right at a 45° angle. Three social welfare curves with this property are shown in Figure 18.1. They indicate that if Bob’s utility is reduced by 1 unit while Ann’s utility is increased by 1 unit, social welfare is unchanged. These curves imply that society is

493

Equity and Social Welfare

Figure 18.1

The Utilitarian Social Welfare Function and the Maximum Social Welfare.

indifferent as to the distribution among the two individuals of any given total of utility. It does not matter to society whether the distribution of utility favors Bob as at point A on social welfare curve Wl or it favors Ann as at point B. The GUPF is also shown in Figure 18.1 as the line GG'. Social welfare is maximized at that point where a social welfare curve is just tangent to the GUPF. The social welfare maximum is point C in Figure 18.1, where a social welfare level of W2 is achieved. As the example of Figure 18.1 shows, the utilitarian social welfare function can lead to a welfare maximum with quite an unequal distribution of utilities. This is because utilitarianism treats all individuals as equally deserving no matter what levels of utility they have already attained. This value judgment may not be acceptable to many because of its tolerance for inequality. There is a more fundamental objection to utilitarianism in particular and to all social welfare functions based on cardinal utilities. They assume that the additional utility one individual experiences from consuming an additional unit of, say, chicken, can be meaningfully compared with the additional utility another individual experiences by, say, listening to an additional hour of music. Can it be that one individual can have a higher capacity than another for deriving enjoyment from the consumption of a given bundle of goods? The issue is whether it is meaningful to say that different people can have different capabilities of producing utility from consumption. For if the answer is yes the utilitarian social welfare function would call for allocating a larger portion of society’s resources to those individuals with the more highly developed “capacity for enjoyment.” On the other hand, if all individuals have identical utility functions and therefore

494

Welfare Economics

equal capacities for enjoyment, a utilitarian social welfare function leads to an equal distribution of income and utility among all individuals. If Ann has more income and therefore has more consumption opportunities, she will be farther out on her diminish¬ ing marginal utility schedules for the goods she is consuming. Suppose that a dollar of income is taken away from Ann and given to Bob who has a lower income. Because Ann has a lower marginal utility of consumption, her loss of utility will be smaller than the utility Bob gains from consuming the extra dollar’s worth of goods. The sum of their utilities is therefore increased. Given identical utility functions, if incomes are unequal, the sum o^ utilities can always be increased by taking income away from the higher income individual and giving it to the lower income individual. Social welfare is maximized only when incomes and the marginal utilities of consumption are equal for all individuals in the economy.1

A Bergson Social Welfare Function According to Abram Bergson, the interpersonal comparison of utility is an ethical matter that must be dealt with in the context of the value judgments underlying the social welfare function.2 He postulated that social welfare was a function of the cardinal utilities of the individuals in the society but that the exact nature of the relationship between the utilities and welfare must be spelled out by the members of the society. Different societies could choose social welfare functions with quite different properties. One plausible property is diminishing marginal social welfare. Marginal social wel¬ fare is the change in welfare for a 1 unit change in the utility of one individual (e.g., &W/MJA). A social welfare function is characterized by diminishing marginal social welfare if, other things equal, equal successive increases in the utility of one individual lead to smaller and smaller increases in social welfare. Diminishing marginal social welfare is sufficient to yield social welfare curves that are convex to the origin such as those shown in Figure 18.2. Can you see why this is so?3

'Even if the utility functions of individuals are not known and cannot be presumed to be equal, the conclusion that social welfare maximization requires equal incomes can be reached from a modification of the utilitarian social welfare function. See Abba Lerner, The Economics of Control, New York: Macmillan, 1944. Lerner argued that in the absence of any better information, any randomly chosen individual is just as likely to have an above average capacity for enjoyment as a below average capacity. Because true social welfare cannot be computed, the problem becomes one of, in the language of probability theory, maximizing the expected value of social welfare. The expected value of social welfare is maximized when the expected values of the marginal utilities of consumption are the same for all individuals. And because any individual is equally likely to have an above average or below average capacity for enjoyment, this condition is satisfied only when money income is distributed equally to all individuals. zSee Abram Bergson, A Reformulation of Certain Aspects of Welfare Economics, Quarterly Journal of Economics, February 1938, 52(1), 310-334 and his Essays in Normative Economics, Cambridge, Mass.: Harvard University Press, 1966. 5Hint: The analysis is similar to that used to establish the relationship between diminishing marginal productivity or diminishing marginal utility on the one hand and the convexity of isoquants or indifference curves on the other hand. See Chapter 3 or Chapter 7.

495

Equity and Social Welfare

Figure 18.2

A Bergson Social Welfare Function and the Maximum Social Welfare.

If marginal social welfare does not diminish at all, as with the utilitarian social welfare function, the social welfare curves are downward-sloping straight lines. The more rapidly marginal social welfare diminishes with increasing individual utility, the more sharply curved are the social welfare curves. The shape and position of the social welfare curves reveals society’s ethical judgment about the relative deservingness of different individuals. If the social welfare function has diminishing marginal social welfare, then the relative deservingness of an individual at the margin depends on that individual’s present level of utility relative to the other individuals in the society. And other things equal, additional utility to a relatively low utility person will add more to social welfare than the same increment of utility to a high utility person. The second plausible restriction on the nature of the social welfare function posits that individuals in similar circumstances are treated equally in terms of the social evaluation of their utility. Specifically, if two individuals have achieved the same level of utility, the marginal social welfare associated with increasing one individual’s utility must be equal to the marginal social welfare of increasing the other individual’s utility. Notice that this condition is an explicit interpersonal comparison of utility levels. This condition imposes a specific requirement on the shape and position of the social welfare curves. At each point where individual utilities are equal, the social welfare curve through that point must have a slope equal to — 1. In Figure 18.2 the dashed line emerging from the origin at an angle of 45° is the locus of all points of equal utilities for Ann and Bob. Each social welfare curve has a slope of — 1 where it intersects the 45° line. Can you see why this is the case? Figure 18.2 also shows the GUPF GG' defined in terms of cardinal utilities. Social welfare is maximized at that point where a social welfare curve is just tangent to the GUPF. This is at point D'. Notice that in this case social welfare maximization does

496

Welfare Economics

not require equalization of utilities. If both individuals had equal capacity for enjoy¬ ment and identical utility functions, the GUPF would also have a slope of — 1 where it intersected the 45° line. In that case social welfare maximization requires equalization of utilities. And this can only be accomplished by equalizing money incomes.

Rawls’s Maximin Criterion The philosopher John Rawls has proposed a novel approach to the question of distribu¬ tive justice or equity.4 He asked what rules might a society of rational, self-interested individuals choose for itself to govern the distribution of welfare among its members? In practice, it seems reasonable to suppose that a self-interested individual’s view of what constitutes equity and economic justice in the distribution of utility might be influenced by her own position in the economy. A person who has achieved a relatively high level of utility in comparison with other members of the society might be less willing to vote for or agree to a social program designed to achieve equality, whereas someone who has attained a low level of utility might highly favor a program designed to achieve equality in the distribution of utility. In order to abstract from the influence of economic position on individuals’ views of social justice, Rawls proposed a hypothetical construct termed the “veil of igno¬ rance.” Assume that the members of society meet before the first day of the society’s existence in order to agree on constitutional rules for their self-governance. The mem¬ bers of society are presumed to be ignorant of what their own economic positions in the society will be. Thus they can consider rules for distributive justice without the corrupting influence of economic position, status, and power. What rules for distributive justice might rational individuals choose while behind the “veil of ignorance”? Rawls argued that since everyone would realize that they were equally likely to wind up being the least well off in the society, they would (or should) all vote for the following rule: Maximin Rule: Any social and economic inequalities that are allowed to exist must be to the greatest expected benefit of the least advantaged members of the society. In other words, there should be no inequalities in economic or social status except those that work to the benefit of the least well off in the society.

This rule is a form of social welfare function. It generates social welfare curves such as those shown in Figure 18.3. These curves are drawn as dashed lines rather than as solid lines to emphasize a difference between these social welfare curves and those of Figures 18.1 and 18.2. Those curves are defined as locuses of points of equal social welfare. The Rawlsian social welfare curves of Figure 18.3 are boundaries between

4See John Rawls, A Theory of Justice, Cambridge, Mass.: Harvard University Press, 1971. For a short discussion of the implications of the Rawlsian approach for economic welfare criteria, see John Rawls, Some Reasons for the Maximin Criterion, American Economic Review, May 1974, 64(2), 141-146.

497

Equity and Social Welfare

Figure 18.3

Rawls’s Maximin Criterion and the Maximum Social Welfare.

points of improved social welfare and points of decreased social welfare. Consider point C at which the utilities of the two individuals are equal. A move from point C to

D

increases Bob’s utility and increases the degree of inequality. But because this increase in inequality does not work to the benefit of the least well off (Ann), it is not sanctioned under the maximin rule. It generates a lower level of social welfare than point

C.

However, if the increase in Bob’s utility were accompanied by even a slight increase in Ann’s utility, such as the move to point

E, this move would pass the maximin test.

That is, the increase in inequality does work to the benefit of the least well off (Ann). Given a GUPF that slopes down to the right, the only position that satisfies the maximin rule is that where utilities are equal. See, for example, point Compared to point

F in Figure 18.3.

F any other point on the GUPF involves an inequality; but that

inequality does not work to the benefit of the least well off. Therefore it must be rejected.

Social Welfare and Income In this section we consider defining social welfare as a function of the money income of the members of society. This approach has obvious intuitive appeal because an increase in money income, other things equal including prices, leads to an increase in an individual’s well-being. And money income, unlike utility, has the virtue of being measurable and comparable across individuals. Nevertheless, there are two problems in implementing a money income-based social welfare function. The first problem is that goods and services purchased with money income need not be the only source of utility for an individual. For example, in Chapter 12 we hypothe¬ sized that individuals derive utility from leisure time activities. Suppose that an individ¬ ual’s money wage rate increases. She might reduce the number of hours worked so that

498

Welfare Economics

money income would only increase slightly. The increase in money income would not be an accurate reflection of the increase in utility associated with the additional hours of leisure. Individuals can also derive utility from nonmarket production activities such as home vegetable gardens and doing their own home and automotive repairs. Finally, government-provided public goods and environmental amenities such as clean lakes and streams for recreation and fishing and clean air also contribute to individuals’ welfare. In principle, it would be possible to calculate for each individual the amount of money that would be necessary to compensate her for the loss of the nonmarket sources of utility, in other words, the consumer surpluses associated with each of the nonmarket goods. This sum should be added to money income to create a measure of “full income.” In what follows we will assume that the income measures used in defining social welfare are full income. The other problem is less easily resolved. Money income or full income can only be a proxy for welfare if the prices of the goods and services purchased with money income are constant. For example, if money income doubles but the prices of all goods double, then the individual’s utility is unchanged. We saw in Chapter 8 that a price index could be used to compute real income or purchasing power when prices are changing. We also saw that using a price index may lead to an overestimate or an underestimate of the change in real income depending on what set of quantities was used as weights in computing the price index. For purposes of finding a social welfare maximum, we need to derive a real full income frontier, analogous to the GUPF, showing the full range of alternative distributions of real full income among the individuals of a two-person economy. But it is at least possible that the general equilibrium positions associated with the range of income distributions might involve quite different sets of relative prices. If the relative prices change over the range of income distributions being evalu¬ ated, it is just not possible to use price indexes to measure real income precisely. In what follows, we will ignore the implications of the index number problem in computing real full income. Assume that the locus of alternative distributions of real full income has been derived for our simple two-person, two-good economy. It is shown in Figure 18.4. Each of the three utility-based social welfare functions discussed in the preceding section have their analogue in income-based social welfare functions. First, the strict utilitarian social welfare function has its analogue in a function that measures social welfare by the size of aggregate real full income. In other words,

W = Ma + Mg where

MA and MB are the real full incomes of Ann and Bob. According to this social

welfare function, society is indifferent as to who receives additional dollars of income. This social welfare function reflects no concern for equity in the distribution of real full income. The social welfare curves associated with this function are straight lines with slopes equal to — 1. As shown in Figure 18.4, they lead to an optimum social welfare at point C. A Bergson type of social welfare function can be defined in terms of real full incomes.

499

Equity and Social Welfare

Ann’s income per period, dollars Figure 18.4

The Aggregate Income Criterion and the Maximum Social Welfare.

Suppose that the social welfare function is

W = W(Ma, Mb) and that the society’s value judgments and preferences for more equal income distribu¬ tion are embodied in the following conditions: 1. Diminishing marginal social welfare for increases in income to each individual, other things equal; and 2. Equal treatment of equals; that is, for

MA = MB the marginal social welfare of

income to Ann equals the marginal social welfare of income to Bob. The first condition makes the social welfare curves convex to the origin. The second condition requires that social welfare curves have a slope equal to -1 where they intersect the 45° equal income locus. Social welfare curves with these properties are shown in Figure 18.5. In that figure the maximum social welfare position is point C where a social welfare curve is just tangent to the real full income frontier. Finally, the Rawls maximin rule can be applied with income rather than utility being used as the basis for determining inequality and for identifying the least well off in the society. The social welfare curves associated with the maximin rule are dashed lines parallel to the axes that meet at the 45° locus of equal incomes. As long as the real full income frontier slopes down to the right, the Rawls maximin rule calls for complete income equality. Figure 18.6 shows a case where the maximin rule permits some inequality of incomes because the inequality works to the advantage of the least well off. In that example equality is achieved at point C. But social welfare is maximized at point

D because the increase in inequality benefits Ann, the least well off, as well as Bob.

500

Welfare Economics

Bob’s income per period, dollars

Ann’s income per period, dollars Figure 18.5

A Bergson Social Welfare Function for Incomes and the Maximum Social Welfare.

Figure 18.6

Rawls’s Maximin Criterion for Incomes and the Maximum Social Welfare.

Achieving the Social Welfare Maximum Assume that a society has chosen one of the social welfare criteria discussed here and has successfully identified the social welfare maximum position. What must the society do to assure that it reaches this maximum position? In principle, the selection of one point on the GUPF is sufficient to determine the appropriate values for all other variables in the economy, including the levels of outputs of all goods, their prices, input

501

Equity and Social Welfare

combinations, and so on. In the simple, two-good, two-person economy the determina¬ tion of the values for the relevant variables would proceed as follows: 1. The welfare maximum is a point on a unique utility possibilities curve corresponding to one point on the production possibilities curve. This determines

2.

the outputs of the two goods, X and Y. The welfare-maximizing point on the GUPF corresponds to one point on the exchange locus. This determines the distribution of both goods between the two

individuals. 3. The optimum point on the production possibilities curve corresponds to a unique point on the efficiency locus in the production box. This gives the appropriate combinations of inputs in the production of both goods. This solution for the welfare-maximizing quantities of inputs and outputs and their distribution could be the basis for an economic plan issued by the planning agency in a centralized command economy. With centralized management of the quantities produced and consumed, there would be no role for prices and markets in such an economy. There is an alternative to management of quantities. It is also possible to solve for the shadow prices that are consistent with the welfare maximum position. 1. Given the optimum point on the production possibilities curve, the prices of the two goods are determined by the slope of the production possibilities curve (the marginal rate of transformation of X for T). 2. The slopes of the isoquants at the optimum input combinations determine the optimum prices for factor inputs. The factor price ratio must equal the marginal rates of technical substitution of labor for capital for both goods. A centrally planned or socialist economy could post these shadow prices as a set of governmentally fixed or administered prices and direct that all transactions in the economy take place at these prices. The agency could then order all production facilities to make their input and production decisions so as to maximize their “profits

com¬

puted according to these prices. Production managers would equate marginal costs and values of marginal product with the relevant fixed prices, and so would be led to produce the welfare-maximizing outputs. The agency would also have to compute the money incomes that are required to allow each individual to attain his welfare-maximizing utility level given product prices. If money incomes were distributed in this way, individuals would respond to fixed prices by choosing the welfare-maximizing consumption bundles. In this way the planning agency could achieve the welfare maximum by managing prices and income distribution rather than by quantities. An unmanaged market system can also achieve the social welfare maximum under certain conditions. One additional piece of information is required: Given the optimum factor prices, there is a single distribution of the income from the ownership of factors that is consistent with the optimum allocation of

502

Welfare Economics

goods between the two individuals. Any other distribution of income would result in the individuals reaching a different point on the exchange locus where their

MRS's would be different from the MRT and the economy would be inside

the GUPF. If the society wishes to rely on decentralized markets with private ownership to achieve the social welfare maximum, it must do two things. First, it must establish the appropriate distribution of rights to receive factor income by an appropriate vesting of property rights. And second, because the social welfare maximum position is on the GUPF, the society must remove all economic and institutional barriers to attaining the GUPF. This means that all those potential sources of market failure such as monopoly or monopsony power, externalities, and public goods must be dealt with through appropriate institutional, legal, and economic changes. The Pareto optimum conditions make up a set of necessary but not sufficient conditions for achieving a social welfare maximum. And appropriate steps must be taken to assure that these conditions are satisfied. If the economy is organized in a way that assures that the Pareto optimum conditions will be satisfied, and if the correct distribution of the rights to income has been achieved, then the decentralized decisions of rational, self-interested individuals operating in perfectly competitive markets will lead the economy not only to the GUPF but to the predetermined social welfare-maximizing point on the GUPF. In order for perfect competition to lead to a social welfare maximum, the society must first decide what it means by a social welfare maximum by choosing a social welfare function defined in terms of cardinal utilities that are comparable across individuals. Then it must assign the right to receive factor incomes in a manner consistent with this social welfare maximum. Only then can perfect competition be said to lead to a welfare maximum. This description of how to achieve a social welfare maximum has ignored the historical context of real-world economies. At any point in time a real-world economy has a specific distribution of ownership of the factors of production that is the result of past patterns of saving and investment, innovation and technological change, inheri¬ tance, and so forth. Only by accident would this actual distribution of ownership and its resulting general equilibrium correspond to the social welfare maximum. Thus the society must consider how to achieve the redistribution of income necessary to attain the maximum position. One approach is to levy taxes that fall on those whose utilities are too high relative to the welfare maximum and to use the proceeds to make transfer payments to raise the utilities of those whose utilities are too low. But virtually all forms of taxation that might be used to achieve this redistribution result in distortions of the price structure and violations of one or more of the Pareto optimum conditions. Taxation to achieve distributive aims tends to push the economy inside the GUPF and to prevent the attainment of a true social welfare maximum. For example, we saw in Chapter 11 that an excise or sales tax on a product raised product price above marginal cost. Also, a tax on labor income would result in the value of marginal product of labor being greater than the individual’s marginal rate of substitution between leisure and income. And as

503

Equity and Social Welfare

the discussion of welfare and negative income tax programs in Chapter 12 showed, transfer payments can also distort labor supply decisions and lead to violations of the Pareto optimum conditions. Taxation of economic activity and transfer payments based on economic status cannot be neutral with respect to resource allocation and the Pareto optimum condi¬ tions. The only neutral taxes are those that are unrelated to any economic activity or economic characteristic of individuals. Examples include taxes on pure rents and a uniform head tax or a poll tax (a tax on the act of voting). But their very neutrality makes it unlikely that they can be used as instruments to achieve a substantial redistri¬ bution of income. The only way a society can avoid the distorting effects of nonneutral taxation is to undertake a once and for all redistribution of existing wealth and rights to receive factor income. Also, this redistribution must be entirely unanticipated, lest the owners of large quantities of wealth take steps such as hiding their wealth in order to avoid the full impact of the redistribution. Although either some form of taxation and transfer payments or confiscation and redistribution of wealth may be necessary to achieve a social welfare maximum that reflects society’s value judgments concerning equity, both types of actions involve a conflict with another social value, one that some would say is more fundamental than equity in the distribution of income and well-being. That value is freedom from coer¬ cion. Taxation and redistribution are forms of economic coercion, unless these pro¬ grams are agreed to by unanimous vote.5 Thus any income redistribution program must involve some resolution of the conflict between the social values of a greater degree of equality in the distribution of well-being and freedom from coercive taxation.

Choosing a Social Welfare Function Thus far we have discussed social welfare and the welfare of society without examining the meaning of these terms very closely. A fundamental premise of welfare economics is that an economic system exists only to serve the individuals who are part of it and that each individual is the best judge of her own welfare. Social welfare does not exist except as perceived and evaluated by the individual members of the society. Thus a social welfare function must be derived somehow from the social attitudes and ethica views of the members of society. How can a society reach agreement on the nature and form of the social welfare function it will use to guide its economy? The most attractive idea is to use a democratic political process to select the social welfare function. But work on the theory of social choice has cast doubt on whether voting can be used to resolve fundamental issues such as the choice of a social welfare function even in principle. The Nobel Prize winning economist Kenneth Arrow has proved the impossibility that any democratic voting system can satisfy four apparently

-Tor a spirited advocacy of this point of view, see Charies K Rowley and Alan T. Peacock, Welfare Economics: A Liberal Restatement, London: Martin Robertson, 1975.

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Welfare Economics

reasonable criteria that embody democratic processes and the notion of consistent choice.6 These conditions are: 1. Consistent ordering. The choices made by any social choice mechanism must rank all alternatives and must be consistent in the sense that the ranking is transitive. 2. Nondictatorship. Social choices must not be dictated by anyone outside the society or by any single individual in the society. 3. Responsiveness to individual preferences. Social choices must not respond in the opposite direction to changes in individual preferences. In other words, if starting from a given pattern of preferences, one person increases her preference for alternative A, the social choice cannot switch from A to B. And if B was originally chosen, and one by one individuals shift their preferences so that they prefer A, at some point, the social choice must shift to A. 4. Independence of irrelevant alternatives. The social choice between two alternatives must depend only on people’s rankings of those two alternatives and not on their preferences regarding other social states. The presentation of the proof to Arrow’s theorem is beyond the scope of this book. But the conclusion can be demonstrated through a useful, but simple example. Suppose that there are three people: Ann, Bob, and Charles. They are asked to choose from among three alternative social welfare functions: X, Y, and Z. The preference orderings of the three individuals for the three alternatives are shown here: Alternatives Individuals

X

Y

Z

Ann

1st

3d

2d

Bob

2d

1st

3d

Charles

3d

2d

1st

If the three alternatives are listed on the ballot and individuals are asked to mark their most preferred choice, the outcome is a tie. The social choice procedure is not conclusive. Suppose instead that option Z is left off the ballot. Then option Y wins because it is preferred over X by Bob and Charles. Now, let us have a “runoff” between Y (the winner) and the third alternative, Z. Charles switches his vote to Z. Charles and Ann together make Z the winner over Y. Since Y has been preferred to X, and Z has been preferred to Y, transitivity in social choice requires that Z be preferred to X. But if these two alternatives are put to a vote, Ann and Bob vote for X and X is revealed preferred to Z. Thus the voting procedure produces an intransitive social ordering that

‘See Kenneth J. Arrow, Social Choice and Individual Values, New York, Wiley, 1951 and his A Difficulty in the Concept of Social Welfare, Journal of Political Economy, 1950, 58, 328-346. Arrow uses the term “social welfare function” to refer to a procedure such as a voting rule for making social choices, rather than as a preference ordering over alternative distributions of utility.

505

Equity and Social Welfare

violates one of the conditions. This conclusion is often referred to as the “voting paradox.” The voting paradox demonstrates the validity of Arrow’s theorem. And his theorem shows that in general, no society can count on a democratic choice mechanism such as voting to choose a social welfare function to guide it in its search for a social welfare maximum.

Conclusions All in all we must conclude that the search for a practical basis for identifying a maximum social welfare position that is consistent with widely acceptable value judg¬ ments has been unsuccessful. We have reviewed social welfare functions that embody value judgments ranging from those that give no weight to equity (the strict utilitarian and aggregate real income criteria) to the Rawlsian criterion that places a high pre¬ mium on equality. We have seen that there is no a priori logical basis for selecting one social welfare function over another. The choice is a matter of personal value judgment. It might be useful for you to pause at this point and consider how you would rank the alternatives. But it must be recalled that even after individuals have established their own preference orderings over alternative social welfare functions, in principle, there is no effective political mechanism for translating the preferences of many individuals into a consistent social choice. In summary, there are insuperable conceptual, political, and practical problems in defining and achieving a social welfare maximum. But although the maximization of welfare may be an elusive social ideal, the principles of welfare economics may still prove to be of some help in determining whether or not a particular policy change is in some sense an improvement. We turn to this question in the next section.

THE PRINCIPLES OF APPLIED WELFARE ECONOMICS We now abandon the search for a social welfare maximum. Instead, we take the initial position of the economy as given and ask how to determine whether a proposed change is an improvement in some sense. What criteria can be employed for evaluating policy changes'? The criteria considered in this section differ with respect to their underlying value judgments, for example, as to whether equity matters. But they all have the virtue of not requiring measurable, cardinal utility in order to be implemented.

Correcting a Market Failure Suppose that because of a market failure, one Pareto optimum condition for an efficient allocation of resources is not satisfied. This means that the economy is presently inside the GUPF. Consider a policy that would correct that market failure and move the economy to the GUPF. This criterion says to accept any policy that corrects an existing market failure. Broadly speaking, this is the criterion that is invoked to justify interven¬ tions to curb monopoly power, regulate monopoly prices, provide public goods, and correct for negative externalities such as air and water pollution.

506

Welfare Economics

As long as the policy intervention is designed to correct the market failure so that the Pareto efficiency conditions are satisfied, there is a presumption that the benefits of the policy outweigh the costs) In other words, it would be possible to redistribute the benefits so that no one lost from the policy intervention and at least some people gained. It is important, however, to note that this criterion does not require any redistribution of the benefits to compensate those who bear the costs of the policy change. And the criterion ignores the distributional consequences of the policy. It does not matter whether the benefits of an efficiency gain go primarily to the poorer members of the society or to those who already have the most. This criterion ignores equity considerations entirely.

The Theory of Second Best.

The proposition that whenever a market failure is

corrected welfare will be improved is intuitively appealing. But unfortunately it is not necessarily true. It is true if the initial position is characterized by only one market failure and the policy fully and completely corrects that market failure. Then the position after the policy is one in which all Pareto optimum conditions are satisfied and the economy is on the GUPF. But consider the following situation. In the initial position there are two market failures, but because of some constraints on policy making, only one market failure can be corrected. Then after the policy is implemented, the Pareto optimum conditions are still not fully satisfied, and the economy must still lie below the GUPF. Without further information and an additional criterion it is not possible to determine whether the new position is better in any sense than the initial position. This inability to apply the correcting market failure criterion when there are two or more market failures is termed “the second best problem.” That is, when there are two market failures, the “first best” solution is to correct both market failures at the same time, thus moving to the GUPF. If for some reason only one of the market failures can be corrected, a “second best” policy is to correct one market failure. But the problem with the second best policy is that we cannot be sure that the result will be an improvement in social welfare. Consider the following example. There is a monopoly firm that discharges a polluting substance. One source of market failure is the monopoly power that leads the firm to raise the price and restrict the output below the efficient level. The negative externality caused by the pollution is a second source of market failure. Pollution results in the marginal social cost of production being greater than the marginal private cost that is guiding the monopolists’ output and pricing decisions. In Figure 18.7 the negative externality is the vertical distance between the marginal social cost curve, the marginal private cost curve,

MCS, and

MC P.

Because the monopolist takes into account only private costs, the profit-maximizing output is where marginal private cost equals marginal revenue. This is an output of

XP and results in a price of Pp. Pareto optimality requires that the negative externality be taken into account and that output be set where marginal social cost is equal to the

X as shown by the demand curve. This leads to a socially optimum output of XQ and a price of P0. The Pareto optimum output is greater marginal willingness to pay for

than the profit-maximizing output and the Pareto optimum price is less than the

507

Equity and Social Welfare

Px, dollars

X per period Figure 18.7

The Monopoly Polluter and the Principle of Second Best: Correcting Pollution Can

Make Matters Worse.

profit-maximizing price. If public policy permitted the correction of both market failures simultaneously, the outcome would be the lower price and higher output that satisfies the Pareto optimum conditions. Now suppose that there is some political or institutional constraint that makes it impossible to deal with the monopoly power of the firm. But suppose that a pollution control agency has been established to correct the market failure that is associated with the pollution discharges. The agency could correct the market failure by imposing a tax on this firm equal to the external cost of its pollution. The pollution tax internalizes the cost of pollution to the firm. The firm’s marginal cost curve including the tax is

MCS. The firm maximizes profits by choosing that output where marginal revenue equals marginal social cost. This is X'P in Figure 18.7 and results in a price of PP.

now

Correcting only the pollution market failure has pushed price and output farther away from the efficient or Pareto optimum levels. Thus in this case, at least, the second best policy of correcting only one market failure has actually made things worse. This need not always be the case. The principal conclusion to be drawn is that whenever a second best policy is proposed, there is no presumption that it is an improvement. It must be carefully evaluated according to some other criterion, for example, the Hicks-Kaldor criterion described subsequently.

The Pareto Criterion This criterion says that a policy should be accepted if no one is made worse off by the policy and at least some people are made better off. In other words, this criterion rules out any policy that imposes costs on any individual, no matter how small the cost, and no matter how large the benefits to any other members of the society.

508

Welfare Economics

Suppose the economy were initially at point C in Figure 18.8. The Pareto criterion only accepts policies that move the economy above and/or to the right toward the grand utility possibilities curve GG'. Consider a policy that would move the economy from point C to F. It creates large utility gains for Ann who was initially in a relatively poor position. These gains come at the expense of a modest reduction in Bob’s utility. But this criterion says, in effect, that no matter how small Bob's loss, the policy cannot be accepted. This is a very stringent criterion in practice. There are very few policy proposals that do not impose some costs on some members of the society. For example, a policy to curb monopoly power reduces the incomes and utilities of those who own the rights to receive monopoly profits. Thus although curbing monopoly power passes the market failure test, it is rejected by the Pareto criterion.

The Hicks-Kaldor Compensation Criterion This criterion asks whether the beneficiaries of a policy would still prefer the policy if they were required to fully compensate any people who might lose from the policy.7 The Hicks-Kaldor criterion does not require that the compensation actually be paid. It accepts the policy if the potential for compensation exists. Suppose the economy is inside the GUPF at, say, point C in Figure 18.9. Consider

Figure 18.8 The Grand Utility Possibilities Frontier and the Pareto Criterion for a Welfare Improvement.

This criterion was proposed independently at about the same time by John Hicks and Nicholas Kaldor. See John R. Hicks, The Foundations of Welfare Economics,” Economic Journal, December 1939, 49(4), 696-712 and Nicholas Kaldor, Welfare Propositions of Economic and Interpersonal Comparisons of Utility, Eco¬ nomic Journal, September 1939, 49(3), 549-552.

509

Equity and Social Welfare

Ann’s utility per period

Figure 18.9

The Hicks-Kaldor Compensation Criterion for a Welfare Improvement.

D. This policy makes Bob better off; {UU') that goes through point D. Since UU' passes above and to the right of point C, it is possible for

a policy that would move the economy to point

but it imposes costs on Ann. There is a utility possibilities curve

Bob to compensate Ann for her losses so that she is no worse off than before. And if the compensation is paid, Bob is still better off than at point C. Exact compensation would result in point

E. In fact, there is a potential to compensate Ann so that both E in Figure

Bob and Ann are better off after the policy has been adopted (see point

18.9). . . , „ Implementation of the Hicks-Kaldor criterion is straightforward in principle. Once the policy alternative has been specified, the first step is to calculate the willingness to pay the gamers from the policy. This willingness to pay, which is a money measure of the utility increase to the beneficiaries, is the addition to consumer surpluses and/or factor surpluses accruing to the gainers. It provides a measure of their ability to compensate the losers without being made worse off themselves. Call this sum t e benefits (B). , ., . The second step is to compute the amount necessary to compensate the losers so that they are no worse off than they would be without the policy. Again, the required compensation is the sum of the (negative) changes in consumer and/or factor surpluses experienced by the losers. Call this sum the costs (C). The policy should be undertaken if the benefits (B) exceed the costs (C). The Hicks-Kaldor criterion is the conceptual foundation for the benefit-cost analysis of public policies. For example, suppose that good X is produced by a monopolist who charges and produces

FXm Xm. Consider a proposed policy to regulate the monopolist’s price so that

price equals marginal cost. The gamers from the policy would be consumers of X who

510

Welfare Economics

benefit by the increase in consumer surplus. If price is reduced to PXe, the benefits would be equal to the area PXmACPXe in Figure 18.10. The loser from this policy would be the owner of the monopoly firm. If price is reduced to PXe, this person loses monopoly profits equal to the area PXmABPXe. If consumers were required to compensate the monopolist, they would still have a net gain equal to the area ABC. They would be willing to compensate the monopolist because they would still be better off after making the payment. Regulating monopoly price passes the Hicks-Kaldor test. Should the compensation actually be paid in the case of policies that pass this test? The Hicks-Kaldor criterion itself is silent on this question. If the compensation is paid in all instances, this criterion coincides with the Pareto criterion because with compen¬ sation there will be no losers from any acceptable policy change. Requiring compensa¬ tion increases the range of opportunities for moving toward the GUPF without impos¬ ing losses on any individuals in the society. Alternatively, one might argue that whether compensation should be paid or not depends on the relative utility or income positions of the gainers and the losers. In the case of the policy move from points C to D in Figure 18.9 Bob was already relatively well off. And in the absence of compensation the policy would increase the degree of inequality between Bob and Ann. Thus one might argue that compensation should be paid if the policy is undertaken. A policy move from points C to F would also pass the Hicks-Kaldor test. But because the benefits go to Ann who is less well off, and because the degree of inequality is reduced, some people would argue that equity is better served by undertaking the policy without a requirement for compensation. If the compensation is never paid, the Hicks-Kaldor criterion is equivalent to one that seeks to maximize the sum or aggregate of real full income for the members of the economy. Any policy that passes this test must have benefits exceeding costs. The difference between benefits and costs is a net increase in aggregate real full income. So

X per period Figure 18.10

The Hicks-Kaldor Test and Regulating Monopoly Price.

511

Equity and Social Welfare

all policies that pass this test yield increases in aggregate real full income. But if society accepts this criterion, it means society is indifferent as to who the gainers and losers are. One of the most clear expressions of this absence of concern for equity as a criterion for policy evaluation was made by the U.S. Congress in passing the Flood Control Act of 1936. The act states that the government will undertake only those flood control investments for which the benefits exceed the costs, “to whomsoever they may accrue.” All moves to the GUPF will pass the Hicks-Kaldor test. Therefore any policy that avoids the second best problem and which passes the test of correcting market failures will pass the Hicks-Kaldor test as well. But the market failure and Hicks-Kaldor tests differ in the following ways. Under the market failure test one need not measure the benefits and costs of the policy provided that the policy is known to reproduce the effects of a perfectly functioning competitive market by correcting all market failures. Examples of such policies include a charge equal to the external cost per unit on the discharge of a polluting substance and the regulation of monopoly price so that price exactly equals marginal cost. Whenever the economy is known to be inside the GUPF, there is some policy change that will pass the Hicks-Kaldor test. But there are also many possible policies that would fail the test. Therefore it is necessary to compute the benefits and costs of the proposed policy to see if the potential for compensation exists. Automobiles with their smog-creating tailpipe emissions provide an example of market failure. The drivers of automobiles impose external costs on those who must breathe the polluted air and experience eye and nose irritation and on farmers and others who find that smog damages crops and other plants. Because this market failure leaves the economy inside the GUPF, there must be some public policy toward automo¬ bile emissions and use that will pass the Hicks-Kaldor test. Congress has established a policy imposing strict controls on emissions from all new cars built after 1970. But it appears that this particular policy does not pass the Hicks-Kaldor test and actually reduces the welfare of the society. It has been estimated that the benefits of the established policy toward automotive pollution are unlikely to be any larger than $5 billion per year. But the costs of building and operating automobiles that meet the congressionally mandated emission standards are more than twice this amount, ap¬ proximately $11 billion per year.8

Scitovsky’s Double Criterion There is an ambiguity in the Hicks-Kaldor criterion that was first noted by Tibor Scitovsky.9 Suppose that the economy is initially at point C in Figure 18.11. Point C is on the utility possibilities curve

UU'. Consider a policy proposal to move the

*For further discussion of the benefit and cost estimates and for an explanation of why this particular policy does not pass the Hicks-Kaldor test see Eugene P. Seskin, Automobile Air Pollution Policy, in Paul R. Portney, ed„ Current Issue in U.S. Environmental Policy. Baltimore, Md.: Johns Hopkins University Press, 9See Tibor Scitovsky, A Note on Welfare Propositions in Economics, Review of Economic Studies, November 1941, 9, 77-88.

512

Welfare Economics

Bob’s utility per period

Ann’s utility per period Figure 18.11

Inconsistent Ranking from the Hicks-Kaldor Compensation Criterion.

economy to point

D on the utility possibilities curve VV'. The move from C to D would

pass the Hicks-Kaldor test, because it would be possible to compensate the losers by moving along

VV to a position such as point E where everyone is better off. The

ambiguity arises because once the policy has been implemented and the economy has been moved to point

D, and provided the compensation has not actually been paid, a

proposal to move the economy back to C would also pass the Hicks-Kaldor test. A

UU' to point F would leave everybody in an improved position relative to the new starting point, point D.

move to C accompanied by compensation along

Scitovsky proposed to resolve the ambiguity by requiring a double test. A policy would only be accepted if it met the following two conditions: 1. The move to the new position passes the Hicks-Kaldor test; and 2. The reverse move back to the original position does not pass a Hicks-Kaldor test. It is generally accepted that the ambiguity discovered by Scitovsky is a theoretical curiosity rather than a problem of practical significance in applied welfare analysis.

A Bergson Social Welfare Function In an earlier section we discussed a Bergson social welfare function defined on the real full incomes of the members of society. The social welfare curves generated by this function can be used to identify the position that maximizes social welfare. The social welfare curves can also be used to evaluate any specific policy even though the position of the real full income frontier is not known. Suppose the economy is originally at point

D in Figure 18.12. A policy to move to point E would impose costs of MB1 — MB2 on Bob while generating benefits equal to MA2 — MAX for Ann. As shown, Ann’s

513

Equity and Social Welfare

Ann’s ircome per period Figure 18.12

Welfare Weighted Income Changes and Welfare Improvements.

benefits are smaller than Bob’s loss. Therefore the policy would not pass the HicksKaldor test. But point

E is on a higher social welfare curve, indicating that the policy

is a welfare improvement for society. This is because society values Ann’s income gain more highly than Bob’s loss. This reflects the social judgment that Ann is relatively more deserving because she starts off with a lower income than Bob does.10

The Rawls Maximin Criterion The Rawls maximin criterion can also be used as a basis for determining whether a policy is a welfare improvement. The maximin rule accepts only such inequalities that work to the benefit of the least advantaged members of the economy. Only those policies that increase the well-being of the least well off are accepted as improving welfare. This criterion can be interpreted as placing a zero weight on any income or utility gains to anyone but those at the bottom of the ladder and placing an infinite weight on income or utility losses to the least well off. Thus no policy could be accepted if it reduced the well-being of the least well off, no matter how large the gains to others.

THE MARKET SYSTEM AND WELFARE What has our analysis of the microeconomics of welfare theory shown us about how to organize an economic system? This analysis has indicated that the principal virtue

10For a further discussion of the use of social welfare functions to evaluate policy changes, see A. Myrick Freeman, III, Project Design and Evaluation with Multiple Objectives, in Robert H. Haveman and Julius Margolis, eds., Public Expenditure and Policy Analysis (2nd ed.), Chicago: Rand McNally, 1977.

514

Welfare Economics

of a market system is its ability, if all markets are competitive and there are no market failures, to achieve an efficient allocation of resources as defined by the Pareto optimum criterion. This is perhaps the single most important and noncontroversial conclusion to emerge from the normative analysis of microeconomic theory. But there are two kinds of limits on the significance of this conclusion as a guide for public policy and for choosing from among alternative economic systems. The first concerns the ability of a real-world market economy to attain an efficient or Pareto optimum allocation in practice. The second involves questions and reservations about the appropriateness of economic efficiency as an objective and its place in the hierarchy of economic goals. We have already shown that a variety of market failures due to such factors as monopoly power, externalities, and public goods can leave the economy inside the GUPF. And although in principle government policies can be adopted to correct for these market failures, there are a variety of problems in the practical implementation of such policies that make it likely that efforts to move the economy to the GUPF will fall short of achieving full efficiency. And the theory of second best shows that piece¬ meal efforts at correcting market failures could actually make things worse. The proofs that have been presented to demonstrate that a perfectly competitive economy will achieve efficiency are based on the assumption of maximizing behavior on the part of all economic agents. Firms must seek to maximize profits and individuals must strive to maximize utility. To the extent that what Herbert Simon has called “satisficing” is a common characteristic of economic behavior, the economy will ap¬ proach but not attain Pareto optimality even with perfectly competitive markets.11 Of course, before this point can be used as an argument against a market system as an economic organization, one must offer an alternative set of economic institutions that does not suffer from the same set of problems. As for the goal of economic efficiency we have seen that in principle there is an infinite number of possible efficient allocations and that the one that is actually attained need not yield an equitable distribution of welfare. If equity matters, efficiency is not a sufficient criterion for judging social welfare. Any criterion that takes account of society’s value judgments concerning equity must make comparisons of the relative deservingness of individuals on the basis of utility or income. But there is in principle no objective way to make such comparisons. And society may find it impossible to find a satisfactory political mechanism for making the necessary social choice from among alternative social welfare functions and their different subjective ethical value judg¬ ments. Thus although economic efficiency is a necessary condition for achieving a social welfare maximum, it is not a sufficient condition, at least if equity matters. Economic reasoning alone, however, is incapable of deducing the sufficient conditions for welfare maximization. These sufficient conditions can only be deduced after some set of value judgments concerning equity has been made. A second reason for discounting the significance of the conclusion that competition

"Recall the discussion in Chapter 9. See also Harvey Leibenstein, Allocative Efficiency vs. “X-Efficiency,” American Economic Review, June 1966, 56(3), 392-415, which focuses on problems of incentives, informa¬

tion, and management as reasons to believe that efficiency will not be achieved at the level of the firm.

515

Equity and Social Welfare

yields efficiency is that economic efficiency is a purely static, equilibrium concept. Yet a key feature of the modern economy is its dynamism, especially in terms of technologi¬ cal change and innovation. It has already been noted that equilibrium is best viewed as a theoretical construct and that a real-world economy is never in equilibrium. Rather, the economy is always being pushed in new directions through investment in new capital equipment, technological change that shifts isoquants and production possibilities curves, and the introduction of new products and improved versions of old products. All these changes have the effect of pushing the GUPF up and to the right. From a long-run dynamic point of view it may be unimportant whether the economy ever reaches the GUPF and satisfies the Pareto conditions, provided that it stays reasonably near an ever expanding GUPF. From a dynamic point of view the question becomes, what set of economic institu¬ tions best promotes technological change, innovation, and the expansion of welfare possibilities? Joseph Schumpeter and others have argued that an economy comprised of perfectly competitive firms would be poorly suited to the promotion of long-run welfare maximization through innovation and growth.12 Small firms would have neither the financial resources nor strong incentives to undertake the research and development that is an essential ingredient of growth. In competition, profits tend to 0, so any firm wishing to undertake research and development would have to borrow funds in the hope that profits would eventually repay the loan and interest. And with perfect information and free entry, any innovation leading to temporary profits for a firm would be quickly imitated. Profits would be transitory. Thus Schumpeter argued that large firms and some degree of industrial concentration and monopoly power were necessary to provide the economic climate and financial resources for promoting innovation. Although monopoly may be accompanied by static inefficiency, over time there would be an erosion of the market power of existing firms as innovators introduce new products, develop cheaper ways of making existing products, and so forth. Schumpeter called this the process of “creative destruction.” Thus although the economy may be inside the GUPF at any point in time, Schumpeter argued that the static efficiency costs are more than outweighed by the welfare gains over time as the GUPF shifts out to the right. The Schumpeterian argument is in principle subject to empirical testing. But efforts to determine the relationship between firm size and/or market power on the one hand and research and development spending and innovation on the other have been incon¬ clusive. There is no solid evidence that large firms spend more relative to sales or innovate more rapidly in comparison with smaller firms in any given industry. But this is not a direct test of the Schumpeterian hypothesis, which refers to a comparison between a perfectly competitive industry for a good and the same good produced by a concentrated industry. Although the Schumpeterian argument calls into question the virtues of perfect competition as an ideal, there are other reasons for preferring a market system even with its imperfections over alternative economic institutional arrangements. These

12See Joseph Schumpeter, Capitalism, Socialism and Democracy, New York: Harper & Row, 1942.

516

Welfare Economics

include the fact that a market system is a decentralized mechanism for economic decision making and coordination. And for this reason it can maintain a high degree of flexibility in response to changes in technology, factor endowments, and tastes and preferences.13 Also, because it is decentralized, the market system may be able to preserve a greater degree of individual freedom of choice in comparison with alternative economic institutions. A major challenge to economic policy makers is to devise ways of promoting and preserving an appropriate degree of equity and of correcting the most serious forms of market failure (e.g., pollution externalities) while preserving the flexi¬ bility and freedom that a market system can provide.

SUMMARY If an optimum position on the GUPF is to be found, the GUPF must be defined in terms of cardinal utilities that can be compared across individuals. A social welfare maximum can be defined in terms of a social welfare function reflecting value judgments concern¬ ing equity. The utilitarian social welfare function defines the welfare maximum in terms of the highest attainable aggregate or sum of utilities. The Bergsonian social welfare function allows for the introduction of weights to reflect society’s value judgments about the relative deservingness of individuals. The Rawls social welfare function is strongly egalitarian in that it tolerates inequality only if it works to the benefit of the least well off in the society. Once a point on the grand utility possibilities frontier has been identified as a social welfare maximum, the appropriate prices, outputs, factor supplies, and distribution of goods and services can all be determined, at least in principle. Because modern preference theory denies the possibility of measuring utility in cardinal terms or making interpersonal comparisons, there have been proposals to define social welfare functions in terms of the incomes received by individuals. The conceptually correct income measure is real full income, including a money measure of the value of nonmarket production and leisure activity. Accurate measurement of real full income may not be possible because of the price index number problem. Each of the three types of social welfare functions previously described has its counterpart in a social welfare function that is defined on income. As economists came to appreciate the immense problems involved in defining a social welfare maximum, they turned to the problem of determining whether any economic change was an improvement. Under alternative welfare criteria, a change could be considered to be an improvement if it corrected a market failure so as to move the economy to the GUPF (achieving efficiency); it made at least one person better off while making no one worse off (Pareto criterion); it brought income and consumer surplus

l3For further discussion of some of these issues, see Tibor Scitovsky, Can Capitalism Survive?—An Old Question in a New Setting, American Economic Review, May 1980, 70(2), 1-9, and Richard R. Nelson, Assessing Private Enterprise: An Exegesis of Tangled Doctrine, Bell Journal of Economics, Spring 1981, 12(1), 93-111.

517

Equity and Social Welfare

gains to some individuals that were larger in aggregate then the monetary measure of the losses to all those made worse off by the change (Hicks-Kaldor compensation criterion); the welfare weighted gains to some individuals were greater than the welfare weighted losses to all losers; or the change benefited the least well off (Rawls). Virtually all these applied welfare criteria have at least one negative feature. For example, the principle of second best tells us that correcting a particular market failure may actually make things worse if there remain other uncorrected market failures in the economy. The Pareto criterion rules against virtually all real-world policy proposals (e.g., regulating monopoly power or externalities) because they involve losses to some individuals in the economy. The Hicks-Kaldor criterion is silent on the equity question of whether or not losers should in fact be compensated. For the criterion involving welfare weighted gains and losses the question remains as to who will determine the weights to be applied to the gains and losses of different individuals. The most significant positive conclusion of welfare economic theory is that a per¬ fectly competitive market system will achieve economic efficiency. In practice, eco¬ nomic efficiency might not be attained because of market failures. An additional possi¬ ble

impediment

to

achieving

efficiency

through

a

market

system

would

be

nonmaximizing behavior on the part of individuals. For example, satisficing behavior of individuals as described by Simon could lead to systematic divergences from the Pareto efficiency conditions. But in contrast to the case of market failure, these diver¬ gences could not be corrected by government action. In fact, government policies in the realm of resource allocation would be subject to the same kinds of problems and constraints as those that might lead to satisficing behavior on the part of individuals in the market system. Thus it would be reasonable to conclude that government policymakers would also satisfice rather than attempt to maximize social welfare how¬ ever it is defined. The conclusion that competitive markets yield an efficient outcome must be tempered with the recognition that efficiency is not the only possible social goal. Equity in income distribution may be a major social criterion. If so, it is possible that an inefficient but equitable outcome might be preferred to an efficient outcome with a highly unequal distribution in income. Also, the Pareto conditions’ focus on static efficiency diverts attention from the dynamic nature of a modern economy and the role of innovation and technological change in enhancing economic welfare over time.

KEY CONCEPTS Utilitarianism

The Pareto criterion

Bergson social welfare function

Second best

Rawls maximin criterion

The Hicks-Kaldor criterion

The Arrow voting paradox

Creative destruction

518

Welfare Economics

QUESTIONS AND PROBLEMS For Basic Review 1. Define and explain the economic significance of each of the key concepts. 2. (a) Show that in an economic system with perfect competition a market economy will satisfy the marginal conditions for a Pareto optimum. Discuss the value, limitations, and relevance for policymaking of this model of the general equilibrium of a competitive economy and the Pareto optimum conditions. (b) Use the appropriate box diagrams, and so on to explain the derivation of the grand utility possibility frontier from the underlying data on factor endowments, technology, and demand for a two-person, two-good, two-factor economy with fixed factor supplies. (c) * Suppose that the government confiscates part of the wealth of a rich man and transfers it to a poor man. Can the economy still attain the grand utility possibility frontier? Is the new position a Pareto optimum position? If it is, is it a better one than that attained in part (a)? Discuss alternative welfare criteria for evaluating such situations.

For Discussion 1. * “One defect of a price system for allocating resources is that it may reduce welfare since a high cost but highly valued good such as medical care might not be produced in sufficient quantity to meet people’s needs.” Evaluate this statement. Consider only a purely competitive economy, that is, one with no market power or external costs or benefits. 2.

Consider a policy proposal to regulate the price charged by a monopolist so as to achieve economic efficiency. What price should the regulators establish? Evaluate this policy in terms of the alternative welfare criteria discussed in the text. Discuss the problems in making unambiguous policy judgments on

3.

questions of this sort. Use the diagrammatic general equilibrium model developed in this book to explain the basic economic questions that must be answered by all societies. Show that any solution to these questions that can be called a social welfare maximum implies a set of shadow prices for outputs and inputs. Explain the role of these shadow prices in assisting the economy to reach the social welfare maximum. What advice would you give to economic planners in centralized socialist economies concerning techniques for attaining socialist planning objectives?

4.

Many states have laws that make it illegal for one person to pay (bribe) another person to vote in a specified way in an election. From the point of view of economic welfare, are these good laws?

5.

It has been said that one of the central questions of microeconomic analysis is:

519

Equity and Social Welfare

“Will the independent maximizing behavior of each economic agent eventually result in a social organization that, in a normative sense, maximizes the well-being of society as a whole?” What have you learned about the ability of microeconomic theory to provide a definitive answer to this question? Your answer should deal with both the issue of defining “the well-being of society as a whole” and the conditions under which an affirmative answer can be given.

Overview: Questions for Review of the Whole Course 1.

(a) State the two rules for maximization that are offered in Chapter 2. Explain

in your own words why these rules are valid. (b) Use these rules to derive the conditions for consumer equilibrium, producer’s equilibrium in the utilization of inputs, profit-maximizing output under competition, profit-maximizing output under monopoly, and the profit-maximizing input combination for a monopsonist. (c) Discuss the role of these rules in the development of positive theories of economic behavior. 2. Discuss the role and usefulness of the concept of equilibrium in analyzing the behavior of individuals and firms in competitive markets. 3. * The principal technique for deriving testable hypotheses and behavioral relationships about economic agents is to assume maximizing behavior and to examine the implications of efforts to maximize in the face of changing external or exogenous conditions. Choose some economic agent and provide an example of the application of this technique. You should be specific about what is being maximized, the constraints, which variables are endogenous and exogenous, the equilibrium conditions, and the behavioral relationship and testable hypotheses you have derived. 4.

(a) Use the analytical tools developed in this course to make a

positive

statement about the consequences of the imposition of an excise tax on a good sold by a monopolist. Do the same for a tax on labor income. (b) Make a normative statement about the impact of the imposition of an excise tax on a good produced by a monopolist. Make a normative statement about the impacts of a tax on labor income. Be explicit about the value judgments that underlie your normative statements. (c) Use these examples to discuss the distinction between positive and normative analysis and the proper approaches to deriving positive and normative statements.

SUPPLEMENTARY READINGS Bator, Felix M. The Simple Analytics of Welfare Maximization,” American Economic

Review, March 1957, 47(1), 22-57.

520

Welfare Economics

Bator, Felix M. The Anatomy of Market Failure, Quarterly Journal of Economics, August 1958, 72(3), 351-379. Coase, Robert H. The Problem of Social Cost, Journal of Law and Economics, October 1960, 3, 1-44. Henderson, James M. and Quandt, Richard E. Microeconomic Theory: A Mathematical Approach (3rd ed.). New York: McGraw-Hill, 1980, Chapter 11. Lipsey, Richard A. and Lancaster, Kelvin. The General Theory of Second Best, Review of Economic Studies, 1956-1957,24, 11-32. Mishan, Ezra J. A Survey of Welfare Economics: 1939-1959, Economic Journal, 1960, 70(278), 197-256. Peacock, Alan T. and Rowley, Charles K. Welfare Economics: A Liberal Restatement. London: M. Robertson, 1975. Rawls, John. Some Reasons for the Maximin Criterion, American Economic Review, May 1974, 64(2), 141-146. Samuelson, Paul A. Foundations of Economic Analysis. Cambridge, Mass.: Harvard University Press, 1947, Chapter 8.

Glossary

Annual equivalent For a given stream of unequal payments over any period of time the annual equivalent is that equal annual payment over the same number of years that has the same discounted present value. Average cost The total private cost of production divided by output, that is, cost per unit of output. Average variable cost The total (private) variable cost of production divided by the level of output. Bilateral monopoly A market with one monopoly seller and one monopsony buyer. Budget constraint The constraint on the purchases of goods and servces imposed by given money income and market prices because the sum of money expenditures cannot exceed money income. Capital An input to the production of goods and services that is durable, yields its productive services over time, and is itself the output from a production process. Cardinal utility A measure of the level of satisfaction from consumption based on a fixed unit of measurement of utility, for example, 1 util, 2 utils, and so on. Ceteris paribus See other things equal. Comparative static analysis The prediction of the change in an endogenous variable of the model as a consequence of a postulated change in one of the exogenous variables of the model. Complements in consumption Two goods for which if the price of one good increases (decreases), the quantity demanded of the other good decreases (increases), other things equal. Complements in production Two inputs in the production of a good for which when the price of one input increases (decreases), the quantity of the other input de¬ creases (increases), other things, including the level of output, held constant. 521

522

Glossary

Constant cost industry An industry with a horizontal long-run supply curve, that is, an industry in which output can change without affecting factor prices and cost curves of firms. Constant returns to scale A characteristic of production functions in which a change in all factor inputs by a given proportion leads to a change in output of the same proportion. Consumer sovereignty The doctrine that in a market economy producers respond to consumers’ preferences by adjusting output in accordance with market prices. Consumer surplus The difference between the total amount of money an individual would be willing to pay for a certain quantity of a good rather than do without and the actual expenditure on that good. Contract curve See exchange locus. Cost function An expression giving the minimum possible total cost of production as a function of the prices of factors and the level of output. Cross-elasticity of demand The percentage change in the quantity demanded of one good in response to the percentage change in the price of another good. Decreasing cost industry An industry with a downward-sloping long-run supply curve, that is, an industry in which as output increases, at least one factor price decreases and cost curves of firms shift down. Decreasing returns to scale A characteristic of production functions in which when all inputs are increased by a given proportion, output increases by a smaller proportion. Degree of monopoly power The excess of price over marginal cost as a percentage of monopoly price; measured by the reciprocal of the elasticity of the monopolist’s demand curve. Demand curve Shows the quantity demanded of a good as a function of its own price, other things equal. Demand function An expression giving the quantity demanded of a good as a function of its own price, the prices of other goods, and money income. Economic efficiency See efficient allocation of resources. Economic profit The excess of total revenues over all private costs of production, including implicit costs. Edgeworth box A diagram for analyzing the distribution of goods through exchange between two individuals. Its dimensions are given by the total quantities of the two goods that are available for distribution. Efficiency See efficient allocation of resources. Efficiency locus A locus of all points in the production box where the marginal rates of technical substitution for the two inputs are equal for both goods. Efficient allocation of resources An allocation of resources is efficient in economic terms if it is not possible to increase the welfare of one individual without decreas¬ ing the welfare of at least one other individual. Elasticity of substitution A property of the isoquants of a production function; mea¬ sured by the percentage change in the capital to labor ratio divided by the percent¬ age change in the marginal rate of technical substitution.

523

Glossary

Endogenous variable A variable in a model whose value is determined within the economic model being analyzed. Engel curve A curve showing the consumption of a good as a function of income, holding all prices constant. Equilibrium A property of an economic model; a state in which there is no tendency for any of the variables of the model to change. Excess burden of taxation A measure of the loss of economic efficiency caused by some forms of taxation, for example, when an excise tax leads to price being greater than marginal cost; measured by the reduction in the sum of consumers’ and factor surpluses. Exchange locus A locus of all points in the Edgeworth box where the marginal rates of substitution between the two goods are the same for both individuals. Exogenous variable A variable in a model whose value is determined outside the model and which is assumed to be given for purposes of analyzing the model. Expansion path The locus of optimum input combinations in production for different levels of output, given constant factor prices. Explicit costs Those costs of production that are represented by transactions between the producing firm and others. External benefit A positive externality; see externality. External cost A negative externality; see externality. Externality A situation in which one economic agent’s action directly confers a benefit or imposes a cost on some other agent without that consequence being reflected in market prices and exchange transactions. Factor surplus The excess of factor receipts over the minimum payment that is neces¬ sary to bring forth the quantity supplied. Fixed cost Those costs of production that in the short run are independent of the level of output; those total costs that remain when output is reduced to 0. Giffen good A good whose demand curve is upward sloping, that is, for which the quantity demanded increases as price increases. Grand utility possibilities frontier A locus showing the maximum level of a utility attainable by one individual for any given level of utility for the other individual, given the factor endowments, production technologies, and preferences. Homogeneous production function A production function having the property that if all inputs are increased by a factor of t, the output increases by a factor of tk, where k is termed the degree of homogeneity. Hypothesis A conditional statement that is derived from a model for the purposes of testing the model; usually of the form: If A, all other things held constant, then B. Implicit costs The opportunity costs of production incurred when a firm uses inputs it already owns. Implicit price of a characteristic The additional money an individual would have to pay to purchase a unit of a good with one more unit of this characteristic embodied in it. Income-consumption curve A locus of optimum consumption bundles for different levels of income.

524

Glossary

Income effect of a price change The change in the quantity demanded of a good due solely to the change in real income that is associated with a price change. Income elasticity of demand The percentage change in the quantity demanded of a good for a given percentage change in money income. Increasing cost industry An industry with an upward-sloping long-run supply curve, that is, an industry in which as output increases, at least one factor price increases and cost curves of firms shift up. Increasing returns to scale A characteristic of production functions in which when all inputs are increased by a given proportion, output increases by a larger propor¬ tion. Index number A weighted average of prices or quantities, where the weights reflect the relative importance of each item in the aggregate. Indifference curve A locus of all bundles of goods among which an individual is indifferent. Inferior good A good whose income elasticity of demand is less than 0, that is, one for which consumption decreases as income increases. Internal rate of return A measure of the profitability of an investment; the discount rate that would make the computed net present value of the investment just equal to 0. Isocline A locus of all the points in an isoquant mapping that have the same marginal rate of technical substitution. Iso-cost line A locus of alternative input combinations that can be utilized for the same total cost. Isoquant A locus of all technically efficient combinations of inputs of labor and capital that will produce a given rate of output. Law of demand The principle that for any commodity that can be purchased in a market the quantity demanded in a given period of time varies inversely with the price, other things equal. Law of diminishing marginal productivity The principle that the marginal product of a variable factor input decreases with increases in that input at least beyond some point, other things equal. Law of diminishing marginal utility The principle that as the consumption of a good increases, other things equal, each additional unit adds less to the total utility of consumption. Long run A planning horizon or time period that is sufficiently long so that it is possible to vary the quantities of all inputs in production. Marginal cost The change in total cost with a small change in output. Marginal expenditure on input The increase in total expenditure on an input associated with a 1-unit increase in the quantity purchased of that input. Marginal net return If the magnitude of some desirable variable Y (e.g., utility, output, revenue, or profit) is influenced by some other variable X, the marginal net return of X is the change in variable Y for a 1-unit change in X, other things equal. Marginal opportunity cost The amount of one good that must be given up in order to free the resources for increasing the output of the other good by 1 unit.

525

Glossary

Marginal product The increase in output realized for a 1-unit increase in one factor input, holding all other inputs constant. Marginal rate of substitution The amount of one good that must be added to a consumption bundle to replace a 1-unit reduction in the amount of the other good, holding the level of satisfaction or welfare constant. Marginal rate of technical substitution The amount of capital that must be added to production to replace a 1-unit reduction in the input of labor, holding the level of output constant. Marginal rate of transformation The quantity of the output of one good that must be given up in order to increase the output of the other good by 1 unit, holding technology and factor supplies constant; the slope of the production possibilities curve. Marginal revenue The change in total revenue for a 1-unit change in quantity sold. Marginal revenue product The change in the total revenue of a firm realized from a 1-unit increase in the quantity of a factor input, other things equal. Marginal utility The change in total utility for a 1-unit increase in the consumption of a good, other things equal. Marginal willingness to pay The maximum amount of money that an individual is willing to give up in order to obtain one more unit of a good. Market structure A property of a market that reflects the numbers of buyers and sellers. Maximand The variable to be maximized in a maximization or optimization problem. Maximin A decision rule in which alternative strategies are ranked by their worst possible or minimum payoffs and that strategy with the highest minimum payoff is chosen. (See also Rawls's maximin rule for social welfare.) Monopolistic competition A market with many producers selling differentiated products. Monopoly A market in which there is only one seller. Monopsony A market in which there is only one buyer. Natural monopoly A market in which economies of scale make it possible for one firm to supply the market without experiencing decreasing returns to scale. Normal good A good whose income elasticity of demand is between 0 and 1. Normative analysis The evaluation of the performance of alternative economic institu¬ tions or given institutions under alternative conditions on the basis of some spe¬ cified norm or criterion. Objective function A relationship that gives the variable to the maximized (the maxi¬ mand) as a function of the choice variables under the control of the decision maker. Oligopoly A market with few sellers, each of which has the ability to influence market price and must take account of the price and output choices of the other sellers in the market. Oligopsony A market with few purchasers, each of which has the ability to influence market price and must take account of the actions of the other purchasers in the market. Opportunity cost See marginal opportunity cost.

526

Glossary

Ordinal utility A measure of the level of satisfaction from consumption based only on a ranking of different consumption alternatives, for example, first, second, third. Other things equal A phrase meaning that except for those variables explicitly being analyzed, all other variables are assumed not to change in the analysis. Pareto optimality See efficient allocation of resources. Perfect competition A market with many buyers and many sellers in which no partici¬ pant in the market has any influence over market price, the product is homoge¬ neous, there is free entry and exit of producers, and all participants have full information. Positive analysis The process of developing a better understanding of how particular economic institutions work and of explaining their functioning. Prediction See hypothesis. Present value The maximum amount of money a rational person would pay to obtain the right to the stream of future monetary returns from an asset. Price The terms on which two goods are exchanged in a market. Price-consumption curve The locus of all the optimum consumption bundles when the price of one good changes, the price of the other good and money income being held constant. Price discrimination When sellers with market power charge different prices for differ¬ ent units of a homogeneous product. Price discrimination can be by units pur¬ chased by each buyer or by purchasers. Price elasticity of demand The percentage change in the quantity demanded for a given percentage change in the price of a good. Production function A quantitative expression that specifies the relationship be¬ tween the level of inputs to the production process and the resulting output level. Production possibilities frontier The locus of the maximum attainable production combinations; the maximum amount of one good that an economy can produce for any given level of production of the other goods, given technology and factor endowments. Profit See economic profit. Property rights The legal structure of rights that govern the use of a good, the exclu¬ sion of others from the use of the good, and the transfer of the rights of use and exclusion. Public good A good that once produced is available in equal quantities to all individu¬ als without restriction. Consumption of a public good is nonrivalrous, and exclu¬ sion is not possible. Pure rent See rent. Quasi-rent The excess of total revenue over total variable cost for a firm. Rawls’s maximin rule for social welfare Choose the economic outcome that generates the highest utility for the least well-off individual. Reduced form equation An expression that gives an endogenous variable of a model as a function of the model’s parameters and its exogenous variables.

527

Glossary

Rent The income received by a factor owner for the services of a factor in perfectly inelastic supply. Satisficing Behavior characterized by acceptance of less than optimum or maximizing outcomes on the rationale that perfect optimization is too difficult, too costly, or not possible because of uncertainties, analytical problems, or absence of required data. Second best problem The principle that when two or more market failures exist, correcting only one of them may not lead to a social welfare improvement. Shadow price An indicator or measure of relative scarcity or value in a specific setting. Short run A planning horizon or time period during which, for technological, institu¬ tional, or contractual reasons, at least one of the inputs cannot be varied; that is, it must be held fixed. Short-run supply curve of the firm The relationship between the price of output and the quantity produced by a firm in the short run. Short-run supply curve of the industry A locus showing the outputs of a competitive industry at different prices, holding the number of firms and their fixed inputs constant. Shut-down price That price at which the firm will be indifferent between continuing production and reducing output to 0 in the short run. Single-factor productivity The ratio of total output to the input of a factor; the average product of that factor. Social welfare curve A locus of all combinations of utilities for two individuals that result in the same level of welfare for society as a whole. Social welfare function A rule for measuring the aggregate welfare of society as a whole as a function of the welfares or utilities of the individual members of society. Substitutes in consumption Two goods for which if the price of one good increases (decreases), the quantity demanded of the other good increases (decreases), other things equal. Substitutes in production Two inputs in the production of a good for which when the price of one increases (decreases), the quantity of the other input increases (de¬ creases), other things, including the level of output, held constant. Substitution effect of a price change The change in quantity demanded due solely to a change in the price ratio, holding the preference level constant by assumption. Superior good A good whose income elasticity of demand is greater than 1. Technological change Any invention or innovation that permits the same total output to be produced with fewer inputs or allows for a greater total output from a given level of inputs. Total factor productivity The ratio of some measure of output to an aggregate or index measure of total factor inputs. Transactions costs The economic cost of negotiating and executing transactions or market exchanges. User cost A measure of the opportunity cost of using a machine in production; the sum of the foregone interest on the market value of the machine at the beginning of the period and the loss of market value of the machine over the period of its use.

528

Glossary

Utilitarianism The doctrine that society’s welfare is measured by the sum of the (cardinal) utilities of all individuals. Utility A numerical measure of the satisfaction or welfare obtained by an individual from consumption. Utility possibilities curve A locus of all possible utility combinations for two individu¬ als that can be obtained from a given total output of the two goods. Value of marginal product The money value of the additional output produced when one more unit of a factor is employed, holding everything else constant. Also, the contribution to the total revenue of a competitive firm made by one additional unit of the factor, other things equal. Variable cost Those private costs of production that vary when the firm alters its output level in the short run.

Answers to End-ofChapter Questions

CHAPTER 1 For Basic Review 2. (a) positive; (b) normative; (c) positive; (d) normative. 5. Primarily by the validity of its predictions.

For Discussion 1. All the questions have at least some economic content because they entail production to meet material wants and needs, scarcity, and/or responsiveness to economic conditions such as prices and incomes. 2. An increase in the tax rate lowers the net or aftertax wage received by workers. You want data on hours worked and net wages for a large sample of individuals. Also, you must be sure that variation in hours worked is not due to some other causal factor. See Chapter 12 for a model that can lead to this prediction and a review of the evidence.

CHAPTER 2 For Basic Review 3. (a) The quantity supplied of A is a function of (depends on) the price of X and the price of a factor input F. (b) The quantity supplied of X is a function of the price of X, holding other things including the price of F constant. 529

530

Answers to End-of-Chapter Questions

Problems 2. (a) Algebraically, substitute the values of PY and PF into XD and Xs. Set the quantity demanded equal to the quantity supplied and solve for the equilibrium price Px: XD = Xs 1000 - 50P* + 100 = 75 + 25Px - 250 P x = IV

Now substitute the equilibrium price into the demand function: XD = 1000 - 50 • 17 + 100 = 250

Alternatively, use the supply function: X5 = 75 + 25 • 17 — 250 = 250

(b) (c) (d) (e)

As Py increases, Px increases and X increases. Px = 18; X = 275. As PF increases, Px increases and X decreases. Px —— 18; X —— 200.

CHAPTER 3 For Basic Review 2. For the law, see p. 53. Let the quantity of capital be fixed at K*. If Li of labor is used, suppose output is Xx. Then the Xl isoquant goes through the input combination of Lu K* (see Figure A3.1(a)). As labor is increased successively to L2 and L3, output increases to, say, X2 and X}. Each of these input combinations and isoquants is shown in the figure. The total product curve is the plot of the following points: Lu Xy, L2, X2; L3, X} (see Figure A3.1(b)). The marginal product curve plots the changes in output for each level of labor input L\, Xi — 0; L2, X2 — X-c, L3, X} — X2 (see Figure A3.1(c)). Be sure to plot the marginal products at the midpoints of the intervals on the horizontal axis. If the fixed factor is increased to, say, 2K*, then the output produced by Lj and 2K* is greater than that produced by Lx and K*. The isoquants through the new input combinations are each above and to the right of Xu X2, and X3. Also, new total and marginal product curves can be derived in the same manner as previously described. 4. Decreasing returns to scale might occur when all inputs are increased by the same proportion. Diminishing marginal productivity always occurs when one input is increased while all others are held fixed. 7. (a) Production possibilities curve (PPC) shifts out. (b) PPC shifts out. (c) No change; a movement along the PPC. (d) PPC shifts out with the vertical intercept unchanged.

531

Answers to End-of-Chapter Questions

X per period

Total product *3

*2

X\

O

Li

L2

^3

L per period (b) Figure A3.1

532

Answers to End-of-Chapter Questions

X per period (*1“0)

(*2-Xi)

(X3 -x2)

o

Figure A3.1

(Continued)

(e) PPC shifts upward and to the right. (f) No change; a movement from a point inside the PPC to the PPC.

Problems 2. (b) With sheet steel plotted on the horizontal axis, the slope of a line tangent to the PPC at 200 tons of sheet steel (S) and 75 tons of girders (G) is approximately 0.2, that is, AG/AS = i Thus the marginal cost of one unit of S is 0.2 tons of G. (c) At S = 100, the slope is approximately ^ or 0.15. At A = 300 the slope is

approximately ^ or 0.35. This demonstrates increasing marginal opportunity cost for S. (d) The marginal opportunity cost of G is AS/AG = 1/(AG/AS) = _1_ marginal opportunity cost of sheet Thus at G = 50, marginal cost is ^ ss 2.9; at G = 75, marginal cost is 5; and at G = 92, marginal cost is ^ ss 6.7. (e) This is inside the PPC. Fire the plant manager!

=

(f) The relative values or prices of sheet steel and girders. See Chapters 5, 14, and 16.

CHAPTER 4 Problem 1. (a) See Figure A4.1. (b) A is preferred to E because it has more of good Y; B is preferred to C because a convex indifference curve through A and B must pass above C; A

533

Answers to End-of-Chapter Questions

is also preferred to C because of transitivity; the ranking of B and D cannot be determined without more information because the convex indifference curve through A and B could pass either above or below D, or through it; D is preferred to C because it contains more Y.

CHAPTER 5 For Basic Review 4. Normative, based on the norm or criterion of efficiency.

Problem 1. Increase X production by 1 unit at an opportunity cost of 2 units of Y. Thus one individual’s consumption of Y would have to be reduced by 2 units. But either individual would be willing to give up as much as 3 Y to obtain the additional X.

For Discussion 2. If workers have no alternative uses for their time, there is no opportunity cost associated with working. The shadow price of labor would be 0. But workers may have opportunities for leisure activities or nonmarket production (tending a vegetable garden, repairing the car). Then the shadow price of labor would be the value of these activities given up at the margin.

534

Answers to End-of-Chapter Questions

CHAPTER 6 For Basic Review 1. Fish in the oceans; water in a river; clean air to breathe.

CHAPTER 7 For Basic Review 6. False; Figure 7.23 shows a Giffen good with diminishing MRS.

Problems 1. True. £pv = 0 means that a change in Px has no effect on the quantity demanded and the expenditure on Y. If there is no change in the expenditure on Y, then the expenditure on X is also unchanged as a consequence of the change in Px. This is a characteristic of demand curves with elasticity equal to 1, or with a horizontal price-consumption line. 3. Four units of food; 2 units of clothing. If the price of clothing doubled, the optimum combination would be four food and one clothing.

For Discussion 2. (a) Shift out if travel is a normal or superior good. (b) Shift in since the bus is a substitute. (c) Shift in. At a given nominal fare, fewer business trips will be taken, because the net or aftertax price to businesspeople is increased. (d) Shift in; the quality or availability of a substitute good is increased. (e) Shift out. 3. This means that for a given income, there is some price of X for which the optimum bundle contains no X, only Y. The indifference curves must cross the Y axis, as shown in Figure A7.1.

CHAPTER 8 Problems 2. At a quantity of 2, the elasticity of demand is 1.5; at quantity = 4, elasticity = 0.25. (Note: Ex = AX/AP ■ P/X, and AX/AP =1.) 3. (a) X = 480,000. MR can be found by four different methods: (1) graphically by constructing the MR curve; (2) numerically by calculating total revenue for 480,000 rides and for 480,001 rides; (3) by calculus (multiply the demand function by P to obtain the total revenue function, rearrange to get TR as a

535

Answers to End-of-Chapter Questions

function of X, and take the derivative with respect to X); (4) or by calculating the elasticity of demand and using the relationship

MR =

P( 1 - 1 /Ex). Ex = 0.0417. MR = -2.3. (b) Raise the fare since MR < 0 and Ex < 1. Revenue is maximized where MR = 0, or P = $1.25 and X = 250,000. (c) Reducing the fare from 10 cents to 0 would increase ridership by 20,000 per day, a drop in the bucket compared to the almost 2 million car trips (25 percent of 1.96 million total trips is 480,000 bus trips).

(d) The consumer surplus or area under the demand curve—$6.25 million per day. (e) Raise price of substitutes—parking fees, highway tolls; improve service, schedules, routes of bus system. 5. (a) A 3.6 percent increase in the quantity sold (1.2 X 3 percent). (b) A 6 percent increase (3.0 X 2 percent). (c) A 20.4 percent increase (-1.2 X 8 percent + 3.0 X 10 percent). Errors in estimating elasticities; errors forecasting auto prices and incomes. Are the auto price increase and income increase measured in real terms (holding everything else constant) or do they reflect general price and wage inflation?

(d) Increase. The demand curve for used cars shifts out as the price of a substitute (new cars) goes up. No; we don’t know what happened to the prices of the goods he purchases. 8. (a) (b) (1) John is better off. He could have purchased his 1980 bundle in 1981 (the 1981 budget line lies outside the 1980 bundle). His actual 1981 bundle must have been preferred.

(2)

0.12 X 245 + 0.25 X 80

pP Pl

0.15 X 245 + 0.20 X 80 0.12 X 200 + 0.25 X 100

= 0.936 = 0.929

0.15 X 245 + 0.20 X 100

To calculate real income for 1981 in 1980 terms, divide the 1981 income by the

536

Answers to End-of-Chapter Questions

appropriate price index. Using Pr: $49.40 -t- 0.936 = $52.75 > $50.00. Using PL: $49.40 -f- 0.929 = $53.17 > $50.00. (c) (1) The 1980 bundle could not have been purchased with the 1981 income and prices; and the 1981 bundle could not have been purchased with the 1980 income and prices. So nothing is revealed about which bundle is preferred. (2) Pp = 0.902; $47.40 -4- Pp = $52.50 > $50.00 PL = 0.98; $47.40 A PL = $48.37 < $50.00 The two price indexes give different answers about the change in real income.

CHAPTER 9 For Basic Review 4. No. The engineer’s data describe the isoquants; but to find the optimum point on an isoquant, we need to know the prices of factor inputs. 5. If F is the free input, the iso-cost lines are horizontal, and the optimum point on an isoquant is where its MRTS = 0 (see Figure A9.1). If a price is charged for F, the iso-cost lines become more steep and less of F is used. Example: river water for processing and carrying off wastes; land on the American frontier.

Problems 2. MPL/PL = 1; MPk/Pk = 0.5. Reducing K by 1 unit saves $10 and reduces output by 5 units. Spending the $10 to purchase 10 units of L increases output by (approximately) 10 units. The net effect is higher output at no increase in cost. Why is the increase in output only approximately 10 units? Because each of the 10 extra units of labor is subject to diminishing marginal returns. 4. (a) If L = K = 5, X = 51/2 • 51/2 = 5 For L = 12.5, K = 2, X = 12.5I/2 • 21/2 = 5 For L = 2, K = 12.5, X = 2xn • 12.51/2 = 5

F Figure A9.1

537

Answers to End-of-Chapter Questions

(b) Solve 5 = L1/2 ■ 141/2 for L = 50 Solve 5 = L1/2 • 1/101/2 for L = 250 (c) Yes. X = 0 for L = 0.

For Discussion 2. If the output is lives saved, the problem is to equate the marginal productivities of dollars spent on advertising in each area. 4. The environment provides a service to producers—carrying off wastes. In the absence of an effluent charge or other effective regulation the waste removal service is free to producers. See the answer to Basic Review question 5. 6. The subsidy lowers the effective price of L N to producers. (a) Use more LN and less Ls. (b) Use more of both LN and Ls. (c) Use more LN and less K.

CHAPTER 10 For Basic Review 3. See Figure 10.6. 5. As Figure 10.7 shows, at this output the short-run and long-run total cost curves are tangent. Since marginal cost is the slope of the total cost curve, SMC

= LMC at the tangency point. 7. Average fixed cost curve, short-run total cost curve, and short-run average cost curve—all shift up. Other curves do not change.

Problems 1. (a) Decrease in value Foregone interest (12 percent X $8000) Insurance User cost (b) Operating cost — 20 MC. Social cost is the area of triangle in Figure A11.3. Social

cost = iX 5 X 5000 = $12,500.

For Discussion 2. (a) The price of apples to consumers falls; the price received by growers, including $5, increases. The price of labor is unchanged, because the supply curve of labor is horizontal. The price of land increases as growers bid for more land to grow apples on. Profits increase in the short run but fall again to 0 in the long run. Output and the utilization of all factors increase. (b) Beneficiaries: landowners, consumers. Losers: those whose taxes go up to pay for the subsidy. (d) No. Price is less than marginal cost. Output is excessive.

540

Answers to End-of-Chapter Questions

Figure All.l

CHAPTER 12 For Basic Review 4. The tax reduces the net or aftertax wage and makes the budget line less steeply sloped. The substitution effect increases the demand for leisure (reduces labor supply), but the effect of reduced money income tends to reduce the demand for leisure (increase labor supply). 6. See Figure A 12.1. No, because the individual will always wind up in that range where his indifference curves slope downward to the right (where work is a bad and leisure is a good). 9. See Figure A 12.2. The same principles apply. See the answer to Basic Review question 4.

541

Answers to End-of-Chapter Questions

Pi, dollars

Figure A11.3

Figure A12.1

Problem 1. (a) Calculate the value of the marginal product of labor schedules for the three classes by multiplying the marginal product by the price of wheat. Plot the three

VMPL schedules and derive the market demand curve for labor by

horizontal addition. Add the vertical supply curve of labor to find the equilibrium wage rate. The wage is $26.00. Each

A farm takes 3j workers,

B farm takes H workers; and C farms are not profitable to operate. Rents per farm are equal to the areas under the VMPL schedules above the price of labor. Rents for A farms = $24.50; rents for B farms $4.50, and each

rents for C farms = 0. (h) The wage falls to $20.00.

A farms take 5 workers; B farms take 3 workers; and C farms take j worker. Rents are A = $50; B = $18; C = $1.

(c) Wages are lower because the increase in the number of workers resulted in a lower marginal productivity of labor on the fixed quantity of land. Land is

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Answers to End-of-Chapter Questions

relatively more scarce resulting in a higher rent for land. (d) Labor is more productive on A farms, perhaps because of higher soil fertility. now

For Discussion 2, If labor is in perfectly elastic supply to farmers, landlords capture all the benefits in higher rents. But if the farm labor supply curve is upward sloping, the increased demand for labor will generate factor surpluses for workers as well. 4. Rents of domestic oil well owners would increase if the price of domestic oil were allowed to rise. The increase in demand for coal as a substitute fuel would increase coal prices and rents to mine owners. Increased costs of agricultural production could lower rents to farmland in real terms. An increase in the demand for wood as a fuel could offset higher harvesting costs and increase rents to forest land. If energy is a complement to capital and a substitute for labor, the price and income share of capital would fall relative to the price and income share of labor.

CHAPTER 13 Problems 1. (a) To calculate the present value, you need to know: (1) the interest rate; (2) the expected life of the goose, and (3) the net receipts per year—number and weight of eggs, price of gold, and the cost of feed and other operating expenses (e.g., security). (b) This is a sign that the market interest rate has risen. Bonds are relatively more attractive as assets. The present value of the goose falls. (c) The annual net receipt and its present value fall.

543

Answers to End-of-Chapter Questions

3. (a) The cost of acquiring the car is only $200. You give up $2000 in monetary assets but have a car that can be sold for $1800.

(b) Simply possessing the car for two years has a user cost of: loss of value $1800-$ 1400 —

$400

foregone interest $180 in the first year plus 1.1 X

$180

in the second year (interest on the interest) =

$378

User cost =

$778

(c) The cost stream is

End of first year

End of second year

$300

$350

50

50

$350

$400

Gas, etc. Additional depreciation Total

(d) The present value of the cost of owning and operating the car is the sum of

A, B (discounted), and C, or PV = 200 +

(200 + 180)

(200 + 198)

1.1

l.T

648.76

= 1523.14 or 7.61^ per mile. You would rent if the rental rate payable in advance were less than this. If the rental rate per mile payable at the end of the year were

r, the present

value of that stream of costs would be: 10,000 R 10,000 R PVr = —- + -I1.1

l.l2

PVr you would be willing to incur is 1523.14. Substitute this in the preceding expression and solve for R . The maximum r is 8.78^ per mile. You are willing to pay more than \