Macroeconomics 8120343069, 9788120343061

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MACROECONOMICS Chandana Ghosh Ambar Ghosh

MACROECONOMICS

MACROECONOMICS

CHANDANA GHOSH Assistant Professor Economic Research Unit Indian Statistical Institute Kolkata

AMBAR GHOSH Professor Economics Department Jadavpur University Kolkata

New Delhi-110001 2011

` MACROECONOMICS Chandana Ghosh and Ambar Ghosh

© 2011 by PHI Learning Private Limited, New Delhi. All rights reserved. No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher. ISBN-978-81-203-4306-1 The export rights of this book are vested solely with the publisher.

Published by Asoke K. Ghosh, PHI Learning Private Limited, M-97, Connaught Circus, New Delhi-110001 and Printed by Mudrak, 30-A, Patparganj, Delhi-110091.

To Dr. MAHESH GOENKA This book would never have been possible without his Midas touch

Contents

Preface

xiii

PART I SUBSTANTIVE MACROECONOMICS 1.

Introduction Reference

2.

3–5 5

National Income Accounting 2.1 2.2 2.3

2.4

2.5 2.6

6–71

Introduction 6 Performance of Economic Activities and Circular Flow of Income 7 National Income Accounting (NIA) and GDP Measurement 8 2.3.1 The Value Added Method 8 2.3.2 The Income Method 11 2.3.3 The Spending/Expenditure Method of Estimating GDP and NDP 2.3.4 Incorporation of the Government 17 2.3.5 National Income Accounting in an Open Economy 23 Measures of Production 27 2.4.1 Gross Domestic Product (GDP) and Net Domestic Product (NDP) 28 2.4.2 Domestic Products and National Products 30 Production and Income 32 Different Concepts of Income, Saving and Investment 33 vii

14

viii

Contents

2.7

Balance of Payments 41 2.7.1 Saving, Investment and Current Account Balance 2.8 Real and Nominal GDP 48 2.9 Composition of India’s GDP 50 2.10 Employment and Unemployment in India 53 2.11 Poverty 57 2.12 Measures of Inflation 59 2.13 Conclusion: India’s Position Relative to the World 64 Problems 69 References 71

3.

46

Aggregate Demand and Determination of GDP

72–118

3.1 3.2

Introduction 72 Simple Keynesian Model 75 3.2.1 Simple Keynesian Model (SKM) for a Closed Economy without Government 75 3.3 Stability of Equilibrium 80 3.4 Comparative Static Exercises 82 3.4.1 Effect of an Increase in the Autonomous Expenditure on Y and C 82 3.4.2 Mathematical Derivation of the Increase in Y and C 83 3.5 Multiplier Process at Work 85 3.6 Inflationary and Deflationary Gap 87 3.7 Relationship between GDP, Actual and Planned Consumption and Actual and Planned Investment 89 3.8 Simple Keynesian Model for a Closed Economy without Government in Terms of Saving and Investment 92 3.9 Stability of Equilibrium 94 3.10 An Exogenous Increase in the Autonomous Component of Saving 95 3.11 Simple Keynesian Model for a Closed Economy with Government 96 3.11.1 The Model 97 3.11.2 Comparative Static Exercise 98 3.12 SKM with Government in Terms of Saving and Investment 111 3.13 Fiscal Policy and Government’s Budget 113 3.14 Conclusion 116 Problems 116 References 118

4.

Financial Sector, Money Supply and Interest Rates 4.1 4.2

Introduction 119 Financial Markets 120 4.2.1 Money Market 120 4.2.2 Market for Foreign Exchange

121

119–162

Contents

Pricing of Securities 123 4.3.1 Pricing of Treasury Bills 123 4.3.2 Pricing of Certificate of Deposits (CDs) 125 4.3.3 Pricing of Bonds 125 4.3.4 Comparison of Different Types of Securities 127 4.4 Financial Institutions in India 129 4.4.1 The Reserve Bank of India 131 4.4.2 Commercial Banks 133 4.4.3 Cooperative Banks 134 4.4.4 Specialized or Development Financial Institutions 135 4.4.5 Insurance Companies 135 4.4.6 Unit Trusts and Mutual Funds 136 4.4.7 Non-Bank Financial Companies (NBFCs) 136 4.5 Money Supply 137 4.5.1 Regulation of Money Supply 146 4.6 Term Structure of Interest Rates 146 4.6.1 Unbiased Expectations Theory 146 4.6.2 Liquidity Preference Theory 150 4.6.3 Market Segmentation Theory 151 4.6.4 Preferred Habitat Theory 152 4.7 Monetary Policy and the Term Structure of Interest Rates 152 4.7.1 Liquidity Adjustment Facility (LAF), Open Market Operation (OMO) and Monetary Stabilization Scheme (MSS) 4.8 Conclusion 161 Reference 162

ix

4.3

5.

IS-LM Model 5.1 5.2

5.3

5.4

Introduction 163 The Model 163 5.2.1 The Commodity Market 163 5.2.2 The Money Market or the Financial Sector 170 5.2.3 Equilibrium in the IS-LM Model 177 Fiscal Policy 179 5.3.1 Increase in Government Expenditure by dG Financed by Internal Market Borrowing 179 5.3.2 Mathematical Derivation of the Result 181 5.3.3 The Multiplier or the Adjustment Process 183 5.3.4 Note on Crowding-out Effect 184 5.3.5 Efficiency of Fiscal Policy 184 5.3.6 Built-in Stabilizers 186 Monetary Policy 186 5.4.1 The Multiplier and the Adjustment Process 189

155

163–204

x

Contents

5.5

Inter-Linkage between the Real and the Financial Sectors in the IS-LM Model 191 5.5.1 LM Schedule in the Liquidity Trap 192 5.5.2 The Classical Zone of the LM 193 5.6 Short-Run Economic Fluctuations and the IS-LM Model 5.6.1 Money and Economic Fluctuations 196 5.7 Comparison of Fiscal and Monetary Policy 197 5.7.1 Monetary and Fiscal Policy Mix 197 5.8 Conclusion 202 Problems 203 References 204

6.

195

Classical Theory

205–229

6.1 6.2 6.3

Introduction 205 Say’s Law: Markets for Goods and Credit 206 Aggregate Supply: Aggregate Production and Labour Market 6.3.1 Supply of Labour 211 6.3.2 Equilibrium in the Labour Market 216 6.4 Money Market 218 6.4.1 Neutrality of Money 220 6.5 Problems with the Classical Theory 221 6.6 Conclusion 229 References 229

7.

Complete Keynesian Model

207

230–259

7.1 7.2

Introduction 230 Complete Keynesian Model: Aggregate Demand 230 7.2.1 Shifts in AD 233 7.3 Complete Keynesian Model: Aggregate Supply 234 7.3.1 Supply Price of Labour 239 7.4 Equilibrium in the Complete Keynesian Model 242 7.4.1 Equilibrium with Involuntary Unemployment 243 7.5 Working of the CKM: Comparative Static Exercises 245 7.5.1 Effect of an Increase in Government Consumption Financed by Internal Borrowing 245 7.5.2 Effect of an Increase in Money Supply 252 7.6 Conclusion 256 Reference 259

8.

The Real Sector and the Financial Sector 8.1

Introduction

260

260–266

Contents

The Model 261 8.2.1 The Financial Sector 261 8.2.2 The Real Sector 262 8.3 Interaction between the Real and the Financial Sectors 8.4 Conclusion: Evaluation of the Model 265 Reference 266

xi

8.2

9.

263

Consumption Function

267–286

9.1 9.2 9.3

Introduction 267 Keynesian Consumption Function 268 Discrepancy between the Short-Run and Long-Run Consumption–Income Relationship 269 9.3.1 Fisher’s Model of Intertemporal Choice 270 9.4 Life Cycle Hypothesis of Consumption 274 9.4.1 Implication of the LCH for the Keynesian Multiplier 9.4.2 Evaluation of LCH 277 9.5 Permanent Income Hypothesis 278 9.5.1 Cross Section Budget Studies and the Permanent Income Hypothesis (PIH) 281 9.5.2 Evaluation of PIH 284 9.6 Conclusion 285 References 286

10. Investment Function: Keynesian Theory of Investment in Fixed Capital 10.1 Introduction 287 10.2 Investment in Fixed Capital 287 10.3 Conclusion: Volatility of Investment Reference 290

287–290

289

11. Demand for Money 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8

277

Introduction 291 Demand for Money: Definition and Sources 291 Transaction Demand for Money 292 Baumol’s Theory of Transaction Demand for Money Precautionary Demand for Money 296 Speculative Demand for Money 296 Keynesian Theory of Speculative Demand for Money Tobin’s Reformulation of the Keynesian Theory of Speculative Demand for Money 298 11.9 Conclusion 303 References 305

291–305

293

297

xii

Contents

PART II MACROECONOMICS GONE ASTRAY 12. New Classical and New Keynesian Theories

309–368

12.1 Introduction 309 12.2 Stagflation and Demise of the Keynesian Orthodoxy 310 12.3 The Phillips Curve 313 12.3.1 Oil Shock and Phillips Curve 317 12.4 New Classical Theory 318 12.4.1 Expectation Augmented Phillips Curve 319 12.4.2 Expectation Augmented Phillips Curve, Aggregate Supply and Natural Rate Hypothesis 322 12.5 New Classical Theory and Rational Expectations 338 12.5.1 Simple Formal Model of Rational Expectations 341 12.5.2 Evaluation of the New Classical Rational Expectation Theory 12.6 Theory of Real Business Cycle 349 12.7 New Keynesian Theory 350 12.7.1 Nominal Rigidities and Economic Fluctuations 350 12.7.2 Real Rigidities 358 12.7.3 Rigidities in Interest Rates and Credit Rationing 362 12.8 Conclusion 367 References 368

13. Modern Theories of Growth: A Critique 13.1 Introduction 369 13.2 Harrod–Domar Model 375 13.3 Neoclassical Theory of Growth 382 13.3.1 Transitional Dynamics 387 13.3.2 Central Result of Solow Model 388 13.3.3 Effect of Increase in s 388 13.3.4 Evaluation of the Central Results of the Solow Model 13.3.5 Golden Rule of Capital Accumulation 395 13.3.6 Dynamic Efficiency in a Market Economy 398 13.3.7 Unconditional and Conditional Convergence 402 13.4 Endogenous Growth Theory 403 13.4.1 Human Capital Formation and Growth 404 13.4.2 Investment in R&D and Growth 412 13.5 Empirical Results and Concluding Remarks 415 References 417

Index

346

369–418

391

419–421

Preface

We grew up in a crisis-ridden period of large-scale unemployment precipitated by the food crisis of the mid 1960s and reinforced by the oil shocks of the 1970s. Unemployment and poverty were the twin evils that haunted us and we wanted desperately to know what exactly caused them and what could be done to remove them. We learnt that economics is the subject that holds key to these questions. So we chose to study economics. Little did we know then how much poison economics could contain and spew. In our childish innocence we thought that economics as a science objectively and relentlessly pursued the truth. We did not know then economics is an instrument of class war; it doggedly pursues not the truth but the class interests. It seeks to present a distorted make-believe world that favours the interest of the dominant class, which sets up a detailed apparatus to establish the distorted reality as the true economic reality. Since in today’s world only one class dominates and competition among different classes is conspicuous by its absence, economics today is highly distorted and untrue. We write this book to substantiate these claims in the context of macroeconomics. The book is written in the hope of showing economics in its true light to the hapless innocent students who are swayed by the kind of emotion that moved us into studying economics more than three decades ago. Chandana Ghosh Ambar Ghosh

xiii

Part

I

Substantive Macroeconomics

1

Introduction

Economics in general and macroeconomics in particular are at the core of politics. Economics may suggest policies which favour a class at the expense of others. It is very much an instrument of class war over the division of the aggregate social production and assets. Needless to say, driven by class interests, economics tends to stray from its true objective of unravelling the working of modern market economies so as to identify the sources of crises that these economies are often afflicted with and to suggest ways of resolving them. To further class interests, economics can distort truth to elicit results that favour a specific class. The only way to keep economics on course is to have equally strong opposing schools of thought representing different classes vigorously competing with one another. Governments are necessary in modern states. However, they are also a source of tremendous stress to the people. They can tax people at high rates. They can confiscate private property, as seen in some Socialist states. They can usurp all means of production turning the people not running the governments into paupers overnight. This fear induces ‘the haves’ to put up an allout effort to develop an economics that shows how unnecessary it is for the government to interfere with economic matters. Its objective is to show that a market economy left to itself can do much better than what an ideal ‘command economy’ can. The macroeconomics that emerged since the beginning of the 1970s precisely worked with that end in view. The developments are broadly classified into three categories, namely, new classical macroeconomics, new Keynesian macroeconomics, and long-run macroeconomics. Although the proponents of the new classical and new Keynesian schools of thought differ in their views as to how a market economy functions, their differences are largely superficial. Both the schools repose unflinching faith in the efficacies of market economies and both of them lend their unanimous support to long-run macroeconomics. With the collapse of the Soviet bloc, the capitalist bloc usurped power and the balance in the world order was lost. To suppress the resurgence of bloc any government-centric power, the powers that be considered it necessary to block the development of any type of economics that points to the necessity of government intervention in the management of market economies or 3

4

Macroeconomics

any type of economics that extols the supremacy of command economies over market economies. How could one achieve it? It was easy and was achieved through the following steps. As the capitalist bloc gained ascendancy, the political parties the world over, even many of the communist parties, were eager to owe their allegiance to the new powers that be. The capitalist bloc forged alliance with these parties and shoved down their throat a package of economic reforms, which sought to convert all the economies into a homogeneous market economy with government’s regulation, and economic activities were reduced to the minimum and relegated to the background. This process is referred to as globalisation (as it implies the removal of restrictions on global flows of trade and capital), liberalisation (of government controls over different economic activities) and privatisation (of government enterprises). To create support for this process, it was necessary to control academics. Journals were globally ranked, obviously, with the journals of the capitalist bloc occupying the top spots. The lower ranked journals also under the control of the same bloc published poor, watered down versions and extensions of the stuff that came out in the top journals. Journals that did not toe the desired path were not recognised or ranked. For recruitment and promotion in universities and research institutes, publications in prestigious journals were made mandatory. This norm for promotion and recruitment was accepted by all the political parties that matter the world over. In return, these parties were given access to these journals so that they could monopolize all seats of higher learning. This was how all the alternative avenues of research were blocked. To get recruited and promoted even in Indian universities, one has to publish at least in B-grade or C-grade journals, which published only poor imitations of the articles published in the topnotch journals. This ensured that the world over only one kind of theories, the theories favoured by the capitalist bloc, held sway. This was how thinking was conquered by just one school of thought. To cloak the pathetically absurd assumptions necessary to show that market economies perform much better than the best of the planned economies managed by someone like the omniscient God, mathematicians were hired. Efforts were on to use complex mathematical tools to lend respect to the childishly absurd economic theories. In this context, it may be relevant to quote Keynes (1936) who explained why the Ricardian economics gained wide acceptance despite its complete incongruity with the behaviour of market economies that are typically subject to trade cycles: “But although the doctrine itself has remained unquestioned by orthodox economists up to a late date, its signal failure for purposes of scientific prediction has greatly impaired in the course of time, the prestige of its practitioners. For professional economists, after Malthus, were apparently unmoved by the lack of correspondence between the results of their theory and the facts of observation—a discrepancy which the ordinary man has not failed to observe, with the result of his growing unwillingness to accord to economists that measure of respect which he gives to other groups of scientists whose theoretical results are confirmed by observation when they are applied to the facts” (General Theory, Chapter 3, p. 33). This book is an attempt at substantiating these claims. The book is divided into two parts. Part I, called Substantive Macroeconomics, presents in detail, and in an easy-to-understand manner, the part of macroeconomics that constitutes a genuine attempt at comprehending how modern market economies work, how they get derailed, and what the government can do to keep them on an even keel. Obviously, Part I deals mainly with macroeconomics of John Maynard Keynes. This part contains 11 chapters covering National Income Accounting, Simple

Introduction

5

Keynesian Model, Financial Sector in Modern Economies, IS-LM Model, Classical Theory of Income Determination, Complete Keynesian Model, a model that deals with the issue of interaction between the real and the financial sectors, Theories of Consumption, Keynesian Theory of Investment, and finally Theories of Demand for Money. Chapter 3 presents the simple Keynesian model, which captures, in the simplest possible framework, the Keynesian explanation of the short-run cyclical fluctuations in GDP in modern market economies. Chapter 4 gives a brief introduction to the financial sector in modern market economies; it gives a brief overview of the major instruments, markets and institutions of the financial sector. Chapter 5 presents the IS-LM model in detail. Chapter 6 discusses the classical model which summarizes the macroeconomic ideas of the predecessors of Keynes. It also makes an assessment of the model to explain why Keynesian objections to the classical theory are valid. Chapter 7 discusses the complete Keynesian model in detail and points to the major Keynesian innovations that make his theory distinct from his predecessors’ and enable it to explain the phenomena of involuntary unemployment of labour and capital and trade cycles in modern market economies. It makes a thorough evaluation of the complete Keynesian model to examine its applicability to India and points to the areas where the theory may be improved upon. One major shortcoming of the complete Keynesian model or the IS-LM model is its treatment of the financial sector and the links between the real and the financial sectors. The next chapter develops a model that seeks to redress this shortcoming. Part II, named Macroeconomics Gone Astray, contains two chapters—one on New Keynesian and New Classical Economics and the other on Long-run Macroeconomics. Chapter 12 explains how the Keynesian theory was put aside in the seventies on a false pretext and how the Keynesian economics was fully capable of explaining the stagflation of the seventies produced by the oil shocks. It then proceeds to discuss the new classical and the new Keynesian developments and points to the reasons why one cannot accept them. The chapter on Long-run Macroeconomics discusses the natural rate hypothesis, and points to its flaws. It presents and assesses the major theories of growth, points to their theoretical inconsistencies and weaknesses and shows that the results of the endogenous growth theory are completely contradictory to the facts.

REFERENCE Keynes, J.M. (1936), The General Theory of Employment, Interest and Money, Macmillan, London, Chapter 3, p. 33.

2 2.1

National Income Accounting

INTRODUCTION

One of the most important objectives of macroeconomics, as we have pointed out in Chapter 1, is to explain how aggregate output and aggregate income are determined in an economy. This raises several difficult questions. One of them being the meaning of aggregate output of an economy. A country in any given period produces hundreds of thousands of different goods and services. They are all heterogeneous and therefore cannot be added. In these circumstances, definition and measurement of aggregate output are important issues which need to be addressed and resolved first. Aggregate income is also an intriguing concept. A person earns income from various sources. She earns wage or salary as an employee of an organization, interest from her bank deposits and securities, rent by renting out her house or land or mine, and profit from her business. Retired government employees get pensions from the government. The victims of natural calamities and accidents get assistance or compensation from the government, both in cash and kind. People also get remittances from their children or spouses working abroad. Houses and consumer durables used by their owners yield services to their owners. These services can also be regarded as income in kind. In this situation, defining and measuring aggregate income are by no means easy. These tasks have to be accomplished first before embarking on the job of determining aggregate income. Obviously, production and income are closely related to each other, as production generates income. People owning companies engaged in production of different goods and services earn profit. They pay wages and salaries to their employees, interest to their lenders, and rent to the landlord, and so on. Thus, the interrelationship between aggregate production and aggregate income should be an important subject of study. It should be understood first before taking up the task of determining aggregate production and income. Finally, both income and production are fruits of activities of the people. To define and measure aggregate production and income and to comprehend the interrelationship between the two, in Section 2.2 we start with a description of the day-to-day activities which are undertaken in an economy. 6

National Income Accounting

2.2

7

PERFORMANCE OF ECONOMIC ACTIVITIES AND CIRCULAR FLOW OF INCOME

Economics is concerned with economic activities. These are defined as those activities that yield some income or involve buying and selling. Economic activities are broadly divided into two categories—production and exchange. Production refers to three types of activities, namely transformation of one kind of material into a different kind of more useful material; transportation of goods from one place to another to make them more useful; and storage of goods from one point of time to another so that the goods become more useful. Economic exchange in modern economies means buying and selling in the market. Goods and services which enter into production are called inputs of production or factors of production. Inputs of production are again broadly classified into three categories: land, labour and capital. Land refers to all kinds of natural resources that enter into production such as land in the usual sense of the word, mines and forests. Labour refers to all kinds of contribution made by human beings to production. Capital is defined as produced means of production, i.e. all the produced goods that are used in production are capital. Let us illustrate these categories with an example. Consider a transport company which is engaged in the business of transporting goods from one place to another. It does not produce a good, but provides a service. When a company produces something tangible, it produces a good. When it produces something intangible, it provides a service. When you are paying fees to your doctor or to your school or college, or when you are buying tickets to watch a movie or a game, like cricket or football, you are paying for a service. A transport company provides service using a large number of inputs such as a fleet of trucks, a large staff consisting of drivers, mechanics, helpers, managers, accountants, clerks, bearers and others, office buildings and garage space built on pieces of land, and fuels to run the trucks. All these inputs must belong to one or the other of the three categories of factors of production mentioned above. Service rendered by the staff is obviously labour. The pieces of land on which the office buildings and garages are built are natural resources and hence belong to the category of land. All the other inputs are produced goods being used in production. Hence they belong to the category of capital. Those who perform economic activities are called economic agents. They are divided into two broad categories: households and firms. Individuals or families are referred to as households. They own all the factors of production. In modern societies, government also owns some factors of production and performs economic activities. But, here, as we wish to keep the discussion simple, we ignore government. Firms are defined as units of production. They carry out production. However, the inputs they use, i.e. the natural resources, labour and capital they use, are all owned by the households. Households have to make a living. They do so by allowing the firms to use the services of factors of production they own. In exchange of factor services, the firms make factor payments to the households. For labour, firms pay wages to households who supply labour. If firms hire houses, land, forests or mines from the households, they pay the households rent for the services of these inputs. Besides the inputs mentioned above, firms use many other non-labour inputs which they do not hire but purchase. Firms hire labour and the services of inputs mentioned above and purchase other inputs either with the firms’ owners’ wealth or with loans taken from the households. For the services of the loan, which include services of factors purchased with loans,

8

Macroeconomics

firms pay interest to the lending households, and for the services of owners’ wealth, which include the services of factors purchased with it, firms pay profit to their owners. Thus there takes place a flow of factor services from households to firms and a reverse flow of factor income from firms to households. Firms use the factor services to produce goods which they sell to households and use the sale proceeds to make factor payments. Households, in their turn, use their factor income to purchase produced goods and services from firms. Thus, the economic activities of economic agents generate a circular flow of factor services from households to firms and that of produced goods from firms to households and a reverse circular flow of income from firms to households and that of spending from households to firms. These flows are depicted in Figure 2.1.

Figure 2.1 Circular flow of income and expenditure.

2.3

NATIONAL INCOME ACCOUNTING (NIA) AND GDP MEASUREMENT

National Income Accounting deals with the measurement of aggregate production and income. One of the most commonly used measures of aggregate production is called Gross Domestic Product (GDP). GDP of a country in a given year is defined as the total value of all the physical goods and services produced within the geographical boundary of the country in the given year. We shall now discuss different methods of measuring GDP. There are actually three methods of doing this, namely, the value added method, the income method, and the expenditure or the spending method. We shall discuss each of these methods in turn. To begin with, we shall consider a very simple economy which is closed and has no government. An economy is closed if it has no transactions with the rest of the world, i.e. if it neither buys, borrows or receives gifts from the rest of the world nor sells, lends or gives gifts to the rest of the world. There are three methods of measuring GDP. Here we shall discuss each of these methods. For simplicity, we consider here a closed economy without government. Once these methods are understood for this simple case, it will be easier to comprehend them for the more complex cases.

2.3.1

The Value Added Method

Suppose that in a given year there existed in the simple economy under consideration N number of firms. Suppose that the output the ith firm produced in the given year was Xi and the price

National Income Accounting

9

it charged for its produce in the same year was Pi so that the value of its output in the given year was (PiXi). Shall we get GDP of the given year by summing up the value of output of each of the N firms that existed in the economy in the given year? The answer is No.

Ç

È N Ø Pi X i Ù É Êi 1 Ú

will

not give the GDP of the country in the given year except under very special circumstances. The reason may be explained as follows. In modern economies, firms are interdependent, i.e. almost every firm uses goods and services produced by other firms as inputs. Under these conditions,

Ç

È N Ø Pi X i Ù É Êi 1 Ú

overestimates GDP by a substantial margin. Let us elaborate. If in the given period

in the given economy, the ith firm used the whole of the jth firm’s output as input and completely used it up in the production of the given year, (PiXi) definitely would not give the true value of the ith firm’s production in the given year. This is because, in producing (PiXi) worth of goods and services, the ith firm completely used up (PjXj) worth of goods and services produced by the jth firm in the given period. Therefore, the true value of production of the ith firm is given by (PiXi – PjXj). Hence the value of the output of the ith firm in the given year included the value of output of the jth firm of the given year, and if we add (PiXi) to (PjXj), the value of the output of the jth firm is counted twice. Let us illustrate this with an example. Suppose that a milkman in a given year produced milk worth ` 1000 and sold it in the same year to a confectioner, who in turn used this milk to produce sweets worth ` 2000 in the given year. The true contribution of the confectioner to the country’s production in the given year is obviously not ` 2000 since, in producing sweets worth ` 2000, he completely used up milk worth ` 1000 produced by the milkman in the given year. Clearly, the value of sweets produced by the confectioner includes the value of the milk used in the production of sweets, and the ‘true’ value of production of the confectioner is only (` 2000 – ` 1000). Therefore, if we add up the value of output of sweets to the value of milk produced by the milkman, the value of milkman’s output will be counted twice. This problem is referred to as the problem of double counting. It arises because of the presence of one kind of inputs called intermediate inputs. Intermediate inputs are those of a firm’s inputs, (i) which get completely absorbed in the process of production, and (ii) which are produced either by other firms or by the same firm (user firm) in the previous periods. Thus the output of milk of the milkman in the example given above is an intermediate input used by the confectioner as it satisfies both criteria (i) and (ii). Since intermediate inputs used by a firm in a given year are completely absorbed in its production in the given year, the value of the output of a firm in a given year, as we have explained above, includes the value of the intermediate inputs it used in the same year. The values of intermediate inputs are also included in the values of outputs of firms producing these intermediate inputs. Therefore, if we add to the value of output of a firm the values of outputs of those firms from which it bought its intermediate inputs, the value of intermediate inputs will be counted twice. This will be the case if the output of the firm using the intermediate inputs and the intermediate inputs are produced in the same period. If the intermediate inputs are produced in the earlier periods, addition of the value of the output of the firm using the intermediate inputs in a given year to the values of outputs of the firms supplying these intermediate inputs in the given year will not lead to double counting of the value of intermediate inputs since they were produced

10

Macroeconomics

in earlier years. But the value of output of the firm using the intermediate inputs will be overestimated by the value of the intermediate inputs. Let us illustrate. In the example given above, if the milk used by the confectioner in the given year was produced by the milkman in the previous year, addition of the output of the confectioner in the given year to the output of the milkman in the given year will not lead to double counting of the output of the milkman since the value of the output of the confectioner includes the value of the output of the previous year of the milkman. Nonetheless, the value of the output of the confectioner in the given year will exceed the value of its true output in the given year by the value of the milk it used in the given year. To avoid this problem of double counting or of overestimation of the value of production of a firm, we have to arrive at a measure of true production of every firm in a given year. Clearly, to get this we have to subtract the value of intermediate inputs used by the firm in a given year from the value of the output of every firm in that year. The figure that we get following this subtraction is called the gross value added (GVA) of the firm in the given year. Clearly, we get the value of all the goods and services produced by all the firms located within the geographical boundary of a country together in a given year, i.e. we get the GDP of a country in a given year by adding up the GVA of every firm located within the geographical boundary of the country in the given year. There is, however, one caveat here. In producing its output, a firm not only uses intermediate inputs, but also durable inputs. They are produced goods, but they differ from intermediate inputs because they are not completely used up in production. They remain intact even after the production process of a given year is over and are used again in production in subsequent years. Machinery, equipment, buildings and other constructions used by a company are examples of these durable inputs. However, the durable inputs lose a part of their productive capacity as a result of their wear and tear during the year. Therefore, in producing its output a firm uses up completely not only the value of the intermediate inputs it uses but also a part of the productive capacity of the durable inputs it employs. Therefore, the value of the output of a firm in a given year includes not merely the value of the intermediate inputs that went into its production in the given year but also the value of wear and tear of the durable inputs it used in the given year. The value of the wear and tear of the durable inputs is called depreciation. Hence the true value of production of a firm in a given year is given by the value of output of the firm in the given year net of the value of the intermediate inputs and depreciation of the durable inputs the firm used in the given year. Alternatively, since in producing its output in a given year a firm not only used up the intermediate inputs but also a part of the value of the productive capacity of the durable inputs it used in the given year, its true contribution to production of the country in the given year is the value of its output net of the value of the intermediate inputs it used up in the given year and the depreciation of the durable inputs it used in the given year. Thus, the GVA of a firm in a given year, net of the depreciation of the durable inputs it used in the given year, which is called net value added (NVA) of the firm in the given year, is a better measure of a firm’s true production. Therefore, a more satisfactory measure of aggregate production of a country in a given year is given by its net domestic product (NDP) in the same year, where NDP is obtained by summing up the NVA of every firm located within the geographical boundary of the country in that year. Hence the NDP of a country in a given year

National Income Accounting

11

is given by the GDP of the country in the given year net of the depreciation of all the durable inputs used in production by all the firms located within the geographical boundary of the country together in the given year. EXERCISE 2.1 (a) Suppose in 1999 there existed only three firms in the economy, a bakery (Firm 1), a flour mill (Firm 2), and a wheat producing farm (Firm 3). Suppose in the given year the bakery produced bread worth ` 500 using the entire output of flour of ` 300 of Firm 2. Firm 2 in turn produced its output using half the output of wheat of ` 300 of Firm 3. Calculate the true value of the output of each firm giving the reason. If you add output of Firm 3 to that of Firm 2, which item is counted how many times? If you add value of output of Firm 1 to that of Firm 2, how many times do you count the output of each firm? If you add outputs of all the three firms, then how many times do you count output of each of the three firms? (b) Suppose that Ram owns a fleet of taxies. In 2009, he earned ` 10 lakh in passenger fares, paid ` 2 lakh to drivers and other employees, ` 1 lakh on repair and maintenance, ` 1 lakh as rent for garage space, and ` 5 lakh on fuel. What is Ram’s true value of production in 2009? Explain your answer.

2.3.2

The Income Method

The GDP and NDP of an economy in a given year can also be measured by summing up the different types of factor incomes generated within the geographical boundary of the economy in the given year. To show this, we have to break up the GVA of a firm into its income components. To bring out the interrelationship between the GVA of a firm and the total factor income that originates within it, we have to start with the concept of gross profit of a firm. The gross profit of a firm from its production in a given year is defined as the value of the output of the firm net of its cost of production excluding depreciation in the same year. (Note that there is no guarantee that the whole of the output of a firm in a given year will be sold in the same year. If a part of the output remains unsold, the value of that unsold output is taken to be equal to the cost of producing it.) The cost of production of the output of a firm in a given year consists of wage, rent and interest payment made to households by the firm for the factor services purchased from them for the production of the given year plus the value of intermediate inputs used by the firm in the production of the given year. (Note that payments made by firms to other firms for the factor services purchased from them, such as payments for labour hired from labour contractors or interest paid on loans taken from banks, should be regarded as part of the value of intermediate inputs used in the production of the given year and not as payment for factor services. If they are not regarded as payments for intermediate inputs, the problem of double counting will arise. Explain the reason.) From the definition of gross profit, therefore, we get the following identity

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Macroeconomics

Gross profit of a firm from its output in a given year º (value of output of the firm in the given year) – (value of intermediate inputs used by the firm for production in the given year) – (wages + interest + rent ) paid to households by the firm for its production in the given year

(2.1)

The difference of the first two terms on the right-hand side of (2.1) is nothing but the gross value added of the firm. It therefore follows from (2.1) that the gross value added (GVA) of a firm in a given year is nothing but the sum of the wage, rent, and interest it paid to the households for the factor services used in its production of the given year plus its gross profit from the production of the given year. This is given by the following identity: GVA of a firm in a given year º (wages + rent + interest) paid to households by the firm for factor services used in the production of the given year + gross profit of the firm from production of the same year

(2.2)

Summing up each side of (2.2) for all firms located within the geographical boundary of the country, we get the following identity: GDP of a country in a given year º sum of GVAs of the given year of all the firms located within the geographical boundary of the country º (aggregate wage + aggregate rent + aggregate interest) paid by all these firms to the households for factor services used in the production of the given year + aggregate gross profit of these firms from production in the given year

(2.3)

From the above identity, it follows that, by adding up the wages, rent and interest paid or payable to the households by all firms located within the geographical boundary of a country together in a given year for the households’ contribution of factor services to production of the same year and the aggregate gross profit of these firms from the production of the given year, we get the GDP of the country of that year. This is the income method of estimating GDP. When depreciation is included in the cost of production of a firm, then the value of output of a firm net of cost of production gives us the net profit of the firm from its output. In other words, if we subtract the depreciation of durable inputs used by the firm in a given year from the gross profit of a firm (from the output of the given year), we get the net profit of the firm from its output in that year. From this it follows that:

National Income Accounting

NDP of a country in a given year º GDP of the country in the given year – aggregate depreciation of the durable inputs in the given year º Aggregate (wages + rent + interest) paid or payable to the households for factor services used in production of the given year by all the firms located within the country together in the given year + aggregate net profit of these firms from the production of the given year

13

(2.4)

At this point it may be instructive to point to certain features of firms which are commonly found in market economies today. These firms may be divided into two broad types: joint stock companies or corporations and proprietorship firms. The latter are small enterprises owned by a single individual or by a few individuals together on a partnership basis. Profit of these enterprises is simply regarded as a part of their owners’ income. Joint stock companies or corporations are large-scale companies of today. The finance needed to set up these companies is raised by selling shares in the market to the public. Shares are also alternatively called stocks or equities. A new share is issued at a price of ` 10 or ` 100. Every shareholder of a company is its owner. If you buy even one share of a company such as Maruit Udyog or ITC or ACC, you become at once its owner jointly with other shareholders. Thus, a modern large-scale company of today is owned by hundreds of thousands of owners. However, management of these companies rests with only a few of them. Shareholders elect a few of them as their representatives. The elected members form the board of directors and manage the company. As there is alienation between the ownership and management of a corporation, the profit of a corporation is regarded separately from its owners’ income. Even though the whole of the profit of a corporation accrues to its shareholders, the board of directors may retain a part of the corporation’s profit as reserves. The part of the profit that is distributed among the shareholders is called dividend. The rest is called undistributed profit or retained earning of the corporations. Thus we get the following identity: Aggregate net profit of a country from production of a given year º aggregate net profit of the proprietorship firms located within the country from production of the given year + aggregate net profit of the corporations located within the country from production of the given year

(2.5)

EXERCISE 2.2 (a) Consider a firm, Hindusthan Uniliver Limited (HUL). In 2006, it produced output worth ` 40 crore, purchased intermediate inputs of ` 20 crore, paid ` 20 crore, ` 5 crore and ` 2 crore respectively in wages and salaries, interest on outstanding loans and repair and maintenance. It did not pay any rent. What are its gross value added and net value added? How are these value added related to the total factor incomes originating in this firm? (b) (i) Consider a bank. It receives deposits and uses them to extend loans. Its output is the service rendered by loans disbursed. In 2007, the bank received ` 10 lakh in interest from borrowers. It paid depositors who, we assume, are all households,

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Macroeconomics

` 5 lakh as interest. It also paid ` 2 lakh and ` 50,000, respectively in wages and salaries, and repair and maintenance. Calculate its gross value added. (ii) Suppose that the bank lent to only one firm, which used the loan to set up its production facility and using this facility, it produced goods and services worth ` 25 lakh in 2007, paid ` 10 lakh as interest to the bank, and ` 8 lakh in wages and salaries. It did not make any other payments for purchasing inputs. Suppose that you treat interest payment by the firm as a factor payment and not as a payment for intermediate inputs. Now if you add the value added of the firm to the value added of the bank, will the output of the bank, which is the service rendered to the firm by the bank loan, be counted twice? Explain. In the light of your answer, how will you treat the bank’s interest payments on deposits, if depositors are all firms? Explain.

2.3.3

The Spending/Expenditure Method of Estimating GDP and NDP

Here we discuss an alternative way of measuring the GDP and NDP of an economy. For this we focus on the fact that every firm carries a stock of goods always. If we observe a firm at any point of time, we find that it carries a stock of goods and we find in its stock various types of goods such as the goods that it produces, the inputs that it will use as intermediate inputs later, goods in process which refer to the firm’s unfinished products at different stages of production, and durable inputs such as machinery, equipment and buildings. The stock of goods that a firm carries is called its capital stock. It has two components, namely, stock of fixed capital and inventory. Stock of machinery, equipment and construction is called the stock of fixed capital, while the stock of all other types of goods held by the firm is called inventory. Investment of a firm in a given year is defined as the change in its capital stock that takes place from the beginning to the end of the given year. Aggregate investment made by all firms together located within the geographical boundary of a country in a given year, which we denote by IF, is accordingly defined as the change in the stock of goods held by all these firms together in the given year. Thus: IF º Stock of capital held by all the firms located within the geographical boundary of a country together at the end of a given year – stock of capital held by all these firms together at the beginning of the given year

(2.6)

To understand why stock of capital of all the firms of a country change from the beginning to the end of a given year, we have to identify the sources of this change. Obviously, changes in the aggregate capital stock held by all the firms together are due to inflows into and outflows from the aggregate capital stock of the firms that take place in the course of a given year. These inflows and outflows are shown in Figure 2.2. Let us explain these two concepts. Here, we consider all the firms together. The economy is also closed. In a closed economy, the stock of goods held by all the firms together can increase only through production. Goods produced by

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15

the firms enter at once into the stock of goods held by them and increase it directly. Production by all firms together or GDP is the only inflow into the stock of goods held by all the firms together in a closed economy. In an open economy, firms located within the geographical boundary of the domestic economy can purchase goods from foreign countries and add to the stock. However, this route is closed in a closed economy. A single domestic firm can increase its capital stock by purchasing goods from other firms and adding them to stock, but this is not possible when we consider all the domestic firms as a single entity. If a firm raises its capital stock by buying goods from other firms, the capital stock of the seller firms will go down exactly by the same amount. Hence the aggregate capital stock held by all the firms together will remain unchanged. Therefore, in a closed economy, the aggregate stock of goods held by all firms together can increase through production only. So, GDP is the only inflow into the aggregate capital stock held by all firms together in a closed economy.

Figure 2.2 Sources of change in the aggregate stock of capital of firms.

Let us now focus on the outflows. There are in fact two reasons why the stock of goods held by all firms together can decline. One, which is by far the most important, is sales by all firms together to non-firm economic agents. The other is depreciation. Goods held in stock depreciate in the course of a given year. Therefore, there are only two outflows from the aggregate stock of goods held by all firms together, namely, sales to non-firm economic agents and depreciation. Obviously, the aggregate capital stock of the firms will change if inflows and outflows are unequal. We can, therefore, calculate the change in the aggregate capital stock of firms by subtracting from the GDP both aggregate sales by these firms to non-firm economic agents and depreciation of the aggregate capital stock of these firms. This will give us the aggregate net investment of the firms or the net change in the aggregate capital stock of the firms. If we do not subtract depreciation, we shall get the aggregate gross investment of the firms or the gross change in the aggregate capital stock of the firms. Denoting the aggregate gross investment and the aggregate net investment of firms by IF and IF , respectively, we get the following identity: IF (of a country in a given year) º gross change in the stock of goods held by all firms located within the geographical boundary of the country together in the given year º aggregate production of these firms in the given year, which is the GDP of the country in the given year – sales by all these firms together to other economic agents, which are the households in this case

(2.7)

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Macroeconomics

In any given year, the sales made by all firms together to households must be equal to the purchases made by households in that year from the firms. Households’ purchases of or expenditures on goods produced by firms consist of their consumption expenditure and investment expenditure. Households’ purchase of houses from firms comprise their gross investment expenditure (which we denote by IH); all other types of purchases made by them from firms are referred to as consumption expenditure (C). Therefore, (2.7) reduces to IF º GDP – (C + IH) From the above identity, we get GDP º C + I

(2.8)

where I (aggregate gross investment) º IF + IH. Hence, NDP º GDP – depreciation º C + IF – depeciation of goods held by the firms during the year + IH – depreciation of houses held by households during the year º C  IF  IH œ C  I

(2.9)

where I º aggregate net investment and IH œ aggregate net investment of the households. We, therefore, can compute GDP and/or NDP also from the data on aggregate consumption and investment expenditures. These consumption and investment expenditures represent spending on final goods and services produced by firms. Final goods and services are those goods and services which do not enter into production as intermediate inputs in the same year. Expenditures on final goods, which are also referred to as final expenditures, should be distinguished from expenditures on intermediate inputs and factor payments made by firms to households. Let us illustrate the above identity with a simple example. Consider a closed economy without government. Suppose that in a given year in this economy all the firms together produced goods worth ` 1000, i.e. the GDP of the economy was ` 1000. Also suppose that in the given year they sold nothing to other economic agents who consisted only of households. Obviously, in the given year the whole of the production was held in stock by the firms. Accordingly, at the end of the year the capital stock of all these firms together, ignoring depreciation, increased by ` 1000. Since the economy is closed, it was not possible for the firms of the given economy to raise their capital stock by purchasing goods from abroad. Hence the capital stock of all these firms increased exactly by ` 1000 from the beginning to the end of the given year. In this case, C + IH = 0 and IF = ` 1000. Now suppose that, instead of selling nothing to the households, they sold to households goods worth ` 800 (or ` 1200) in the given year. In this case, therefore, the capital stock of all these firms together on the one hand rose by ` 1000 because of production and declined on the other hand by ` 800 (on ` 1200) because of sales to households from the beginning to the end of the given year. Hence the net aggregate capital stock of all these firms together, ignoring depreciation, increased (decreased) by ` 200. In this case C + IH = ` 800 (` 1200) and IF = ` 200(IF = – ` 200).

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EXERCISE 2.3 Suppose in an economy in a given period households purchased goods and services worth ` 20,000. Firms purchased goods worth ` 10,000 and added to the stock. However, all the firms together produced goods and services worth ` 35,000 (` 25,000). They, therefore, could not sell (had to sell) ` 5000 worth of goods (from their inventory) and had to hold them in their inventory, i.e. their inventory increased (decreased) involuntarily by ` 5000 in the given year. What is IF in this case? Will the identity (2.8) of the text hold in this case? Give reasons for your answer.

2.3.4

Incorporation of the Government

We now extend the framework of our analysis to incorporate government’s economic activities even though the economy is still assumed to be closed. The government undertakes different kinds of economic activities such as production, collection of taxes, making transfer payments, and paying subsidies. Let us discuss each of these activities in turn. Governments in all countries produce certain goods, referred to as social or public goods, which are not and/or cannot be bought and sold in markets. Examples of these goods are: national defence, administration (maintenance of internal law and order), roads, etc. We do not buy the services of national defence or administration. Similarly, we do not purchase the services of roads provided by the corporations, municipalities or panchyats. The government in India—both the central government and state governments—produces not only social goods, but also goods that are bought and sold in markets such as electricity, transport services, steel, machinery, etc. Government-owned firms can thus be divided into two categories, viz. those which supply their products free of charge or at non-remunerative prices to the households and firms and those which charge remunerative prices for their products. All the firms belonging to the former category together are referred to as government administration and defence, while government-owned firms of the latter category are called public sector enterprises (PSEs). Government collects taxes. One of the main objectives of tax collection is to defray the cost of provision of social goods. There are other objectives too. However, they need not be discussed in the present context. Taxes are broadly divided into two types—direct taxes and indirect taxes. Direct taxes are taxes on individuals, while indirect taxes are taxes on goods. Examples of direct taxes are income tax, wealth tax and gift tax, which are all imposed on individuals. Sales tax, excise duty (tax on manufacturing) and customs duty (tax on imports) are examples of indirect taxes. These taxes are imposed on sales, manufacturing and imports of different types of goods and services. Government also gives monetary assistance to firms that are engaged in the production of socially desirable goods such as education, healthcare, and foodgrains. This monetary assistance is called subsidy. Many of the private educational institutes in India receive large amounts of subsidy from the government. Government also makes transfer payments, i.e. payments made to those persons who are either unable to earn any income owing to old age, physical infirmity, inadequate demand for labour, etc., or victims of natural calamities, accidents, etc. Pension payments to disabled soldiers and retired government servants, unemployment doles, grants given to the people of a state hit by a natural calamity, and so on are examples of transfer payments.

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How do these activities affect the methods of national income accounting? In order to explain this, we focus on the value added method first.

Value added method for a closed economy in the presence of government activities Value added, as we have explained above, gives the true value of a firm’s production. Hence the GDP of a country in a given year identically equals the sum of GVAs in the given year of all the firms located within the geographical boundary of a country. In the presence of government, as we have seen above, there are three categories of firms in an economty, viz. private firms, public sector enterprises, and government administration and defence. Accordingly, GDP º Sum of gross value addeds of all private firms or private sector enterprises + sum of gross value added of all pubic sector enterprises + gross value added of government administration and defence

(2.10)

Products of public sector enterprises are bought and sold in the market at market prices. Hence the gross value added of a public sector enterprise can be calculated in the same way as that of a private firm, which is alternatively referred to as a private sector enterprise. The gross value added of government administration and defence cannot be calculated applying the usual method since most of its products do not have a price. Hence the value added of government administration and defence is evaluated at cost. Note that the GVA of a firm, as we have already shown in (2.2), is equal to the aggregate factor payments made to the households by the firm. Hence, the GVA of government administration and defence could be taken to be equal to the aggregate factor payments made to the households by government administration and defence. However, by convention, only wages and salaries paid to households by government administration and defence are taken into account in computing its GVA, i.e. the GVA of government administration and defence is taken to be equal to the wages and salaries paid by government administration and defence to households. Moreover, NVA and GVA are taken to be the same. Interest and rent payments to households by government administration and defence are excluded from its GVA. Thus, there is no value added or production corresponding to interest and rent payments to households by government administration and defence. Hence these payments cannot be said to have been made for any kind of productive service rendered. These payments, therefore, are regarded as transfer payments and not as factor payments. Thus, in the presence of government: GDP of a country in a given year º sum of gross value added of private and public sector enterprises located within the country in the given year + wages and salaries in government administration and defence in the given year

(2.11)

EXERCISE 2.4 Suppose that in an economy in a given year there existed three firms: a private firm, a public sector enterprise, and government administration and defence. The private firm in the given year

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produced goods and services worth ` 1000, purchased intermediate inputs worth ` 200 from the public sector enterprise and paid to households ` 500 as wages, interest and rent. Depreciation of its capital stock was ` 50. The public sector enterprise produced goods and services worth ` 1500 and paid ` 500 to households in wages, rent and interest. It also bought intermediate inputs worth ` 300 from the private firm. Depreciation of its capital stock was ` 100. Government administration and defence purchased goods and services worth ` 1000 from the other two firms. It paid ` 600 in salaries and wages and ` 500 in interest to households. Compute the GVA and NVA of each of these firms and thereby compute the GDP and NDP of the economy in the given year.

Income method in a closed economy in the presence of government In the presence of government activities, subsidies constitute a source of income of the firms besides the value of the output. On the other hand, indirect taxes constitute an additional component of their cost. Let us illustrate these points with examples. Suppose that a farmer in a given year grew 100 kg of paddy and sold it at ` 10 per kg. He also received a subsidy from the government at the rate of ` 1 per kg. His cost of producing 100 kg of paddy, excluding depreciation in the given year, was ` 8000. We shall clearly not get the gross profit of the farmer by deducting from the value of his output the cost of production exclusive of depreciation. This is because for producing 100 kg of rice he received from the government ` 100 as subsidy. Hence to calculate his gross profit, we have to add to the value of his output the subsidy of ` 100 that he received from the government and then subtract from this sum the cost of producing 100 kg of paddy. Similarly, consider the case of a producer of cigarettes. Suppose there is an excise duty at the rate of ` 1 per cigarette produced. This means that he has to pay ` 1 to the government as excise duty for every cigarette he produces. Hence it should be reckoned as a part of the cost of production of every cigarette. If the tax were imposed on sales of cigarettes, the amount of sales tax paid per cigarette should have been reckoned as a part of the cost of production of every cigarette sold. Suppose that cigarettes are produced with imported tobacco and there is customs duty at the rate of 10 percent on import of tobacco. So, if the cigarette manufacturer imports tobacco worth ` 1000, he has to pay ` 100 as customs duty to the government. The customs duty of ` 100 should therefore be regarded as a part of the cost of production of the cigarettes produced with this tobacco. Indirect taxes paid by every firm in a given year for producing or selling the output of the given year should therefore be regarded as a part of the cost of production of the output of the firm in the given year. Therefore, identity (2.1) gets modified in the following way: Gross profit of a private (public) sector enterprise in a given year º value of output of the enterprise in the given year + subsidy received by the enterprise from the government in the given year – indirect taxes paid by the enterprise to the government in the given year for producing or selling the output of the given year – [wages + interest + rent ] paid by the enterprise to the households in the given year – value of intermediate inputs used by the enterprise in the given year

(2.12)

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Macroeconomics

From (2.12), it follows that GVA of a private (public) sector enterprise in a given year º gross profit of the enterprise in the given year + [wages + rent + interest] paid by the enterprise to the households in the given year + net indirect taxes paid by the enterprise to the government in the given year for producing or selling the output of the given year

(2.13)

where Net indirect tax paid by the enterprise to the government in the given year º indirect tax paid by the enterprise to the government in the given year for producing and selling the output of the given year – subsidy received by the enterprise from the government in the given year

(2.14)

From (2.10) and (2.13), it follows that GDP of an economy in a given year º aggregate gross profit of all private and public sector enterprises within the geographical boundary of the economy in the given year + [wages + interest + rent] paid by all these enterprises together to households in the given year + aggregate net indirect taxes paid by all these enterprises to the government in the given year + wages and salaries paid to the households by government administration and defence of the given economy in the given year

(2.15)

EXERCISE 2.5 Consider the economy of Exercise 2.4. Suppose that the private firm in the given year received subsidy of ` 100 from the government and the public sector enterprise paid sales tax of ` 50 to the government in the given year. Compute the GDP and NDP of the economy in the given year using the income method.

Spending method We shall discuss here how the spending method of calculating GDP is modified following the incorporation of the government. Note first that government administration and defence by assumption do not make any investment. The stock of goods held by government administration and defence by convention is not regarded as its capital stock or a part of the capital stock of the economy. Hence a change in this stock is not regarded as investment. Public consumption or government consumption, denoted by G, is therefore defined as the value added of government administration and defence plus the purchase of goods and services of government administration and defence from private and public sector enterprises. This implies:

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21

G º wages and salaries in government administration and defence + value of goods and services purchased by government administration and defence from private and public sector enterprises (2.16) Investment in a closed economy with government is therefore made by the households and the private and public sector enterprises located within the geographical boundary of the economy. Let us first focus on the private and public sector enterprises. Just as in the earlier case, let IF denote the change in the stock of goods held by all private and public enterprises located within the geographical boundary of a given economy together from the beginning to the end of a given year without allowing for the depreciation of the goods held in the stock of these enterprises. Clearly, IF gives the gross change in the stock of goods held by all these firms together in the given year or gross investment of all these enterprises together in the given year. Therefore: IF º total inflow into the stock of goods held by all these enterprises together in the given year – total outflow from this stock during the given year without allowing for depreciation

(2.17)

We have noted earlier that in a closed economy the only inflow into the stock of goods held by all the firms located within the geographical boundary of the economy together is their aggregate production or aggregate gross value added in the given year. The difference between the present case and the earlier case is that here we consider not all firms, but only private and public sector enterprises and these private and public sector enterprises can buy goods from government administration and defence and add to their capital stock. However, the latter supplies only services—think of defence, public administration, etc.—which cannot be held in stock. Moreover, government administration and defence by definition supply their output free of charge to other economic agents. Hence, even if a part of the output of government administration and defence consists of goods and is held by other firms in their capital stock, it is not regarded as constituting an addition to their capital stock. Hence, even in the presence of government administration and defence, the only inflow into the capital stock of all the private and public sector enterprises located within the geographical boundary together of a closed economy is the aggregate gross value added of these enterprises. Hence, (2.17) can be rewritten as IF º Aggregate gross value added of all the private and public sector enterprises together in the given year – sales made by these enterprises together to other economic agents in the given year

(2.18)

Now, Sales by all private and public sector enterprises together to other economic agents in a closed economy in a given year º sales by all these firms to households of the given economy in the given year (º C + IH) + sales to government administration and defence of the given economy (purchases of goods and services by government administration and defence from the private and public sector enterprise of the given economy) º G – wages and salaries of government administration and defence) in the given year (2.19)

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Macroeconomics

Substituting (2.19) into (2.18), we get IF º Aggregate GVA of all private and public sector enterprises of the given economy in the given year – (C + IH) – (G – wages and salaries of government administration and defence) (2.20) From (2.20), it follows that GDP º Aggregate GVA of all private and public sector enterprises + wages and salaries of government administration and defence º IF + (C + IH) + (G – wages and salaries of government administration and defence) + wages and salaries of government administration and defence º C + IF + IH + G

(2.21)

Note that government administration and defence by assumption do not make any investment. If they hold a part of their output or purchases in their stock, it is regarded as a part of public consumption, G. Hence aggregate gross investment of an economy in a given year, denoted by I, is the sum of the gross investment of the households of the given economy in the given year, denoted by IH, and the gross investment of the private and public sector enterprises of the given economy in the given year, denoted by IF. Therefore, I º IH + IF

(2.22)

From the last two identities, it follows that GDP º C + I + G

(2.23)

Thus it is possible to calculate GDP by summing up the consumption and investment expenditures made by the households, investment expenditure made by the private and public sector enterprises and the consumption expenditure made by the government administration and defence. This is the spending method of calculating GDP. These expenditures are referred to as final expenditures. EXERCISE 2.6 (a) Consider the police force of a country. Its job is to maintain law and order of the country. Suppose that in a given year it spent ` 10 lakh in interest on its outstanding loan, ` 20 lakh in wages and salaries, ` 10 lakh on stationery, fuel and power and acquired buildings, equipment and cars worth ` 30 crore. What is its GVA in a given year? Did it contribute anything to G and transfer payments of government administration and defence? Explain your answers. (b) Suppose that in a given year in a closed economy with government, private and public sector enterprises produced goods and services worth ` 10 lakh, i.e. their aggregate GVA in the given year was ` 10 lakh. They sold in the same year goods and services of ` 8 lakh to households and ` 5 lakh to government administration and defence. Besides, government administration and defence paid ` 10 lakh in wages and salaries, and ` 1 lakh in interest to households. What is the aggregate gross investment of the firms in the given year? Explain. Calculate the GDP of the economy by the spending method. Explain each step.

National Income Accounting

2.3.5

23

National Income Accounting in an Open Economy

In an open economy, domestic economic agents can buy goods, services, factor services, and physical and financial assets from foreigners. Similarly, foreigners can also buy all these from domestic economic agents. The objective here is to examine how the methods of national income accounting are modified when these transactions are taken into account.

The value added method As before, the gross value added gives the true value of a firm’s production inclusive of depreciation. Accordingly, the GDP of a country in a given period is given by the aggregate gross value added of all the domestic private and public sector enterprises located within the geographical boundary of the country plus wages and salaries in government administration and defence in the given period. The only point to note is that some of the intermediate inputs used by the domestic firms may have been purchased from foreign firms. To understand the implication, we consider an example. Suppose an automobile is produced by a domestic firm using intermediate inputs supplied by other domestic firms. In this case, the GDP of the economy includes the full value of the automobile. If, on the other hand, some of the intermediate inputs are imported, then the GDP of the economy contains the value of the automobile net of the value of the imported intermediate inputs. EXERCISE 2.7 Consider an open economy where two firms, Firm 1 and Firm 2, existed in a given period. Firm 1 in the given period produced wheat of ` 1000 using imported feritilizer of ` 200. Firm 2 used the output of wheat of Firm 1 and also imported wheat of ` 2000 to produce bread of ` 5000. Is the GVA of each of the two firms the true value of its production? What is the GDP of the given economy in the given period? Explain your answers.

The income method Gross profit of a firm from the output of a given year is defined as the value of the output of the given year net of the cost of production exclusive of depreciation of the given output irrespective of whether the firm is located within the geographical boundary of a closed or an open economy. Therefore, identity (2.12) gives the definition of gross profit of a private or public sector enterprise for an open economy also. The only point is that in an open economy some of the intermediate inputs may be imported (i.e. purchased from foreign countries). Similarly, some of the factors of production used by a domestic firm may also be owned by residents of foreign countries. Let us illustrate this with a few examples. India imports petroleum and petroleum products, which are used as intermediate inputs almost in every industry. Some of the Indian firms are also allowed to borrow from the international credit market. Interests on these loans are paid to lenders who are residents of foreign countries. These Indian firms use these loans to buy capital goods and other inputs. They, therefore, are said to employ foreign capital. Foreign firms dealing in financial assets, referred to as foreign institutional investors (FIIs), are allowed to buy

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shares of Indian firms. Firms use the proceeds from the sale of shares to buy capital goods and other inputs and they pay dividends to the shareholders in return for the services rendered by these inputs. These services are regarded as services of capital. Hence dividends paid to FIIs are in return for services of capital purchased with the proceeds from the sales of shares to the FIIs. These services are accordingly regarded as being rendered by capital owned by foreigners. Dividends paid to FIIs are therefore factor payments made to foreigners. From the above it follows that the GVA of a private or a public sector enterprise of an open economy and hence the GDP of an open economy continue to be given by (2.13) and (2.15), respectively. The only difference is that a part of the factor payments may be paid to foreigners. EXERCISE 2.8 Consider the example given in Exercise 2.7. Suppose that, in addition to the expenditures noted above, Firm 1 paid wages and salaries of ` 200, interest on its outstanding loans, which it took from foreigners only, of ` 100, and Firm 2 paid dividend of ` 100 to foreigners and wages and salaries of ` 200. Find out the GDP of the economy using the income method.

The expenditure method Aggregate stock of goods held by all domestic private and public sector enterprises together can increase in an open economy not only because of production but also owing to imports. Thus, inflows into the aggregate capital stock of these enterprises consist of current production or aggregate GVA of all these enterprises and all kinds of imports made by these enterprises in the given period. The total import made by these enterprises in a given period is denoted by MF. Outflows, ignoring depreciation, on the other hand, consist of sales by all these enterprises together to domestic households, domestic government and foreigners in the given period. Now: Sales by domestic private and public sector enterprises together to domestic households in a given period º purchases by domestic households from domestic private and public sector enterprises in the given period º C + IH – MH

(2.24)

Let us explain identity (2.24) along with the notations. (C + IH) represents value of aggregate purchase made by domestic households in the given period from both domestic private and public enterprises and foreigners (we shall henceforth use the term ‘foreigners’ to refer to economic agents, i.e. households, firms and governments, located abroad) and MH denotes the value of purchases made by domestic households in the given period from foreigners. Accordingly, the value of purchases of goods and services of domestic households from domestic private and public sector enterprises in the given period is given by C + IH – MH. Similarly: Sales to domestic government by domestic private and public sector enterprises in a given period º purchases by domestic government from domestic private and public sector enterprises in the given period º G – wages and salaries in government administration and defence – MG

(2.25)

National Income Accounting

25

Let us explain identity (2.25) along with the notations. G denotes the value of total purchases made by domestic government administration and defence from both domestic private and public sector enterprises and foreigners in the given period plus wages and salaries in the domestic government administration and defence. MG, on the other hand, stands for value of goods and services purchased by the domestic government administration and defence in the given period from foreigners. Hence the value of purchase of goods and services made by domestic government administration and defence from domestic private and public sector enterprises in the given period is given by [G – wages and salaries in domestic government administration and defence – MG]. Sales by domestic economic agents to foreigners are nothing but exports, which we denote by X. These inflows into and outflows from the aggregate capital stock of the domestic private and public sector enterprises are shown in Figure 2.3.

Figure 2.3

Sources of change in the capital stock in an open economy.

Clearly, gross change in the aggregate capital stock of all the private and public sector enterprises located within the geographical boundary of the country from the beginning to the end of a given period, denoted by IF, is given by the total inflow into the aggregate capital stock of these enterprises during the given period net of the total outflow, excluding depreciation, from this capital stock during the given period. Thus: IF = [Aggregate GVA of all private and public sector enterprises in the given period + MF] – [(C + IH – MH) + (G – MG) + X)] + wages and salaries in domestic government administration and defence

(2.26)

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Macroeconomics

Let us illustrate identity (2.26) with a simple example. Suppose that an economy has just one firm within its geographical boundary and it produces only cars. It also uses imported components to produce the car. Suppose that, in a given year, it produced just one car. To produce one car it required foreign components worth ` 50,000. However, it imported components worth ` 1 lakh in the given year. It sold the car in the same year to another economic agent at ` 1 lakh. Its GVA in the given year was therefore ` 50,000. Inflows into its stock in the given year accordingly were its GVA of ` 50,000 and imports of ` 1 lakh. Its outflow, on the other hand, ignoring depreciation, was the sale of the car at ` 1 lakh to another economic agent. Let us now examine how its capital stock changed in the given year. As it sold out the whole of its output, no part of its output was added to the stock. However, it imported components worth ` 1 lakh, half of which went into the production of the car that was sold out. The remaining half of the imported components remained with the firm. Hence, its capital stock in the given period went up by ` 50,000, i.e. the gross investment of the firm in the given year was ` 50,000. You can easily see that this is nothing but the excess of total inflow into the firm’s capital stock in the given year (which is the GVA of ` 50,000 + imports of ` 1 lakh) over the total outflow from its capital stock in the given year (which is ` 1 lakh). To get a clearer picture, consider the above example again. However, make just one change. Suppose that the firm sold in the given year nothing to other economic agents. In this case, clearly, gross increase in the capital stock of the firm in the given year is given by the total inflow of ` 1.5 lakh into its capital stock consisting of its GVA of ` 50,000 and imports of ` 1 lakh. The firm, since it did not sell anything to other economic agents in the given year, had to hold its produced car of ` 1 lakh and imports of ` 50,000, which it did not use to produce the car, in its stock. Hence, again, gross investment of the firm in the given year is given by the excess of the total inflows into its capital stock over the total outflow. To gain more conviction, again consider the first example with just one change. Suppose that the firm, though produced in the given year just one car of ` 1 lakh, sold in the given year two cars at ` 1 lakh each to other economic agents. Obviously, one of the cars was sold out of the inventory of the firm. Let us now calculate its gross investment. It sold a car of ` 1 lakh from its inventory. This reduced its capital stock by ` 1 lakh. It sold out the whole of its output. Of its total imports, half went into the production of the car sold out. This part of its import therefore went out of its stock. It held, therefore, the remaining half of the imports of ` 1 lakh. Its capital stock in the given year, therefore, went down by ` 1 lakh as it sold out a car of ` 1 lakh from its inventory. On the other hand, as it added half of its total imports of ` 1 lakh to its inventory, its capital stock went up by ` 50,000. Its gross investment was, therefore, – ` 50,000 in the given year. You can easily see that this is nothing but the excess of total inflow of ` 1,50,000 (consisting of GVA of ` 50,000 + imports of ` 1 lakh) in the given year net of the total outflow from its capital stock (which is ` 2 lakh, the value of the two cars sold out) in the same year. From (2.26), it follows that {Aggregate GVA of all private and public sector enterprises + wages and salaries in government administration and defence} º C + (IH + IF) + G + X – (MH + MF + MG)

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27

The above identity in turn implies that GDP º aggregate GVA of all private and public sector enterprises + wages and salaries in government administration and defence ºC + I + G + X – M

(2.27)

where M º MF + MH + MG º total imports of the economy, i.e. the total amount of foreign goods purchased by all the domestic economic agents, viz. domestic private and public sector enterprises, domestic government administration and defence and domestic households, together in the given period. EXERCISE 2.9 In a given period in an economy, all the domestic private and public sector enterprises produced goods and services worth ` 10,000, i.e. the sum of their GVAs was ` 10,000. They imported goods worth ` 10,000, the whole of which was used as intermediate inputs in the given year. They also sold to non-firm economic agents goods and services worth ` 10,000. What is the aggregate gross investment of these enterprises? Explain. (Hint: The value of sales includes the value of the imported intermediate inputs used in the production of goods and services sold. If the given enterprises had sold the whole of their output, the value of their sales would be the GVA of ` 10,000 plus the value of the intermediate inputs used, which is also ` 10,000. Similarly, if these given firms had sold half of their output in the given year, value of their sales in the given year would have been half of their aggregate GVA plus half of the value of the intermediate inputs used. Consider the example where there is just one firm in an economy producing just one car of ` 1 lakh in a given year using imported intermediate inputs of ` 50,000. The firm also sold the car to a household in the given year. Its GVA in the given year is clearly ` 50,000, but the value of its sales is ` 1 lakh, which is the GVA of the firm plus the value of intermediate inputs used in the production of the good sold. Value of sales therefore, gives us the GVA of the goods and services sold plus the value of the imported intermediate inputs used in the production of the goods and services sold. Accordingly, (aggregate GVA + the aggregate value of imports) of the domestic private and public sector enterprises in a given year minus the value of sales of these enterprises in the given year gives us the aggregate GVA of the goods unsold plus the value of the imported goods used in the production of these unsold goods plus the value of all the imported goods not used as intermediate inputs in the given year, i.e. it gives us the gross aggregate investment of these enterprises in the given year.)

2.4

MEASURES OF PRODUCTION

There are several measures of aggregate production of an economy. GDP and NDP are only two of them. We shall discuss some of these measures here. However, we shall start with a discussion on GDP and NDP.

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2.4.1

Gross Domestic Product (GDP) and Net Domestic Product (NDP)

GDP is not an accurate index of aggregate production. This is because it does not take into account the wear and tear of the economy’s capital stock that take place during the period under consideration. Before proceeding further, it may be instructive to make clear what is meant by capital stock. It is defined as a stock of only those goods which yield future income. Since all the goods held in stock by private and public sector enterprises will be used by them to earn income in future, these enterprises’ entire stock of goods is defined as their capital stock. Government administration and defence does not earn any income as it provides its services either free of charge or at a price much less than the average cost of production. Hence the stock of goods it owns does not yield any future income. Accordingly, the stock of goods in the possession of government administration and defence is not regarded as capital stock. Since investment is defined as addition to capital stock, i.e. addition to the stock of goods that will yield income in the future, government administration and defence does not make any investment expenditure. All the expenditures of public administration and defence, except for interest or rent payment, are public consumption. Interest and rent are payments for services of capital, i.e. they are payments for services of income-yielding goods. Since public administration and defence does not own or use any income-yielding good (as it does not earn any income), its interest and rent payments are not regarded as factor payments but as transfers. To be consistent, rent and interest paid by government administration and defence are not regarded as a part of the value added of government administration and defence. Had rent and interest payments been a part of the value added of government administration and defence, this part of the value added would have been due to the services rendered by the stock of goods held by government administration and defence and, therefore, rent and interest payment should have been regarded as factor payments, i.e. payments for the contribution of this stock of goods to production or value added of government administration and defence. This is the reason why interest and rent are not included in the value added of government administration and defence. The only issue yet to be explained is why rent and interest payments are not regarded as a part of public consumption. The services rendered by government administration and defence are provided free of charge to the people. In other words, these services are consumed collectively by the community. Since these services do not have a price, what is the value of this collective or public consumption? Conventionally, this in a given year is taken to be the total expenditure of government administration and defence except for payments of interest and rent. How does one explain this omission? It is quite easy to do this. Consider the identity between GDP and aggregate final expenditure as given by (2.27). GDP includes the value added of government administration and defence, which is given by only wages and salaries in government and defence. Public consumption is given by G on the RHS of (2.27). If G includes payments of interest and rent, the RHS of (2.27) will exceed the LHS by the amount of interest and rent payment by government administration and defence. This is the reason why these payments are not included in G. Capital stock of households is defined as the stock of houses they own. The stock of durable consumer goods owned by households is not regarded as a part of the capital stock of households. Of the goods the households use and own, only houses have well-developed rental markets. A

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29

household can hire out his house and earn rent from that. Rental markets for consumer durables are yet to develop. Hence it is not possible for households to rent out their consumer durables and thereby earn income in future. Accordingly, only stock of houses owned by households is regarded as their capital stock. In any given period, goods held in the capital stock of firms and households, as they are used in production of the given period, wear off and thereby lose a part of their productivity. Hence, to get the true value of aggregate production of an economy in a given period, one has to subtract from its GDP of the given period the value of wear and tear of the goods held in its capital stock. The latter is referred to as depreciation. Depreciation is also alternatively referred to as capital consumption allowance. The NDP of an economy in a given period, which is defined as GDP of the given economy in the given period net of depreciation of its aggregate capital stock in the same period is, therefore, a more accurate measure of aggregate production. Table 2.1 shows the figures of GDP, capital consumption allowance, and NDP of India from 1995–1996 to 2005–2006. Table 2.1 India’s GDP, NDP and NNP (` crore) Year1

GDP

Consumption of fixed capital (depreciation)

NDP

NFIA

NNP

1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006

1191813 1378617 1527158 1751199 1952036 2102375 2281058 2458084 2765491 3126596 3250932

114655 132179 147709 166289 185593 206295 232452 254767 284702 332490 379200

1077158 1246438 1379449 1584910 1766443 1896080 2048606 2203317 2480789 2794106 2871732

–13484 –13082 –13205 –14968 –15437 –22733 –20068 –16690 –18250 –22375 –24969

1063673 1233356 1366244 1569942 1751006 1873347 2028538 2186626 2462538 2771730 3163007

Net indirect taxes

117906 125224 135116 165510 176960 180871 192780 216073 270663 316245

Source: RBI 1

Year refers to financial year, which starts from 1st April of a given calendar year and ends on 31st March of the following calendar year. Thus, year 1995–96 refers to the financial year that starts from 1st April, 1995 and ends on 31st March, 1996. In India, values of economic variables are recorded over financial years and not over calendar years.

EXERCISE 2.10 (a) Suppose that Ram owns two houses, which have the same design and space and are located next to each other. He lives in one and rents out the other at an annual rent of ` 20,000. He also has to spend ` 1000 annually for the repair and maintenance of each of the two houses. How much does each of the two houses contribute annually to the GDP and NDP of the country where they are located? How does each of the three

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methods of computing GDP capture the value of services rendered by these two houses as a part of GDP? Explain. (b) Consider a closed economy with just one private firm and government administration and defence producing all the goods and services. The former produced in a given year goods and services worth ` 20,000. The latter provided its output free of charge to people. It paid ` 5000 in wages and salaries. The firm houses from the households and paid them rent of ` 5000, and also borrowed from them and paid them interest of ` 1000. Besides, the firm purchased goods worth ` 5000 from the private firm. Households purchased goods and services worth ` 13,000 from the private firm. Rents paid by households living in rented houses to the households owning them was ` 2000 and imputed rent of the owner-occupied houses was also ` 2000. Compute GDP by value added method. Also compute GDP by the spending method. What exactly is the problem that arises if you include rent and interest payment of government administration and defence in government consumption? Explain.

2.4.2 Domestic Products and National Products The GDP and NDP of a country in a given year are defined respectively as gross and net values of all the goods and services produced by all the firms located within the geographical boundary of the country together in the given year. All the economies in the world are open. The recent spate of globalization has made most of the economies more open than ever. As we have already mentioned, in open economies, domestic economic agents, i.e. economic agents located within the geographical boundary of the domestic economy, can buy foreign produced goods and services, foreign factor services and foreign financial and physical assets. Similarly, foreign economic, agents, i.e. economic agents located outside the geographical boundary of the domestic country, can also buy domestically produced goods, domestic factor services and domestic physical and financial assets. As a result, in open economies, foreign factors of production, i.e., factors of production owned by economic agents located or resident abroad contribute to domestic production, while domestic factors of production, i.e. factors of production owned by economic agents located or resident in the domestic country, participate in foreign production. In this scenario, gross and net values of all the goods and services produced by domestic factors of production the world over in a given year is likely to differ from the given year’s domestic country’s GDP and NDP, respectively, and it may be important to know how much goods and services domestic factors of production have produced in a given year in the world economy. Hence, the concepts of Gross National Product (GNP) and Net National Product (NNP) have been introduced. The latter is nothing but GNP net of depreciation of the domestic capital stock. GNP and NNP of an economy in a given year are defined, respectively, as the gross and net values of all the goods and services produced by the factors of production owned by the residents of the given economy in the given year in the world economy. The reason why GDP and GNP (and therefore NDP and NNP) can differ in an open economy is quite clear. Firms within the geographical boundary of the domestic economy can hire foreign capital. They can sell their shares, bonds, debentures, etc., to foreigners and use the funds raised to buy productive assets and inputs for production. This amounts to using services of foreign capital to produce

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31

goods and services. The contribution of these foreign factors to the GDP of the domestic economy is measured by the factor income the foreign factors earn in return for their contribution to the production of the domestic economy. Thus, the part of domestic economy’s GDP, which is produced by the factors of production owned by the residents of the domestic economy in a given year, is given by the GDP of the domestic economy in the given year net of the factor payments made to the foreign factors of production in return for their contribution to domestic production of the given year. Similarly, the part of foreign GDP of a given year produced by factors of production owned by residents of the domestic economy is given by the factor payments made by foreigners to these factors of production for their contribution to foreign production of the given year. It should be noted that only factor incomes remitted to foreign countries are subtracted from and factor incomes remitted from foreign countries to the domestic country are added to the GDP of the domestic country to get the GNP of the domestic country. Thus, for example, if a company owned by Indians operates in the US and makes profit, but does not remit any part of it to India, then neither that profit is added to India’s GDP in computing its GNP, nor it is subtracted from the GDP of the US to compute its GNP. This gives us the following identity: GNP of an economy in a given year º GDP of the economy in the given year – factor income paid (and remitted) by firms of the given economy to foreigners for the contribution of their factors of production to the GDP of the given economy in the given year – factor income paid (and remitted) by foreigners to factors of production owned by residents of the given economy for their contribution to the foreign GDP of the given year

(2.28)

NNP, on the other hand, is given by the following identity: NNP of an economy in a given year º GNP of the economy in the given year – Depreciation of the aggregate capital stock of the given economy in the given year

(2.29)

For figures of net factor income from abroad and NNP of India, see Table 2.1. EXERCISE 2.11 Suppose that some Indian shareholders of some companies in Japan earned in a given year ` 20,000 in dividend from the Japanese companies and these companies in the given year distributed all their profits. In the same year, the Japanese companies operating in India made a profit of ` 50,000 and distributed only half of it as dividend to its Japanese shareholders. How will you use this information to compute India’s and Japan’s GNPs from their respective GDPs? Substantiate your answer.

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2.5 PRODUCTION AND INCOME Production and income, as we have seen above, are closely related to each other. In fact, in the case of a closed economy without government, the whole of the NDP accrues to the owners of factors of production as factor income. However, for an open economy with government, NDP and the aggregate factor income are different on account of net factor income from abroad, indirect taxes and subsidies. Hence we need a separate measure of aggregate income that residents of a country earn from production. The commonly used measure of this is national income (NI). National income of a country in a given year is defined as the aggregate factor income earned by the factors of production owned by the residents and the government of the country for their contribution to world production in the given year. National income is closely related to NNP. From identities (2.13), (2.27) and (2.28), it follows that the only part of the NNP of a country that does not go into the hands of residents and the government of the country as factor income consists of the indirect taxes that the firms located within the geographical boundary of the country pay to the government. Hence, they constitute a part of the value of the goods and services produced in the world economy by the factors of production owned by the residents and the government of the domestic economy, but they do not accrue as factor income to these factors of production. We also find that, besides NNP, there is another source of factor income for these factors of production. It is the subsidies that the firms within the geographical boundary of the country receive from the country’s government. These subsidies accrue as additional profit to the owners of these firms. The relationship between NNP and NI is therefore given by the following identity: NI of a country in a given year º NNP of the country in the given year – Net indirect taxes paid by the firms located within the geographical boundary of the country to the government for the production of the country of the given year

(2.30)

Alternatively, NI is referred to as NNP at factor cost. If we add depreciation of the aggregate capital stock to NI, we get GNP at factor cost. If we subtract net indirect taxes from GDP and NDP, we get GDP at factor cost and NDP at factor cost, respectively. EXERCISE 2.12 (a) Consider a hypothetical economy, where in a given period, two firms, Firm 1 and Firm 2 existed. Firm 1 produced wheat of ` 2000, paid ` 1500 in wages and ` 100 in subsidy from the government. Firm 2, on the other hand, produced bread of ` 4000 using the whole output of Firm 1, paid ` 3000 in wages, and ` 200 as sales tax to the government. Break up the GVA of each firm into its income components. Is the subsidy received by Firm 1 a part of its GVA? How much factor income originates in Firm 1? Is it equal to its GVA? If not, then by how much does it differ from its GVA? (b) Calculate the values of NNP at factor cost or NI from the data given in Table 2.1 for each of the years from 1995–1996 to 2005–2006.

National Income Accounting

2.6

33

DIFFERENT CONCEPTS OF INCOME, SAVING AND INVESTMENT

National income is a measure of a country’s residents’ income from production. However, production is not the only source of their income. They get assistance from the government in their old age or when they are physically handicapped or when they fall victims to natural calamities or man-made accidents. These incomes are referred to as transfer incomes. Similarly, residents of a country can receive gifts from foreigners. These incomes are referred to as foreign transfers. Personal income (PI) is a country’s residents’ income, which includes both, factor income (i.e. income from production) and all kinds of transfers. Personal income of a country in a given year is defined as aggregate factor income and transfers actually received by the residents of the country in the given year. In the above definition, the words “actually received by the residents” should be taken into account. The whole of the NI of a country of a given year, except for the profit of the public sector enterprises, accrues to the residents of the country in the given year, but they may not actually receive the whole of it. Consider the profit of the joint stock companies or corporations. The whole of it belongs to the shareholders and is a part of the NI. But the corporations may not distribute the whole of it. So the shareholders may not actually receive the undistributed profit of the corporations though it belongs to them. Similarly, profit of the public sector enterprises is a part of national income, but it is paid to the government and not to the individuals since public sector enterprises are owned by the government. Again, transfers, as they are not factor income do not constitute a part of NI. But they are a part of personal income, since the residents receive them as income from the government and foreigners. In fact, there are three components of NI of a country that the residents of the country do not receive. These are the profit of the public sector enterprises, undistributed profit of the corporations, and the corporation income tax or corporate tax that the corporations pay to the government. In every country, corporations’ income is regarded separately from their owners’ and is therefore taxed separately along with their owners’ income. The tax on corporations’ income is referred to as corporation income tax or corporate profit tax or just corporate tax. The part of the corporations’ profit that is paid out as this tax is not received by the shareholders. The relationship between NI and personal income is therefore given by the following identity: Personal income of a country in a given period º NI of the country in the given period – profit of the public sector enterprises of the country in the given period – undistributed profit of the corporations or the retained profit or income of the corporations of the country in the given period – the corporate profit tax payable from the profit of the corporations of the country in the given period + transfer income received by the residents of the country from the government of the country in the given year + tansfer income received by the residents of the country from the foreigners in the given year

(2.31)

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Macroeconomics

Business transfers Transfer payments are made by businesses or firms as well. Firms in a country may give donations to, for example, the victims of war, natural calamities and accidents, meritorious poor students, etc. These payments are referred to as business transfers. Obviously, business transfers are paid out of the value added of the firms and, therefore, they reduce the profit of the firms. In the presence of business transfers, profit of a firm in a given year is calculated by deducting, from the value of output of the firm in the given year and the subsidy received by the firm in the given year, not only the cost of producing the output but also the business transfers made by the firm in the given year. Business transfer made by a firm in a given year is therefore a part of its GVA and NVA of that year, but it is not a part of its factor payments. This is because it is not paid in return for any kind of factor service. Business transfers made in a given year in a given economy, as parts of the GVA and NVA of the firms located within the geographical boundary of the economy in the given year, are components of the GDP and NDP of the economy of the given year, but they are not a part of the NI of the economy of the given year. Business transfers are received by the residents of the country. Hence they are a part of the PI of the country. Thus, components of GDP and personal income in the presence of business transfers are given by the identities (2.32) and (2.33), respectively. GDP of an economy in a given year º Aggregate gross profit of all private and public sector enterprises within the geographical boundary of the economy in the given year + [wages + interest + rent] paid by all these enterprises to households in the given year + aggregate net indirect taxes paid by all these enterprises to the government in the given year + aggregate business transfers made by all these enterprises together in the given year + wages and salaries paid by the government administration and defence of the given economy in the given year

(2.32)

Personal income of a country in a given year º NI of the country in the given year – undistributed profit of the corporations located within the geographical boundary of the country in the given year – corporation income tax paid by these corporations in the given year – profit of the public sector enterprises in the given year + transfers made by the government of the country to the residents of the country in the given year + transfers made by foreigners to the residents of the country in the given year – transfers made by the residents of the country to the foreigners in the given year + business transfers made by the private and public sector enterprises located within the geographical boundary of the country to the residents of the country in the given year

(2.33)

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35

Personal income of a country in a given year gives the total amount of income that the residents of the country actually receive in the given year. However, they cannot use the whole of it for purposes of consumption and saving. In every economy, residents’ income, wealth and gifts are taxed. These taxes, which are referred to as personal taxes, the residents have to pay from their incomes. Hence to get a measure of the total amount of income that the residents can use for purposes of consumption, saving etc., their personal taxes have to be deducted from their personal income. This measure is called personal disposable income. It is given by the following identity: Personal disposable income of a country in a given period º personal income of the country in the given period – personal taxes paid by the residents of the country in the given period

(2.34)

Saving and investment An individual allocates her personal disposable income between consumption and saving. Aggregate saving of all the individuals of a country taken together is referred to as personal saving. Personal saving is defined as the excess of personal disposable income over aggregate consumption of the residents of a country. We thus get the following identity: Personal saving of a country in a given year º personal disposable income of the country in the given year – personal consumption of the country in the given year

(2.35)

Besides domestic households, there are two other types of economic agents in a country, namely the firms located within the geographical boundary of the country and the government of the country. Even though firms’ income belongs to their owners, corporations’ income is regarded separately from their owners’, as there is alienation between management and ownership in the case of joint stock companies. Even though corporations’ income belongs to their shareholders, they reserve the right not to distribute the whole of their profit to the shareholders. They can retain a part of it. In the case of non-joint stock companies, which are referred to as proprietorship firms, their income forms a part of their owners’ and, therefore, the issue of their saving as distinct from that of their owners does not arise. In the case of corporations, however, a clear distinction is made between their income and their owners’ and, therefore, between their saving and that of their owners. Saving of the firms, which is referred to as business saving, consists solely of the saving of the corporations, which in turn is defined as the undistributed profit or retained earning of the corporations. We thus get the following identity: Business saving of a country in a given year º undistributed profit or retained earning of the corporations located within the geographical boundary of the country in the given year

(2.36)

Government saving is defined as the excess of government’s revenue receipts over government’s revenue expenditure. The former consists of receipts from taxes, profit of public sector enterprises,

36

Macroeconomics

and non-tax receipts such as fees. The revenue expenditure of the government, on the other hand, consists of its consumption, G, transfer payments, interest payment on government loans and subsidies. Thus we get the following identity: Government saving of a country in a given year º its receipts from taxes in the given year + profit of the public sector enterprises in the given year + its non-tax receipts such as fees in the given year – its consumption, G in the given year – subsidies it paid in the given year – transfer payments it made in the given year – interest it paid on its loans in the given year

(2.37)

Note that value added in government administration by convention consists solely of wages and salaries in government administration and defence and does not include interest payment of the government. Thus there is no value added or production corresponding to government’s interest payment. Hence it cannot be regarded as factor payment. It is, therefore, treated on the same footing as government’s transfer payment. Aggregate national saving is defined as the sum of personal saving, business saving and government saving. Thus we have the following identity: Aggregate national saving of a country in a given year º personal saving of the country in the given year + business saving of the country in the given year + government saving of the country in the given year

(2.38)

Suppose T º total revenue receipts of the government net of subsidies º total receipts from both direct and indirect taxes + profit of public sector enterprises + receipts from non-tax sources, Rg º total transfer payments of the government including interest payments on government loans, Rb º business transfers, Rf º net foreign transfers received (defined as total foreign transfers received by the domestic households of the country net of the transfer payments made by the domestic households of the country to foreigners), pu º undistributed profit of the corporations and S º aggregate national saving, we can rewrite (2.38) as S º (NNP + Rf + Rg – T – pu – C) + (pu) + (T – Rg – G) Note that Direct taxes º Corporate taxes + Personal taxes

(2.39)

Again, it follows from (2.28)–(2.31) and (2.33)–(2.35), that Personal disposable income º NNP + Rf + Rg – T – pu

(2.40)

National Income Accounting

Hence,

Personal saving º (NNP + Rf + Rg – T – pu – C)

37

(2.41)

Moreover from (2.36) and (2.37), we get Business saving º pu Government saving º T – Rg – G

(2.42) (2.43)

Also note that Rb does not figure anywhere in (2.37) because it is included in NNP. In case domestic government gives and receives foreign transfers, net foreign transfers received by the domestic government is to be added to T to compute government saving. Previously, governments of underdeveloped countries (now called developing countries) used to get aid from governments of rich countries (or developed countres). Even now, poor countries ravaged by major natural calamities receive aid from other countries. From (2.39), it follows that S º NNP + Rf – C – G

(2.44)

Identity (2.44) shows that aggregate national saving of a country in a given period is nothing but the excess of the sum of the NNP and net foreign transfers received by the residents of the country in the given period over the personal and public or collective consumption of the country in the given period. Let us interpret (2.44) in detail. (NNP + Rf) of a country in a given year gives the total amount of goods and services produced and received as gifts from foreigners by the residents of the country in the given year. It therefore gives the total amount of goods and services at the command of the economic agents of the economy in the given year. They can utilize this amount of goods and services without borrowing from the foreigners. Aggregate national saving gives the excess of this amount of goods and services over personal and public consumption. We know that NNP of a country in a given year is nothing but the NDP of the country in the given year plus net factor income received from abroad (NFIA) by the domestic economic agents of the country in the given year. We denote the latter by NFIA. Thus, NNP = NDP + NFIA

(2.45)

Substituting (2.27) into (2.45) and then putting it into (2.44), we get S œ I  [NFIA  R f  ( X  M )]

(2.46)

where I º Net investment º I – Depreciation. We shall now explain (2.46). Let us first focus on the second term within the square brackets on the RHS of (2.46). [NFIA + Rf + X] gives the value of foreign exchange in terms of the country’s currency received by the given country in the given period by selling produced goods and services and factor services to the foreigners and also by way of transfers from the foreigners, while M stands for the value of foreign currency in terms of the country’s currency paid by the country to foreigners for purchasing their produced goods and services. The excess of the former over the latter is referred to as current account surplus of the country in the given period. Let us examine the implications of current account surplus. First note that foreigners need the currency of the domestic country to purchase domestic country’s goods and services. They procure this currency by selling their own currency in the foreign exchange market where

38

Macroeconomics

currencies of different countries are bought and sold for one another. Similarly, the domestic country also buys foreign currency to purchase foreign goods by selling their own currency in the foreign exchange market. Thus, when the domestic country has a current account surplus, value of its export earning exceeds the sum of its payments for its imports, the net factor payment to foreigners and net payment of foreign transfers. In other words, in the period under consideration, the domestic economy receives from foreigners more domestic currency in return for its exports than what it pays to foreigners in return for imports of produced commodities and as net foreign transfers and net factor payments. Since the domestic economy is the sole creator of its currency, foreigners can pay to the domestic economy more domestic currency for purchasing domestic economy’s produced goods than what it receives in return for its imports and by way of net factor payments to foreigners and net foreign transfers from the domestic economy only if they borrow from the domestic economy. Let us illustrate the point with an example. Suppose that, in 2006, India had a current account surplus of ` 100. It means that in 2006 India received from foreigners ` 100 more for its exports than the amount of rupees it paid to the foreigners that year for the imports and by way of net factor payments to foreigners and net foreign transfers. Since India is the sole creator of rupees, foreigners can secure the Indian currency without borrowing from India only from their imports to India and through net factor payments made by India to foreigners and India’s net foreign transfers to foreigners. Thus, in 2006, foreigners paid the extra ` 100 by borrowing from India. Similarly, when India has a current account deficit in a given year, i.e. when its current account surplus is negative in a given year—think over it yourself—it pays more foreign currency to foreigners for its imports of foreign produced goods than what it receives from foreigners for its exports of produced goods and by way of net factor payments and net foreign transfers to India by foreigners. Hence, in the given year, India has to borrow a sum equal to its current account deficit from foreigners to finance its current account deficit. We are now in a position to interpret (2.46). It shows that a country can utilize its national saving, the excess of the total amount of goods and services at its command over and above its private and public consumption, in two ways. It can either invest it or lend it out to foreigners or both. When the country has a current account deficit, it borrows from abroad to invest more than its national saving. Obviously, when net investment of a country in a given year exceeds national saving, the total amount of goods it uses in the given year for purposes of private consumption, public consumption and net investment exceeds the total amount of goods net of depreciation that the country has produced and received by way of net foreign transfers and thereby it can use without borrowing from abroad. Hence, in the given year, the country has borrowed the excess of its net investment over its national saving from foreigners. More precisely, the country in the given year has borrowed the excess of its private consumption, public consumption and net investment over (NNP + Rf). Thus, the foreign goods purchased with foreign borrowing need not necessarily be utilized for investment alone. They may be used for purposes of private and public consumption as well. Two other concepts of saving may be introduced at this stage—gross domestic saving (GDS) and net domestic saving (NDS). They are defined as follows:

and

GDS º GDP – C – G

(2.47)

NDS º NDP – C – G

(2.48)

National Income Accounting

39

Interpret GDS and NDS yourself. How are GDS and NDS related to gross national saving and net national saving respectively? Table 2.3 gives the figures of India’s gross domestic saving and its composition as percentages of India’s GDP. When we break up GDS into government saving, business saving and personal saving, definitions of the first two are the same as those in (2.42) and (2.43) respectively. Personal saving, however, is defined excluding NFIA and Rf. If we refer to this definition of personal saving by domestic personal saving, we get it by subtracting from the RHS of (2.41) NFIA and Rf. Thus Domestic personal saving º NDP + Rg – T – pu – C

(2.49)

Table 2.3 shows that India saved of late more than one-third of its GDP and the households are by far the most important source of saving in India contributing from 70 per cent to 85 per cent of GDS during the period under consideration. (Exercise: Compute in percentage terms shares of different components of saving in GDS). From the identity, GDP º C + I + G + X – M, we find that GDS is used either for gross investment in the domestic economy or for giving away to the foreigners in the form of trade surplus, X – M, or both. From Table 2.2 we find that, every year during the period under consideration, India’s I exceeded her GDS. This means that every year India had a trade deficit, which in turn implies that every year India used a part of the domestic saving of the rest of the world over and above her own GDP, i.e. every year she used more goods and services than what she produced within her geographical boundary and the excess of the amount of goods and services she used over her GDP in any given year was exactly equal to the excess of her gross investment over her GDS in the given Table 2.2

India’s NI, PDI, GDS1 and I2 (` crore)

Year

NI

Personal disposable income

GDS (% of GDP)

I (% of GDP)

1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006

958679 1119238 1244980 1438913 1589672 1647903 1743466 1805830 1963544 2104520 2306894

956193 1141407 1260027 1470397 1614591 1758613 1143509 2058550 2291632 2453380 2772575

24.4 22.7 23.8 22.3 24.8 23.7 23.5 26.4 29.8 31.8 34.3

26.2 24.0 25.3 23.3 25.9 24.3 22.8 25.2 28.2 32.2 35.5

Source: RBI: Handbook on Indian Economy 1 2

GDS refers to gross domestic saving I, which denotes aggregate gross investment, is also referred to as gross domestic capital formation.

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Macroeconomics

Table 2.3 Components of India’s GDS as percentages of GDP Year

HS1

BS2

GS3

Total

1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005 2005–2006

16.9 16.0 17.7 18.8 21.1 21.6 22.1 23.2 24.4 23.0 24.2

5.0 4.5 4.3 3.9 4.5 3.9 3.4 3.9 4.4 6.6 7.5

2.6 2.2 1.8 –0.5 –0.8 –1.8 –2.0 –0.6 1.1 2.2 2.6

24.5 22.7 23.8 22.2 24.8 23.7 23.5 26.5 29.9 31.8 34.3

1

HS—household saving. BS—business saving. 3 GS—government saving. 2

year. X represents the part of the domestic economy’s GDP that is sold to the rest of the world, while M represents the part of the rest of the world’s GDP that is bought by the domestic economy. Clearly, if X exceeds M, the domestic economy is utilizing less goods and services than what it produces and its use of goods and services is less than its GDP by (X – M). Obviously, the rest of the world uses more goods and services than what it produces and the excess of its use of goods and services over its GDP, denoted by GDP*, is given by (X – M). Note that the rest of the world’s exports, denoted by X*, is nothing but M, while the rest of the world’s imports, denoted by M*, is nothing but X. This relationship may also be alternatively shown as follows. From the basic GDP identities, we get GDP + GDP* º C + I + G + X – M + C* + I* + G* + X* – M* º C + I + G + C* + I* + G* From the above identity and the definition of gross domestic saving, it follows that GDS – I º I* – GDS*

(2.50)

where GDS* º gross domestic saving of the rest of the world. Obviously, the excess of GDS over I in any economy gives the excess of the GDP of the given economy over the amount of goods and services used by the economy in the given period. EXERCISE 2.13 (a) Consider the following figures (all given in ` crores) of an economy in a given year. NNP = ` 10,000, X = ` 200, NFIA = ` 10, M = ` 200, and net foreign transfers from abroad = ` 50. (i) How much goods and services can the domestic economic agents

National Income Accounting

41

enjoy in the given year without borrowing from foreigners? Explain. (ii) What is the value in terms of rupee of the foreign exchange received by the country without borrowing in the given year? (iii) What is the value in terms of rupee of the foreign exchange paid by the country for purchasing produced goods and services from abroad? (iv) Is the country using all the goods and services that it can use without borrowing from foreigners? Explain. (v) Suppose that the NDP of the rest of the world in the given period was ` 30,000. How much goods and services could the foreigners use without borrowing from the domestic economy? How much goods and services did they actually use and how much did they borrow from the domestic economy? (vi) Is the domestic economy allowing foreigners to use more goods and services than what they have at their command by giving them credit? In other words, relate your answers to (iv) and (v). (b) Using the data given in Tables 2.1 and 2.2, compute the values of gross national saving and net national saving of every year from 1995–1996 to 2005–2006.

2.7 BALANCE OF PAYMENTS Every country has a balance of payments account (BOP account). BOP account of a country of a given year records all the payments made by foreigners to domestic economic agents and all the payments made by domestic economic agents to foreigners in the given year. It has two sides, a debit side and a credit side. All the payments made by foreigners to domestic economic agents are recorded on the credit side, while all the payments made by domestic economic agents to foreigners are recorded on the debit side. Domestic economic agents need to be paid in domestic currency. An Indian living in India, for example, needs to be paid in rupees. If, for instance, an American tourist comes to India and tries to pay for her travel, boarding, etc., with dollar, she will fail to do so. She will have to first go to a foreign exchange dealer, a person whose job is to buy and sell currencies of different countries of the world, and buy rupee with dollar. The foreign exchange dealer is a participant in the foreign exchange market where currencies of different countries of the world are bought and sold at market determined prices. In this market, price of every currency is quoted in terms of every other currency and currency of every country can be bought with the currency of any other country at the market price of the currency bought in terms of the currency sold. If the price of dollar at a point of time is 48 rupees, one dollar at that point of time will buy 48 rupees, i.e. the sale of one dollar for rupee at that point of time will fetch 48 rupees. We shall show shortly how the price of a currency is determined in terms of any other currency. Since only domestic currency is acceptable to domestic economic agents, to make payments to them, foreigners have to first buy the domestic currency by selling their own currencies. Similarly, to a foreigner only the currency of his own country is acceptable. Hence to make payments to foreigners, domestic economic agents have to first buy foreign currencies of the foreigners’ respective countries by selling their own currency. Domestic economic agents (foreigners) make payments to foreigners (domestic economic agents) if they (i) purchase produced goods and services from foreigners (domestic economic agents), (ii) purchase factor services from foreigners (domestic economic agents), (iii) make transfer payments, i.e. give

42

Macroeconomics

gifts, make remittances, etc. to foreigners (domestic economic agents), and (iv) purchase financial assets such as shares, debentures, and bank deposits, as also physical assets such as houses, land, mines and forests from foreigners (domestic economic agents). Of the four transactions noted above, transaction (iv) has a distinctive feature, viz. it directly adds to the domestic country’s future receipts from and payments to foreigners. For example, if a domestic economic agent buys bank deposit in a bank located in Bangladesh, she will receive interest on her deposit in future. So, India’s future receipt from foreigners will go up. Again, if a resident of Sri Lanka buys bank deposits of a bank located in India, the bank will pay the depositor interests in future periods. India’s future payments to foreigners will therefore go up. Similarly, if an Indian resident buys a house or land in Pakistan, she can earn rent in future by renting it out. Accordingly, the BOP account is divided into two segments, viz. current account and capital account. The former records the first three kinds of transactions, (i), (ii) and (iii), with the foreigners. These three types of transactions have no direct bearing on the future receipts from and payments to foreigners of the domestic economy. The transactions that have, i.e. the transactions listed against (iv) above, are recorded in the capital account. Let us briefly discuss about current and capital account transactions. The sale of produced goods and services to foreigners and purchase of produced goods and services from foreigners are referred to as export and import of produced goods and services, respectively. Similarly, sale of factor services to foreigners and purchase of factor services from foreigners are referred to as export and import of factor services, respectively. How does the domestic economy sell factor service to foreign countries? Let us illustrate it with an example. Suppose that an Indian resident holds shares of a company located in USA. Accordingly, she gets dividend from the firm. Firms use the proceeds from the sale of the shares to purchase produced means of production or capital and pay dividend for the productive services provided by them. The dividend paid to the Indian resident by the US-based firm is the price of the service rendered by the capital purchased with the proceeds from the sale of the shares to the Indian. This dividend is therefore a payment for the purchase of factor services and is recorded on the credit side of the current account. If the dividend is paid in dollar, the Indian (since she cannot buy anything with dollar in India) will sell the dollar in the foreign exchange market to buy the rupee. Similarly, if an Indian holds his savings in a deposit with a bank located in USA, the interest the bank pays him is a factor payment for the service provided by the bank deposit, which is a part of the bank’s capital. Let us elaborate. A bank takes deposits and lends them out. The excess of the interest that it receives from its loans over the interest that it pays to its depositors constitutes its profit or income. Thus, the main productive asset that a bank uses to earn its income or to produce the service it renders, namely, securing savings from the savers and making them available to deserving borrowers, is the deposits. (The service provided by a bank is referred to as financial intermediation, since it acts as an intermediary between economic agents who have surplus funds and the economic agents who need funds to make investment and consumption expenditures). Hence, deposits constitute the main component of a bank’s capital stock. Again, if an Indian resident owns a house or a piece of land in Nepal and rents it out, the rent she receives is a payment for the sale of the service rendered by the house or the piece of land. The service is a factor service and payment for the purchase of this factor service is recorded on the credit side of the BOP account.

National Income Accounting

43

Transfer payments to foreigners mean giving gifts to foreigners. Let us illustrate this with an example. Suppose that an Indian gets a job in USA. She migrates to USA and takes up the job. If she sends a part of her income to her parents who are residing in India, the remittance is treated as a transfer payment made by a foreigner to Indians and is recorded as a credit item in the current account of India’s BOP account. Similarly, if a US citizen works in India and sends a part of her income to her parents residing in USA, the remittance will be treated as a transfer payment made by an Indian resident to foreigners and will be recorded on the debit side of the BOP account. (Exercise: How will these remittances be treated in the BOP account of USA?) Since Indian residents cannot use dollar for purchasing goods and services in India, either the foreigners making transfer payments to the Indians will have to first buy rupee by selling dollar and then make the payment or the Indian residents receiving these remittances will have to sell the dollar received to buy rupee. If the sum of the items on the credit side of the current account exceeds the sum of the items on its debit side, the excess of the former over the latter is referred to as current account surplus. In the opposite case, the excess of the sum of the items on the debit side over the sum of the items on the credit side is referred to as current account deficit. Table 2.4 presents the balance of payments of India of the year 2005–06. Let us focus on the current account first. The items on the current account are broadly divided into two categories—merchandise and invisibles. The former refers to only produced goods as distinct from produced services or factor services. The invisibles consist of three items: non-factor services (i.e. produced services), incomes (which mean payments received from the sale of factor services and payments made for the purchase of factor services), and, finally, transfers received from and given to foreigners. We find that in 2005–06, India had a deficit in trade in merchandise and a surplus in trade in invisibles, and a current account deficit of ` 40,722 crore. Purchases and sales of physical and financial assets by domestic economic agents to and from foreigners are recorded in the capital account of the BOP account of a country. The sales of these assets, which are alternatively referred to as import of capital, are recorded on the credit side, while the purchases of these assets, alternatively referred to as export of capital, are recorded on the debit side. The sales of financial assets (e.g bank deposits, shares, debentures) to foreigners amount to taking loans from foreigners. Similarly, the purchases of financial assets from foreigners amount to giving loans to foreigners. Note that, to purchase physical and financial assets from foreigners, domestic economic agents have to first buy foreign currencies by selling domestic currency and vice versa. If the sum of the items on the debit side of the capital account exceeds (falls short of) the sum of the items on the credit side, there is a deficit (surplus) on the capital account. As shown in Table 2.4, items on the capital account of India’s BOP account are divided into five broad categories—foreign investment, loans, banking capital, rupee debt service and other capital. Foreign investment has two components—foreign direct investment (FDI) and foreign portfolio investment. The former consists of foreigners setting up production facilities or expanding existing production facilities in India or buying Indian companies or purchasing so many shares of an Indian company that they are gaining control over the company. If an individual buys more than 50 per cent of the shares of a joint stock company, he gains management control over the company. When foreigners make foreign direct investment, it is recorded as a credit item. When they do just the opposite, i.e. when they sell off Indian companies they bought earlier or sell off their controlling stakes of Indian corporations,

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Macroeconomics

Table 2.4

India’s balance of payments during 2005–06 (` crore)

A.

Credit

Debit

Net

1. Merchandise

465705

695131

–229426

2. Invisibles (a + b + c) (a) Non-factor services1 (b) Income2 (c) Transfers

409200 272220 25124 111856

220496 166601 49712 4183

188704 105619 –24588 107673

Total current account (1 + 2)

874905

915627

–40722

1. Foreign investment (a + b) (a) FDI3 (b) Portfolio investment4

337301 35213 302088

260982 14251 246731

76319 20962 55357

2. Loans5

166208

139650

26558

95988

90193

5795

0

2557

–2557

28979

32125

–3146

628476

525507

102969

B.

Current account

Capital account

3. Banking capital

6

4. Rupee debt service7 5. Other capital Total capital account (1 to 5) C.

Errors & Omissions

D.

Overall balance

E.

Monetary movement Foreign exchange reserve (– increase, + decrease)

3649

0

3649

1507030

1441134

65896

0

65896

–65896

1

Non-factor services consist of travel, transportation, insurance, software services, business services, financial services, communication services, etc. 2 Income consists of both investment income and compensation of employees 3 FDI (foreign direct investment) consists of foreigners building production facilities in India or buying controlling stakes in Indian companies. 4 It consists of foreigners buying and selling in Indian shares and securities market without gaining control over any Indian company. 5 Loans consist of external assistance, external commercial borrowing, and short term loans to India. The last item refers to suppliers’ credit. 6 It consists mainly of Indian commercial banks’ lending to foreigners, investing in foreign assets and receiving deposits from foreigners. 7 India has outstanding loans with Russia, which India could service with rupee. Rupee debt service refers to the debt service payments by India on this loan.

it is recorded as a debit item. External commercial borrowing (ECB) refers to borrowing by Indian companies from international credit market. The distinction between ECB and foreign

National Income Accounting

45

investment is that the latter refers to real or financial investment by foreigners in Indian money and capital markets, while the former consists in Indian companies taking loans from foreign money and capital markets. Inflow of loans through ECB is recorded on the credit side and repayment of loans taken through ECB is recorded on the debit side. ‘Short term to India’ refers to short term credit given by foreign suppliers to Indian importers and buyers’ credit provided by Indian importers who make advance payments for imports to foreigners. Suppose an Indian company buys intermediate inputs from a foreign company on a three-month credit, i.e. the foreign company allows the Indian company to pay for the intermediate inputs bought three months later. This is a three-month supplier credit given by the foreign company to the Indian company. Inflow of supplier’s credit is a credit item, while buyer’s credit provided by Indian importers to foreigners is recorded as a debit item. ‘Banking capital’ refers to inflow of NRI and foreigners’ deposits into Indian commercial banks and acquisition of foreign assets by Indian commercial banks. When NRIs or foreigners deposit their savings in Indian commercial banks, these inflows are recorded as credit items. When Indian commercial banks purchase foreign financial assets, the outflows are recorded as debit items. Let us now focus on rupee debt service. India took loans from the erstwhile Soviet Union and these loans, unlike other foreign loans, could be serviced with rupee. ‘Rupee debt service’ refers to debt service payments made by India on these loans. These payments are obviously recorded on the debit side. Other capital consists of leads and lags in export. Advance payments by foreigners for export, referred to as leads in export, are loans (short term) or buyers credit and are recorded on the credit side. Similarly, delayed payments by foreigners for imports, referred to as lags in export, are suppliers credit given to foreigners and are therefore recorded on the debit side. Is there any relationship between the sum total of the debit items and that of the credit items taking the current account and the capital account together in the BOP account? The answer is yes. The two sides are always equal. Let us explain. Domestic economic agents are the only source of domestic currency to the foreigners, while foreigners are the only source of foreign exchange to the domestic economic agents. Receipts from foreigners, as you would recall, mean sale of foreign exchange for domestic currency, while payments to foreigners mean purchase of foreign currency with domestic currency. If the total of payments to foreigners in a given period exceeds the total of receipts from foreigners, it means that domestic economic agents in the given period have purchased more foreign exchange with domestic currency than what the foreigners have sold for domestic currency. Clearly, that is impossible since foreigners are the only source of foreign exchange to the domestic economic agents. For similar reasons, total payments to foreigners cannot be less than the total of receipts from foreigners either. Argue it yourself. This means that, if there is a surplus on the current account, there is an exactly equal amount of deficit on the capital account and vice versa. There is, however, one caveat here. The central bank of every country carries a stock of foreign exchange. It often buys foreign exchange with domestic currency or sells foreign exchange for domestic currency in the foreign exchange market to keep the exchange rates stable. Every foreign currency has an exchange rate. Exchange rate of a foreign currency means the price of the foreign currency in terms of the domestic currency. Exchange rates of dollar, Euro and pound sterling, for example, were ` 42.73, ` 66.97 and ` 84.38 respectively on 26 June 2008.

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Macroeconomics

Suppose that the Reserve Bank of India (RBI) wants to keep the exchange rate of dollar at ` 40. If at this exchange rate there is excess demand for dollar, i.e. if at this exchange rate domestic economic agents want to buy more dollar with rupee than what the US residents want to sell for rupee, exchange rate will rise. The RBI can prevent the rise of the exchange rate of dollar by selling dollar for rupee from its foreign exchange reserve. Similarly, if there is excess supply of dollar, i.e. if the US residents want to sell more dollar for rupee than what the Indian residents want to buy, the exchange rate tends to fall. The RBI can stop this decline by buying the excess supply of dollar with rupee and adding it to its foreign exchange reserve. Therefore, when the central bank intervenes in the foreign exchange market, the total of the items on the debit side in the current and capital account taken together may exceed (fall short of) that on the credit side, i.e. there may be a BOP deficit (surplus) taking the current and capital account together. But in that case, the foreign exchange reserve of the central bank will fall (rise) exactly by an equal amount. In a country where the central bank intervenes in the foreign exchange market, there is a third segment in the BOP account. This is referred to as the official settlement account. In this account a fall in the central bank’s foreign exchange reserve is recorded on the credit side, while addition to the central bank’s foreign exchange reserve is recorded on the debit side. Thus, if there is an overall deficit (surplus) on the current and capital account taken together, there should be an equal amount of surplus (deficit) on the official settlement account. From Table 2.4 we find that, taking the current and the capital account together, there was an overall surplus of ` 65,896 crore. Accordingly, we find that there was an addition of the same amount to the RBI’s foreign exchange reserve. Recording of receipts from and payments to foreigners may involve errors and omissions. Thus, if there occurs any discrepancy between change in RBI’s foreign exchange reserve and the overall balance, taking the current and the capital account together, the discrepancy is recorded as “errors and omissions” so that the sum of the items on the credit side and that on the debit side become equal, when all the three segments are considered together.

2.7.1

Saving, Investment and Current Account Balance

Let us go back to (2.46). It shows that the excess of net investment over national saving of the domestic economy is identically equal to its current account deficit. We shall first show that the current account deficit of the domestic economy is in turn identically equal to the excess of national saving of the rest of the world over its net investment. Note that the total amount of goods and services available to the world in a given period is the NNP (or NDP) of the domestic economy plus the NNP (or NDP) of the rest of the world. We shall henceforth denote the former and the latter by NNP and NNP*, respectively. The total amount of goods and services at the command of the domestic economic agents, as we have already explained, is given by NNP plus Rf, which denotes net foreign transfers to domestic economic agents, while total amount of goods and services at the disposal of the foreigners is NNP* – Rf. This is because net foreign transfers received by the economic agents resident in the rest of the world, denoted by Rf*, is the net transfers received by the foreigners from the domestic economic agents, which is nothing but (–Rf). Thus, Rf* = – Rf (2.51)

National Income Accounting

47

The total amount of goods and services used by domestic economic agents and foreigners is given by (C + I + G) and (C* + I* + G*) respectively. Accordingly, domestic economy’s saving, S º NNP + NFTR – C – G < I means that the domestic economic agents in the given period used more goods and services than what they had at their command. This is obviously possible if foreigners had used less goods than what they had at their command in the given period and the gap between (NNP* – NFTR) – (C*+ I* +G*) œ S*  I* had exactly equalled the excess of (C + I + G) over (NNP + NFTR) in the given period. To derive this identity rigorously, let us start with the definition of: S* º NNP*  R f  C * G* º C*  I*  G*  X *  M *  NFIA*  R f  C *  G* º I*  X *  M *  NFIA*  R f

(2.52)

Note that export of the rest of the world is nothing but import of the domestic economy. Hence, X* = M

(2.53)

Similarly, import of the rest of the world is nothing but the export of the domestic economy to the rest of the world, i.e. M* = X

(2.54)

NFIA* º – NFIA

(2.55)

Obviously, Putting (2.53), (2.54) and (2.55) in (2.52), we get S * œ I*  M  ( X  NFIA  R f )

Þ

S*  I * œ M  ( X  NFIA  R f )

(2.56)

From (2.46) and (2.56), it follows that

S*  I * œ I  S

(2.57)

The total amount of goods and services available to the world population in any given year is NNP + NNP*. The domestic economy has in its command NNP + NFTR, while the amount of goods available to the rest of the world is NNP – NFTR. The amounts of goods used by the domestic economy and the rest of the world are respectively (C + I + G) and (C* + I* + G*). Clearly, if (C + I + G) exceeds (NNP + NFTR), the excess must come from foreigners and it can come foreigners only. This means that the excess of what domestic agants use over what the command, given by ( I  S ), must exactly equal the excess of what foreigners command over what they use, given by ( S*  I * ).

48

Macroeconomics

EXERCISE 2.14 (a) Consider the following information: NDP = ` 10,000, NDP* = ` 100,000, NFIA = ` 100, Rf = – ` 100, X = ` 200, M = ` 250. It is also given that the domestic economy did not engage in any kind of capital account transactions in the given year. How much produced goods and services are available to the world economy? How much goods and services are at the command of the economic agents of the domestic economy? How much produced goods and services do they use? If the central bank of the domestic economy intervenes in the foreign exchange market, by how much does its foreign exchange reserve change in terms of rupee. Explain your answer. (Hint: There is a current account deficit of [M – X – NFIA – Rf] = ` 50. The amount of goods and services at the command of the domestic economy in the given year was [NDP + NFIA + Rf]. = ` 10,000. It, however, ran a current account deficit of ` 50. This means that it used in the given year goods and services of ` 50 over and above the amount of goods and services at its command. It did not borrow in the given year. But, it paid foreign exchange of ` 250 to the foreigners, but received only foreign exchange of [X + NFIA + Rf] = ` 200 from foreigners Clearly, it was possible because the central bank of the domestic economy sold to the domestic economic agents foreign exchange of ` 50. Hence the central bank’s foreign exchange reserve in terms of rupee decreased by ` 50.) What is the value of (I – S) in case of the domestic economy? How much goods and services are at the command of the rest of the world? How much goods and services do they use? What is their current account deficit? What is the value of (S* – I*)? (b) From the data given in Table 2.4, can you say whether India in 2005–06 used more or less goods than what she had at her command and exactly how much more or less? Explain.

2.8

REAL AND NOMINAL GDP

The GDP of an economy in a given year gives the gross value of goods and services produced within the geographical boundary of the economy in the given year. Recall that the GDP of a given year is computed at the prices prevailing in the given year. More precisely, The GVAs of firms in a given year, the sum of which gives the GDP of the given year, are computed at the prices prevailing in the given year. It is of course true that, even during a given year, prices of goods and services change from one point of time to another. The GVAs of a given year are accordingly calculated at prices prevailing at some specific point of time in the given year. Hence, for an economy, the GDP over time can change because either (i) the quantities of goods and services produced in the economy have changed over time, (ii) the prices of the goods and services produced have changed over time or, (iii) both. It is in this context that the distinction between real and nominal GDP becomes important. Nominal GDP of a country in a given year gives the value of goods and services produced within the geographical boundary of the country valued at the prices prevailing in the same year. Comparing nominal GDPs of an economy of two periods, one may not always get the true picture of the change in the level of aggregate production from one period to the other for the

National Income Accounting

49

reason mentioned above. To give an example, consider a hypothetical economy having just one firm within its geographical boundary producing only three goods, 1, 2 and 3. Suppose x1, x2, x3 and p1, p2, p3 denote respectively the quantities produced and prices prevailing of these three goods in period t0. The GDP of the economy in period t0 is therefore {p1x1 + p2x2 + p3x3}. Since there is just one firm, the problem of double counting does not arise here. Suppose in a later period, t1, each production level remains the same only the prices double. Nominal GDP in period t1, is therefore (2{p1x1 + p2x2 + p3x3}) and it is double the nominal GDP of period t0. Change in nominal GDP from one period to another therefore does not give any idea as to by how much the aggregate level of production has changed. If, however, production levels in the two periods are valued at the same set of prices, the change in GDP will reflect only the change in the quantities of goods and services produced. If, for example, outputs of the three goods in both the periods are evaluated at the prices prevailing in either period t0 or period t1, the values of GDP in the two periods would remain unchanged and hence give the real picture of the level of aggregate production over the two periods. Real GDP of an economy in a given year is computed on the basis of prices prevailing in some specific year referred to as the base year. Real GDP of India in the year 2007 with the base year 2000 gives India’s GDP of the year 2007 evaluated at prices prevailing in the year 2000. This means that the GVA of every firm located within the geographical boundary of India in the year 2007 is computed using the prices prevailing in the year 2000 in calculating real GDP of India in the year 2007 with the base year 2000. Clearly, the figures of real GDP of a country over time reflect the change in the level of aggregate production of the economy over time. Table 2.5 gives figures of India’s GDP and aggregate private final consumption expenditure (which we denoted by C above) at constant prices, with 1999–2000 as the base year. When Table 2.5

Per capita income and consumption (in 1999–2000 prices) Income1

IX plan avg.3 X plan avg.4 2002–03 2003–04 2004–05 2005–06 2006–07 2007–08 1

Consumption2

`

Growth (%)

`

Growth (%)

19245 24156 20996 22413 23890 25696 27784 29786

3.4 6.2 2.2 6.8 6.6 7.6 8.1 7.2

12392 14677 13352 13918 14413 15422 16279 17145

3.0 4.3 1.1 4.2 3.6 7.0 5.6

Income is taken as GDP at market prices. Consumption is PFCE (Private Final Consumption Expenditure). Per capita is obtained by dividing these by population. 3 Ninth plan covers the period 1997–2001. 4 Tenth plan covers the period 2002–2006. 2

50

Macroeconomics

GDP and consumption are computed at constant prices, their growth reflects growth in aggregate production and that in real consumption. From Table 2.5, we find that during the Ninth Plan (1997–2001), GDP and consumption grew at the annual average rates of 3.4 per cent and 3.0 per cent respectively, while during the Tenth Plan their average annual growth rates were 6.2 per cent and 4.3 per cent respectively. In fact, the period covered by the Ninth Plan and the first year of the Tenth Plan constitute a period of slow growth. We refer to such periods as periods of recession. The period from 2003–04 to 2007–08 is one of high growth. Such periods are called periods of boom. In market economies periods of recession and those of boom alternate each other. One of the main objectives of macroeconomics is to explain why the rate of growth of GDP, instead of being stable, fluctuates erratically over time. It also searches for policies that may be adopted by the government to keep the growth rate stable at the maximum possible level. We shall turn to these issues in the next chapter. EXERCISE 2.15 Suppose in an economy in the years 2006 and 2007, there were only two firms, Firm 1 and Firm 2. Firm 1 produced milk and Firm 2 produced sweets. Firm 2 in both the years used the whole of Firm 1’s output to produce sweets. In 2006 and 2007, Firm 1 produced 100 litre and 200 litre of milk, while Firm 2 produced 30 kg and 60 kg of sweets respectively. Prices of a litre of milk in 2006 and 2007 were ` 10 and ` 15 respectively and those of sweets were ` 15 per kg and ` 20 per kg respectively. Compute nominal GDP of the economy for both the years. Compute the real GDPs of both the years with the base year (i) 2006 and (ii) 2007.

2.9

COMPOSITION OF INDIA’S GDP

It is standard to divide an economy into three sectors, namely agriculture and allied activities, industry and services. Allied activities consist of forestry and fishing. Table 2.6 gives share of each of these three sectors in India’s GDP. Industry consists of mining and quarrying, manufacturing (comprising food processing, manufacturing of beverages and tobacco products, clothing and textiles production units, machinery and equipment production units, chemicals production units and others), and finally, electricity, gas and water supply. Services consist of (i) construction, (ii) trade, hotels, transport and communication, (iii) financing, insurance, real estate and business services, (iv) community, social and personal services. Share of each sector in India’s GDP is computed in the following manner. Aggregate gross value added of any sector is given by the sum of GVAs of all the firms engaged in that sector. The sum of aggregate GVAs of the three sectors gives us the GDP. Dividing the aggregate GVA of any sector by India’s GDP and multiplying it by 100, we get the share of the given sector in GDP, i.e. the percentage of GDP that originates in the given sector. Historically, it has been found that the composition of GDP of a country changes with economic development of the country. In the early stage of development, the bulk of the GDP comes from agriculture. With economic development, agriculture dwindles in importance and the other two sectors become more and more important. India is no exception. The share of agriculture in India’s GDP declined from 55 per cent in 1950–51 to 19.7 per cent in 2005–06. On the other hand, shares of industry and services almost doubled from 10.6% and 33% in 1950–51 to 19.3% and 61.0% in 2005–06

National Income Accounting

51

Table 2.6 Composition of GDP: Sectoral shares Year

Agriculture and allied activities1

Industry2

Services3

1950–51 1960–61 1970–71 1980–81 1990–91 2000–01 2005–06

55.5 50.7 44.3 38.0 31.4 23.9 19.7

10.6 13.3 15.5 17.4 19.8 20.0 19.3

33.9 36.0 40.2 44.6 48.8 56.1 61.0

1

Allied activities consist of forestry and fishing. Industry consists of mining and quarrying, manufacturing: food, beverages and tobacco, clothing and textiles, machinery and equipment, chemicals and others, electricity, gas and water supply. 3 Services consist of construction, trade, hotels, transport and communication, financing, insurance, real estate and business services, community, social and personal services. 2

respectively. In the high income countries of the world in 2004, agriculture and allied activities constituted only 2% of GDP, while industry and services contributed 26% and 72% of GDP respectively. High income countries are those whose per capita GNP in 2004 was $10,066 or more. India belongs to the low income countries whose per capita GNP in 2004 was $825 or less. India’s per capita GNP in 2004 was $620. Average per capita GNP of the high income countries was therefore more than sixteen times that of India in 2004. India accordingly has a lot of catching up to do. In every country of the world government produces what we call the ‘social goods’. Social goods refer to those goods whose use is non-excludable. A good’s use is non-excludable, if its owner cannot prevent others from using the good. Suppose a person sets up a flood control facility to prevent an area from being flooded. Once the facility is put in place, everyone living in the area in question will enjoy its benefits. If the person who has set up the facility asks the beneficiaries to pay for the service and if the beneficiaries refuse, he cannot do anything to deprive them of the benefits of the facility as long as it exists. This is true of national defence, public administration, which maintains internal law and order of the country, etc. Obviously, private producers do not produce social goods. They are essential in every country and they are produced by the governments. In India, government produces not only social goods but also many other goods, which private producers can and do produce. Examples of these goods are steel, electricity, fuel, machinery, transportation, education, healthcare and even consumer durables. India is therefore a mixed economy, which is defined as one where both private producers and the government participate in the production of non-social goods. Table 2.7 shows that the public sector at present contribute more than one-fifth of India’s GDP, i.e. aggregate gross value added of government administration and defence and public sector enterprises constitutes more than 20 per cent of India’s GDP.

52

Macroeconomics

Table 2.7

Shares of the public sector and private sector in India’s GDP (Rupees crore)

Year

GDP at market prices

GDP1 of the public sector

Share of the public sector in GDP(%)

Share of the private sector in GDP(%)

1960–1961 1970–1971 1980–1981 1995–1996 1996–1997 1997–1998 1998–1999 1999–2000 2000–2001 2001–2002 2002–2003 2003–2004 2004–2005

27807 68645 134410 1529453 1645037 1711735 1817752 1952035 2030867 2136635 2216260 2402247 2602235

350117 517148 695361 348736 361505 397073 491219 457006 465149 492321 518787 544425 566788

7.94 13.27 19.33 23.63 21.97 19.06 27.02 23.41 22.9 23.04 23.41 22.66 21.78

92.06 86.73 80.67 76.37 78.03 80.94 72.98 76.59 77.1 76.06 76.59 77.34 78.22

Source: RBI: Handbook of Statistics on Indian Economy 1

GDP of the public sector means the aggregate gross value added of the public sector.

It may also be instructive to divide the economy into unorganized and organized sectors. The latter comprises government administration and defence, public sector enterprises and all non-agricultural private enterprises which are either registered or come under the purview of any of the Acts and/or maintain annual accounts and balance sheets. Unorganized sector, on the other hand, consists of all private agricultural farms and all private non-agricultural enterprises which are not regulated by any of the Acts and which do not maintain annual accounts and balance sheets. The unorganized sector is therefore the traditional sector comprising all private agricultural farms and small private enterprises of industrial and services sectors. The organized sector comprises the entire public sector (the sector owned by the government) and all large non-agricultural private enterprises. Table 2.8 shows the shares of the organized and the unorganized sector in India’s NDP. We find that the share of the unorganized sector is larger, but its share is falling steadily. The share of the organized sector rose from 36.8 per cent in 1993–94 to 43.3 per cent in 2003–04. This implies that the organized sector grew at a higher rate than NDP from 1993–94 to 2003–04. Let us explain. Suppose the share of the organized sector in NDP is denoted by Z. Then Y0 Z ; Y œ organized sector’s aggregate net value added and Y º NDP Y 0 Taking log on both sides of the above equation and then taking total differential, we have dZ Z

dY0 dY  Y0 Y

(2.58)

53

National Income Accounting

Table 2.8

Contributions of the organized (Orgd) sector and the unorganized (Unorgd) sector to the value added of major sectors of production and NDP 1993–94

Industry Agriculture, forestry and fishing Mining, manufacturing, electricity and construction Services NDP

2003–04

Orgd

Unorgd

Total

Orgd

Unorgd

Total

3.5

96.5

100.0

4.1

95.9

100

64.2

35.8

100.0

60.5

39.5

100

47.1 36.8

52.9 63.2

100.0 100.0

53.1 43.3

46.9 56.7

100 100

Source: CSO (2005): National Accounts Statistics 2005, May, Government of India

Let us interpret the LHS of the above equation first. dZ is the increase in Z. So (dZ/Z) expresses the increase in Z as a fraction of the initial value of Z. This is called the growth rate of Z. If we multiply this growth rate by 100, we express it as a percentage. Consider the figures of Table 2.8. We find that the initial value of Z (value of Z in 1993–94) was .368 and it rose to .433 in 2003–04. So the increase in Z was .065. This increase as a fraction of .368 is .177. Now .177 is the growth rate of Z during the period under consideration. If we multiply it by 100, we express the growth rate as a percentage. Thus there took place 17.7 per cent growth in Z from 1993–94 to 2003–04, i.e. the increase in Z that took place from 1993–94 to 2003–04 is 17.7 per cent of the value of Z in 1993–94. Similarly, (dY0/Y0) and (dY/Y) give the growth rates of the aggregate net value added of the organized sector and NDP respectively. It follows from Eq. (2.58) that positive growth rate of Z implies higher growth rate of the organized sector relative to that of the NDP and vice versa.

2.10 EMPLOYMENT AND UNEMPLOYMENT IN INDIA Table 2.9 gives figures of usual principal and subsidiary status (UPSS) employment and unemployment in India. UPSS employment and unemployment figures have a year as the reference period. Let us first explain the meaning of UPSS. A person is considered employed (unemployed) on usual status (US) if he was seeking work or available for work and got work (but did not get work) for the major part of the reference year. A principal worker is one whose sole job is to work. A subsidiary worker is one who has infirmities or other vocations, but seeks part time work out of compulsion. Examples of subsidiary workers are students, pensioners etc. UPSS employment figures give the total number of both principal and subsidiary workers who worked for the major part of the reference year. Table 2.9 shows that in 1993–94, 381.94 million principal and subsidiary workers sought work or were available for work and they constituted the labour force in 1993–94. In the given year 374.45 million principal and subsidiary workers worked for the major part of the year and they constituted the workforce. The rest did not work for the major part of the year. The sizes of the labour force and the workforce rose to 406.05 million and 397 million respectively in 1999–00 and to 469.06 million and 457.82 million

54

Macroeconomics

Table 2.9

Employment and unemployment in India (UPSS) 1993–94

1999–00

2004–05

In million Labour force1 Workforce2 Number of unemployed

381.94 374.45 7.49

1993–94 to 1999–00

1999–00 to 2004–05

Point-to-point annualized growth rate

406.05 397.00 9.05

469.06 457.82 11.24

2.23

2.39

1.03 0.98

2.93 2.89

Per cent Unemployment rate3

1.96

Source: Statement 4.1 of NSS Report No. 515 1

People who are working or seeking or available for work. People who are working. 3 Number of unemployed as percentage of the labour force. 2

respectively in 2004–05. In 1993–94, 1999-2000 and 2004–05 percentages of labour force unemployed (referred to as unemployment rates) were 1.96, 2.23 and 2.39 respectively. Unemployment rate therefore increased steadily in India from 1993–94 to 2004–05. The low rates of unemployment in India are quite surprising in view of the abundance of labour relative to natural resources and capital. We shall seek to explain this point shortly. Table 2.10 gives figures of labour force participation rates (LFPR) by gender and rural– urban location. It shows that during the period 1983–84 to 1993–94, 56 per cent of the rural male population and 33 per cent of the rural female population were in the labour force, while LFPR for urban males and urban females were 54.3 per cent and 16.5 per cent respectively. Table 2.10 also shows that LFPR was more or less stable during 1983–84 to 2004–05. Table 2.10

Labour force participation rate (LFPR)1 by gender and rural-urban location (Unit: per cent)

NSS Round

1983–84 to 1993–94 50th round 1993–94 to 1999–00 55th round 1999–00 to 2004–05 61st round

Rural

Urban

Male

Female

Male

Female

56.1 54.0 55.5

33.0 30.2 33.3

54.3 54.2 57.0

16.5 14.7 17.8

Source: Statement 4.1 of NSS Report No. 515 1

LFPR is the number of persons in the labour force per 1000 persons.

Table 2.11 gives allocation of employment over the three different sectors of the economy, namely industry, agriculture and services. Table 2.11 shows that in 1993–94, 1999–00 and

55

National Income Accounting

Table 2.11 Sectors

Employment (UPSS)1—sectoral shares

1993–1994 million

1999–2000

2004–2005

per cent

million

per cent

million

per cent

Agriculture, forestry and fishing Mining and quarrying Manufacturing Electricity, gas and water supply Construction Trade, hotels and restaurants Transport, storage and communication Financing, insurance, real estate and business services Community, social and personal services

242.46

64.8

237.56

59.8

267.57

58.4

2.70 42.50 1.35

0.7 11.3 0.4

2.27 48.01 1.28

0.6 12.1 0.3

2.74 53.51 1.37

0.6 11.7 0.3

11.68 27.78

3.1 7.4

17.62 37.32

4.4 9.4

25.61 47.11

5.6 10.3

10.33

2.8

14.69

1.7

17.38

3.8

3.52

0.9

5.05

1.3

6.86

1.5

32.13

8.6

8.4

35.67

7.8

Total employment

374.45

100

33.2 397.00

100

457.82

100

Source: NSSO 61st round survey and Report of the Taskforce on Employment Opportunities, Planning Commission 1

Usual principal and subsidiary status. A person is considered unemployed on usual status (US) if he was seeking work or available for work but did not get work for the major part of the reference year. A principal worker is one whose sole job is to work. A subsidiary worker is one who has infirmities or other vocations, but seeks part time work out of compulsion. Examples of subsidiary workers are students, pensioners, etc. UPSS employment figures give the total number of both principal and subsidiary workers who worked for the major part of the reference year. Besides UPSS, NSSO uses two other measures of unemployment, viz. current weekly status (CWS) and current daily status (CDS) unemployment. CWS uses a week as the reference period. This measure considers a person unemployed, if he/she did not work even for an hour during the reference week, but was seeking work or available for work during the reference week. Current daily status (CDS) unemployment also has a week as the reference period. It gives the total person days of unemployment, i.e. aggregate of all the unemployed days of all the persons in the labour force during the reference week.

2004–05, agriculture employed 64.8 per cent, 59.8 per cent and 58.4 per cent of the workforce respectively; industry comprising mining and quarrying, manufacturing and electricity, gas and water supply employed 12.4 per cent, 13 per cent and 12.6 per cent of the work force respectively and the services sector comprising the remaining sub-sectors shown in Table 2.11 employed 22.8 per cent, 25.2 per cent and 29 per cent respectively. It is clear that even though agriculture contributes only about 20 per cent of India’s GDP, it employs about 60 per cent of the workforce. It is by far the largest provider of employment.

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Macroeconomics

Table 2.12 gives figures of employment for the organized sector comprising the modern large-scale production units. We find that it employed only 6.89 per cent and 5.64 per cent of the labour force in 2000 and 2005 respectively. Moreover, employment in both the organized private sector and public sector declined in absolute number from 2000 to 2005. This is all the more surprising in view of the data given in Table 2.8, which shows that from 1993–94 to 2003–04 the organized sector grew at a faster rate than the NDP, while the unorganized sector grew at a slower rate than NDP. It follows from Table 2.8 and Table 2.12 that even though the organized sector contributes about half of India’s NDP, it employs less than 7 per cent of India’s labour force and growth in the organized sector is accompanied by a fall in its employment. Thus a high rate of growth of the unorganized sector is absolutely essential for providing India’s growing labour force with employment and income. Table 2.12

Estimates of employment in organized private and public sectors Unit: Lakh persons as on March 31st of the year

Year (1)

Public (2)

Private (3)

Total (4)

1999 2000 2001 2002 2003 2004 2005

194.15 193.14 191.38 187.73 185.80 181.97 180.07

86.98 86.46 86.52 84.32 84.21 82.46 84.52

281.13 279.60 277.89 272.06 270.00 264.43 264.58

Total as percentage of labour force (5)

6.89

5.64

Source: Columns (2)–(4) have been obtained from Ministry of Labour and Employment (DGE&T). Column (5) has been calculated using these data and the data on labour force.

Table 2.13 divides the workforce into three categories—self-employed, casual labour and regular wage/salaried. The last one refers to the workers who are in permanent employment. Casual labour refers to those workers who are not in any kind of permanent employment. They work on a daily basis. They are not tied to any firm. Every day they have to look for work and only on the days on which they find work, they get paid. On the days on which they do not get any work, they do not earn anything. Self-employed are those who carry out productive or income-yielding activities on their own. Hawkers, farmers cultivating their own land, businessmen running business establishments, artisans manufacturing artifacts on their own are all selfemployed. The problem with the category of self-employed people is that the unemployed may become self-employed. As a result open unemployment may become disguised unemployment. An unemployed person may, for example, start hawking lozenges or incense sticks. He is unemployed in disguise because even if he stops hawking, number of lozenges or incense sticks consumed in any given period will not be affected. This means that he is not making any contribution to consumption or production of the goods he is hawking. His activity is not generating any additional income for the society. Similarly, members of a peasant family

National Income Accounting

Table 2.13

Distribution of workforce by gender, activity-status and rural–urban location (per cent)

Population/segment

Rural male Rural female Urban male Urban female

57

1999–00

2004–05

SE1

RWS2

CL3

SE

RWS

CL

55.0 57.3 41.5 45.3

8.8 3.1 41.7 33.3

36.2 39.6 16.8 21.4

58.1 63.7 44.8 47.7

9.0 3.7 40.6 35.6

32.9 32.6 14.6 16.7

Source: Statement 5.7 of NSS Report No. 515 1

SE—Self-employed RWS—Regular wage/salaried 3 CL—Casual labour 2

cultivating their own land may be unemployed in disguise. In the absence of employment opportunities outside, members of a family may all share the workload of the family farm, which cannot provide fulltime employment to every member of the family. As a result, everyone works part time. In this scenario, if some of the members withdraw from cultivation, others will do their work and the output of the family farm will not be affected. All the members of the family who can be withdrawn without affecting the output of the family farm are all unemployed in disguise. Thus, in India, the low rates of unemployment, as shown in Table 2.9, are a suspect, since quite a large section of the self-employed may be unemployed in disguise. As shown in Table 2.13, more than 55 per cent of the rural workforce and more than 40 per cent of the urban workforce are self-employed. Obviously, this preponderance of the self-employed are a matter of grave concern. Casual labourers have no guarantee of jobs and income. They have to hunt for jobs every day. This is obviously a miserable situation. Table 2.13 thus reveals a disconcerting scenario. It shows that more than 90 per cent of rural male workers and more than 96 per cent of rural female workers are either self-employed or casual labourers. This starkly reveals the poor quality of employment of the rural workforce. The situation, though much better for the urban workers, is far from satisfactory. Even here almost 60 per cent of the urban male workers and about 65 per cent of the urban female workers are either self-employed or casual labour. The state of employment thus calls for drastic qualitative and quantitative improvement. Can we rely on the growth of the organized sector to generate employment?

2.11 POVERTY India is a poor country and quite a large segment of her population is abysmally poor. Planning Commission of India uses the concept of poverty line to estimate the extent of poverty. Poverty line used by the Planning Commission is given by the value of an average consumption basket that gives an individual the minimum amount of calorie needed per month for survival. These minimum nutritional requirements have been fixed at 2400 calories for the rural areas and 2100 calories for the urban areas. The values of the consumption baskets that provide these

58

Macroeconomics

minimum amounts of calories have been estimated at ` 356.30 and ` 538.60 for per month rural and urban areas respectively at 2004–05 prices. Accordingly poverty lines are defined as per capita monthly expenditures (MPCE) of ` 356.30 and ` 538.60 for rural and urban areas respectively at 2004–05 prices. Poverty ratio is given by the percentage of people having less than the poverty line MPCE. Table 2.14 gives the poverty ratios for both the rural and urban areas and also for the country as a whole for 1993–94 and 2004–05. Data on MPCE are provided by the National Sample Survey Organization (NSSO). They estimate MPCE from data on household consumption expenditure using two methods, namely uniform recall period (URP) and mixed recall period (MRP). Under the former, MPCE is calculated by summing up the average per capita expenditure on every item of consumption over a 30-day period. Under the latter, MPCE is calculated by recording data on average per capita expenditure on five infrequently purchased items of consumption, namely clothing, footwear, durable goods, education and institutional medical expenses, over a 365-day period and on all other items of consumption over a 30-day period. Thus, if the average per capita expenditure on the five items mentioned above is found to be ` 200 over the 365-day period, the MPCE on these five items is taken to be equal to ` (200/365) × 30 = ` 54.79 (approx). From Table 2.14 we find that under the URP method, the percentage of rural people below poverty line in the total rural population declined from 37.3 per cent in 1993–94 to 28.3 per cent in 2004–05, the percentage of urban people below poverty line in the total urban population Table 2.14 Poverty ratios1 by URP2 and MRP3 (per cent) By Uniform Recall Period (URP) Method2 Category Rural Urban All India

1993–94 37.3 32.4 36.0

2004–05 28.3 25.7 27.5

By Mixed Recall Period (MRP) Method3 Rural Urban All India

27.1 23.6 26.1

21.8 21.7 21.8

Source: Planning Commission 1

Poverty ratio is the percentage of people on or below the poverty line, which is defined as per capita monthly consumption expenditure of ` 356.30 for rural areas and ` 538.60 for urban areas in 2004–05. 2 Under URP, a recall/reference period of 30 days is used for every item of consumption, i.e. the total expenditure on every item of consumption within the reference period is used to compute per capita monthly expenditure. 3 Under MRP, however, a recall/reference period of 365 days is used for five infrequently used non-food items, namely clothing, footwear, durable goods, education and institutional medical expenses and 30-day recall/reference period for remaining items. From the total expenditures on all the different consumption items within their respective reference periods, per capita monthly consumption expenditure is computed.

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declined from 32.4 per cent in 1993–94 to 25.7 per cent in 2004–05 and the percentage of people below poverty line for the country as a whole in the total population declined from 36.0 per cent in 1993–94 to 27.5 per cent in 2004–05. It is obvious that the monthly consumption expenditure of every household under the MRP method will be more than that under the URP method. Hence poverty ratios will also be less. As Table 2.14 reveals, poverty ratios for rural areas, urban areas and the country as a whole were 27.1, 23.6 and 26.1 respectively in 1993–94. The corresponding ratios in 2004–05 were 21.8, 21.7 and 21.8 respectively. The point to note here is that poverty line is grossly inadequate as a basis for measuring poverty, since a person cannot survive on calories alone. He needs shelter, clothing, education and healthcare services as well. If minimum accepted requirements of all these items are incorporated in poverty line, most of the Indians will be below poverty line.

2.12 MEASURES OF INFLATION Inflation is another phenomenon, which macroeconomics seeks to explain. Inflation refers to the situation where prices of all goods and services increase. If prices of only a few goods and services go up, the phenomenon does not qualify as inflation. There are many different measures of inflation. We shall discuss some of the important ones here. One of the commonest and most important measures of inflation is the consumer price index (CPI). CPIs are calculated for different groups of consumers. For example, it may be computed for industrial workers of Kolkata or for non-manual workers of Kolkata. We shall now explain how CPIs are constructed. CPI, as we have pointed out, refers to a particular group of consumers. To construct CPI for a particular group of consumers, one has to first identify the consumption basket of a typical consumer family belonging to the group. That is, one has to identify which goods are consumed by an average family of that group and in what quantities in a given period (say per day or per week, etc.). The period in which the data regarding the average consumption basket of a typical family of the group are collected is called the base period. We shall refer to the base period as period zero. Suppose it is found that on the average a typical consumer family belonging to the consumer group in question consumes N number of goods in quantities denoted by x10, x20, ..., xN0, where xi0 º quantity of the ith good consumed by the representative consumer family in the base period, i.e. period zero, and i = 1, 2, ... , N. The value of this consumption basket in the base period is given by P10x10 + P20x20 + L + PN0xN0, where Pi0 º price of the ith good in the base period, period zero and i, 1, 2, ..., N. Consumer price index of the consumer group in question can be constructed for any period other than the base period. Let us consider a period, say, period T. To construct the CPI for period T, we have to first derive the value of the consumption basket (x10, x20, ..., xN0) in period T, which is given by P1Tx10 + P2Tx20 + L + PNTxN0, and then divide it by the value of the consumption basket in the base period. The CPI of the consumer group in question for the period T is therefore given by

" P x " P x

P1T x10  P2T x 20  P10 x10  P20 x 20

T 0 N N 0 0 N N

Let us now explain what the above ratio says. Suppose it is 1. It means that the value of the consumption basket is the same in both the periods. This in turn implies that the average

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Macroeconomics

price of the goods and services that the consumer group in question consumes is the same in both the periods. If the ratio is 2 (1.5), it means that the value of the consumption basket in period T is twice (one and a half times) that of the base period. It implies that the average price of goods and services consumed by a typical family of the given consumer group has doubled in period T from the base period, i.e. period 0. To express the CPI in percentage terms, we multiply the above ratio by 100. Thus, for the consumer group in question CPI for period T =

" P x " P x

P1T x10  P2T x 20  P10 x10  P20 x 20

T 0 N N 0 0 N N

× 100

(2.59)

If we subtract 100 from CPI for period T, we get the rate of inflation for the consumer group in question relative to the base period. Suppose that the CPI for period T as given by Eq. (2.59) is 200 (150), i.e. the cost of the consumption basket in period T is 200 (150) per cent of that in period 0. This means that the average price of the goods and services consumed by the consumer group in question in period T is 200 (150) per cent of that in the base period. This implies that from the base period to period T, there has taken place 100 (50) per cent increase in the average price of the goods and services. In other words, from the base period to period T, the rate of inflation for the consumer group in question is 100(50) per cent. There are certain points about CPI that should be taken into reckoning. First, CPI is a measure of the rate of inflation not of all prices but of prices of only those goods and services that the group of consumers in question consumes. Obviously, this group of consumers is bothered only about the prices of those goods and services that they consume. Let us illustrate this point with an example. Consider an agricultural labourer, Vinod. He consumes mainly rice and pulses, lives in his own house (i.e. he does not pay rent), collects fuel from fields and forests and secures clothing from rich neighbours, who give away their old dresses in charity. His daily consumption of rice and pulses in January 2008 was on the average 1 kg and .1 kg respectively. Prices of rice and pulses, the kinds that Vinod consumed, in January 2008 were ` 10 and ` 20 respectively. In June 2008, prices of rice and wheat were ` 12 and ` 30 respectively. CPI of Vinod for June 2008 with January 2008 as the base year is therefore 125%. It shows that average price of the goods and services consumed by Vinod increased by 25% from January 2008 to June 2008. This is the measure of inflation that Vinod is interested in. Obviously, what is happening to prices of computers, automobiles, wine, meat, etc. are of little interest to him. Second, at any point of time every good has usually more than one price. Let us explain. Producers of goods usually do not sell their products directly to consumers. Farmers producing wheat, for example, do not usually sell directly to the consumers of wheat. Similarly, manufacturers of computers or clothing or refrigerators or cigarettes do not sell directly to consumers. There are middlemen between producers and consumers. Producers generally sell their products to wholesalers, who buy and sell in bulk. Wholesalers also do not sell to the consumers directly. They sell to the retailers. The retailers in turn sell to the consumers. The shopkeeper from whom the consumers buy his groceries, stationeries, vegetables, fish, meat, etc. are all retailers. For every good, therefore, there is a price that the producers charge to the wholesalers, another price that the wholesalers charge to the retailers and a third price, the price that the retailers charge to the consumers. There may be more tiers of middlemen than the three described above. The CPI obviously considers only the prices that the consumer pays, i.e. it

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only considers the prices that the retailers charge to the consumers. The other point about CPI is that here prices of both the base period and the current period, the period for which the CPI is computed, are weighted by the quantities of the respective goods and services consumed in the base period. When prices of both the periods are weighted by the base period quantities, the price index is called Laspeyere’s price index. If the prices of both the periods are weighted by the current period quantities, the price index is called Paasche’s price index. CPI is therefore a Laspeyere’s price index. Laspeyere’s index has an upward bias. Let us explain. The CPI should ideally show not the change in the cost of purchasing a given consumption basket from the base period to the current period, but the change in the cost of enjoying a given level of utility from the base period to the current period. The base period consumption basket has a certain level of utility associated with it. The CPI should show the change in the cost of attaining that level of utility from the base period to the current period. However, the consumption basket that gives the same level of utility as the base period consumption basket at minimum cost is different from the base period consumption basket at current period prices. Let us illustrate with an example. Suppose that the consumption basket of the consumer group in question contains only two goods, x1 and x2. Quantities of x1 and x2 in the base period consumption basket are x10 and x20 respectively. Prices of x1 and x2 in the base period and the current period, referred to as period T, are denoted by (P10, P20 ) and (P1T, P2T ) respectively. At (P10, P20 ), the consumption basket chosen is (x10, x20), which, as shown in Figure 2.4, is on the indifference curve, I1. Hence at (P10, P20 ) the least cost bundle for attaining I1 is (x10, x20). Let us explain. Consider the following equation: C

P10 x1  P20 x 2

(2.60)

Figure 2.4 Identification of the least cost bundle on an indifference curve.

In (2.60), C is a constant. (2.59) gives us all the combinations of x1 and x2 each of whose value or cost at the base year prices (P10, P20) is C .C C in Figure 2.4 represents (2.60). Its vertical intercept is (C / P20 ) and the absolute value of its slope is (P10 /P20). It is called an isocost

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Macroeconomics

line. For every value of C , there is a unique isocost line. The larger the value of C , the higher is the isocost line. All the isocost lines corresponding to the base year prices have the same slope, i.e. they are parallel to one another. Of all the points that lie on any given indifference curve the one that costs the least at the base year prices can be identified using these isocost lines. Let us explain. Consider the indifference curve I1 in Figure 2.4. An isocost line passes through every point on I1. The lower the isocost line passing through a point, the less is the cost of the bundle represented by the point. Obviously, the lowest isocost line from which I0 can be attained is the one, which is tangent to I0. This isocost line is labelled C C in Figure 2.4. Clearly, all the isocost lines that lie below C C also lie below I1. Hence none of the points on I1 can be attained from them. As shown in Figure 2.4, (x10, x20) is the point of tangency between

C C and I1. It, therefore, costs the least of all the bundles lying on I1 at the base year prices. Note that (x10, x20) is the point chosen by the representative household at the base year prices. The budget line of the representative household at the base year prices is therefore also given by C C . The equation of the isocost lines at the prices of period T, (P1T, P2T), is given by C

Table 2.15 Year

2000–01 2001–02 2002–03 2003–04 2004–05

P1T x1  P2T x 2

(2.61)

Consumer price index—annual average IU1

UNME2

AL3

1982 = 100

1985–86 = 100

1986–87 = 100

444 463 482 500 520

371 390 405 420 436

305 309 319 331 340

1

IU stands for industrial workers. CPIs for IU have been computed with 1982 as the base year. 2 UNME stands for urban non-manual employees. CPIs for UNME have been computed with 1985–86 as the base year. 3 AL stands for agricultural labourers. CPIs for AL have been computed with 1986–87 as the base year.

The vertical intercept and the absolute value of the slope of the isocost line represented by (2.61) are

C P2T

and P1T/P2T respectively. Of the isocost lines represented by (2.61) for different

values of C , the one that is tangent to I1 is labelled CT CT. It is obviously not tangent to I1 at (x10, x20). Thus at the period T prices, the least cost bundle on I1 is different from (x10, x20). Let us now focus on (2.59). The denominator of the fraction gives the minimum cost of attaining I1 at the base period prices. The numerator should have ideally given the minimum cost of attaining I1 at period T prices. The numerator is larger than that as the cost of (x10, x20)

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is larger than the minimum cost of attaining I1 at period T prices. Therefore the CPI or the Laspeyere’s price index overestimates the increase in the average price of goods and services consumed by the representative household of the consumer group in question.

GDP Deflator GDP deflator is constructed using the concepts of real GDP and nominal GDP discussed in Section 2.5. It is simply given by the following formula GDP deflator of a given year =

Normal GDP of the given year × 100 Real GDP of the given year

(2.62)

Let us illustrate the GDP deflator with an example. Consider the GDP deflator of the year 2007. It is given by the ratio of the nominal GDP of the year 2007 to the real GDP of the year 2007 with, say 2002, as the base year. To express the ratio in percentage terms, it is multiplied by 100. Suppose the ratio multiplied by 100 is 200. It means that the value of GDP of the year 2007 valued at the prices prevailing in 2007 is 200 per cent of the value of GDP of the year 2007 evaluated at 2002 prices. Since the denominator and the numerator evaluate the same basket of goods and services at prices prevailing in 2002 and those prevailing in 2007 respectively, we can say that the prices of 2007 on the average are 200 per cent or twice those of 2002, i.e. prices on the average went up by 100 per cent from 2002 to 2007. If the GDP deflator of the year 2007 were 120, it would mean that the prices on the average went up by 20 per cent from 2002 to 2007. Thus GDP deflator is also a measure of inflation. The difference between CPI and GDP deflator is that the CPI measures the average increase in prices of a specific set of consumer goods consumed by a typical or representative household of a particular group of consumers whereas GDP deflator takes into reckoning prices of all the different goods and services produced within the geographical boundary of the country. As a result, imported products, which are not produced domestically will not figure in the GDP deflator. However, these imported products may be in the consumption basket of the CPI. Moreover, the consumption basket of the CPI remains the same year after year, but the commodity basket underlying the GDP deflator may change every year, as some new goods are produced every year, while some old goods cease to be produced within the geographical boundary of the country. (Exercise: Using the data of Table 2.1 and Table 2.5, compute GDP deflators for each year for the period from 2002–03 to 2005–06. Explain the GDP deflators.)

Wholesale price index This is a popular measure of inflation in India. It is published monthly by the Economic Advisor to the Ministry of Commerce and Industry. It is also a Laspeyere’s price index where both the base period and the current period prices are weighted by the base period quantities. However, in this price index the wholesale prices are taken into account and not retail prices. It is also constructed using the price relatives. The price relative of a good of period T, say, is the ratio of the price of the good in period T to the price of the good in the base period, referred to as period zero. The price relative of the i-th good is therefore (PiT/Pi0), where PiT and Pi0 denote prices of the i-th good in periods T and zero respectively. To construct the wholesale price

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Macroeconomics

index, price relative of every good bought and sold in the wholesale market is weighted or multiplied by the ratio of the value of the total quantity of the good transacted in the wholesale market in the base year to the aggregate value of the total quantities of all the goods transacted in the wholesale market in the base year. This ratio is given by

Pi0 xi0

Çi

Pi0 xi0

, where xi0 denotes the

quantity of the i-th good transacted in the wholesale market in period zero, and it is the weight of the price relative of the i-th good. The wholesale price index is given by the weighted sum of these price relatives weighted by their respective weights specified above. To express this index in percentage, this sum is multiplied by 100. Thus Wholesale price index =

È

T Ø

Çi ÉÊ PPi0 ÙÚ i

Pi0 xi0

Çi Pi0 xi0

– 100

Çi PiT xi0 – 100 Çi Pi0 xi0

(2.63)

It follows from (2.63) that the wholesale price index is the weighted average of the percentage increase in the price of every good transacted in the wholesale market from the base period to the current period. Weight for every good is the proportion of the value of the total quantity of the good transacted in the wholesale market in the aggregate value of total quantities of all the goods transacted in the wholesale market. It, therefore, gives the percentage increase in the average price of goods transacted in the wholesale market from the base period to the current period. Wholesale price indices of India are given in Table 2.16. From the figures we find that the wholesale prices on the average increased by 61% from 1993–94 to 2001–02 and by 66.8% from 1993–94 to 2002–03. This means that the wholesale prices on the average increased by [(66.8 – 61)/61] × 100 = 9.5% from 2001–02 to 2002–03. Compute the rate of inflation in wholesale prices for the other years in the Table. Table 2.16

Wholesale price index (WPI)—annual average All commodities Base: 1993–94 = 100

Year

2001–02

2002–03

2003–04

2004–05

2005–06

2006–07

WPI

161.3

166.8

175.9

187.3

195.5

206.1

Source: RBI: Handbook of Statistics on Indian Economy.

2.13

CONCLUSION: INDIA’S POSITION RELATIVE TO THE WORLD

Per capita GNP of a country, which gives the value of goods and services at the command of the people per head, may be regarded as an index of the average level of well-being of the people of the country. Comparing per capita GNPs of different countries of the world, therefore,

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65

one can ascertain the level of well-being of the people of one’s own country on the average relative to those of the other countries of the world. Table 2.17 gives figures of the per capita GNP of the different countries of the world for the year 2004. However, comparing per capita GNPs of different countries of the world in any given period is the same as that of comparing per capita GNP of any given country of different periods. The problem arises from the fact that GNPs of different countries are evaluated at different sets of prices. GNPs of India and the US in 2004, for example, are evaluated at the sets of prices prevailing in India and the US respectively in 2004. Hence one does not know how much of the difference between the two per capita GNPs is due to difference in physical output and how much due to price differences. It is true that per capita GNPs of different countries are expressed in terms of their respective currencies. To compare them per capita GNP of every country is expressed in terms of a common currency, which is the US dollar in the case of Table 2.17. This is done by multiplying per capita GNP of every country by the price of the currency of the given country in terms of the common Table 2.17

India’s position relative to the world (2004)

Population (Millions)

Surface area (Thousand square kilometres)

Population density (People per square kilometre)

GNP per capita ($)

Rank

High income1 USA UK Japan Korea Republic

1004 294 60 128 48

34595 9629 244 378 99

30 32 247 351 487

32112 41440 33630 37050 14000

Middle income

3018

69070

45

2274

6644

Upper middle income2 Argentina

576

29897

20

4769

10168

38

2780

14

3580

Lower middle income3 Brazil China

2442

39173

63

1686

184 1296

8515 9598

22 139

3000 1500

97 129

7940 5890

86 108

Low income4 India Pakistan World

2343 1080 152 6395

30276 3287 796 133941

80 363 197 49

507 620 600 6329

159 161

2258 3120 2170 8844

144 157

5 13 9 50

93

PPP GNP per capita ($) 31009 39820 31430 29810 20530

5829

High income countries are those whose per capita GNP is $10,066 or more. Upper middle income countries are those whose per capita GNP varies from $3256 to $10,065. 3 Lower middle income countries are those whose per capita GNP varies from $826 to $3255. 4 Low income countries are those whose per capita GNP is $825 or less. 2

3 14 18 46

12530

Source: 2006 World Development Indicators 1

Rank

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Macroeconomics

currency. This clearly does not resolve the basic problem. If the per capita GNP of India, say, is multiplied by the price of rupee in terms of the US dollar, price of each good in terms of rupee is multiplied by the price of rupee in terms of the US dollar, but that does not make Indian prices equal to the US prices. They remain different. To get round this problem, GNPs of all the countries should be evaluated at the same set of prices so that differences in per capita GNPs can be attributed only to differences in the per capita command over goods and services. That is, however, not done, as it is likely to involve tremendous amounts of cost and difficulty. Instead an indirect simple method is used. Let us illustrate this method with an example. Let P be the average price of goods and services in India in rupee. This means that P amount of rupees can purchase 1 unit of goods and services in India on the average. Hence ` 1 can purchase (1/P) amount of goods and services in India. Let P* be the average price of goods and services in the US in dollar. To buy (1/P) amount of goods and services in the US, (P*/P) amount of dollar is needed. Therefore ` 1 in India is equivalent to (P*/P) amount of dollar in the US. To compare India’s per capita GNP with that of the US, therefore, one should multiply India’s per capita GNP in terms of rupee, which we denote by y, by (P*/P) × [y × (P*/P)] is referred to as purchasing power parity (PPP) measure of India’s per capita GNP. Column 7 of Table 2.17 gives PPP per capita GNPs of different countries in the world. From the above discussion, it follows that the ranking of the countries on the basis of PPP per capita GNP is much better than that on the basis of per capita GNP. PPP per capita GNP is also not fully satisfactory, since goods produced in the US may be different from those produced in India. India may specialize in low-tech goods, while the US may produce high-tech goods only and India may import the goods produced in the US in exchange for the goods it produces. Hence India and the US may face different sets in this care the equivalence between ` 1 and $(P*/P) breaks down. In reality, however, the commodities produced by different countries of the world do overlap to a large extent and prices of the same set of goods do vary considerably across countries. Hence PPP per capita GNP, despite the qualification mentioned above, is a better basis for cross-country comparison. Even if commodities produced in the two countries are largely the same, difference in P and P* may simply reflect difference in quality. P*, for example, may be twice P simply because the US goods are far superior to India’s goods qualitywise. In that case PPP measure of India’s per capita GNP will overestimate India’s per capita GNP relative to that of the US. Column 5 of Table 2.17 ranks countries in accordance with their per capita GNPs. On the basis of per capita GNPs countries of the world have been divided into four categories, namely high income, upper middle income, lower middle income and low income countries. In 2004, countries having per capita GNPs of $10,066 or more were regarded as high income countries, upper and lower middle income countries were defined as those having per capita GNPs less than $10,066 but more than or equal to $3265 and less than $3265 but more than or equal to $826 respectively. Low income countries referred to those whose per capita GNPs were less than $826. India in 2004 belonged to the low income countries, with a per capita GNP of $620. It is one of the poorest countries of the world and ranked 159 in a total of 195 countries. If assessed on the basis of PPP GNP per capita, which is a more satisfactory basis of comparison, India’s PPP per capita GNP in 2004 was $3120, which is almost five times its own per capita GNP. We find from Table 2.17 that the gap between high income and low income countries narrows considerably when we consider their PPP per capita GNPs. However, the whole of this narrowing down of the gap may not be real, as there is

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considerable difference in the qualities of the goods produced in the high income and low income countries. Table 2.18 makes a comparison of the poverty levels in different countries in the world. Column 3 of Table 2.18 gives the percentage of the total population of the country below the poverty line consumption expenditure of $1 a day. As prices vary considerably across countries, real value of $1 also varies substantially. This makes comparison unsatisfactory. Still it may be instructive to look at the figures. We find that in 1999–00, 34.7 per cent (more than one-third) of the people were below the poverty line. In Argentina, an upper middle income country, Brazil, a lower middle income country, China, a lower middle income country, percentages of people below poverty line were 7 per cent in 2003, 7.5 per cent in 2003 and 16.6 per cent in 2001 respectively. In 1999–00, $1 was about ` 50. If we raise the poverty line to the per capita consumption expenditure to $2 a day, percentages of people below poverty line rise to 52.4 per cent in India in 1999–00, 23 per cent in 2003 in Argentina, 21.2 per cent in Brazil in 2003 and 46.7 per cent in China in 2001. Poverty gap is a measure of the average shortfall of the consumption of the poor from the poverty line. Poverty gap with consumption expenditure of $1 a day as the poverty line was 8.2 per cent in 1999–00. It was 2 per cent in case of Argentina in 2003, 3.4 per cent in case of Brazil in 2003 and 3.9 per cent in case of China in 2001. Obviously, the poverty gap increases substantially, when the poverty line is raised to $2 of consumption expenditure a day. Table 2.18 Country

Survey year

Inter-country comparison of poverty Population below $1 a day (%)

Argentina 2003 Brazil 2003 China 2001 India 1999–2000 Korea Republic 1998 Philippines 2000

7.0 7.5 16.6 34.7 0

where C¢ º marginal propensity to consume (mpc). Marginal propensity to consume gives the amount of increase in aggregate planned consumption demand or expenditure due to a unit increase in Y. Keynes assumed that an increase in Y usually induces individuals to spend more on consumption, but the increase in consumption expenditure is generally less than that in Y. This explains the restrictions on C¢. Keynes referred to this relationship between C and Y as a fundamental psychological law governing the consumption spending of human beings. He also assumed C¢ to be less than the average propensity to consume (apc) which is equal to (C/Y). Empirical exercises that were later carried out to estimate short-run consumption functions of different countries bore out all the Keynesian assumptions. For simplicity, we shall assume the consumption function to be linear as given by C = a + bY; a > 0, 0 < b < 1 (3.1) where a and b are constants or parameters of the consumption function. a is the autonomous part of the consumption expenditure. This part is called autonomous because it is independent of Y. The other part is dependent on Y and it is called the induced component. b is obviously the marginal propensity to consume. If we divide both sides of (3.1) by Y, we get

C a b Y Y From the above equation it follows that the ratio (C/Y) falls with an increase in Y. Equation (3.1) thus implies that the growth in Y induces growth in C, but the growth rate of C will be less than that in Y. Table 2.5 presents data of growth rates of GDP and consumption at constant prices from 1997–98 to 2007–08 and it shows that the growth rate in C at constant prices and that in GDP at constant prices are quite close to one another and the former is consistently less than the latter. These data, therefore, lend prima facie support to the Keynesian consumption function. (Note: Table 2.5 gives figures of growth rates of per capita GDP and per capita C. However, if we add the rate of growth of population to each of the two growth rates, we shall get the rates of growth of C and Y.) Firms and households make investment expenditure to augment future income. Aggregate real planned investment expenditure, i.e. aggregate planned investment expenditure measured at constant prices is, therefore, governed by individuals’ expectations regarding the future prospect of their business. Henceforth investment expenditure will mean real investment expenditure only. Keynes was of the view that investors’ investment decisions are driven by some kind of optimism, which can hardly be explained in terms of any kind of rational calculations on the part of the investors. Keynes referred to this optimism as animal spirit and did not try to explain it. Thus in SKM aggregate real planned gross investment (denoted by I) is simply regarded as exogenously given. Hence I

I

(3.2)

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Macroeconomics

where I is an exogenously given constant. Real planned aggregate demand (AD) for goods and services is therefore given by (3.2a) AD a  bY  I Economists explain economic phenomena by constructing mathematical models. These models are of two types, viz. static and dynamic. The former are those which do not explicitly incorporate time into the analysis, while the latter consider time explicitly and focus on more than one period. Static models in economics focus exclusively on equilibrium, which is defined as a situation where all variables are in a position of rest. SKM is a static model. The only variables that it explicitly considers are C, Y and I. Recall that in this model, producers keep their prices fixed and adjust their output to demand. Given this assumption regarding producers’ behaviour, if at the level of Y produced, aggregate planned demand equals the given Y, producers have no reason to change the level of Y. If Y remains unchanged, so will C. Aggregate planned investment is exogenously given. Therefore all the variables that the SKM considers explicitly are in a position of rest, i.e. there is equilibrium in the model if the following equation is satisfied Y

[ a  bY ]  I

(3.3)

Note that, even though static models do not explicitly consider time, there is a period of time implicit in them. The period of time that is implicit in SKM, as we have already specified, is a short period, which may be a day, a week, a month, a quarter or a year. If the short period is, for example, a year (quarter), Y is the yearly (quarterly) GDP, C is the aggregate planned consumption demand per year (quarter) and I denotes aggregate planned investment demand per year (quarter). Economic variables which are expressed as quantities per unit of time, as is the case with Y, C and I here, are called flow variables. If we say that aggregate gross production or GDP of a country is ` 1000, it does not make any sense. We have to say whether this is the GDP of the country in a given month, day or year, etc. This is true for C and I as well. Thus, all these variables are flow variables. The model is now fully specified. It contains two key equations (3.1) and (3.3) in two unknowns Y and C. The value of I is exogenously given and therefore known. The model explains the values of Y and C. The variables that a model seeks to explain, which are Y and C in the present case, are called endogenous variables. The variables, the values of which the model takes as given, are called the exogenous variables. Here I and the parameters of the consumption function, a and b, are the exogenous variables. In fact, a model explains its endogenous variables in terms of its exogenous variables. The model presented here contains, as we have already said, two key independent equations (3.1) and (3.3) in two endogenous variables C and Y. The system is therefore determinate and we can solve these two equations for the equilibrium values of the endogenous variables. Equation (3.3) contains only 1 unknown, Y, and hence we can solve it for the equilibrium value of Y. Putting this equilibrium value of Y in (3.1) we get the equilibrium value of C. Solving (3.3), we have aI Ye (3.4) 1b where Ye º the equilibrium level of Y. Clearly, (3.4) gives the equilibrium Y in terms of the exogenous variables of the model. Let us now explain (3.4). The numerator of the expression on the RHS of (3.4) gives the amount of planned aggregate demand (AD) and therefore the

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amount of excess demand [defined as the excess of AD over Y, i.e. (AD – Y)] at Y = 0. Producers will start expanding production to meet this excess demand. The economy will achieve equilibrium when Y rises to such an extent that the excess demand falls by ( a  I ) in absolute quantity, i.e. from ( a  I ) to zero. To know the amount by which Y has to rise to reduce excess demand by ( a  I ) in absolute amount, we have to know by how much excess demand falls in absolute terms per unit increase in Y. An increase in Y by 1 unit, given AD, lowers the excess demand directly by 1 unit in absolute terms. However, this additional unit of Y, given the assumption that business saving is negligible, also raises personal disposable income by the same amount and thereby raises aggregate planned consumption demand and therefore excess demand by b. Thus in the net a unit increase in Y reduces excess demand not by unity but only by (1 – b) in absolute terms. Therefore excess demand falls by ( a  I ) in absolute terms, when Y rises by [( a  I )/(1  b)] . Let us illustrate this point with an example. Suppose an economy produces only rice and the price of 1 kg of rice is ` 1. Suppose ( a  I ) for this economy is ` 100. This means that if no rice is produced, then economic agents plan to purchase rice of ` 100. Hence, if the producers produce nothing, they will face an excess demand of ` 100. The economy will clearly achieve equilibrium if the producers raise the output of rice from zero to such an extent that the excess demand falls to zero, i.e. by ` 100 in absolute terms. If the producers raise output of rice by ` 1 from zero and if this increase has no impact on demand, excess demand for rice will fall by ` 1 as demand of ` 1 is fulfilled. However, the value of this production, ` 1, will go into the hands of the households as personal disposable income and they will spend a fraction b of it for consumption. Let us suppose b = (1/2). Thus the production of this ` 1 of rice will generate demand for rice of ` (1/2). This will raise excess demand by ` (1/2). Thus an increase in the output of rice by ` 1 reduces excess demand in the net by ` (1 –[1/2]) = ` 1/2 in absolute terms. Therefore, excess demand will fall by ` 100 in absolute terms, when Y goes up by [` 100/(1/2)] = ` 200. We show the solution of (3.3) graphically in Figure 3.1 where CC represents the consumption function (3.3). Its position is determined by its vertical intercept, a, and slope, b. The horizontal line I gives the investment function (3.2). Vertically summing up the consumption and investment functions, we get the AD schedule representing (3.2a). The vertical distance between CC and AD is I . The coordinates of every point on the 45° line in Figure 3.1 are equal. Thus at the point of intersection of the 45° line and AD, planned aggregate demand is equal to Y and therefore the economy is in equilibrium. The equilibrium Y corresponds to this point. The point on the consumption function corresponding to this equilibrium level of Y gives the equilibrium level of consumption. We have identified above the equilibrium values of Y and C. At these values of Y and C, there is no tendency for these variables to change. But what is the significance of these equilibrium values of Y and C? The actual values of Y and C may differ substantially from their respective equilibrium values so that equilibrium values of Y and C may not hold any clue as to what values Y and C would actually assume. The equilibrium values become significant if it can be shown that whatever the initial values of Y and C might be, they would move towards their respective equilibrium values over time. In that case the equilibrium values of Y and C give us those values of Y and C which Y and C would eventually assume so that in any given short period we can reasonably expect the actual values of Y and C to be, if not exactly equal, at least

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Figure 3.1 Determination of GDP in the SKM for a closed economy without government.

close to their respective equilibrium values. When the equilibrium values of the endogenous variables satisfy the characteristic noted above, the equilibrium is said to be stable. Let us now examine whether the equilibrium in the model considered here is stable or not. EXERCISE 3.1 Suppose C = 100 + .77Y and I = 25. Derive the equilibrium values of Y and C. Explain the equilibrium value of Y. Illustrate the equilibrium graphically indicating the vertical intercept and slope of each schedule.

3.3 STABILITY OF EQUILIBRIUM We shall now examine whether the equilibrium in the SKM is stable. To examine stability of equilibrium, first we have to specify the adjustment rules for the endogenous variables, which are Y and C in the present case. These rules state how the endogenous variables behave in all possible situations of equilibria and disequilibria. For simplicity we make the simplest possible assumption regarding C. We assume that C is always given by the consumption function, (3.1). Y, however, is the key variable and, as we have already stated, in the SKM Y rises, stays unchanged or falls according as the excess demand for Y is positive, zero or negative. (Y is the key variable because it determines the value of C.) Let us now start from an initial equilibrium level of Y at which excess demand for Y is zero. Consider an increase in Y from this initial equilibrium value. If, following this increase in Y, excess demand becomes negative, i.e. if excess demand falls with a rise in Y, then and only then, given the adjustment rule, Y will tend to move back to its equilibrium level. Similarly, if, following a decline in Y, excess demand becomes positive, i.e. if excess demand rises with a fall in Y, then and only then Y will show a tendency to rise to its equilibrium value. From the above it follows that the equilibrium is stable if and only if excess demand varies inversely with Y , i.e. if and only if d ( AD  Y ) 0 dY

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Given the adjustment rule regarding C, AD in all possible situations is given by a  b ¹ Y  I , or more generally by C (Y )  I . Therefore the equilibrium is stable if and only if d ([ a  bY  I ]  Y )  0 À (b  1)  0 À b  1 dY

Or, more generally d ([C (Y )  I ]  Y )  0 À (C „  1)  0 À C „  1 dY

Thus in SKM, given the adjustment rules, the equilibrium is stable because b (mpc) or C¢ < 1 by assumption, see (3.1). The intuition behind the result may be easily explained as follows. If b or C¢ is less than unity, then following an increase in Y from its equilibrium value, the rise in C and therefore that in AD will be less than that in Y generating excess supply and hence Y will fall. If, on the other hand, b or C¢ > 1, then following an increase in Y from its equilibrium value, C and therefore AD will rise more than Y creating an excess demand situation. Hence Y will rise further instead of falling. If b or C¢ = 1, then following an increase in Y from its equilibrium value, AD will rise by the same amount as Y. Hence there will be equilibrium at this higher value of Y also. Hence Y will show no tendency to move back to its initial equilibrium value. This explains the stability condition. It is clear that, if b or C¢ < 1, for every Y greater than the equilibrium Y, excess demand is negative, i.e. there is excess supply and hence if initially Y > Ye, it will tend to fall to Ye and for every Y < Ye, excess demand is positive and hence if the initial value of Y is less than Ye, it will tend to rise to Ye. Since in SKM b or C¢ is taken to be positive but less than unity, its equilibrium is stable. If the equilibrium is stable, values of the endogenous variables will be more or less equal to their respective equilibrium values, if, given the speeds of adjustment of the endogenous variables, the period underlying the model is not too short. In the context of the SKM, in the absence of any kind of supply bottlenecks, we can expect the values of Y and C to be equal to their respective equilibrium values always, given its assumptions. We shall explain this point shortly. Let us illustrate how C and Y adjust to their respective equilibrium values in the SKM using Figure 3.1, when the short period is a quarter (year). Suppose that the producers initially planned to produce Y0 < Ye for the given quarter. This means that they planned to produce (Y0/90) daily on the average. But if they produce that much, the daily AD would be [AD (Y0)/90] > (Y0/90) on the average. Thus on the average there will be excess demand for Y daily, given by [AD (Y0)/90 – Y0 /90]. In the simple Keynesian model it is assumed that firms carry adequate amount of inventory of the goods they produce and also that of the intermediate inputs they use. Hence in the event of excess demand they sell from their inventory and also, if necessary, raise output using their inventory of intermediate inputs. Accordingly, daily output will adjust to its equilibrium value within the day. Given the assumptions of SKM, therefore, output and the other endogenous variables will be equal to their equilibrium values almost always. Thus, in the SKM, we can always take the values of its endogenous variables to be equal to their respective equilibrium values.

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EXERCISE 3.2 (a) Examine the behaviour of the economy if initially Y = Y1 > Ye with the help of Figure 3.1, assuming that Y denotes quarterly GDP. (b) Suppose the annual level of aggregate demand is given by AD = 50 + 0.9Y, where Y º annual GDP. Find out the amount of the daily rate of involuntary change in inventory, when producers planned (i) Y = 450, and (ii) Y = 600. How will Y and C behave over time in the two cases?

3.4

COMPARATIVE STATIC EXERCISES

One important objective of the static models in economics is to examine how the endogenous variables behave, i.e. in which direction they will change and by how much, following changes in the exogenous variables of the model. This they do by deriving the directions and magnitudes of changes in the equilibrium values of the endogenous variables. Obviously, directions and magnitudes of changes in the equilibrium values will indicate those of the actual values of the endogenous variables if and only if the equilibrium is stable. The exercises that are carried out for this purpose are called comparative static exercises. Since the equilibrium of the SKM developed above is stable, we can carry out comparative static exercises to examine how Y and C behave following the changes in the exogenous variables—the parameters of the consumption function, a and b and the exogenously given gross investment, I . Let us denote the autonomous component of aggregate demand, given by ( a  I ) , by A. This is the autonomous component of AD or autonomous expenditure, since this component of AD is independent of Y. The remaining component, bY, is dependent on Y and is therefore called the induced component of AD or induced expenditure.

3.4.1

Effect of an Increase in the Autonomous Expenditure on Y and C

We shall first work out the effect of an exogenous increase in autonomous expenditure (A), which is the sum of a and I , by a given amount dA on Y and C graphically with the help of Figure 3.2, where the AD schedule gives the value of AD, A + bY, corresponding to every Y. To ascertain graphically how Y and C will change following the given change in A, first we have to figure out how the given change in A affects the AD schedule, since the equilibrium value of Y is given by the point of intersection of the AD schedule and the 45° line. Following the increase in A by dA due to an increase in either a or I or both, AD corresponding to every Y goes up by dA. Hence the AD schedule shifts upward by dA. The new AD schedule is labelled as AD¢ in Figure 3.2. Hence the equilibrium Y and therefore the equilibrium C go up. The new equilibrium value of Y is denoted by Y1e. From Figure 3.2, we can derive the magnitude of the increase in the equilibrium Y, given by the distance GH. Focus on the triangle GHJ. tan 45° =

JH GH

JK + HK GH

dA  bY1e  bY e GH

1

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Figure 3.2 Increase in the autonomous expenditure.

or or

dA + b(Y1e – Ye) = GH = (Y1e – Ye)

Y1e  Y e

GH

dA 1b

(3.5)

Let us now derive the increase in Y mathematically.

3.4.2 Mathematical Derivation of the Increase in Y and C To derive mathematically the increase in the equilibrium Y, we have to use the equilibrium condition Y = A + bY as it gives the equilibrium value of Y. Substituting the equilibrium value of Y denoted by Y e into the above equation, we get the following identity:

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Ye º A + bY e

(3.6)

(3.6) is an identity, as opposed to the equilibrium condition, since the equality of its two sides follows from the definition of Ye. Hence its two sides are always equal. Taking the total differential of the two sides and treating b as constant, we get the following equation: dY e

Þ

˜[ A  bY e ] ˜[ A  bY e ] ˜[ A  bY e ] e dA  db  dY ˜A ˜b ˜Y

dYe = dA + b dYe

(Q db = 0)

(3.7)

Let us now explain Eq. (3.7). The LHS gives the change in the value of Y from the initial to the new equilibrium. The RHS gives the change in the aggregate planned demand for goods and services from the initial to the new equilibrium. Let us elaborate. The determinants of planned aggregate demand are A, b and Y—see (3.2a). Of these, A changes by a known quantity dA from the initial to the new equilibrium. b remains unchanged by hypothesis. Y is an endogenous variable. It is, therefore, likely to change and it is assumed to change from the initial to the new equilibrium by dYe, which is an unknown quantity. The RHS gives the change in planned aggregate demand for goods and services when Y changes by dYe and A changes by dA. Hence the RHS gives the change in the planned aggregate demand from the initial to the new equilibrium. Since Y and AD are equal in both the equilibrium situations, the change in Ye from the initial equilibrium to the new one should be equal to the change in AD from the initial equilibrium to the new one. Hence the two sides of (3.7) must be equal. This explains (3.7). Equation (3.7) contains only one unknown dYe and we can solve it for its value. It is given by dY e

dA 1b

(3.8)

Note that (3.8) and (3.5) are the same. We need the stability condition to sign (3.8). We know that the equilibrium is stable if and only if b < 1. This implies that dYe > 0. One important assumption of the SKM is that b > 0. This assumption along with the stability condition means 1 that dYe > dA or dY e dA . This leads to a significant result of the SKM, which we state 1b as follows: Result 1: A given increase in the autonomous expenditure raises GDP by a multiple of it. The multiplier [1/(1 – b)] is called the autonomous expenditure multiplier. It gives the amount by which Y rises following a unit increase in the autonomous expenditure. Let us now explain the RHS of (3.8). The numerator gives the amount of excess demand (ED) that is generated following an increase in A by dA at the initial equilibrium Y. Once the producers become aware of this excess demand they will begin to raise output. The new equilibrium is achieved when through the rise in Y the excess demand falls from dA to zero, i.e. when the rise in Y reduces excess demand by dA in absolute terms. An increase in Y by 1 unit lowers excess demand by 1 unit in absolute terms, given AD. However, a rise in Y by 1 unit also raises demand by b. Thus ED (= AD – Y) falls in absolute terms not by 1 unit but by (1 – b) amount in absolute terms per unit increase in Y. Hence ED will fall by dA in absolute terms when Y rises by (dA/[1 – b]). Let us illustrate this point with a numerical example. Suppose b = (1/2). A rise in Y by 1 unit reduces ED by 1 unit in absolute terms, given demand.

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However, following a unit rise in Y, AD does not remain unchanged. It goes up by (1/2) and thereby, given supply, raises ED by (1/2). Therefore, in the net, per unit increase in Y causes excess demand to fall in absolute terms by [1 – (1/2)] = (1/2). Therefore to reduce excess demand by any given amount, dA, in absolute terms, Y has to rise by twice that amount, i.e., by (dA/[1 – b]), where b = (1/2). This explains the RHS of (3.8). One important point to note is that the value of the multiplier is an increasing function of b. This may be easily explained following the line suggested above. The autonomous expenditure multiplier gives the amount of increase in Y that is brought about by a unit increase in autonomous expenditure. Since a unit increase in autonomous expenditure creates an excess demand of 1 unit at the initial equilibrium level of Y, we can also interpret the autonomous expenditure multiplier as the amount of increase in Y that reduces the excess demand in absolute terms by 1 unit. The larger the value of b, the less is the absolute value of reduction in excess demand per unit increase in Y. Hence to reduce excess demand by 1 unit or by any given amount, Y has to rise by a larger quantity. Thus, when b = (3/4), a unit increase in Y reduces excess demand in absolute terms by (1/4). Hence to reduce excess demand by any given amount in absolute terms Y has to rise 4 times the given amount of excess demand. Whereas, when b = (1/2), a unit increase in Y reduces excess demand in absolute terms by (1/2). Hence to reduce excess demand by any given amount in absolute terms Y has to rise 2 times the given amount of excess demand. When b = 0, the multiplier is 1, i.e. there is no multiplier. EXERCISE 3.3 Why does an exogenous increase in the autonomous expenditure by a given amount raises equilibrium Y by a larger amount? Note: An alternative way of explaining the RHS of (3.8): Following an increase in the autonomous expenditure by dA, the new equilibrium is achieved when Y rises by such an amount that the excess demand falls from dA to zero, i.e. by (– dA). Now partially differentiating the excess demand function, ED (º AD – Y) = (A + bY) – Y, with respect to Y, we find that per unit increase in Y lowers the excess demand by –(1 – b). Now, the excess demand falls by –(1 – b) when Y rises by 1 unit. Therefore, the excess demand falls by 1 unit when Y rises by [1/ – (1 – b)] amount. Therefore, the excess demand falls by (– dA) units when Y rises by [–dA/ – (1 – b)] amount.

3.5 MULTIPLIER PROCESS AT WORK We shall show here how the multiplier process works following an exogenous increase in the autonomous expenditure by dA. Suppose AD (= A + bY) gives quarterly demand for goods and services. The initial equilibrium value of quarterly GDP was therefore [A/(1 – b)] = Ye. The initial equilibrium values of both daily demand and daily production on the average were therefore (Ye/90). Following the increase in A by dA, daily demand goes up by (dA/90) creating daily excess demand of (dA/90) at the initial daily equilibrium GDP of (Ye/90). Producers will increase the level of daily production by (dA/90). This additional production, ignoring business saving, will accrue as additional factor income to the households. Hence average daily income of the households rises by (dA/90). Hence daily demand will go up by b × (dA/90) creating excess demand of the same amount on the average daily again. Producers will therefore raise

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daily level of production again by b × (dA/90). This will again accrue as additional factor income to the households. They will therefore receive this additional income daily and hence their daily demand will go up again by b2 × (dA/90). This in turn will raise the level of daily GDP by the same amount. Clearly, the expansionary process will continue until the additional demand that is created due to the increase in income in the previous round falls to zero. Note that, since b < 1 the additional demand that is created in every round falls over successive rounds and steadily approaches zero. Once the additional demand created drops to zero, the expansionary process stops and the economy achieves new equilibrium. The total increase in daily production from its initial equilibrium level of (Ye/90) to the new equilibrium level is the sum of the increases in daily output in all the different rounds specified above. It is thus given by (dYe/90) = (dA/90) + b × (dA/90) + b2 × (dA/90) + b3 × (dA/90) + L The above is an infinite geometric series of which b is the common ratio. Hence ( dY e /90)

( dA /90)  b ¹ ( dA /90)  b 2 ¹ ( dA /90)  b 3 ¹ ( dA /90) 

If the daily GDP goes up by

Ë 1 È dA Ø Û Ì É ÙÜ , Í 1  b Ê 90 Ú Ý

"

1 È dA Ø 1  b ÉÊ 90 ÙÚ

the quarterly GDP will rise by

Ë 1 Ì1  b Í

Û

dA Ü . Ý

Note that the higher the value of b, the larger is the increase in Y in every round except in the first and therefore the greater will be the total increase in Y. Thus we can explain the reason why the autonomous expenditure multiplier is an increasing function of b with the help of the multiplier process also. We can also explain why there is no multiplier if b = 0. The SKM contains the basics of a powerful theory of determination of GDP. It identifies investment and the parameters of the consumption function—the autonomous consumption expenditure, a, and the marginal propensity to consume, b—as the determinants of GDP and employment. Equation (3.4) implies that if in an economy in a given year a, I and b are sufficiently low, GDP will be much less than its full employment or potential level giving rise to large-scale unemployment of labour and capital. Many workers will not get jobs and many firms will not be able to utilize quite a substantial part of the productive capacity of their plants. This is the principal feature of a year of recession. Thus, for example, a car manufacturing company, which has a capacity to produce 100 cars a day, may have to produce only 50 cars a day on the average utilizing only half of its productive capacity in a recession year owing to low level of demand. The model, therefore, explains why unemployment of labour and capital may exist in a market economy. The model also contains a theory of short run fluctuations of GDP, i.e. year-to-year fluctuations of GDP. It states (see Result 1 derived earlier) that GDP changes from one year to the next due to exogenous shifts in I, a and b. The power of Result 1 in explaining the fluctuations is evident from the fact that it implies that a given change in I (or a) brings about a change in Y, which is many times more than the change in I (or a). More precisely, it shows that due to per unit change in I (or a) aggregate output changes in the same direction by a multiple of the amount of change in I (or a) and the multiplier is given by (1/[1 – b]). Thus, if mpc is 0.9, not unusual in market economies, then the multiplier is 10. This means that a fall in I (or a) will lead to a decline in Y, which is ten times the fall in I (or a). Thus, according to (3.4) small changes in I and a can produce large changes in Y in the same

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direction and thereby generate booms and busts in the market economies. How can we use this model to explain the data provided in Table 3.1? The model says that the real GDP grows from one year to the next because of the increases in I and a. But, why should I and a increase from one year to the next. The model says nothing regarding that. However, we can give some reasons why I and a are likely to increase over time. Let us explain. a summarizes the influence of all factors other than Y that affect C. These factors are not explicitly taken into reckoning because they are likely to remain constant in the short-run. The most important factors are households’ wealth and their tastes and preferences. The former, though does not change much in the short-run, goes up from one year to the next through saving made by the households. The increase in households’ wealth exerts a positive impact on C and this gets reflected in an increase in a. Moreover, technological progress at home and abroad brings new consumer goods in the market. Thus in every year some new consumer goods, which did not exist in the previous year, enter the market. This may tilt consumers’ tastes and preferences in favour of consumption and this also gets reflected in an increase in a. I is also likely to increase from one year to the next for the following reasons. Note that I, which consists in setting up of new production units or expanding productive capacities of the existing production units, in any given year augments productive capacity of the country next year. Moreover, investment is usually concentrated in those areas where there are shortages. Hence investment in any given year eases up the supplies of those goods and services next year which were in short supply in the given year. Investment in any given year therefore gives a boost to investors’ confidence and expectations next year. This coupled with the increase in consumption demand discussed earlier induces investors to undertake larger amounts of investment next year. The AD schedule in Figure 3.1 therefore shifts upward from one year to the next leading to growth in GDP. If for some reason or the other investors’ expectations get substantial fillip, AD shifts upward by a large amount leading to a high growth rate of GDP and thereby creating a boom. If just the opposite happens to business sentiments, I and therefore AD shift upward by a small amount giving rise to low rate of growth of GDP and large unemployment of labour and capital plunging the economy in recession. Why should there emerge large-scale unemployment of labour and capital in a recession year despite growth, though modest, in GDP? This may be explained as follows. In any given year capital stock is larger than that in the previous year because of the investment made in the previous year. Population growth also makes the size of the labour force larger in the given year than that in the previous year. During a recession year the increase in GDP from the previous year’s level is so small that the increase in employment of labour and capital becomes significantly less than the additions that take place to the stocks of labour and capital in the given year leading to substantial increase in the unemployment of both labour and capital. In times of severe recession, business sentiments are so bleak that I may fall instead of rising leading to negative growth in GDP. Note that, to apply SKM to explain the growth rate of GDP from one period to the next, one has to make sure that in the periods under consideration there were no supply bottlenecks so that output could adjust smoothly to demand expansion.

3.6

INFLATIONARY AND DEFLATIONARY GAP

As discussed above, investment in any given year creates additional capital and thereby additional productive capacity next year. Population growth also increases the size of the labour force

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from one year to the next. The growth in the supplies of both labour and capital increases the level of full employment output from one year to the next. SKM assumes that normally the growth in AD from one year to the next is such that the GDP that meets the AD in the later year is less than the later year’s full employment output. SKM therefore assumes that normally every year the equilibrium level of GDP is less than its full employment level, i.e. AD corresponding to the full employment level of output is normally less than the full employment level of output every year. The shortfall of AD corresponding to the full employment level of output from the full employment level of output is referred to as deflationary gap. The situation is shown in Figure 3.3 where the full employment level of output is denoted by Yf and the AD corresponding to Yf is denoted by AD(Yf) and AB indicates the deflationary gap, given by [Yf – AD(Yf)], which is nothing but the excess supply that would emerge if Yf were produced.

Figure 3.3 Deflationary gap.

In times of boom, however, if investors’ expectations are particularly buoyant, growth in demand from one year to the next may outstrip the growth in full employment output to such an extent that there would emerge in the later period excess demand even if full employment output were produced. The excess of aggregate demand corresponding to the full employment level of output over the full employment level of output is referred to as the inflationary gap. The situation is shown in Figure 3.4. Keynes was of the view that in the presence of inflationary gap GDP will be stuck at its full employment level and prices will be rising generating inflation. Either dissatisfied buyers will be offering higher prices to bid the scarce goods away from the others or the firms perceiving the excess demand at the maximum level of output may start raising prices without the fear of losing their clients to others. When all the producers are producing at their maximum possible levels, none of them is in a position to accommodate any additional demand. Producers know that this is the case in times of inflationary gap and hence they realize that in such periods they can raise prices without risking any loss in market shares to others. In periods of strong boom conditions both the above-mentioned mechanisms through which prices rise operate generating inflation.

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Figure 3.4 Inflationary gap.

3.7

RELATIONSHIP BETWEEN GDP, ACTUAL AND PLANNED CONSUMPTION AND ACTUAL AND PLANNED INVESTMENT

We have seen in Chapter 2 that the GDP is identically equal to the sum of actual gross aggregate investment and actual aggregate consumption. This must hold in the context of the SKM as well, though here the sum of aggregate planned consumption expenditure and aggregate planned gross investment expenditure equals GDP only in equilibrium. Let us illustrate using Figure 3.5. Focus on a level of Y, Y1 > Ye. At this Y, as we find from Figure 3.5, there is an excess supply. Hence households and firms are able to purchase as much goods and services as they plan from the market. Aggregate planned consumption demand is therefore fully satisfied. Aggregate planned consumption expenditure and aggregate actual consumption expenditure are accordingly equal at Y1. Households investment plans are also fulfilled, as they are able to purchase as many houses as they plan to from the market. Firms are also able to purchase as much goods as they plan to from the market. However, even after meeting all the market demand for goods and services, firms are unable to sell the whole of their output. The amount of goods unsold with the firms is given by the length KL in Figure 3.5. These unsold goods remain with the firms in their inventory. Thus the capital stock of households and firms goes up not just by their planned purchases for investment purposes, given by I , but also by the involuntary increase in the firms’ inventory given by the unsold part of the firms’ output. Aggregate actual investment is accordingly given by I plus the unsold part of GDP. Sold part of Y1 is given by C(Y1) + I of which C(Y1) is both planned and actual consumption. I + unsold part of Y1 is the actual investment. Therefore Y1 is identically equal to actual consumption and actual investment corresponding to Y1. Again, consider a level of Y, Y0 < Ye. At this Y, as we find from Figure 3.5, there is excess demand. In the SKM it is usually assumed that firms carry adequate inventory of the goods they produce and in the event of excess demand, they meet it by selling from their inventory. Hence households and firms are able to purchase as much goods

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Figure 3.5 Identity between GDP and actual aggregate expenditure.

and services as they plan to from the market. Aggregate planned consumption demand is therefore fully satisfied. Aggregate planned consumption expenditure and aggregate actual consumption expenditure are accordingly equal at Y0. Households investment plans are also fulfilled, as they are able to purchase as many houses as they plan to from the market. Firms are also able to purchase as much goods as they plan to from the market. However, to meet all the market demand for goods and services, firms have to sell from their inventory an amount of goods equal to that of excess demand, given by PQ in Figure 3.5. Thus the capital stock of households and firms goes up by their planned purchases for investment purposes, given by I , net of the involuntary decrease in the firms’ inventory given by the excess demand at Y0. Accordingly, Aggregate actual investment at Y0 º I  [C (Y0 )  I  Y0 ] Þ

Aggregate actual investment at Y0 º Y0 – C(Y0)

Þ

Aggregate actual investment at Y0 + Aggregate actual consumption at Y0 º Y0

Finally, in equilibrium the whole of the GDP is purchased by firms and households for purposes of investment and consumption and their aggregate planned consumption and aggregate planned investment demands are exactly met. There is no involuntary addition to or depletion of inventory. This implies that aggregate planned investment and aggregate planned consumption are exactly equal to their actual counterparts in equilibrium. Hence in equilibrium GDP is equal to the sum of actual consumption and actual gross investment expenditure. The above identity will hold even if firms do not carry any inventory of the goods they produce. Note that services cannot be held in inventory. The difference between this case and the previous case arises only in the event of emergence of excess demand. In the kind of economy considered here, GDP is purchased only for the purposes of investment and consumption.

Aggregate Demand and Determination of GDP

91

When there is excess demand, GDP is fully sold off, i.e. it is equal to actual purchases of produced goods and services for consumption and investment. Hence the sum of actual consumption expenditure and actual investment expenditure has to be equal to GDP. EXERCISE 3.4 (a) Consider an economy, which produces only one final good, bread. Everyone is engaged directly or indirectly in its production. Those who produce only the intermediate inputs that go into the production of rice are indirectly engaged in the production of bread. Suppose the sellers sell bread at a fixed price of ` 1. Suppose the aggregate planned annual demand for bread is given by AD = 1000 + 0.75Y where Y º annual level of aggregate output of bread (A) Find out the equilibrium level of the annual output of bread. (B) Now suppose the annual level of planned autonomous demand for bread rises by 365 from 1000. (i) Then how much excess demand is generated every day on the average at the initial equilibrium level of GDP? (ii) Suppose producers realize after seven days that there has emerged an excess demand for their products. Then by how much will the inventory get depleted in these seven days? (iii) Producers will expand average daily level of output of bread to meet this excess demand. What is the absolute value of decline in average daily excess demand following a unit increase in the average daily GDP? What is the absolute value of decline in average daily excess demand following an increase in average daily GDP by k units? By how much the average daily excess demand has to fall in absolute terms through the rise in average daily GDP to restore equilibrium in the system and which value of k will achieve this? Explain. How is the required value of k affected if marginal propensity to spend were .5 instead of .75. Explain your answer. Describe the multiplier processes in the two cases. (b) Gross investment may be an increasing function of Y. The reason may be briefly stated as follows. Every firm has a given productive capacity in the short run determined by its installed capital stock. Thus a firm, given its capital stock, can produce only a given maximum number of units of its product per unit of time (i.e. per day or per month, etc.) and not more than that. Even though there is in general idle productive capacity in the SKM, the rate of utilization of productive capacity may vary from firm to firm. At a high level of Y some firms may be operating near their full capacity. They know from experience that normally, for reasons we have already explained, demand grows over time and hence they might decide to add to their productive capacity by increasing their capital stock, i.e. by making investment. The higher the level of Y, the larger is likely to be the number of such firms and therefore the larger is likely to be the aggregate planned investment. Hence aggregate planned investment may be an increasing function of Y. Set up the SKM in this case. Derive the stability condition. Find out the autonomous expenditure multiplier in this case. Compare it to that in the earlier case where investment is exogenously given and explain the difference interpreting the multiplier expressions and also by comparing the multiplier processes.

92

3.8

Macroeconomics

SIMPLE KEYNESIAN MODEL FOR A CLOSED ECONOMY WITHOUT GOVERNMENT IN TERMS OF SAVING AND INVESTMENT

The SKM for a closed economy without government may be specified in terms of aggregate planned saving and aggregate planned investment as well. We shall present that version here. Note that in a closed economy without government the whole of GDP accrues as gross private disposable income, and actual and planned private gross saving are therefore given by (GDP – actual C) and (GDP – planned C) respectively. Denoting the latter by S, we have S = Y – C(Y) º S(Y);

0 < S¢ = 1 – C¢ < 1

(3.9)

Note that in the kind of economy considered here aggregate gross private saving is the same as aggregate gross saving. S¢ is the marginal propensity to save. It gives the amount by which S increases following a unit increase in Y. From the definition of saving, as given by (3.9), it follows that the aggregate gross private disposable income has only two uses, consumption and saving. The part of Y that the households do not plan to spend for consumption is by definition S. Hence, if Y goes up by a unit, and the households plan to use C¢ of it for the purposes of consumption, the remaining part by definition is added to S, i.e. S goes up by S¢ with an increase in Y by unity. In other words, C¢ + S¢ º 1 or S¢ º 1 – C¢. Since by assumption C¢ lies between 0 and 1, so does S¢. This explains (3.9). In (3.9), Y and C(Y) denote real GDP and aggregate real planned consumption expenditure respectively. Hence S(Y) gives aggregate real planned saving. We get aggregate nominal planned saving by subtracting aggregate planned nominal consumption expenditure from nominal GDP. We have already pointed out that aggregate real gross investment may be either exogenous or an increasing function of Y, see Problem (b) of Exercise 3.4. Here, however, we consider the latter. The investment function is therefore given by I = I(Y); I¢ > 0

(3.10)

The equilibrium condition of the earlier version of the SKM, (3.3), is given by Y = C(Y) + I Þ Y – C(Y) º S(Y) = I. Therefore this equilibrium condition in terms of saving and investment may be written as S(Y) = I(Y) (3.11) Note that all the variables considered here, namely S, I and Y are real variables, i.e. they are measured at a fixed set of prices Let us explain (3.11). The LHS, S(Y), gives corresponding to every Y the excess of GDP or aggregate supply over aggregate planned consumption demand. If it is equal to aggregate planned investment demand, then aggregate supply equals aggregate planned demand. If S(Y) > I(Y), then the excess of aggregate supply over aggregate planned consumption demand is greater than aggregate planned investment. Hence there is excess supply and the amount of excess supply is given by [S(Y) – I(Y)]. By similar reasoning [I(Y) – S(Y)] gives the amount of excess demand. The three Eqs. (3.9), (3.10) and (3.11) constitute the SKM in terms of saving and investment. It contains three endogenous variables, S, I and Y, in three independent equations. We can therefore solve this system for the equilibrium values of the three endogenous variables.

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Aggregate Demand and Determination of GDP

For simplicity, let us take linear forms of the saving and investment functions. The linear saving function is given by

S  s ¹ Y;

S

0  s 1

(3.9a)

If the consumption function underlying the saving function (3.9a) is given by (3.1), then

S

1C

and

s

1b

The linear investment function is given by I

I  i ¹Y; 1 ! i ! 0

(3.10a)

The equilibrium condition, accordingly, is given by

S  s ¹Y

I



i ¹Y

(3.11a)

We can solve these three equations for S, I and Y in terms of the parameters of the saving and investment functions, S , s, I and i, which are the exogenous variables of the model. Solving (3.11a), we get the equilibrium value of Y. Putting this in (3.9a) and (3.10a), we get the equilibrium values of S and I respectively. Denoting the equilibrium value of Y by Ye, we get Ye

I S si

(3.12)

From (3.12), it follows that if I ! S and s > i, there will exist a unique positive value of equilibrium Y. In what follows, we shall assume these conditions to be true. These conditions constitute a set of sufficient conditions for the existence of a unique meaningful equilibrium value of Y. Let us now explain (3.12). Focus on the RHS. The numerator gives the excess of aggregate planned investment over aggregate planned saving at Y = 0, i.e. it gives the amount of excess demand at Y = 0. Given the assumptions of the SKM, the producers will raise Y from zero to remove this excess demand, i.e. they will go on raising output until the excess demand as measured by (I – S) falls in absolute quantity by ( I  S ) , i.e. from ( I  S ) to zero. Now, per unit increase in Y the fall in (I – S) in absolute quantity is (s – i). Let us explain. A unit increase in Y raises S by s and thereby, given I, lowers (I – S) by s in absolute terms. However, the unit increase in Y also raises I by i and thereby raises (I – S) by i, given S. Thus, in the net (I – S) falls in absolute terms by (s – i). Therefore (I – S) falls in absolute quantity by

( I  S ) , when Y goes up by ( I  S )/(s  i ) . Thus, if at Y = 0, there is positive excess demand, i.e. I ! S , and if a rise in Y lowers excess demand, i.e. if (s – i) > 0, then the economy will achieve equilibrium at a unique positive Y. The solution of the three equations, (3.9a), (3.10a) and (3.11a), is shown graphically in Figure 3.6, where the SS and II schedules represent the saving and investment functions respectively. We have drawn the schedules in such a way that the sufficient conditions for the existence of a meaningful equilibrium mentioned above are satisfied. The equilibrium values of saving, investment and Y correspond to the point of intersection of the SS and II schedules.

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Macroeconomics

Figure 3.6

Determination of equilibrium GDP using saving and investment schedules.

EXERCISE 3.5 Suppose quarterly S and I are given by S = –100 + .25Y and I = 20 + .1Y. Derive the equilibrium quarterly GDP denoted by Y. What is the average daily level of excess demand measured in terms of saving and investment at Y = 0? By how much does the daily excess demand (in terms of saving and investment) fall per unit increase in the average daily level of GDP? By how much will the average daily and therefore quarterly GDP have to rise to remove the average daily and therefore quarterly excess demand? Explain.

3.9 STABILITY OF EQUILIBRIUM To examine the stability of equilibrium, first we have to specify the adjustment rules governing the behaviour of all the endogenous variables, S, I and Y , in all possible situations. Regarding S and I we make the assumption that they are given by the saving and investment functions respectively in all possible situations. The assumption in respect of Y in the SKM is that it falls, stays unchanged or rises according as excess demand [= I(Y) – S(Y)] is positive, zero or negative. Let us now start from equilibrium. If a rise in Y from its equilibrium value makes excess supply, [S(Y) – I(Y)], positive, i.e. if [S(Y) – I(Y) rises (from zero) with an increase in Y, then Y will show a tendency to fall. Similarly, if a decline in Y from its equilibrium value makes [S(Y) – I(Y) negative, i.e. if [S(Y) – I(Y)] falls (from zero) with a decline in Y, then Y will, given the adjustment rules, show a tendency to rise back to its equilibrium level. Thus, if [S(Y) – I(Y)] varies directly with Y, then the equilibrium is stable. If [S(Y) – I(Y) is an increasing function of Y at every value of Y, then the equilibrium is stable globally (i.e. stable whatever be the magnitudes of the deviations of the initial values of S, I and Y from their respective equilibrium values). Let us explain. Consider any given value of Y. If it is greater (less) than the equilibrium value of Y at which [S(Y) – I(Y)] = 0, then at this Y, the value of [S(Y) – I(Y)] will be positive (negative) because [S(Y) – I(Y)] is an increasing function of Y at every Y. Hence Y will tend

Aggregate Demand and Determination of GDP

95

to fall (rise). This is true of every Y > ( 0. EXERCISE 3.7 Consider the following equations: C = 100 + .75Y

and

I = 20

Suppose these consumption and investment functions give quarterly values of consumption and investment, i.e. here Y denotes quarterly GDP. Derive the average daily involuntary change in inventory function. Explain its parameters. Present the functions graphically. Find out the change in the average daily involuntary change in inventory function when (i) Y = 400 and (ii) Y = 500. Explain these quantities in detail.

3.11 SIMPLE KEYNESIAN MODEL FOR A CLOSED ECONOMY WITH GOVERNMENT In a market economy, as we have already pointed out, GDP does not grow steadily over time. Its growth rate, as we find in Table 3.1, fluctuates a great deal. SKM attributes this to shifts in aggregate demand function due to volatility of investment. If business sentiments are depressed, aggregate planned investment is low and the economy in consequence is in recession, with low rate of growth of GDP and large-scale unemployment. If, however, investors are optimistic

Aggregate Demand and Determination of GDP

97

about future, aggregate planned investment may be so high, that there may emerge an inflationary gap putting upward pressure on prices. Thus a market economy is caught between the twin dangers of unemployment and inflation. Too large levels of investment lead to inflation, while too low levels of it create unemployment and both cause untold suffering to the people. The question that therefore emerges is whether the government can do anything to stabilize the economy at the full employment level of output, i.e. keep the economy in equilibrium at the full employment level of output despite fluctuations in aggregate planned investment. To answer this question the government has to be incorporated into the SKM. In what follows, we shall present the SKM, with the government’s activities incorporated into the system.

3.11.1

The Model

In the presence of the government, GDP is identically equal to the sum of aggregate consumption expenditure, aggregate gross investment expenditure and aggregate government consumption expenditure. This means that the GDP is purchased only for these three purposes—personal consumption, gross investment and public consumption. These are the only sources of demand for GDP in a closed economy with government. Aggregate planned demand for GDP is therefore given by aggregate planned consumption expenditure/demand, aggregate planned gross investment expenditure/demand and aggregate planned public consumption expenditure/demand. Note that GDP here refers to the real GDP, i.e. it is measured at constant prices and it is expressed in terms of rupees. Similarly, every component of aggregate planned demand represents real planned demand and is expressed as planned expenditure measured at constant prices. Prices are fixed in SKM and both GDP and aggregate planned expenditure are measured at this fixed set of prices so that changes in GDP and those in aggregate planned expenditure are due respectively to changes in physical production and changes in real demand for goods and services only. We shall denote aggregate planned public consumption expenditure by G. In the SKM, GDP is determined by aggregate planned demand for goods and services. We shall accordingly try to identify the major factors that determine aggregate planned demand, which is the sum of aggregate planned personal consumption expenditure (C), aggregate planned gross investment expenditure (I) and aggregate planned government expenditure (G). C, as we have noted already, depends, according to Keynes, only on the personal disposable income in the short-run. In the presence of government, there are subsidies, taxes and transfers that make GDP and personal disposable income differ from each other even after ignoring business saving, which we assume to be zero here. We have seen in the previous chapter that, when business saving is zero, gross personal disposable income is identically equal to GDP minus all taxes (both direct and indirect) plus government transfers plus subsidies Hence, under the assumption that business saving is zero so that private and personal disposable incomes are equal, we can write the consumption function as C = C(Y – T + TR);

0 < C¢ < 1

(3.13)

where T º all taxes net of subsidies and TR º government transfers. Usually taxes net of subsidies in a country are an increasing function of income. In most countries the tax structure is progressive, i.e. the amount of tax burden or tax obligation as a

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Macroeconomics

proportion or percentage of income rises with income. However, for simplicity, we assume the tax to be a lump sum for the time being. Thus T T (3.14) Transfers refer to the financial assistance given by the government to the unemployed and the victims of natural disasters, accidents, etc. In periods of high levels of output, unemployment is likely to be low and the natural factors are also likely to be less unfavourable. For these reasons transfers are likely to be a decreasing function of Y. However, for the present, we ignore transfers, i.e. assume transfers to be zero.

TR = 0

(3.15)

Using (3.14) and (3.15), we can write (3.13) as C

C (Y



T );

0



C„  1

(3.16)

The investment function remains the same as before and is given by I I (3.17) Public consumption expenditure is determined by government’s policies. Hence we shall regard it as an exogenous variable. Thus

G G (3.18) Aggregate planned demand is therefore given by C (Y  T )  I  G . For reasons explained earlier, there is equilibrium in SKM when GDP equals aggregate planned demand. The equilibrium condition is thus given by Y

C (Y  T )  I  G

(3.19)

The specification of the model is now complete. It contains two independent key equations, namely Eqs. (3.16) and (3.19) in two endogenous variables, C and Y. It is clear from (3.16) and (3.19) that the equilibrium value of Y is a function not only of I but also of government’s policy parameters, G and I . (Verify this statement by taking a linear consumption function and then solving for the equilibrium value of Y.) By changing its consumption expenditure and tax the government is therefore able to exert substantial influence on the equilibrium level of Y. In what follows we shall examine in greater detail the extent of government’s influence over aggregate output and employment. The solution of (3.16) and (3.19) is shown in Figure 3.7. Explain the Figure yourself. Following the line suggested in the context of the SKM without government, examine the stability of equilibrium in this model stating the adjustment rules for all the endogenous variables. In this model also the equilibrium is stable, if C¢ < 1 for all Y. Also derive the stability condition when I is an increasing function of Y and explain it.

3.11.2

COMPARATIVE STATIC EXERCISE

Let us now carry out a comparative static exercise. The government can control directly G and T , but it has no direct control over C or I, since consumption and investment decisions are taken

Aggregate Demand and Determination of GDP

Figure 3.7

99

Determination of GDP in the SKM with government

by the households and firms. The government can influence C only indirectly through T. G and T are therefore policy parameters of the government and we shall examine here the effect of a policy induced increase in G and T by dG and dT respectively. First, we shall do this graphically with the help of Figure 3.8 and then mathematically. To carry out the exercise graphically, we have to examine how the policy-change affects the AD schedule in Figure 3.8. This change in government’s policy has two opposite effects on AD. The increase in G, ceteris paribus (i.e. other things remaining the same), raises aggregate demand at every Y by dG . The increase in T, on the other hand, lowers personal disposable income at every Y by dT and thereby lowers C by C¢ × dT . Therefore in the net aggregate planned demand at every Y goes up by ( dG  C „ ¹ dT ) . This is positive if dT is not larger than dG by a sufficiently larger amount. When this is the case, the AD schedule will shift upward by the amount ( dG  C „ ¹ dT ) in Figure 3.8. Hence the equilibrium values of Y and C will go up. (Derive the exact magnitude of the increase in Y graphically). The new equilibrium value of Y is labelled Y1e in Figure 3.8 (Derive the exact magnitude of the increase in Y graphically.) Let us now derive the result mathematically. Substituting the equilibrium value of Y denoted by Ye into (6) and then taking total differential of both sides of the resulting identity treating I as a constant, we have

dY e

C „(dY e



dT )  dG

(3.20)

The LHS of Eq. (3.20) gives the change in the value of Y from the initial equilibrium to the new one. The RHS gives the change in the aggregate planned demand from the initial equilibrium

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Macroeconomics

Figure 3.8

Impact of fiscal policy on GDP.

to the new one, since the determinants of aggregate planned demand that have changed from the initial equilibrium to the new one are Y e , T and G . Since Y and AD are equal in both the initial and the new equilibrium situations, changes in the former and the latter from the initial equilibrium to the new one must be equal. This explains (3.20). Equation (3.20) contains only one unknown dYe, since dG and dT are known to us. C¢ is also known and constant, as it is evaluated at the initial equilibrium level of Y and the consumption function is given and therefore known to us. We can as a result solve (3.20) for dYe. Thus dY e

dG  C „dT 1  C„

(3.21)

Let us explain Eq. (3.21). Following an increase in G and T by dG and dT respectively, AD goes up by dG at the initial equilibrium Y. At the same time the increase in T by dT reduces disposable income by dT at the initial equilibrium Y and hence lowers the aggregate planned consumption demand by C¢ dT . Hence planned aggregate demand at the initial equilibrium Y goes up and thereby creates an excess demand of [ dG  C „dT ] . (There is of course no guarantee that this amount is positive. It may be negative as well if dT is sufficiently large relative to dG . In that case there emerges an excess supply at the initial equilibrium Y.)

Aggregate Demand and Determination of GDP

101

In case there is excess demand, producers will begin to expand Y and a new equilibrium is established when the rise in Y reduces excess demand to zero, i.e. by [ dG  C „dT ] in absolute terms. Now, an increase in Y by 1 unit, given AD, reduces excess demand, (AD – Y), by 1 unit in absolute terms. However, it also raises personal disposable income by the whole of 1 unit since the amount of tax does not change with Y. Hence C goes up by C¢. Thus in the net per unit increase in Y excess demand falls in absolute terms by (1 – C¢). Therefore, excess demand will fall by [ dG  C „dT ] in absolute terms when Y goes up by {[ dG  C „dT ]/(1  C „)} . Let us now explain the multiplier process that takes place following the increase in G and T by dG and dT respectively. Let us suppose that the short period implicit in the model is a year so that Y and AD represent annual GDP and annual planned aggregate demand respectively. G and T therefore represent annual public consumption expenditure and annual tax collection respectively. Following the given increase in them, as we have already explained, there emerges an annual excess demand of [ dG  C „dT ] at the initial equilibrium Y, when dT is not sufficiently larger than dG . When the government plans to spend dG extra annually, its planned daily spending on the average goes up by ( dG /365) . Again, when the government cuts down annual tax burden of the people by dT lowering their annual planned consumption spending by C „dT , their planned daily consumption spending on the average falls by (C „dT /365) . On the average, therefore, there will be an excess demand of ([ dG  C „dT ]/365) daily at the initial equilibrium level of average daily output. Hence producers initially will raise average daily GDP by ([ dG  C „dT ]/365) . Since taxes are a lump sum here, they do not increase with the rise in Y. Moreover, business saving is also zero by assumption. Hence the whole of this additional Y will accrue as personal disposable income of the people. This will raise annual planned consumption

spending and thereby average daily planned consumption spending by C „ ¹ [ dG  C „dT ] and (C „ ¹ [ dG



C „dT ]/365) respectively creating a situation of excess demand again. Producers

will therefore raise average daily GDP by (C „ ¹ [ dG  C „dT ]/365) , which in turn will lead to a further round of expansion in income, demand and production and so on. This process of expansion will stop and the economy will achieve a new equilibrium, when the additional demand that is generated in each round eventually falls to zero. Thus the total increase in the average daily GDP is given by

[(dG  C „dT )/365]  C „ ¹ [(dG  C „dT )/365]  (C „)2 ¹ [(dG  C „dT )/365]  ¹ ¹ ¹ Ë Í

(dG  C „dT )/365ÛÝ 1  C„

Hence annual GDP, Y, will go up by dY e

[(dG  C „dT )] 1  C„

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Macroeconomics

EXERCISE 3.8 (a) Explain the value of dYe in the case where [ dG  C „dT ] < 0 by explaining the expression giving the value of dYe and also the multiplier process. (b) Consider the following equations: C

1000  .75(Y  T ), I

100  .15Y , G = 50 and

T 40 . Suppose the short period implicit in the model is a year. Set up the SKM. Identify the endogenous and exogenous variables. Derive the equilibrium levels of the endogenous variables. Is the equilibrium globally stable? Derive and explain the stability condition. Examine the impact of increase in G and T by 20 and 10 respectively. Examine graphically first and derive the changes in the values of the endogenous variables graphically. Derive the result using calculus. Explain it. Describe the multiplier process. Suppose to reach the full employment level, the annual GDP has to be raised by 500 units. By how much will T has to be lowered, with G remaining unchanged, to accomplish the desired increase in annual GDP? Explain. e dG dT , i.e. Ye goes up by the same From (3.21) it follows that, if dG dT , then dY amount as G or T . When G and T change by the same amount, we say that there has taken place a balanced budget change in G and T. The amount of increase in Ye that takes place per unit balanced budget increase in G or T is called the balanced budget multiplier (BBM). It follows from the above that it is unity.

EXERCISE 3.9 (a) Explain why BBM is unity by explaining the multiplier expression and also by describing the multiplier process. (b) Suppose the tax is a proportional function of Y: T = tY. Derive the government expenditure multiplier in this case. Explain the difference in its value from that in the earlier case by explaining the multiplier expressions in the two cases and also by describing the multiplier processes. Hint: Here when Y rises by 1 unit, disposable income goes up by (1–t) amount, since from the additional unit of income t amount has to be paid as tax. Hence following a unit increase in Y, consumption demand does not increase by C¢ as in the earlier case, but by C¢.(1–t) < C¢. Therefore in the present case excess demand falls in absolute terms by a larger quantity than in the earlier case, since (1 –C¢(1 – t)) > (1 – C¢). Hence to reduce excess demand by any given quantity, Y has to rise by a smaller quantity in the present case. An important objective of the government’s economic policy, as we have already stated, is to close inflationary and deflationary gaps. The latter is defined as the amount of positive excess supply at the full employment level of Y. Obviously, if the aggregate demand function is such that there is a deflationary gap in the economy, then there will be unemployment of both labour and capital. Unemployment of labour and expensive capital is costly to the unemployed workers and owners of capital respectively. Inflationary gaps are also undesirable. Even though in the SKM prices are fixed, an inflationary gap, as has been explained above, generates inflation. Inflation is costly for an

Aggregate Demand and Determination of GDP

103

economy. It hurts those people whose nominal or money income does not rise in steps with the prices. Their real income goes down. Let us explain this point with an example. Divide the people of a country into two groups, wage earners and non-wage earners. Let us denote the aggregate money income of the wage earners by W. The remaining part of the nominal GDP, PY, where Y is the real GDP, accrues to the non-wage earners. An economy caught in an inflationary gap produces the full employment real GDP, which we denote by Yf. In this economy, the following equation will hold PYf = W + (PYf – W)

(3.22)

Let us explain (3.22) by elucidating the concepts of nominal GDP and real GDP once again. Suppose an economy produces N number goods. Full employment quantities of these goods in a given year are denoted by x1f, x2f, ..., xnf respectively. Suppose prices of these goods that prevailed at the beginning of the given year are p10, p20, ..., pn0. Suppose in the given year the economy was caught in an inflationary gap. Everyday therefore on the average there aggregate daily planned demand exceeded daily full employment GDP driving up prices. Suppose the average prices of the goods during the given year were p1t, p2t, ..., pnt. Obviously, these prices will be higher than those that prevailed at the beginning of the given year. Real annual GDP

Çp x N

of the given year evaluated at the initial set of prices is

0 f i i

( œ Y f ) . The price level of the

i 1 N

given year is the price index

pit x if Ç i 1 N

Ç

( œ P ) . The nominal GDP of the given year is therefore

pi0 xif

i 1

pit x if Ç i 1 N

PY f

(3.23)

Note that if prices go up, with Y remaining at Yf, as happens in the event of an inflationary gap, the nominal GDP rises. However, the whole of the nominal GDP accrues to the owners of the factors of production as factor income. If average prices in a given year are double their initial values, the nominal GDP in the given year will be double the real GDP of the given year evaluated at the initial prices. Accordingly, nominal factor income would also be double of what it would have been had prices remained at their initial levels. Hence real value of aggregate factor income is not affected when prices change alone, while production remains unchanged. Hence, if we consider all the individuals together, then inflation alone cannot affect the real value of their aggregate factor income. However, even though inflation cannot affect the real value of aggregate factor income of the people as a whole, it can, as we shall presently show, redistribute the aggregate real factor income from one class of people to another. To see this divide both sides of (3.22) by P. This gives N

Yf

W P

È  ÉY f  Ê

WØ P ÙÚ

W0

W W0

Ç pi0 xif i 1 N

Ç

i 1

È  ÉYf  Ê f

pit x i

WØ P ÙÚ

(3.24)

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where W0 º aggregate income of the wage earners if money wage rates remained unchanged at the levels attained at the beginning of the given year. Consider first the situation where prices and money wage rates remain unchanged at their beginning-of-the-year levels (referred to as pit xif Ç i 1 N

initial levels). In this situation P

Ç N

1 and W

W0 and hence, as follows from (3.24),

pi0 x if

i 1

from Yf wage earners get W0 and the non-wage earners get the rest. However, suppose P = 3 and W = W0. This means that the average prices in the given period are three times their initial levels, while money wage rates are equal to their initial values. In this case, as follows from (3.24), wage earners get W0/3) from Yf, i.e. they get from Yf only one-third of what they would have got if prices had stayed unchanged at their initial levels. What they lose goes to the nonwage earners. From Yf they get 2W0/3) amount more because of the price increase. Thus, even though inflation does not affect the aggregate real income of the people as a whole, it redistributes income from the wage earners to the non-wage earners, if money wage rates do not increase in the same proportion as the prices. It is clear from (3.24) that, if (W/W0) = 3, when P = 3, wage earners continue to get W0 from Yf. From the above it follows that in times of inflation, people as a whole are not worse off, but those whose nominal incomes do not rise in steps with prices suffer a decline in their real income and what they lose accrues to the others. Usually wage rates of unskilled and semiskilled labour, who is in abundant supply in India, cannot force a proportionate rise in their nominal wage rates, when prices increase. It is these workers who lose out in the main in times of inflation in countries like India. In fact, on the basis of the kind of redistribution of income that inflation brings about Kaldor (1969) suggested a mechanism that removes the inflationary gap through inflation. Let us present it below. The poor can hardly afford to save. Hence their average and marginal propensities to consume are much larger than those of the rich. The unskilled and semiskilled labour households constitute the bulk of the poor. Let us denote their aggregate wage income in terms of money by W. The real income of these households is therefore (W/P), where P is the price level or the average price of goods and services. Kaldor assumes that the average and marginal propensities to consume of these people are equal and constant and denotes them by cw. The rest of the real GDP, (Y – [W/P]), accrues to others. Their average and marginal propensities to consume are also assumed to be equal and constant and denoted by cc. Aggregate planned consumption expenditure of these two groups of people is therefore given by C = cw(W/P) + cc(Y – [W/P])

(3.25)

Equation (3.25) is the aggregate consumption function of the economy. Using (3.25), the equilibrium condition of the SKM for a closed economy without government may be written as Y

cw (W / P )  cc (Y  [W / P ])  I

(3.26)

In the situation of deflationary gap, both W and P are constant and (3.26) determines Y. In the situation of inflationary gap, there is excess demand at the full employment output, denoted Y , with W and P at their initial levels. In this situation, producers will produce Y and P will rise. The equilibrium condition in this situation may therefore be written as Y

cw ¹(W / P )  cc ¹(Y



[W / P ])  I

(3.27)

Aggregate Demand and Determination of GDP

105

In (3.27), Y is exogenously given, but (W/P) is endogenous and it determines (W/P). Denoting (W/P) by w, the initial value of w by w0, we can write w as w0  w ;

w

w œ w0  w

(3.28)

Substituting (3.28) into (3.27) and manipulating terms, we can write it as Y

[c w ¹w0



cc ¹(Y



w0 )  I ]  (c w



cc ) ( w )

(3.29)

Euation (3.29) contains only one endogenous variable, w . We can therefore solve it for the equilibrium value of w given by w

[ cw ¹w0



cc ¹(Y  w0 )  I ]  Y (cw  cc )

(3.30)

We may explain the RHS of (3.30) as follows: The numerator gives the inflationary gap that exists at w0. This puts upward pressure on prices. P starts rising reducing w and thereby raising w . The rise in P and w will continue until AD falls by the amount of the inflationary gap. Per unit fall in w and therefore per unit rise in w , the poor lose 1 unit of real income, which reduces their consumption expenditure by cw. This loss in the poor’s income accrues as gain to the others. Their real income therefore goes up by unity. Consequently, their real consumption demand rises by cc. In the net aggregate planned consumption demand falls, since cw > cc and it falls by (cw – cc). Aggregate planned consumption demand and therefore AD falls by (cw – cc) per unit rise in w . Hence AD will fall by [ cw ¹ w0  cc ¹ (Y  w0 )  I ]  Y removing the inflationary gap, when w goes up by {[ cw ¹ w0  cc ¹ (Y  w0 )  I  Y ]/(cw  cc )} . Let us illustrate with an example. Suppose inflationary gap at w0 was ` 20 and it started raising P and thereby w . With the per unit increase in w , AD falls by, say, ` 0.25, assuming cw = 1 and cc = 0.75. AD therefore will fall by ` 1 when w goes up by [1/(1/4)] (= 4). AD will therefore decline by ` 20, when w increases by (20) × [1/(1/4)] (= 80) closing the inflationary gap. In times of boom therefore inflationary gap opens up driving up prices and hurting thereby the economically vulnerable sections of the population who do not have the bargaining strength to achieve following the increase in the price level a proportionate increase in their nominal income. We show the solution of (3.29) graphically in Figure 3.9 where the AD schedule representing the equation AD

[ c w ¹ w0



cc (Y



w0 )  I ]  ( c w



cc ) (w )

(3.31)

gives the value of AD corresponding to every w and the horizontal line, Y Y , shows the level of full employment output, Y , corresponding to every w . Obviously, the equilibrium w corresponds to the point of intersection of AD and Y Y . The equilibrium w is labelled w e in Figure 3.9. We can derive the equilibrium value of graphically also. For that, first focus on the AD schedule. Its vertical intercept, [ c w ¹ w 0



c c (Y



w 0 )  I ] , which exceeds Y , gives the

value of AD at w 0 . When w 0, w = w0. This means that at the initial value of w, w0, there is inflationary gap in the economy and the size of the inflationary gap is given by

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Macroeconomics

Figure 3.9 Inflationary gap, inflation and redistribution.

Z

[ c w ¹ w0  c c (Y  w0 )  I ]  Y . It also follows from (3.31) that AD is downward sloping

and the absolute value of its slope is (cw – cc). This means that due to per unit increase in w from zero, AD falls by (cw – cc). Hence to reduce AD by Z, w has to rise by [Z/(cw – cc)]. We can derive this value graphically also. From Figure 3.9, it follows that tan R

AY YB

(c w  cc ) À Y B

w e

AY

Z

(c w  cc )

(cw  cc )

Note that inflation also redistributes income from lenders to borrowers. Increase in prices lowers the real value of both the principal and the interest payments, which are all fixed in nominal terms. Hence the lenders lose. What they lose accrues to the borrowers. In India, about 80 per cent of aggregate national saving comes from the households and they hold most of it in safe financial assets such as government securities, bank deposits, etc. They are therefore the net lenders and inflation makes them worse off. The rich households, who are usually the entrepreneurs, and the government are the net borrowers and inflation benefits them. W in (3.26) may include households’ income from loans as well. In the absence of the government, the poor have to hold their savings in the form of the financial assets of private firms owned by the rich, i.e. they have to lend out their savings to the rich. EXERCISE 3.10 Suppose the real GDP in a given year evaluated at prices prevailing at the beginning of the year (henceforth referred to as the initial prices) was ` 10,000 of which ` 6000 accrued to those whose nominal income remained unchanged at ` 5000 in the face of price increase. Suppose this real GDP was the full employment real GDP of the given year. Suppose the marginal and average consumption propensities of the poor and the rich were 1 and 0.75 respectively. The level of autonomous real planned investment expenditure in the given year evaluated at the prices prevailing at the beginning of the given year was ` 2000. Was there any inflationary gap in the economy at the initial prices? If the answer is yes, what was the average daily inflationary gap and average daily level of involuntary depletion in inventory at the initial prices? By how much will the price level rise to close the inflationary gap? How long are the prices likely to take to reach their equilibrium levels?

Aggregate Demand and Determination of GDP

107

From the above it follows that both inflationary and deflationary gaps are harmful to the people, and governments in market economies undertake economic policies to remove them. This activity on the part of the government is called stabilization. Suppose the government has to change Y by a given amount A to achieve full employment equilibrium in the economy. The government can accomplish this, as we have already seen, by changing its consumption or by changing its tax-transfer policies or both. The policy of influencing the equilibrium levels of GDP by changing government’s taxes and expenditures are referred to as fiscal policy. We assume, for simplicity, that taxes are lump sum and transfers are zero. Under these conditions the equilibrium value of Y is given by Y

C (Y  T )  I  G

We shall now derive all the different policies—each policy is represented by a (dG, dT )—that the government can undertake to achieve its objective. Substituting the equilibrium value of Y, Ye, into the above equation, taking total differential of both sides of the resulting identity and setting dI 0 , we have dY e

C „ ¹ dY e  C „ ¹ dT  dG

Substituting A for dYe into the above equation, we get

A C „ ¹ A  C „ ¹ dT  dG (3.32) Let us explain the above equation. The LHS gives the change in aggregate supply, when Y changes by the targeted amount, A. The RHS gives the change in aggregate planned demand, when Y changes by the targeted amount, A and G and T change by dG and dT respectively. Thus at the values of dG and dT that satisfy (3.32), the goods market will be in equilibrium if Y changes from its initial equilibrium value by A. This implies that, if the government changes G and T by dG and dT respectively such that they satisfy (3.32), Y will change by the targeted amount A, since the equilibrium is stable. Thus, solving (3.32), we get all the different combinations of dG and dT each of which achieves the government’s objective. We plot all these combinations in Figure 3.10 in the (dT, dG) plane. It is given by the GT schedule. Rewriting (3.32), we have dG

Figure 3.10

(1  C „) ¹ A  C „ ¹ dT

Government’s tax-expenditure programme for stabilization.

(3.33)

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Macroeconomics

Let us now explain (3.33). It shows that, when dT 0 , the value of dG that raises Y by A is (1 – C¢) × A. This is quite easy to explain. We know that Y rises by [1/(1 – C¢)], when G goes up by 1 unit. Hence Y will rise by 1 unit when G rises by (1 – C¢). Therefore Y will rise by A if G goes up by (1 – C¢) × A. Let us illustrate this with an example. Suppose C¢ = 1/2. Then Y will rise by 2 per unit increase in G . Hence to raise Y by 1 unit, G has to be raised by (1/2). Therefore to raise Y by any given unit, say A, G has to be raised by (1/2) × A. This explains the vertical intercept of GT. It gives the amount by which the government has to raise G to achieve A amount of increase in Y, when it decides to keep its tax collection unchanged. From (3.33), it follows that (dG/ dT )

C „ . This is the slope of GT. It gives, starting from

a (dG, dT ) that satisfy (3.33), the amount by which dG has to be raised per unit increase in dT to keep the goods market in equilibrium at the targeted level of Y. Let us explain this slope. Consider any ( dG, dT ) on GT. At such a ( dG, dT ), the goods market is in equilibrium at the targeted level of Y. If dT rises by 1 unit, with dG remaining unchanged, disposable income will go down by 1 unit and thereby lower AD by creating an excess supply of C¢ at the targeted Y. Therefore to keep the goods market in equilibrium at the targeted Y, dG has to be raised by C¢. EXERCISE 3.11 (a) Suppose an economy is given by the following equations. C = 100 + .5YD, I = 10, T = 40, G = 10 and Yf = 250, where YD is the private and personal disposable income. Is there an inflationary or a deflationary gap in the economy? What is its value? What policies can the government adopt to keep the economy in equilibrium at the full employment level of output? Derive mathematically and explain. (b) Suppose all the equations in Problem 1 remain the same except for the fact that the tax collection instead of being a lump sum is a proportional function of income. Thus T = tY, where t º the tax rate. Suppose t = 0.25. Derive the equilibrium levels of Y and C. Suppose G goes up by 2 units. By how much will the equilibrium GDP rise? Derive graphically as well as mathematically. Will it increase less following the 2-unit increase in G, if the tax is a lumpsum? Derive the result mathematically. Derive the result graphically as well. While graphically working out the result, take a value of t so that the initial equilibrium Y is the same in both the cases. Explain this value of t. Explain why GDP does not increase by the same amount in the two cases interpreting the multiplier expressions as well as by describing the multiplier processes. How is the equilibrium GDP affected, if G and T increase by the same amount in the present case of proportional tax function? By how much the government will have to change t to make dT equal to dG? Explain. How does a given increase in the tax rate affect the equilibrium level of GDP? Derive the result graphically and mathematically. Explain interpreting the mathematical expression, using the multiplier process and also with the help of a graph. Governments in all modern economies continuously monitor economic activities to ascertain signs of emergence of inflationary or deflationary gaps. In India, for example, the government

109

Aggregate Demand and Determination of GDP

observes the quarterly growth rates of GDP and also those of its different components as shown in Table 3.2 to discern signs of slackening in the growth momentum or those of ‘overheating’ or inflationary gap. We find that the growth rate of real GDP at factor cost in the first quarter (April–June) of 2008–09 is less than those in the previous two quarters by almost 1 percentage point. It is also less than the growth rates of GDP in the first two quarters of 2008–09 and the annual growth rates of GDP in 2005–06, 2006–07 and 2007–08 by about 1.5 percentage points. These indicate a slackening in the growth momentum. However, deceleration in the growth rate in just one quarter may not be a sufficient indication of a recession. Hence, in addition to the quarterly growth rates, the government also observes the changes in the indices indicating the state of business expectations. These indices are prepared by many different agencies. Some of these indices are shown in Table 3.3. From this table we find that the Business Confidence Index prepared by NCAER (National Council of Applied Economic Research) in the last quarter of 2008 declined by 8.8 percentage points from the level it attained in the last quarter of 2007 and was less than its level in the previous quarter by 15.4 percentage points. Expectation Index prepared by FICCI (Federation of Indian Chambers of Commerce and Industry) in the last quarter of 2008 was less than that in the last quarter of 2007 by 20.3 percentage points and that of the previous quarter by 5.1 percentage points. Similar worsening of business expectations are also indicated by the Business Expectation Index and Business Optimism Index prepared by the RBI and Dun & Bradstreet respectively. Deceleration in the quarterly growth rate in the first quarter of 2008–09 and the decline in the expectation indices in the first quarter of 2008 reflect telltale signs of a recession, which the government has to combat through its tax-expenditure policies, which are referred to as fiscal policies. However, along with the indicators noted above, the government also takes the price situation into reckoning. The reason is quite obvious. A situation of overheating or inflationary gap is given away by a higher quarterly growth rate of GDP and a higher rate of inflation, while a recession is indicated by a fall in the quarterly growth rate of GDP and a decline in the rate of inflation. Even though in the SKM, we have presented here, prices are assumed to be stationary in the situation of deflationary gap, in reality prices on the average are always on the rise. However, the rate of their increase, i.e. the rate Table 3.2 Sectors

Agriculture and allied activities Industry Services GDP at factor cost

Growth rates of real GDP at factor cost (at 1999–2000 prices) (per cent) 2000–01 to 2007–08 (Average)

2005–06

2.9 (20.9) 7.1 (19.6) 9.0 (59.5) 7.3 (100)

5.9 (19.6) 8.0 (19.4) 11.0 (61.0) 9.4 (100)

Source: RBI Bulletin (November 2008).

2006–07

3.8 (18.5) 10.6 (19.6) 11.2 (61.9) 9.6 (100)

2007–08

4.5 (17.8) 8.1 (19.4) 10.7 (62.8) 9.0 (100)

2007–08

2008–09

Q1

Q2

Q3

Q4

Q1

4.4

4.7

6.0

2.9

3.0

9.6

8.6

8.6

5.8

5.2

10.6 10.7 10.0 11.4

10.2

9.2

9.3

8.8

8.8

7.9

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Macroeconomics

Table 3.3 Organisations

NCAER FICCI RBI Dun & Bradstreet

Business expectations forecast

Business expectations

Growth over Growth over a year ago previous round

Period

Index

July–December 2008 July–December 2008 October–December 2008 July–September 2008

Business Confidence Index Expectation Index Business Expectation Index Business Optimism Index

–8.8 –20.3 –4.4 –28.1

–15.4 –5.1 –2.6 1.8

Source: RBI Bulletin (November 2008)

of inflation, responds to demand–supply situation. In the situation of inflationary gap, the rate of inflation goes up and in times of recession or deflationary gap, the rate of inflation usually falls. However, Table 3.4, which gives data on wholesale price inflation, reveals a paradoxical situation. It shows that in the first quarter of 2008–09, the quarterly growth rate of real GDP dipped, but the wholesale price inflation rate increased from 3.2 per cent on 10 November, 2007 to 8.3 per cent on 26 April, 2008 and finally to 11.9 per cent on 25 June, 2008. The spurt in the rate of inflation in the present case was surely not due to inflationary gap, as the growth rate was much less than the average of the previous three years. It was mainly on account of soaring petroleum prices in the world market. Prices of petroleum and petroleum products are administered by the Government of India. Petroleum marketing companies in India, which are all public sector enterprises, buy oil from the world market at the world prices and sell it in the domestic market at government administered prices. In 2008, the world oil prices exceeded the domestic administered prices by a substantial and fast growing margin saddling these companies with large and ballooning losses. These companies in their turn put pressure on the government to hike domestic administered prices of oil to arrest the growth in their losses. The government finally succumbed to their pressure and hiked the administered prices of oil. This raised cost of production in general and the transport cost in particular putting firms’ profit margins under Table 3.4 Wholesale price inflation Period

WPI inflation

Period

WPI inflation

April 14, 2007 April 28, 2007 August 4, 2007 November 10, 2007 April 26, 2008 May 10, 2008 May 24, 2008 June 12, 2008 June 25, 2008

6.3 6.0 4.4 3.2 8.3 8.6 8.9 11.7 11.9

July 5, 2008 July 19, 2008 July 30, 2008 August 30, 2008 October 11, 2008

12.2 12.5 12.5 12.1 11.4

Source: RBI Bulletin (November 2008).

Aggregate Demand and Determination of GDP

111

pressure. This forced many of the firms to raise their prices despite slack in demand. This explains the spurt in the rate of inflation even in the face of a deflationary gap. India is a small player in the international oil market. It cannot influence oil prices by buying more or less oil. So a rise in oil prices in the world market is completely beyond its control. It is given to India. The primary impact of an increase in oil prices is on the cost of production. Hence it is a shock on the supply side (i.e. on the side of production) and is referred to as a supply shock. Of course, the SKM presented here is too simple to capture the impact of a supply shock. In the presence of a deflationary gap and a supply shock, the government is faced with a policy dilemma. The former calls for expansionary programmes, i.e. programmes such as cuts in taxes, stepping up of public expenditure, etc., that induce an expansion in GDP, while the latter requires just the opposite. The less the level of demand, the smaller is the scope of the firms to absorb the rise in the cost due to the supply shock by raising their prices. Hence contractionary programmes (programmes that bring about a contraction in GDP) are likely to reduce the inflation rate. The policy choice in face of a deflationary gap together with a supply shock depends upon the relative importance of the two evils—unemployment and inflation—to the government and also on their relative magnitudes. If the rate of inflation is within tolerable levels, but the rate of unemployment is not, the government will go in for expansionary programmes and vice versa.

3.12

SKM WITH GOVERNMENT IN TERMS OF SAVING AND INVESTMENT

We can rewrite the SKM denote aggregate planned consumption expenditure subtracting from GDP all

with government in terms of saving and investment as well. Let us private saving by Spv. We get it by subtracting aggregate personal from aggregate private disposable income (DY). We get DY by taxes net of subsidies and adding to it government transfers. Thus DY = Y – T + TR

where T º total direct and indirect tax collection net of subsidies and TR º government transfers. Let us assume for simplicity that T = tY

and

TR

TR

Then

S pv

[(1  t )Y



TR]  C ((1  t )Y



TR) œ S pv ((1  t )Y



„ TR); 0  S pv



1

(3.34)

Government saving denoted by Sg is given by

Sg

tY  TR  G

(3.35)

Aggregate planned domestic saving denoted by S is, therefore, given by S = Spv + Sg Þ

S

S pv ((1  t )Y  TR)  [tY  TR  G]

(3.36)

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Macroeconomics

It follows from (3.34) and (3.36) that

Þ

S

Y  tY  TR  C(¹)  tY  TR  G

S

Y  C (¹)  G

(3.37)

Thus S gives the excess of aggregate production or GDP over aggregate planned private and public consumption. Clearly, if S equals aggregate planned investment, there is equilibrium in the goods market. If aggregate planned investment demand exceeds the excess of aggregate production or GDP over aggregate planned private and public consumption, then obviously, there is excess demand and its amount is given by (I – S). Aggregate planned investment is given by I = I(Y); I¢ > 0 (3.38) There is therefore equilibrium, as we have already explained, when

S pv ((1  t )Y  TR)  [tY  G  TR]

I (Y )

(3.39)

Equations (3.34)–(3.39) give the SKM for a closed economy with government in terms of saving and investment. It contains 5 independent equations in 5 endogenous variables, Spv, Sg, S, I and Y. We can solve these equations for the equilibrium values of the endogenous variables. (Show the solution graphically). To examine the stability condition of this model, we have to first state the adjustment rules regarding the endogenous variables. Regarding Spv, Sg, S, and I we make the assumption that their values are always given by (3.34)–(3.38). Regarding Y the assumption is that it rises, stays unchanged or falls according to [I(Y) – S] is positive, zero or negative, since [I(Y) – S] measures the amount of excess demand corresponding to every Y. We have already pointed out that (S or Spv+ Sg) gives the excess of GDP over aggregate planned personal and public consumption. Hence if I is greater than (Spv + Sg), there is excess demand and vice versa. Clearly, the equilibrium is globally stable, given the adjustment rules, if corresponding to every Y > () 0. Since at Ye excess demand as given by [I(Y) – Spv(×) – Sg(×)] = 0, the condition for global stability as stated above is satisfied if

˜[ I (Y )  S pv (¹)  Sg (¹)]  0 À I „  (S „pv (1  t )  t ). ˜Y

EXERCISE 3.12 (a) Examine the impact of an increase in on private, public and aggregate domestic saving. (b) Suppose an economy is given by the following equations: C = 100 + .8DY), I = 10 + .25Y, T = 10 + .2Y, G 10 . Recast the model for this economy in terms of aggregate domestic saving and investment. Is the equilibrium globally stable? Derive the impact of an increase in the autonomous component of the tax function by 1 unit on the endogenous variables of this model graphically and mathematically. The above version of the SKM with government yields some interesting results. It shows that government saving is an endogenous variable and therefore cannot be controlled directly by the government. In fact it shows that government’s efforts at raising it may in the end lower it and therefore may turn counterproductive. This result is significant in view of the Fiscal

Aggregate Demand and Determination of GDP

113

Responsibility and Budget Management Act, 2003 under which the Government of India is legally bound to take measures that will reduce revenue deficit to zero by 2008 and make it negative in subsequent years. Revenue deficit is nothing but the negative of government saving. Obviously, as the SKM shows, this kind of an act makes little economic sense, as government’s revenue deficit falls largely outside government’s direct control.

3.13 FISCAL POLICY AND GOVERNMENT’S BUDGET The government, as the SKM shows, can control India’s GDP through its tax-expenditure programmes. Its fiscal policy stance is contained in its budget, which is an account of its receipts and expenditures. Government’s budget or tax and expenditure programmes are formulated not only for the purposes of stabilization but also for many other purposes, which fall outside the scope of this chapter. However, stabilization remains an important objective of government’s budget and to design a fiscal policy, it is necessary to have some idea about government’s budget. India is a federation of many states (twenty-eight states to be precise). Each state has a state government. At the top, there is a central government. Government’s economic powers and responsibilities, which are usually referred to as fiscal powers and responsibilities, are divided between the state governments and the central government. Stabilization is one of the most important responsibilities of the government and in India it is vested in the central government. Besides stabilization, governments provide social goods and seek to achieve optimum distribution of income. Social goods are those goods, which are essential for a society but which cannot be bought and sold in markets. Take, for example, national defence. Once a system of national defence is in place to protect a country from foreign invasion, all the people living in the country will reap its benefits and the provider of the service will not be able to make anyone pay for the service. This is because if anyone refuses to pay for the service, the provider of the service cannot deprive him of the benefits of the service. Obviously, such a service will not be provided by the private sector. Similarly, think of the roads, bridges, etc. These facilities are used free of charge by the people. It is not possible to impose user charges on roads, etc., as attempts at collecting such charges in cities will cause tremendous traffic snarls. Given the economic condition of the rural people, it is not feasible to impose user charges on rural roads. Services provided by national defence, roads, bridges, public administration, etc., are all social goods and they are provided by the government. Governments in India also seek to achieve optimum income distribution by making transfer payments to the poor through a number of poverty alleviation and employment generation schemes. The objective of these schemes is to provide every person with a minimum level of income. Moreover, both the central and the state governments own a large number of public sector enterprises, which make investment expenditures. Governments also provide subsidies to firms engaged in socially desirable lines of production. Government has the power to tax. It taxes people to meet the cost of providing social goods, to make transfer payments and also to stabilize the economy. In India tax powers are concentrated in the centre, though responsibilities or functions are more or less evenly distributed between the centre and the states. The state governments therefore have to depend upon transfers and grants from the centre to perform their functions. State governments’ expenditures therefore crucially depend upon the bounty of the

114

Macroeconomics

centre. Since the expenditures of both the central and the state governments and the taxes are largely at the control of the central government, it has been assigned the responsibility of stabilization. Table 3.5 shows the consolidated budget of revenue receipts, revenue expenditures and revenue deficit of the central and the state governments of India. The budget is a record or an account of the receipts and expenditures of the government. The budget has two accounts, namely revenue account and capital account. Each of these two accounts has a receipt side and Table 3.5

Combined receipts and disbursements of the central and state governments1 (Rs., crore)

I. Total receipts (A+B) (As per cent of GDP) A. Revenue receipts (1+2) (As per cent of GDP) 1. Tax receipts (As per cent of GDP) 2. Non-tax receipts2 (As per cent of GDP) B. Capital receipts3 (As per cent of GDP) II. Total disbursements (a+b+c) (As per cent of GDP) (a) Revenue4 (As per cent of GDP) (b) Capital5 (As per cent of GDP) (c) Loans and advances (As per cent of GDP) III. Revenue deficit (As per cent of GDP) IV. Gross fiscal deficit (As per cent of GDP)

02–03

03–04

04–05

7,10,177 28.9 4,46,749 18.2 3,52,899 14.4 2,93,850 3.8 2,63,428 10.7 6,95,203 28.3 6,11,809 24.9 64,757 2.6 18,637 0.8 1,65,060 6.7 2,33,594 9.5

8,40,675 30.5 5,11,038 18.6 4,08,097 14.8 1,02,941 3.7 3,29,637 12.0 7,86,112 28.5 6,72,702 24.4 85,821 3.1 27,589 1.0 1,61,664 5.9 2,32,059 8.4

8,75,621 27.8 6,05,180 19.2 4,85,375 15.4 1,19,805 3.8 2,70,441 8.6 8,57,644 27.2 7,22,675 22.9 1,12,241 3.6 22,728 0.7 1,17,495 3.7 2,33,236 7.4

05–06

06–07

10,14,689 11,24,687 28.3 27.1 7,07,054 8,69,940 19.7 21.0 5,76,596 7,18,788 16.1 17.3 1,30,458 1,51,152 3.6 3.6 3,07,635 2,54,747 8.6 6.1 9,59,855 11,48,824 26.8 27.7 8,06,366 9,58,942 22.5 23.1 1,32,585 1,70,106 3.7 4.1 20,904 19,776 0.6 0.5 99,312 89,002 2.8 2.1 2,39,560 2,63,944 6.7 6.4

07–08 13,11,122 27.9 9,96,266 21.2 8,34,094 17.8 1,62,173 3.5 3,14,856 6.7 13,09,897 27.9 10,55,770 22.5 2,33,920 5.0 20,207 0.4 59,504 1.3 2,56,286 5.5

Source: Reserve Bank of India. 1

Data pertaining to state governments relates to budget of 28 state governments and are provisional from 2006--07 onward. The data do not cover union territories with legislature, i.e. national capital region territory of Delhi and Puducherry. 2 Non-tax receipts consist mainly of profit of the public sector enterprises (PSEs) and fees charged by the governments for various services. 3 Capital receipts consist mainly of proceeds from the sale of PSE shares commonly referred to as disinvestment proceeds, proceeds from the sale of land and property, recovery of loans and loans and advances taken by the government in the given year. 4 Revenue disbursement or revenue expenditure consists of government consumption (G), subsidies, interest payments and transfer payments. 5 Capital disbursement or capital expenditure consists of investment expenditures of PSEs.

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an expenditure side. The receipts recorded on the receipt side of the revenue account and the expenditures or disbursements recorded on the expenditure side of the revenue account are referred to as revenue receipts and revenue expenditures respectively. Revenue receipts and revenue expenditures are those receipts and expenditures which have no direct bearing on the future receipts and expenditures of the government. Revenue receipts comprise tax receipts and non-tax receipts. The latter includes public sector enterprises’ profit and fees collected by the governments. Revenue expenditures, on the other hand, consist of government consumption (G), subsidies, interest payments and transfers. The excess of revenue expenditures over revenue receipts is referred to as revenue deficit. Note that revenue deficit is nothing but the negative of government saving. Receipts and expenditures recorded respectively on the receipt and expenditure side of the capital account are referred to as capital receipts and capital expenditures respectively. They comprise those receipts and expenditures which directly affect government’s future receipts and expenditures. Capital receipts consist mainly of proceeds from the sale of shares of public sector enterprises and physical assets of the governments. Obviously, such sales directly reduce future revenue receipts of the government. They also include loans taken by the government. They directly contribute to future interest payments of the government. Capital expenditures consist mainly of investment expenditures of public sector enterprises and loans and advances given by the government. They also directly add to future receipts of the government. In the Indian context, as we find from Table 3.4, besides government consumption expenditure, government investment expenditure constitutes an important component of aggregate final demand for goods and services. This part of aggregate investment should be treated separately and shown explicitly as it is in the direct control of the government and can be used by the government for purposes of stabilization. There is a complementarity between private and public investment. Public investment in infrastructure such as roads, power, etc., induces larger doses of private investment as it implies more plentiful supplies of crucial infrastructural inputs. Hence public investment is more powerful than public consumption in influencing GDP. Table 3.4 shows that India had revenue deficit every year during 2002–2008, i.e. in all these years government saving in India was negative. However, India’s revenue deficit declined steadily over time from 2002–03 to 2007–08. During the given period, it should be noted, rates of direct and indirect taxes were cut. Despite that, tax revenue as a percentage of GDP rose consistently. This is perfectly consistent with the SKM. However, efforts were also made all through this period to broaden the tax base by bringing in services in the ambit of taxation. Previously, there were taxes only on goods and not on services. Aggregate public expenditure as a percentage of GDP declined only slightly during the period under consideration. To get an idea about the nature of government’s fiscal policy, one has to examine carefully how it is proposing to change each component of revenue and expenditure at the beginning of every fiscal year. Information regarding this becomes available, when central and state governments place their budget proposals in the parliament and state legislatures at the beginning of every fiscal year. If they propose to cut tax rates and to raise subsidies, transfers, public consumption and investment expenditures, they are planning to undertake expansionary fiscal policy and vice versa. EXERCISE 3.13 Derive the conditions under which government’s efforts at raising its saving by raising taxes or reducing its expenditure may lower its saving.

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3.14

CONCLUSION

The SKM brings the demand side factors to the centre stage in the determination of GDP in the short run. Even though demand side factors play a crucial role in the determination of GDP, the SKM is too simple to apply to Indian reality. First, the bulk of the investment expenditure is financed with loans. Consumption expenditure is also partly loan financed. Hence price and availability of loans should be important determinants of aggregate demand. The SKM ignores the loan market altogether and thereby commits a serious error. Keynes was of the view that in times of recession business expectations are usually so bleak that the investors undertake only essential investments and they cannot be induced to invest more by offering them more loans at lower interest rates. In other words, Keynes thought that aggregate demand is largely interest inelastic in times of recession. Even though this might be true, one cannot a priori rule out cost of borrowing and availability of loans as important determinants of aggregate demand. Moreover, the assumption that aggregate supply is perfectly elastic at a fixed set of prices may be far too extreme in Indian context. One reason for this is the importance of agriculture in aggregate production. Agricultural markets are competitive and agricultural prices are highly flexible. Moreover, since land is scarce, law of diminishing marginal return to inputs applies to agriculture. This means that the input requirement for one additional unit of agricultural output and therefore marginal cost of agricultural production rise with an increase in the supply of agricultural output. Under competitive market conditions, which is the case in Indian agriculture, this means that the supply price of agricultural output increases with a rise in agricultural supplies, i.e. agricultural supply is an increasing function of its price. Marginal cost of production rises in other sectors as well because of shortages of crucial infrastructural inputs such as power, roads, transport, etc. In case of power shortage, for example, to raise output beyond a certain level, producers have to set up power generating units of their own and this raises marginal cost of production. Moreover, prices do respond to changes in demand and supply conditions. Finally, India is an open economy. Quite a sizable part of its GDP is exported and a large portion of its aggregate demand is met with imports. For all the reasons mentioned above the SKM presented here has to be extended in many directions to capture India’s macroeconomic reality. This is what we shall seek to do in the following chapters.

PROBLEMS 1. Consider a simple Keynesian model for a closed economy without government. At GDP (Y) = 1000, producers have to sell 20 units from their stock to meet the customers’ demand fully. It is given that the equilibrium level of GDP is 1040. (i) Find out the impact of an increase in autonomous expenditure on the equilibrium level of Y. (ii) Suppose due to technological progress input requirement per unit of output becomes half of what it was before. What impact is it likely to have in this model? Explain. 2. (a) In a simple Keynesian model for a closed economy without government, there are two groups of income earners. Group 1 earns 800, while the income of Group 2 is Y – 800, where Y denotes NDP. Average consumption propensities of Group 1 and Group 2 are 0.6 and 0.5 respectively. Investment function is given by 400 + 0.1Y.

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Derive the aggregate saving function and the equilibrium amount of saving. Now suppose there takes place a transfer of income from Group 1 to Group 2 of 100 units. How will it affect the aggregate saving function? Do you observe paradox of thrift here? Explain. 3. Suppose that an economy is given by the following equations: C = 100 + 0 .8(Y – T), I = 20, G = T = 10. Find out the equilibrium level of Y. What is the value of the involuntary change in inventory at Y = 500? By how much will Y rise following an increase in G by 10? How does your answer to the last question change if marginal propensity to consume out of disposable income is 0.9 instead of 0.8? Explain. 4. Suppose that an economy is given by the following equations: C = 100 + 0.8(Y – T), I = 20, G = T = 10. The full employment level of output of the economy is Yf = 800. (i) By how much will the government have to change its consumption expenditure to achieve full employment equilibrium? (ii) If the government wants to achieve the same target by changing the level of lump sum tax, by how much will it have to change T? In case your answers to (i) and (ii) are different, can you explain the difference? 5. Following a deterioration of investors’ expectations regarding the future course of business, investment will fall autonomously leading to a reduction in output and employment. This will reduce firms’ profit and depress business sentiments further. Investment therefore is likely to fall again. Can this scenario be captured by assuming that in addition to an autonomous component investment function has an induced part, which is an increasing function of Y? Does the explanatory power of the simple Keynesian model in explaining economic fluctuations increase if investment function is of the type mentioned above instead of being just an exogenously given amount? Explain. 6. In the Keynesian cross (simple Keynesian model) the consumption function is given by C = 200 + 0.75(Y – T), T = 10 – 0.25Y, and I = 100. (a) Graph the planned expenditure as a function of Y. (b) What is the equilibrium level of income? (c) If government purchases increase to 125, by how much the equilibrium income rise? (d) What level of government purchases is needed to achieve an income of 1600? (e) How does your answer to (d) change if the tax rate is zero instead of being .25. Explain your answer. 7. Consider the following functions: C 50  0.8YD ; I 70; G 200; TR 100; t 0.2. (a) Suppose t rises to 0.25. Calculate the change in the budget surplus. Would you expect the change in the budget surplus to be more or less if C = 0.9 instead of 0.8? Explain. (b) Can you explain why the multiplier is 1 when t = 1? (c) Suppose the economy is operating at equilibrium with Y0 = 1000. If the government undertakes a fiscal change so that the tax rate, t, rises by 0.05 and the government spending increases by 50, will the budget surplus go up or down? Why? 8. In the simple Keynesian model for a closed economy the amount of change in inventory at Y = 200 is 10 units and the equilibrium level of NDP goes up by 10 units following an increase in autonomous expenditure by 5 units. There is a lump sum tax and its value is 50. By how much will the government have to raise the level of output to

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achieve equilibrium with full employment level of output, which is 230 units? By how much will the government have to lower its lump sum tax to raise the equilibrium level of output to its full employment level? (Do you have to make any assumption to answer this?) Explain your answer. If the marginal propensity to consume out of NDP was (3/4), what would be the required reduction in the lump sum tax to bring about the same amount of increase in NDP? Explain the difference, if any. Derive the aggregate saving function of the initial situation where I = 50. 9. Suppose the equilibrium level of NDP in the simple Keynesian model is ` 150 and it goes up by 2 units following an increase in the lump sum transfers by 1 unit from its initial value of zero. Derive the value of the involuntary change in inventory of the initial situation as a function of NDP. Plot it in a diagram. Identify the parameters of this function and explain their meanings. Derive the initial equilibrium level of NDP in terms of the parameters of this function. If the equilibrium level of NDP had risen by 3 units instead of 2 following the unit reduction in the lump sum tax, which of the parameter or parameters of the function you have derived would have been affected? By how much the initial equilibrium level of NDP, with transfers equal to its initial value, zero, would change following the change in this (these) parameter (parameters)? Explain the result. 10. Suppose the tax function is proportional, with the tax rate, 0.1, but the maximum amount of tax the government can collect is ` 100. If NDP (Y) goes up by ` 8 at Y = 500 following an increase in the autonomous expenditure by ` 2, then by how much will it increase at Y = 1200 following the same amount of increase in the autonomous expenditure when all components of aggregate planned final expenditure other than consumption are autonomous? Explain your answer. Derive the private saving function and plot it in a diagram under the assumption that C = 10, where C º autonomous component of the consumption expenditure.

REFERENCES Rakshit, M. (1989), Studies in the Macroeconomics of Developing Countries, Oxford University Press, Delhi. Samuelson, P. (1948), “The Simple Mathematics of Income Determination” in Income Employment and Public Policy: Essays in Honor of Alvin Hansen, W.W. Norton & Co., Inc., New York.

4 4.1

Financial Sector, Money Supply and Interest Rates

INTRODUCTION

The financial sector refers to the sector that mobilises funds from the economic agents with surplus funds to those who are in need of funds. Financial sector provides the former with opportunities for deploying their surplus funds securely and profitably and enables the latter to secure funds readily at reasonable costs. The efficiency of the financial sector is assessed on the basis of how exhaustively it can mobilize the surplus funds of the economic agents and how adequately and cheaply it can meet all the legitimate demands for funds. Corporations and the government can raise funds by selling securities in the market. Securities are pieces of papers which specify the legal rights of the holders of the securities on the incomes and properties of the issuers of the securities and the conditions under which the right can be exercised. A corporation can raise funds, for example, by selling equities or shares in common stock. The holders of equities of a corporation are legally the owners of the company and the profits made by the company belong to them. Consider a corporation, which has issued and sold 100 equities. The holder of one of these equities is an owner of this company and has claim on (1/100)th of the profit of the company. Securities may be secured or unsecured. A security is secured if it is issued against a property of the issuer. This property is called collateral. In case of default, the holder of the security has the legal right to get hold of the collateral and sell it off to cover the losses. Similarly, a loan, which is given against collateral, is a secured loan. An unsecured security is one, which is not backed by collateral. It simply contains a promise of the issuer that he will make all the payments specified in the security. Such securities are called promissory notes. The securities that are issued against a specific property or a specific set of properties of the issuer pledged as collateral are called mortgage bonds, while securities that are issued against all the properties of the issuers are called debenture bonds. Most of the securities, other than equities, have 119

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specific dates of maturity. A security ceases to yield any income to its holder after the date of its maturity. Let us illustrate these points with some specific examples. One important kind of securities issued by the government is treasury bills (T-bills). In India the central government issues treasury bills. Treasury bills have fixed maturity periods. Government of India in 2009 issued only 91-day, 182-day and 364-day T-bills, which mature in 91 days, 182 days and 364 days respectively after the day of their issue. T-bills only have a face value, which is paid on the day of maturity. If a 91-day T-bill is held for more than 91 days after the day of its issue and then presented to the government for redemption, the government will pay the holder only the face value and no extra amount for the days it was held after the day of its maturity. The government borrows by selling T-bills. A bond is a security, which has a coupon and a face value. It pays a fixed sum, the coupon, at regular intervals until it matures. On the day of its maturity it pays not only the coupon but also the face value. The face value may be called the principal and the coupon, the interest. There are firms, which issue and sell securities to use the sales proceeds mainly to lend and to buy securities of other firms. These firms are called financial institutions or financial intermediaries. A bank, for example, issues and sales various kinds of deposits, which are all securities, and uses the proceeds to lend or to buy securities of other economic agents. Commercial banks, cooperative banks, specialized financial institutions, insurance companies, mutual funds and non-bank financial companies (NBFCs) are all financial institutions. The markets of all kinds of securities are referred to as financial markets. Financial markets and the financial institutions together constitute the financial sector of the economy. In this chapter, we shall give a brief overview of how the financial institutions and the financial markets operate. We shall focus on the financial markets first and then examine how prices of securities are determined in these markets.

4.2 FINANCIAL MARKETS Financial markets may be decomposed in many ways. From the point of view of the length of maturity of securities or loans, financial markets are divided into money market and capital market. The former is the market for securities/loans of maturity periods of one year and less. Securities and loans of maturity periods of more than one year are traded in the capital market. Again, from the point of view of whether markets deal with newly issued securities or old ones, financial markets are divided into primary and secondary markets. In the primary market, newly issued securities are traded, while old securities, i.e. securities that have been sold at least once, are traded in the secondary market. Most of the government securities and securities issued by corporations of substantial business standing have active secondary markets. In what follows, we shall briefly discuss the money market, as it plays a very crucial role in the regulation of money supply.

4.2.1 Money Market The major segments of India’s money market are the call money market, repo market and market for collateralized borrowing and lending obligations (CBLOs). The call money market is the market for loans on call, i.e. the loans in the call money market are payable on demand, i.e. they have to be paid back whenever lenders want them to be paid back. Maturity periods

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of these loans vary from overnight to 14 days. Only commercial and cooperative banks are allowed to operate in the call money market. It is an interbank market in India. Banks which have surplus funds in the short run lend in this market, while banks that are deficient in funds in the short run borrow from this market. Besides banks, all other financial institutions and corporations with surplus short-term funds and in need of short-term funds can participate in the other segments of the money market.

Repo market Repo refers to selling of securities by a seller to a buyer with the commitment to buy the securities back at a specific date in future. This amounts to borrowing by the seller against the collateral of the securities sold. An interest rate applies to the loan. This interest rate is referred to as the repo rate. This implies that the seller entering into the repo agreement buys back the securities at the agreed upon specific date in future at a price higher than the sale price. Reverse repo refers to the purchase of securities by a buyer with the obligation of selling them back to the seller at a specific date in future. Reverse repo is therefore lending against the collateral of the securities bought. The lender charges an interest on the sum lent. This is referred to as the reverse repo rate. The reverse repo rate makes the sell-back price higher than the purchase price. In the repo market, repos are traded. Since repos and reverse repos represent borrowing and lending against collaterals, they are quite safe. This is particularly true, if securities involved are government securities. Repos and reverse repos are usually short-term loans with the maturity period varying from overnight to 14 days.

Market for CBLOs In the market for collateralized borrowing and lending, loans are given and taken against collateral. They are therefore highly safe. In the CBLO market maturity period of loans do not exceed 1 year. All economic agents with surplus funds in the short-run and all economic agents in need of short-term funds can participate in the CBLO market.

4.2.2

Market for Foreign Exchange

Besides securities and loans, foreign currencies are also traded for domestic currency in the financial markets. Why is foreign exchange traded for domestic currency? The reason is the following. India is an open economy and Indians may want to buy foreign goods and assets. However, they will have to pay for these foreign items with foreign currencies. Hence, to make these purchases, they will first buy foreign currency with Indian rupee. Again, to buy Indian goods and assets, foreigners will have to pay with Indian currency, which they will have to secure by selling their own currencies for rupee. Thus Indians’ demand for foreign goods and assets and foreigners’ demand for Indian goods and assets give rise to trading in foreign currencies for Indian currency. There is obviously a market for each kind of foreign currency where the given foreign currency is traded for Indian rupee and these markets determine prices of all the foreign currencies in terms of Indian rupee. To illustrate, consider the market where

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the US dollar is traded for Indian rupee. In this market demand for the US dollars comes from the Indians wanting to buy goods and assets of the US and supply of the US dollars come from the US residents wanting to buy Indian goods and assets. Note that prices of Indian goods and assets are quoted in Indian rupee, while those of the US goods and assets are quoted in the US dollar. Corresponding to any given price of the US dollar in terms of the Indian rupee, there are unique prices of Indian goods and assets in terms of the US dollar and also unique prices of the US goods and assets in terms of Indian rupee. To illustrate, suppose the price of the US dollar is ` 40, i.e. to buy 1 US dollar one has to pay ` 40. Thus, if the price of Basmati rice in India is ` 40 per kg, to the people in the US, its price is $1. Similarly, if a particular model of Compaq computer sells at $1000 in the US, to Indians its price will be ` 40,000. If the price of the US dollar goes up in terms of rupee, prices of Indian goods become cheaper in terms of the US dollar leading to an increase in the USA’s demand for Indian goods and assets. If the USA’s demand for Indian goods and assets is elastic, the value of the USA’s demand for Indian goods in terms of the US dollar will go up bringing about an increase in the supply of the US dollar for the purchase of rupee. Again, the increase in the price of the US dollar in terms of Indian rupee will make the US goods and assets dearer to the Indians in terms of rupee bringing about a decline in India’s demand for these goods and assets. So Indians’ demand for the US dollar in exchange for rupee will go down. Thus, if the USA’s demand for Indian goods and assets is elastic, supply of the US dollar for purchasing rupee will be a decreasing function of the price of the US dollar in terms of rupee, which we shall henceforth refer to simply as the price of dollar. India’s demand for dollar in exchange for rupee is a decreasing function of the price of dollar which is also called exchange rate. We show these demand and supply functions in Figure 4.1 where DD and SS represent respectively demand for US dollar in exchange for rupee and supply of the US dollar for purchasing rupee. The equilibrium exchange rate corresponds to the point of intersection of the DD and SS schedules. The equilibrium price of the US dollar is indicated in Figure 4.1 as e*. These schedules are drawn for given prices of Indian goods in terms of rupee and given prices of the US goods in terms of the US dollar and also for given interest rates in the US and India. We shall explain the reason why interest rates also play a part in the formation of demand and supply of the US dollar in exchange for Indian rupee shortly. If these prices and interest rates change, these curves will shift and so will the

Figure 4.1 Determination of the exchange rate.

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equilibrium exchange rate in consequence. If all other factors remaining unchanged, there takes place an increase in the interest rates in India, lending to Indian residents will be more lucrative and the US residents with funds to lend may be induced to lend to Indian residents rather than to the US residents in need of loans. To lend to Indian residents, the US residents with surplus funds will have to first buy Indian rupee by selling the US dollar. Thus supply of the US dollar for purchasing rupee will go up at every price of dollar leading to a rightward shift in the SS schedule in Figure 4.1 engendering a fall in the exchange rate. When foreigners lend to Indians, capital flows into India. On the other hand, if Indian residents lend to foreigners, capital flows out of India. Since prices and interest rates are volatile, the exchange rate is likely to fluctuate a great deal. One of the major objectives of the central bank of a country, which is the Reserve Bank of India (RBI) in India, is to keep the exchange rate stable. How does the RBI do it? Let us explain. Suppose the RBI wants to keep e at e*. Consider the situation where initially DD and SS intersect at e*. Now, suppose there takes place a rightward shift in DD engendering an excess demand for the US dollar at e* and thereby putting an upward pressure on e. What does the RBI do in this situation to keep e at e*? Let us explain. The RBI keeps stocks of all foreign currencies including that of the US dollar. To keep e at e* following the emergence of excess demand for the US dollar for purchasing rupee at e*, the RBI will supply the US dollar from its stock, buy up rupee and meet this excess demand and thereby prevent e from changing. Similarly, in the event of excess supply emerging at e*, the RBI will buy up the US dollar in excess supply by selling rupee and thereby keep e at e*. We have given some idea about financial markets and the instruments that are traded there. We shall now discuss briefly how these instruments or securities are priced. EXERCISE 4.1 Suppose supply and demand of the US dollar in exchange for Indian rupee are given respectively by S = aP + b e and D = g P – rP* – j e; (gP – rP*) > 0, where P º average price of goods and services in India in Indian rupee, e º price of the US dollar in Indian rupee, P* º average price of goods and services in the US in the US dollar and finally, a, b, g, r and j are parameters. Derive the equilibrium price of the US dollar. What should the RBI do to keep the exchange rate unchanged, if (i) P goes up by dP and (ii) P* rises by dP*? Illustrate your answer graphically.

4.3

PRICING OF SECURITIES

There are many different types of securities bought and sold in the financial markets. Some of them are treasury bills (T-bills), certificates of deposits (CDs), bonds, equities, etc. In what follows we shall explain how these securities are priced.

4.3.1

Pricing of Treasury Bills

How is a T-bill priced? To illustrate, consider a 91-day T-bill with the face value F. This T-bill promises to pay its holder a sum, F, 91 days after its issue. At what price will it sell in the

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market at the time of its issue? To derive this price, one has to take into account the interest rate on similar securities (i.e. securities with a maturity period of 91 days and as safe as T-bills) in the market. Suppose the interest rate on such securities is 10 per cent, i.e. if ` 100 is invested in such a security, the investor will get back after 91 days ` 110. Once this is known, it is easy to derive the price of the T-bill, which we shall denote by P. The interest income the T-bill yields is (F – P). This must be 10 per cent of P, i.e. (F – P) should be equal to (1/10)P. If (F – P) exceeds (1/10)P, everyone will want to invest in this T-bill instead of in the other similar securities creating an excess demand for this T-bill and thereby driving up its price. Similarly, if (F – P) falls short of (1/10)P, no one will want to invest in this T-bill. They will invest in the other similar securities instead, creating an excess supply of this T-bill and thereby driving down its price. Thus we get P from the following equation

FP

È 10 Ø É 100 Ù Ê Ú

P

À

P

F 10 1 100

More generally, if the interest rate on securities similar to the 91-day T-bill is r, i.e. if ` 1 invested in such securities yields an interest income of ` r after 91 days, the price of the T-bill will be given by F P (4.1) 1r It may be useful to introduce the concept of the present value here. Present value relates to a given sum of money of a future date. Present value in the current period of a given sum of money of a future date is defined as the sum of money, which, if lent in the current period at the interest rate prevailing in the market, will yield the given sum of money at the given future date in principal and interest. Now, consider (4.1). The interest rate prevailing in the current period on 91-day loans without any risk of default is r. If ` (F/(1+r)) is invested in the current period in such loans, it will yield ` F after 91 days in principal and interest. Hence ` (F/(1+r)) is the current period’s present value of ` F of a date, which is 91 days after the current date on which the investment in the T-bill is being made. Obviously, the T-bill will be sold at the time of its issue at the present value at the time of its issue of its face value. If a higher price is quoted, no one will be willing to buy it, as by lending out a smaller sum at the market rate of interest at the time of the issue, the face value of the T-bill can be earned 91 days later. Again, if a lower price is quoted, everyone will want to buy this T-bill, since to earn F after 91 days from the date of the issue of the given T-bill one has to lend a larger sum at the date of the issue of the T-bill in the market. This will drive up the price of the T-bill. Often the interest rate is expressed as an annualized interest rate or an annual effective rate. The interest rate is annualized in the following manner. Suppose the total interest income yielded by a 91-day security is R. R is obviously given by the excess of the face value of the security over the price of the security at which it was bought at the time of its issue. The interest income yielded by the security per day on the average is therefore (R/91). If the security had yielded daily interest income at this rate on the average over a period of 365 days, it would have yielded a total interest income of (R/91) × 365. If we express this as a percentage of the issue price of the security, which is the price at which the security was bought and sold at the time of its issue,

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we get the annualized interest rate or the annual percentage rate (APR) on the security. If the issue price of the security is P , the APR is given by APR =

R 365 ¹ ¹ 100 P 91

To get the actual interest rate on the security, which is ( R / P ) ×100, we have to multiply the APR by (91/365). EXERCISE 4.2 Suppose a 182-day T-bill was issued on 6 November 2009. It has a face value of ` 1000. The APR on risk-free 182-day loans on 6 November 2009 was 10 per cent. At what price was this T-bill sold on 6 November 2009? Explain your answer.

4.3.2 Pricing of Certificate of Deposits (CDs) CDs are issued in India by commercial banks and financial institutions. CDs issued by commercial banks have a specific date of maturity and a face value. Maturity periods of these CDs vary from 7 days to 1 year. These CDs are negotiable, i.e. they are tradable in secondary markets. CDs issued by nationalized banks are as safe as T-bills. Suppose that APR on 182-day T-bills is 5 per cent. At what price will a 182-day CD with the face value of ` 1000 issued by the SBI be sold at the time of its issue? The actual interest rate on 182-day T-bills, as derived from the 5 182 ¹ . This means that every rupee invested in an 182-day T-bill at the time of APR, is 100 365 5 182 its issue fetches ` ¹ in interest at the time of its maturity. Therefore, the price of the 100 365 1000 . More generally, a T-day CD with CD in question at the time of its issue will be 5 182 1 ¹ 100 365 a face value of F, with the APR on risk-free T-day loans of R per cent at the time of its issue, F will be sold at a price of . R T 1 ¹ 100 365 Repos and CBLOs backed by the government securities are as safe as CDs of nationalized banks and T-bills. Accordingly, their prices can also be derived following the line suggested above.

4.3.3 Pricing of Bonds A bond usually has a fixed maturity period, a face value and a coupon. The coupon is normally written as a percentage of the face value. When the coupon is expressed as a percentage of the face value, it is called coupon rate. The coupon in most cases is paid semi-annually, i.e. every six months. Let us illustrate these concepts with an example. Consider a two-year bond with a

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face value of ` 1000 and a coupon rate of 10% paid semi-annually. This means that the bond has a maturity period of 2 years. It also has an annual coupon of ` 100, which it pays semiannually, i.e. it pays ` 50 every 6 months. On the day of its maturity it will pay the face value of ` 1000 and coupon of ` 50. At what price will the bond be sold at the time of its issue? For this we have to derive the present value (PV) at the time of the issue of the bond of all the incomes yielded by the bond. Six months after the date of its issue it will yield coupon of ` 50. What is its PV at the time of its issue? Suppose the interest rate on 6-month loans at the time of the issue of the bond was 5%, i.e. ` 100 lent out for 6 months at the date of the issue of the bond yielded on maturity interest income of ` 5. So the PV of the coupon of ` 50 at the 50 . If the interest rates on 1-year loans at the time of the issue of the bond would be ` 5 1 100 time of the issue of the bond was 8%, the PV of the second coupon payment paid 1 year after 50 . Similarly, if interest rates on 1.5-year loans and 2-year the date of issue would be 8 1 100 loans at the time of issue were 12% and 15% respectively, PV of the third coupon payment of ` 50 and that of the payment on maturity of the face value (principal) and coupon of ` 150 50 150 would be and respectively. To earn ` 50 after 6 months from the date of issue 12 15 1 1 100 100 50 at the date of issue. Similarly, to earn ` 50 5 1 100 after one year, ` 50 again after 1.5 years and ` 150 after 2 years from the date of issue of the bond one has to lend respectively their PVs at the date of issue of the bond. Thus to earn the income stream yielded by the bond, one has to lend at the date of issue of the bond the sum of these PVs as given by

in principal and interest, one has to lend

50 50 50 150    5 8 12 15 1 1 1 1 100 100 100 100 At the time of the issue of the bond, it will be bought and sold at Z. The reason is quite simple. If a higher price for the bond is quoted, no one will be interested in buying the bond, as by lending a smaller sum of money at the interest rates prevailing at the time of issue of the bond, the income stream yielded by the bond can be earned. Hence the price of the bond will fall. If the price quoted is less, everyone will be interested in buying the bond, since to earn the income stream yielded by the bond one has to lend out a larger sum of money. There will, therefore, be an excess demand for the bond and the bond price will rise. More generally, the price of a T-year bond with the face value, F, and A% coupon rate paid semi-annually will be sold at the time of issue of the bond at Z

A 1 A 1 F 100 2  100 2  1  r1 (1  r2 ) 2

F P

"

A 1 100 2   (1  rm ) m F

"

A 1 100 2  (1  r2T ) 2T F

(4.2)

Financial Sector, Money Supply and Interest Rates

where r1 r2 rm r2T

º º º º

interest interest interest interest

rate rate rate rate

on on on on

127

(1/2)-year loan, 1 (=2/2)-year loan, (m/2)-year loan, and T(=2T/2)-year loan.

EXERCISE 4.3 (a) Suppose Ram invested ` 1000 in a 1-year CD with a face value of ` 1200. He sold it off with 182 days still remaining to maturity. At the time he sold it, the APR on 182day T-bills was 10%. At what price did he sell it? Explain your answer. (b) Consider a 2-year bond with a face value of ` 1000 and a coupon rate of 10% paid annually. Consider also a zero coupon bond which does not have a coupon, but has a face value. Both the bonds were issued at the same time. They were also sold at the same price. Suppose that the APR on loans of all maturities at the time the bonds were issued was 15%. What was the face value of the zero coupon bond? Explain.

4.3.4

Comparison of Different Types of Securities

To compare different types of securities, we have to use the concept of market yield to maturity or market yield in short of a security. The market yield to maturity of a security is an indicator of the interest income yielded by the security if it is held up to the date of its maturity. It is expressed as an annual rate. Let us illustrate the concept with a simple example. Take the case of a 1-year CD that offers a one time interest payment on maturity at the annual rate of interest of 15%. This means that if ` 100 is invested today in this CD, it will yield after 1 year ` 115. The interest income that it yields is ` 15 in one year on a principal of ` 100. Its market yield or market yield to maturity is therefore 15%. We shall henceforth refer to this CD as the first CD. Consider now a more complicated example of a 6-month CD with an APR of 12% and monthly compounding. This means that the CD will calculate the interest payable on the amount invested in the CD every month. Not only that every month the CD will calculate interest income on the amount invested, but also on the interest income accumulated in the previous months. This payment of interest on interest income is called compounding and the intervals at which the interest is calculated on the principal as well as on the accumulated interest is called compounding periods. Here the compounding period is a month. This means that the interest on the sum invested and also on the accrued interest will be calculated every month. The points we have made above will be clear from the following discussion. We have to derive the monthly interest rate on this CD from the APR. From the APR we find that the daily interest income on ` 1 invested in the CD is (12/100)/360 (assuming 1 year to have 360 days for simplicity). Therefore, monthly interest income on ` 1 invested in the CD is [(12/100)/360] × 30 =(12/12.100)=1/100. Thus the monthly interest rate on the CD is 1%. Let us now see how much this CD will pay on its maturity if ` 1 is invested in it today, which is the day of its issue. After one month, the principal plus the interest becomes 1 + (1/100). At the end of the second month, it regards the whole of 1 + (1/100) as the principal and calculates the interest payable on the whole of it. This means that at the end of the second month the CD calculates interest at the

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rate of 1% not only on the principal of ` 1 but also on the interest income of ` (1/100) that accrued at the end of the first month. Thus at the end of the second month, the amount payable to the investor becomes 1 + (1/100) + [1 + (1/100)] × (1/100) = [1 + (1/100)]2. Again at the end of the third month, the amount of payable becomes [1 + (1/100)]2 + [1 + (1/100)]2 × (1/100) = [1 + (1/100)]3. Thus at the end of the sixth month, the amount payable becomes [1 + (1/100)]6. We shall refer to this CD as the second CD. To derive the market yield of the second CD, we have to calculate what we call the effective annual interest rate (EAR) on the second CD. For that we have to find out how much interest income would it have yielded had its maturity period been 1 year instead of 6 months. Obviously, if its maturity period were 1 year, it would have yielded on an investment of ` 1 a sum of ` [1 + (1/100)]12. The EAR of a security is defined as the total amount of interest income yielded by a security on an investment of ` 1 in one year. The principal in our case is ` 1. So the interest income that the second CD would yield in one year is the total amount of income that it would yield in one year over and above ` 1. Therefore EAR = [1 + (1/100)]12 – 1

(4.3)

To express it in percentage terms, we have to multiply the RHS of (4.3) by 100. Let us now compare the first CD and the second CD. The first CD’s EAR is (15/100). Obviously, the CD with the higher EAR is better. Consider a two-year bond with a face value of ` 1000 and a coupon rate of 10% paid semiannually. Suppose it was sold at a price of ` 800 at the time of its issue. To derive its market yield to maturity, we have to first derive the uniform discount rate that makes the PV of its income stream equal to its price. Denoting this uniform interest rate by r, we get 800

50 50   1  r (1  r ) 2

"  (11050  r)

24

(4.4)

From (4.4), it follows that if ` 800 is lent out at the interest rate, r, which is compounded every 6 months or semi-annually, it can yield in principal and interest the income stream yielded by the bond. Hence, we may interpret r as the interest rate on the bond, which is compounded semi-annually. To derive the market yield on the bond, we have to annualize it, i.e. we have to convert it into EAR. The EAR, as we have already defined it, is the interest income the bond will yield in one year on an investment of ` 1. If ` 1 is invested in the bond, the interest rate r will apply to it and it will be compounded semi-annually. Hence in one year ` 1 invested in the bond will become (1 + 2)2. Therefore, the interest income the bond will yield on an investment of ` 1 in one year is (1 + r)2 – 1. Thus EAR of this bond is given by EAR = (1 + r)2 – 1 To express it in percentage terms, we have to multiply the EAR derived above by 100. This EAR is the market yield of the bond. Following the line suggested above, we can derive the market yield or market yield to maturity of securities of all maturities. Corresponding to any given maturity period, there will usually be a large variety of securities of different degrees of risk. We can calculate the market yield of the risk-free securities of every given maturity period and plot them in a graph.

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129

The curve that we shall get showing the risk-free market yield of securities of every different maturity period is called the yield curve. Let us now focus on the following question. Suppose the buyer who bought the first CD at the time of its issue chooses to sell it at the beginning of the fourth month. At what price will he sell it? At the beginning of the fourth month, the first CD in which he invested ` 100 at the time of its issue will mature after three months. It is therefore comparable to similar 3-month securities. If the CD is issued by a nationalized bank, for example, it is comparable to a 91-day T-bill. Suppose that the interest rate on such T-bills or securities is 10% so that ` 1 invested in such a security yields an interest income of ` (1/10) after 3 months. The payment that the CD in question will make on maturity is ` 100. [1 + (1/100)]6. The present value of this sum at the beginning of the fourth month discounted at the market interest rate on similar securities is

100 ¹ [1  (1 / 100)]6 . It will, therefore, sell at this price. Explain it yourself. 1 1 10

EXERCISE 4.4 (a) Consider a 3-month T-bill with a face value of ` 110. Suppose it was sold at ` 100 at the time of its maturity. What is its market yield to maturity? Compare it with a 6-month T-bill with a face value of ` 120 and sale price of ` 100 at the time of its issue. Explain. (b) Consider a 5-year zero-coupon bond with a face value of ` 2000. Suppose it was sold at ` 1400 at the time of its issue. What is its market yield to maturity?

4.4 FINANCIAL INSTITUTIONS IN INDIA Financial institutions are the key players in the financial sector. At the top of the financial institutions is the central bank of the country, which is the Reserve Bank of India (RBI) in India. It supervises, monitors and regulates all the other financial institutions. Next in importance comes the commercial and the cooperative banks. There are also specialized financial institutions or development financial institutions such as the EXIM Bank of India, Small-Scale Industrial Development Bank of India (SIDBI), National Bank of Agriculture and Rural Development (NABARD), National Housing Bank, etc., insurance companies such as the LIC, GIC and its subsidiaries, the mutual funds and the non-bank financial companies. We shall discuss about these financial institutions briefly below. Commercial and cooperative banks raise their funds mainly by selling deposits. They use these funds to lend and also to invest in securities. To run their business, banks have to be ready all the time to meet depositors’ demand for withdrawal from their deposits. If banks fail to meet these demands, people’s faith in the banks gets shaken. They become hesitant in buying bank deposits and banks have to go out of business. However, if the banks hold on to all the deposits they get, they will only be paying interest on the deposits, but the deposits will not yield any income for them. They will only lose. To make profit, the banks have to lend out the deposits. But, if they lend out all their deposits, they may not be able to meet depositors’ demand for withdrawal. They have to therefore strike a balance between

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profitability and remaining ready all the time to meet depositors’ demand for withdrawal. Actually, to meet depositors’ demand for withdrawal, banks need not hold all their deposits in the form of cash. Everyday some deposits are withdrawn, but everyday some new deposits are made. Lenders also repay their loans and pay interest on their loans. Thus everyday banks receive some cash and everyday they have to make payments. The banks are in trouble only if the outflow of cash exceeds the inflow. Hence, the banks have to keep in their hands that amount of cash that is sufficient to bridge the excess of the outflow over the inflow, when such situations occur. For this, banks need to keep only a small fraction of their deposits in the form of cash. Moreover, in case of trouble, i.e. if on some day their holding of cash falls short of the amount that is needed to bridge the gap between the outflow and the inflow mentioned above, they can borrow from the market. They can borrow from the RBI as well. The RBI is the lender of last resort to the banks. If banks fail to secure loans from the market to tide over the temporary shortfall of cash, they can always borrow from the RBI. It is the duty of the RBI to lend to the banks, if they approach the RBI for loans to meet their temporary need for cash. The RBI issues all the currency notes and coins in India. Hence, it is always able to lend. The part of deposits that the banks hold in the form of cash is held in two ways. A part is held in the form of currency and coins with themselves. This part is referred to as vault cash or cash on hand. The remaining part is held in the form of deposits with the RBI. The RBI stipulates a minimum fraction of deposits which the banks have to hold in cash. This is called cash reserve ratio (CRR). In August 2009 CRR was 5% in India, i.e. the banks at that time had to hold at least 5% of their deposits in the form of cash reserves. The amount of reserves the banks have to hold under the stipulation of the CRR is called the required reserve (RR). Over and above this RR, banks may choose to hold a fraction of their deposits in the form of additional reserves or excess reserves. Since banks have to be ready all the time to show to the RBI that they are fulfilling the CRR requirement at least on the average, they cannot use the RR much to meet the shortfalls of the outflows of funds over the inflows. Hence they maintain excess reserves. The amount of excess reserves banks choose to hold depends on various factors. We shall discuss some of the important ones here. The fund banks hold as excess reserve yields either no income or very little income. Had the banks lent out their cash reserves, they would have earned much larger interest income. Hence the higher the interest rates on loans, the less is the incentive on the part of the banks to hold excess reserves. The amount of excess reserves banks want to hold is therefore likely to be a decreasing function of the interest rates on bank loans. If the banks hold excess reserves, their requirement of loans for meeting the temporary shortfalls of inflows over outflows goes down. They save on the cost of borrowing. Banks usually borrow from the call money market, which is also the interbank loan market in India, to bridge temporary shortfalls of cash. We shall discuss the call money market shortly. The interest rates prevailing in the call money market are called call rates. Banks can also borrow from the RBI. The higher the call rates or the rates of interest at which they can borrow from the RBI, the greater will be the incentive for holding more excess reserves. Excess reserves are therefore likely to be an increasing function of the call rate and the reverse repo rate, which is the rate at which the RBI gives loans to the banks. We are now in a position to discuss in a greater detail about the major financial institutions in India. We shall start with the RBI.

Financial Sector, Money Supply and Interest Rates

4.4.1

131

The Reserve Bank of India

The RBI performs very important functions. It may be instructive to describe them in the light of its asset–liability balance sheet, which is presented in Table 4.1. Start with the liabilities. Notes in circulation refer to the currency notes held outside the RBI. All the currency notes in circulation are the principal liability of the RBI. It issues, distributes and manages these notes. Government’s currency liabilities to the public refer to the rupee coins and small coins held outside the RBI. Even though these coins are the liabilities of the central government, the responsibility of issuing, distributing and managing these coins rests with the RBI. It is the responsibility of the RBI to see that currency notes and coins are universally accepted as the medium of exchange. Table 4.1

Balance sheet of RBI

Liabilities

Assets

Currency ((i) + (ii)) (i) Notes in circulation (ii) Government’s currency liabilities to the public comprising rupee coins and small coins

1. Domestic credit ((i) + (ii) + (iii)) (i) Credit to government (ii) Credit to commercial sector (iii) Claims on banks

Other deposits ((a) + (b) + (c) + (d)) (a) Deposits of quasi-government and other financial institutions (b) Balances in the accounts of foreign central banks and governments (c) Accounts of international agencies such as the IMF, etc. (d) Provident, gratuity and guarantee fund, of the RBI staff (e) Profit of the RBI held temporarily under the deposits pending transfer to the central government

2. Net foreign exchange assets of the RBI

1. Bankers’ deposits

3. Capital account 4. Other items

RBI is the apex bank of India. It is the issuer of all the currency notes and coins. Its liabilities are universally accepted as the medium of exchange in India. For this reason, foreign governments and international agencies such as IMF hold deposits with the RBI to settle payments in rupee, when necessary. RBI also acts as bankers to all financial institutions and quasi-government institutions. Other deposits of the RBI, the second item on the liabilities side, comprise of deposits of foreign governments and foreign central banks with the RBI, deposits of quasi-government institutions and financial institutions other than banks with the RBI, deposits of international agencies such as the IMF with the RBI, provident, gratuity and guarantee funds of the RBI staff held as deposit with the RBI and profits of the RBI held temporarily as deposit pending transfer to the central government.

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The RBI also acts as the banker to the banks. Commercial and cooperative banks hold the major part of their reserves as deposits with the RBI. Since all the banks have deposits with the RBI, it acts as the clearing house for the banks, i.e. all the interbank debts are settled through the RBI. This brings us to the last item on the liabilities side. Bankers’ deposits refer to the deposits held by the scheduled commercial banks, the state cooperative banks, regional rural banks and non-scheduled banks with the RBI. RBI supervises, monitors and regulates the activities of all the banks and the financial institutions. It is also the lender of the last resort to the banks. We shall dwell on this point later. Let us now focus on the assets side. It includes four items, namely domestic credit, net foreign exchange assets of the RBI, capital account and other items (net). Domestic credit consists of RBI’s credit to central and state governments and credit to the commercial sector. RBI is the banker to both the central and the state governments. Hence they hold their balances as deposits with the RBI. The central and the state governments also borrow from the RBI either directly or indirectly by selling securities to the RBI. Direct RBI loans to the central and the state governments constitute loans and advances to the central and the state governments. The central government takes loans from the RBI also by selling treasury bills and dated securities. Government securities are called dated securities because their dates of maturity are written on the securities. State governments also issue dated securities and they often borrow from the RBI by selling it their dated securities. Rupee coins and small coins issued by the RBI on behalf of the central government are also regarded as loans given by the RBI to the central government. Finally, RBI credit to the government as recorded in the assets–liability balance sheet of the RBI is a net concept. It reports total loans extended by the RBI to the central and the state governments net of the deposits which these governments hold with the RBI. Thus RBI credit to central and state governments consist of (i) loans and advances to the central and the state governments, (ii) RBI’s holding of treasury bills and dated securities of the central and state governments and (iii) rupee coins and small coins net of deposits held by the central and state governments with the RBI. The RBI is a major lender to the financial institutions including banks. It lends to the financial institutions directly and also by buying shares, bonds and debentures issued by the financial institutions. The RBI’s credit to the commercial sector refers to its lending both direct and indirect to all financial institutions other than banks. It is the sum of holdings of (i) shares and bonds of financial institutions other than banks, (ii) ordinary debentures of the cooperative sector, (iii) debentures of cooperative land mortgage banks. It also includes (direct) loans to financial institutions other than banks. Cooperative land mortgage banks are not regarded as banks in India, as they do not raise their funds by selling deposits. The RBI is the lender of last resort to the banks. Claims on banks refer to RBI’s loans and advances to banks and holdings of banks’ shares, bonds, debentures, etc. Since, as we have seen above, the RBI intervenes in the market for foreign currencies to keep the exchange rates stable, it has to hold stocks of foreign currencies and other foreign assets. In case of excess demand for foreign currencies emerging at the targeted exchange rate, the RBI has to sell from its stock of foreign currencies to keep the exchange rates stable. Net foreign exchange assets of the RBI consist of (i) gold coins and bullions, (ii) eligible foreign securities and (iii) balances held abroad. The balances held abroad are held with the foreign central banks whose liabilities are foreign currencies.

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The capital account of the RBI is composed mainly of paid-up capital, which refers to the contributions of the shareholders of the RBI. Other items (net) constitute liabilities such as bills payable, balances under the RBI employees’ pension/cooperative guarantee/provident funds, compulsory deposit schemes and other sundry liabilities netted from other assets such as the value of premises, furniture and fittings, loans and advances granted to members of the staff for purchasing houses, cars, etc. All the liabilities of the RBI together constitute, what is called, the stock of high-powered money or the monetary base of the economy. We shall explain the reason later.

4.4.2 Commercial Banks We have already given a brief introduction to what commercial banks do. Their activities will be clearer further, if we go through their asset-liability balance sheet. Commercial banks take loans from other economic agents by selling deposits; hold a part of these loans as cash reserve; and uses the rest to invest in government and other securities and to lend out directly to firms and households. Deposits therefore constitute the liabilities of the banks, while its cash reserves, investments in securities, and loans extended, besides paid-up capital and accumulated undistributed profits (which are denoted simply by reserves), constitute its assets. For reasons that will be clear later, banks’ liabilities, which consist solely of banks’ deposits, are divided into demand liabilities and time liabilities. The former refers to deposits which the banks have to pay on demand, i.e. these deposits can be withdrawn or money can be withdrawn from these deposits whenever the depositors want. These deposits are the current account deposits and balances in savings account deposits over and above the minimum balance. The minimum balance in the savings accounts refers to the minimum balance which the depositors have to keep in their savings accounts all the time. Time liabilities are those deposits which cannot be withdrawn before their maturity. These deposits are the fixed deposits, cash certificates, cumulative and recurring deposits and minimum balances in the savings accounts. Other time liabilities include CDs issued by the banks. Assets, on the other hand, consist of cash reserves of the commercial banks, referred to as cash with banks, credit extended by the commercial banks, paid-up capital contributed by the shareholders and reserves of accumulated undistributed profits. The last two items constitute the capital account in the asset column of Table 4.2. In Table 4.2 credit extended by commercial banks is decomposed into domestic credit and credit given to foreigners. Domestic credit refers to credit given to domestic economic agents. It is further subdivided into credit given to domestic government and credit given to the commercial sector of the domestic economy. The former consists of the banks’ investments in short-term and long-term government securities. The latter consists of loans given to domestic firms and households in both rupee and foreign currencies and investments in non-government securities including those of PSUs. Commercial sector of the domestic economy, the way it is defined here, consists of the private sector of the domestic economy and the PSUs of the domestic government. Banks give loans to foreigners as well. By foreigners we mean economic agents resident in foreign countries. Credit given to foreigners is referred to on the asset side of Table 4.2 by foreign currency assets. It consists of banks’ investments in foreign securities net of the banks’ foreign borrowings including repatriable foreign currency deposits of the NRIs.

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Table 4.2

Balance sheet of commercial banks

Liabilities 1

1. Demand liabilities ((i) + (ii) + (iii)) (i) Current deposits (ii) Demand liabilities portion of savings bank deposits (iii) Other demand liabilities2 2. Time liabilities ((iv) + (v) + (vi) + (vii) + (viii)) (iv) Fixed deposits (v) Cash certificates (vi) Cumulative and recurring deposits (vii) Time liability portion of savings bank deposits (viii) Other time liabilities3

Assets 1. Domestic credit (1a + 1b) 1a. Credit to government (1a1 + 1a2) 1a1. Investment in short-term4 government securities 1a2. Investment in long-term5 government securities 1b. Credit to commercial sector (1b1 + 1b2 + 1b3) 1b1. Bank credit in India in rupees and foreign currency6 1b2. Investments in other approved7 securities 1b3. Other investments 1c. Net foreign currency assets of commercial banks8 1d. Capital account9 1e. Cash with banks

1

Liabilities that are to be paid on demand. Other demand liabilities include items such as balances in overdue fixed deposits, demand drafts, outstanding telegraphic transfers, etc. 3 Other-time liabilities include CDs, etc. 4 Short-term means maturity of 1 year or less 5 Long-term means maturity of more than one year 6 Bank credit includes loans and advances, cash credit, overdrafts, bills purchased and discounted, etc. 7 Approved securities emanate from the statutory stipulation that banks at the close of business on any day have to hold a minimum proportion of their demand and time liabilities in India in the form of cash, gold and unencumbered approved securities, which consist of government securities and other approved securities. 8 Net foreign currency assets of commercial banks consist of foreign currency assets net of non-resident foreign currency repatriable fixed deposits and foreign currency borrowings. 9 Capital account consists of paid-up capital and reserves. 2

4.4.3

Cooperative Banks

Cooperative banks are organized and managed on the basis of cooperation or mutual help. Cooperative banks are set up by a group of persons who are called members of the cooperative. They make equal contributions to the setting up of the cooperative. Every member has one vote. They operate on “no profit no loss basis”. They operate mainly in rural areas. However, there are many state cooperative banks (SCBs), central cooperative banks (CCBs) and urban cooperative banks that operate in urban areas also. Cooperative banks have a three-tier structure. At the top, i.e. at the state level there are state cooperative banks and state land development banks. At the district level there are central cooperative banks or district central cooperative banks and at the village level there are the primary agricultural credit societies and the primary land development banks. The banks in the higher tier are the members and shareholders of those in the immediate

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135

lower tier. Note that for our purpose we shall not regard primary agricultural credit societies and cooperative land development banks as banks for reasons that we shall explain shortly. Cooperative banks are supervised and also funded partly by the governments, RBI, and NABARD. Cooperative banks’ functions are the same as those of commercial banks. This is reflected in the asset–liability balance sheet of the cooperative banks presented in Table 4.3. They mobilize demand deposits (deposits that are payable on demand) and time deposits (deposits with fixed maturity periods and payable on and after maturity), hold a part of these deposits as cash reserves (referred to as cash with banks) and use the rest to lend and also to invest in government and other securities. Cooperative banks are subject to the same CRR stipulations as the commercial banks. Table 4.3

Asset–liability balance sheet of cooperative banks

Liabilities Aggregate deposits with the cooperative banks (1 + 2) 1. Demand deposits 2. Time deposits

4.4.4

Assets Domestic credit of cooperative banks (1 + 2) 1. Credit to the government 2. Credit to the commercial sector (2.1 + 2.2 + 2.3) 2.1 Loans and advances, cash credit, overdrafts and bills purchased and discounted 2.2 Investment in other approved securities 2.3 Other investments 3. Other items (net) 4. Capital account (4.1 + 4.2) 4.1 Paid-up capital 4.2 Reserves 5. Cash with banks

Specialized or Development Financial Institutions

Banks initially supplied mainly short-term loans. Hence, to meet the requirement of mediumterm and long-term loans, the Government of India set up a few specialized or development financial institutions. With the economic development of India in general and that of the financial sector in particular, the banks started supplying medium-term and long-term loans as well. Hence the government converted developed financial institutions into banks. Some of these institutions, which have now been converted into banks, are the Small Industrial Development Bank of India (SIDBI), Exim Bank of India, National Bank of Agriculture and Rural Development (NABARD) and National Housing Bank (NHB).

4.4.5

Insurance Companies

Insurance companies insure risks of life, health, cars, households, etc. Their chief source of finance is the premia they receive from the insurance policies. They use these funds to invest

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principally in government securities. They invest in shares and debentures of corporations as well. They also extend loans for housing development and development of infrastructure facilities. They lend to corporations as well.

4.4.6

Unit Trusts and Mutual Funds

Unit trusts and mutual funds refer to the same kind of financial firms. The first term is used in the UK, while the second term is used in the USA. These financial firms sell units to the public to raise funds and use the sales proceeds to invest in corporate securities. These firms pool the resources of the individuals (small investors) to construct highly diversified portfolios of corporate securities. Diversification reduces risks associated with investment in securities. Investment in corporate securities is highly risky. Prices of corporate securities are highly volatile. There is also default risk. In a diversified portfolio, securities of a large number of corporations from different sectors of production are held. The advantage of such a portfolio is that even if some firms in the portfolio perform below the average, some others will perform better than the average and the return on such a portfolio will therefore be stable. These financial firms can also engage financial experts to construct and manage their portfolios. These factors enable these firms to induce the individuals to invest in their units. The portfolios are referred to as funds. There are open ended funds in which people can put in their money whenever they want. The unit trust or the mutual fund taking subscriptions in these funds have to be ready all the time to redeem the units at their NAV. The NAV of a unit corresponding to a portfolio at a given point of time is given by the value of the securities held in the portfolio at the given point of time divided by the total number of units sold to construct the portfolio. This is the case when the portfolio is constructed by selling units only. If, however, funds from other sources are also used to construct the portfolio, such funds have to be subtracted from the value of the securities held in the portfolio and then this net value has to be divided by the number of units to get the NAV of the units. Since security prices are highly volatile, so must be the NAV of the equities. However, in a highly diversified portfolio, some security prices will rise and some other security prices will fall lending some amount of stability to the NAV of the units. In close-ended funds, subscription to units is open for some specific time period. The amount of subscription is also often fixed. Moreover, they also have a specific period of maturity or a specific redemption date. Units of close-ended schemes are not redeemed before the redemption date. However, these units may be traded in secondary markets in the stock exchange.

4.4.7

Non-Bank Financial Companies (NBFCs)

Non-bank financial companies refer to a whole host of relatively small financial companies such as the loan companies, investment companies, hire-purchase companies, equipment leasing companies, etc. Many of these companies secure funds by selling deposits. In addition, they have net-owned funds which consist of paid-up capital and accumulated reserves of undistributed profits. Loan companies give loans to small entrepreneurs and traders who do not get access

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to bank loans. They charge high interest rates on their loans and also pay high rates of interest on their deposits. These loans are unsecured. Investment companies give loans for both consumption and commercial purposes. These are also unsecured loans. The hire-purchase companies give loans to purchase consumer goods as well as capital goods. The difference between hire-purchase credit and installment credit is that in the case of the former, the ownership of the goods purchases remains with the lender until all the dues to the lender are cleared. In the case of the latter, the ownership of the goods purchased remains always with the borrower. The equipment leasing companies lease out equipments. Those who take the lease, referred to as lessees, make a fixed payment to the lessors at regular intervals of time during the period of the lease. One important kind of NBFC is merchant banks. Corporations hire them to handle the marketing of the securities they issue.

4.5

MONEY SUPPLY

Any commodity that is universally accepted as medium of exchange is called money. To put it more simply, it is a commodity with which one can buy anything one wants to from sellers in the markets in a country. Obviously, currency notes and coins issued by the RBI fit the bill. Demand deposits of banks, i.e. current account deposits and balances in the savings account deposits over and above the minimum balance that has to be maintained always in the savings accounts, are payable on demand and hence can be converted into currency and coins whenever the depositors want without any cost. Hence, they also qualify as money. Moreover, cheques can be drawn on the demand deposits of most of the banks and demand deposits of these banks are also universally accepted as medium of exchange in case of large transactions. This means that the holders of the chequable demand deposits can make payments directly with these demand deposits. They need not convert these deposits into currency and coins to make payments. Let us illustrate with an example. Suppose an individual buys a refrigerator from a shop. In most cases he need not pay for the fridge with currency. He has the option of paying for it with demand deposits also. When he pays with demand deposits, he draws a cheque on his account instructing his bank to pay the price of the fridge to the seller of the fridge. The seller of the fridge deposits this cheque in his own bank and through a process that we shall explain shortly an amount equal to the price of the fridge gets transferred from the buyer’s account to the seller’s account. In this case, no exchange of currency notes and coins takes place between the buyer and the seller, only demand deposits get transferred from the buyer’s account to the seller’s account. Since money is universally accepted as the medium of exchange, it is the most liquid of all goods. Liquidity of a commodity is a measure of the readiness with which it can be exchanged for any other good without any loss of value. When prices are stable, one can buy whatever one wants with money without any loss of value. Hence money (currency and coins and demand deposits of banks) is the most liquid of all goods. Note that bank deposits are also securities. Explain this point yourself using the definition of securities. Shares in common stock and securities (other than bank deposits), as they have secondary markets, are also quite liquid. So are units of mutual funds. However, their liquidity is marred by the fact that their prices are highly volatile. As a result, their sale at a short notice may involve substantial loss of value. They are therefore much less liquid than the assets mentioned

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above. Let us illustrate with an example. Note first that one cannot buy goods and services from market directly with shares and securities other than bank deposits. One has to first sell them for currency notes or demand deposits of banks. When securities are paid for with cheques drawn on the buyers’ accounts, the securities get traded for demand deposits of banks. However, prices of shares and securities change substantially even over short periods of time. Hence sales of shares and securities at a short notice may mean selling them at prices much lower than those at which they were bought. Thus such sales may saddle the seller with huge losses. Hence shares and securities are much less liquid than money. In every country, the central bank seeks to control the supply of money for reasons that we shall explain in detail in the chapters that follow. However, to control it, the central bank has to first identify the assets that it regards as money. The set of assets identified by the central bank as money is called a monetary aggregate. Central banks usually define four kinds of monetary aggregates denoted by M1, M2, M3 and M4. Assets included in these aggregates, however, vary across countries. In India these aggregates are defined as follows. Let us first focus on M1 and M3, which are by far the most commonly used. The former is referred to as narrow money, while the latter is called the broad money. In India M1 is defined as currency with the public, i.e. currency held by economic agents outside the banking sector, other deposits of the RBI and demand deposits of the banks (excluding the RBI). Other deposits of the RBI are included in M1 because they are held by economic agents other than the domestic banks and they are universally accepted as medium of exchange in India. Other deposits of the RBI are a liability of the RBI, which issues all the currency notes and coins. Hence depositors can always withdraw currency and coins from these deposits whenever they want. There is no risk of default. Moreover, depositors can also make payments with cheques drawn on these accounts, i.e. they can make payments with these deposits directly. Hence other deposits of the RBI is included in M1. The broad money, M3, is defined as M1 plus time deposits of banks. M3 is therefore given by currency and coins held by the public, other deposits of RBI and all deposits of banks. Time deposits are included in the definition of broad money because they can be converted into currency and coins or into demand deposits whenever the depositors want at a very low cost. Fixed deposits have a fixed maturity period and they cannot be withdrawn before their maturity. However, banks allow pre-mature withdrawal of time deposits against the payment of a fine, which is usually quite small. So M3 includes time deposits of banks. The RBI and the banks constitute the banking sector. The banking sector is the supplier of money. Supply of narrow money and that of broad money mean respectively the amount of M1 and the amount of M3 in the possession of economic agents other than the banks and the RBI. These economic agents are referred to as the public. We get M2 by adding to M1 all the savings bank deposits of post offices. The sum of M1 and the time deposits of banks gives us M3. Finally, if we add to M3 all the deposits of post offices, we get M4. We shall now explain how the supply of M3 is determined. For the present, to simplify matters, we shall ignore other deposits of RBI so that M3 will consist of currency with the public (denoted by N) and all deposits of banks (denoted by D). Thus M3 = D + N

(4.5)

Financial Sector, Money Supply and Interest Rates

139

The public allocate their holding of money between currency and bank deposits. Usually the public hold currency and deposits in a fixed ratio, which we denote by l. Thus

N À N MD D (Think yourself which factors are likely to determine l .) Substituting (4.6) into (4.5) and then solving for D, we get

M

D

M3 1M

(4.6)

(4.7)

Again, substituting (4.7) into (4.6), we get

M

N

1 M

M3

(4.8)

Let us explain (4.7) and (4.8). The public hold broad money in currency and bank deposits. Moreover, they maintain a fixed ratio between N and D, as shown by (4.6). Given this fixed 1 ratio, l, (4.7) and (4.8) show that the public will hold fraction of any given amount of 1 M M3 in the form of D and

M

fraction of any given M3 in the form of N. 1 M We mentioned earlier that banks hold a fixed fraction of their deposits as reserves of cash. These reserves consist of required reserve and excess reserve. Let the amount of cash reserves that banks want to hold be denoted by R. Suppose the fixed fraction of deposits that banks want to hold as cash reserve is r. Therefore R = rD

(4.9)

RBI is the issuer of currency. Hence currency or cash is a liability of the RBI. RBI’s liabilities are called high-powered money or monetary base of the economy for reasons that will be clear shortly. We shall denote them by H. Ignoring other deposits of the RBI, whatever H exists in the economy is held in the form of cash reserves of banks and currency held by the public. Thus H=R+N

(4.10)

From (4.9) and (4.7), it follows that corresponding to any given R, there is a unique M3. Again, from (4.8) we find that there is a unique M3 corresponding to every N. Thus, corresponding to every H there is a unique M3 and vice versa. This will be evident from (4.11), which we get by substituting (4.7), (4.8) and (4.9) into (4.10). H

S

1 M

M3 

M

1 M

M3

SM M 1 M 3

(4.11)

Equation (4.11) shows that there is a one-to-one correspondence between H and M3, given

l and r. Thus (4.11) must hold in equilibrium where the public hold their money balances in

the forms of currency and bank deposits in the desired quantities and the banks hold the desired fraction of their deposits in the form of cash reserve. But does there exist any causal relationship between the two? In fact, it does and the direction of causality moves from H to M3, i.e. given

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l and r, H determines M3. We therefore rewrite (4.11) to express M3 as a function of H. It is given by

1 M

M3 Since

1M

SM

SM

H

(4.12)

! 1 , (4.12) implies that a given amount of RBI’s liabilities can create an amount

of M3 which is a multiple of the given amount of RBI’s liabilities. Hence RBI’s liabilities, as we have already mentioned, is called the high-powered money or the monetary base, while 1M is called the money multiplier. We shall now explain below how RBI’s liabilities create

SM

M3. This we shall do with the help of Table 4.4, which shows simplified asset-liability balance sheets of the RBI and of two banks referred to as Bank 1 and Bank 2. In the simplified balance sheet of the RBI, which is a simplified version of Table 4.1, we have ignored other deposits of the RBI on the asset side and claims on banks, capital account and other items on the liabilities side. Moreover, instead of credit to the government we have written net credit to the government, which is nothing but credit to the government net of government’s deposit with the RBI. Banks’ balance sheets presented in Table 4.4 are simplified versions of Table 4.2. Here we have clubbed together demand and time liabilities into deposits on the liabilities side. On the asset side, credit given by banks to domestic economic agents (consisting of domestic government and domestic private economic agents) and foreign currency assets are all clubbed together and decomposed into loans and advances and investments in securities. Table 4.4

Balance sheet RBI

Liabilities Currency with the public Banks’ deposits with the RBI

Assets Net RBI credit to the government Credit to the commercial sector Foreign exchange assets with the RBI Bank 1

Liabilities Deposits

Assets Deposits with the RBI Investments in securities Loans and advances Bank 2

Liabilities Deposits

Assets Deposits with the RBI Investments in securities Loans and advances

Financial Sector, Money Supply and Interest Rates

141

The RBI often undertakes open market operations (OMO). It means buying and selling securities in the market. The RBI does this to regulate money supply. Suppose the RBI buys government’s dated securities of ` 100 from Bank 1. The RBI will credit this amount in the account of Bank 1 with itself. So banks’ deposits with the RBI on the liabilities side of the RBI’s balance sheet will go up by ` 100. On the asset side, the RBI’s net credit to the government will go up by ` 100, since the dated securities are the liabilities of the government. Thus the buying of security creates H. It raises H by ` 100 in our example. Through the OMO therefore the RBI raises or lowers the stock of high power money in the economy. Selling of securities by RBI reduces H. The buying of government’s dated securities of ` 100 by the RBI from Bank 1 will affect Bank 1’s balance sheet as well. On the assets side, its deposit with the RBI will go up by ` 100, while its investment in securities will fall by ` 100. This marks the end of Round 1 transactions. At the end of these transactions we find that the supply of highpowered money, given by the liabilities of the RBI, has gone up by ` 100. On the other hand, cash reserves of Bank 1 have gone up by ` 100, while its deposits remain unchanged. Bank 1 therefore holds more reserves than what it wants to, assuming that initially it was holding the desired fraction of its deposits in the form of cash reserves. Bank 1 is thus in disequilibrium. This starts the second round of transactions. Before going into the details of the second round transactions, note that in Round 1, DN = DD = 0 and DH = ` 100.. Bank 1 now finds that it has surplus cash reserve of ` 100, which it will either invest in securities or lend out. Suppose it lends it out. The borrower will obviously use it to buy goods and services, since he takes the loan for purposes of either consumption or investment. Bank 1’s balance sheet now changes as follows. It pays ` 100 to the borrower by withdrawing ` 100 in currency from its account with the RBI. Thus Bank 1’s deposits with the RBI go down by ` 100 and its loans and advances go up by the same amount. Its liabilities remain unaffected. In the RBI’s balance sheet, banks’ deposits with the RBI goes down by ` 100, while currency held by the public goes up by ` 100. Its assets remain unchanged. Suppose Mr. A is the seller to the original borrower from the bank and he banks with Bank 2. Upon receiving this sum of ` 100, his money holding goes up by ` 100. He, however, will not hold the whole of this additional money balance in the form of currency. He will allocate it between currency and 1 fraction of bank deposits—see (4.7) and (4.8). From (4.7), it follows that he will hold 1 M the additional money balance in the form of bank deposit and the remaining

M

1 M

fraction of

1 100 in his account with 1M Bank 2. Bank 2 in its turn will deposit this sum in its account with the RBI. In the balance sheet ` 100 in the form of currency. He will therefore deposit `

of Bank 2, its deposits are now larger by ` the RBI are larger by `

1 100 , while on the asset side its deposits with 1 M

1 100 too. In the RBI’s balance sheet, additional currency held by 1 M

the public will go down from ` 100 to `

M 1 100 , as it gets back ` 100 as deposit from 1 M 1 M

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Macroeconomics

Bank 2. Thus total amount of liabilities of the RBI remains unchanged. Its composition, however, is now different. Of its additional liability of ` 100, it is now holding ` currency holding of the public and `

M

1 M

100 as additional

1

100 as additional deposits of the banks with the 1 M RBI. The second round of transactions is now complete. At the end of the second round of transactions we find that Bank 1 is in equilibrium. It is no longer holding any idle reserve and its loans and advances are larger by ` 100. Its deposits are unchanged. The second round of transactions has not affected the total amount of liability of the RBI. It is still the same as that in Round 1. Only its composition has changed. At the end of Round 1 the RBI’s liability was larger by ` 100 and it held the whole of it in the form of additional deposits of banks with the RBI. At the end of the second round of transactions, its total liability is the same as that at the end of Round 1. But it is now holding the additional liability of ` 100 partly in the form of

1 100 , and partly in the form of 1M currency with the public. The stock of high-powered money therefore is not affected by Round 2 transactions. Let us now focus on Bank 2. On the liabilities side, its deposits are larger by banks’ deposit with the RBI, which is now larger by `

`

1

100 , while on the assets side, its deposit with the RBI is larger by the same amount. 1M It is therefore not in equilibrium. It is holding its entire additional deposit in the form of additional reserve. This will start the third round of transactions. To sum up, at the end of

M 1 100 and ' D C 100 . 1 M 1 M This means that DM3 = ` 100 as a result of Round 2 transactions. Round 3 transactions begin as Bank 2, which was holding the whole of its additional deposit in the form of cash reserves at the end of Round 2 transactions, lend out 1 ` (1  S) 100 . Bank 2 withdraws this amount from its account with the RBI in currency 1M and pays it to the borrower who spends it on goods and services. Bank 2 will therefore achieve Round 2, as a result of Round 2 transactions,

'H

0, ' N

C

1 100 , while its loans and 1M advances rise by the same amount. In the balance sheet of RBI on the liabilities side, the banks’ equilibrium, as its deposit with the RBI goes down by ` (1  S)

1 100 , while currency holding of the public 1M rises by the same amount. The total amount of liability of the RBI therefore remains unchanged. Let us now focus on the borrower. He will spend his loan to purchase goods and services. The

deposit with the RBI goes down by ` (1  S)

seller receives this amount. His money holding therefore goes up by ` (1  S )

1 1M

100 . Of this

È M Ø 1T additional money holding, he will hold ` É 100 as additional currency and the rest Ê 1  M ÙÚ 1  M

Financial Sector, Money Supply and Interest Rates

`

È 1 Ø É1  M Ù Ê Ú

143

2

(1  S ) ¹ 100 as additional deposit. Suppose he banks with Bank 1. His deposit with È 1 Ø É1  M Ù Ê Ú

this bank and therefore Bank 1’s total deposit will go up by `

2

(1  S ) ¹ 100 . Bank 1

will deposit this amount with the RBI raising its deposit with the RBI. In the RBI’s balance sheet, on the liabilities side banks’ deposit with the RBI will rise by this amount, while currency holding of the public will fall by the same amount leaving the total amount of liability unchanged. The assets side will remain unaffected. This is the end of Round 3 transactions. As a result of Round 3 transactions therefore DH = 0, the seller’s currency holding and bank deposits and therefore economy’s currency holding of the public (N) and total bank deposits (D) are larger by È

Ø Ù Ê1  M Ú

` MÉ

1

2

(1  S) ¹ 100 and `

a result of Round 3 transactions and ' M 3

C

È 1 Ø É1  M Ù Ê Ú

'H

2

(1  S ) ¹ 100 respectively. To sum up, therefore, as

0, ' N

C

M (1  S )100, ' D (1  M ) 2

C

1 (1  M ) 2

(1  S)100

1 S 100 . (1  M ) 2

È1 SØ Round 4 transactions will begin when Bank 1 lends out ` É ¹ 100 to optimally Ê 1  M ÙÚ allocate its additional deposit of `

È 1 Ø É1  M Ù Ê Ú

2

(1  S ) ¹ 100 between cash reserves and loans. One

can easily check that as a result of Round 4 transactions following changes will occur: DH = 0, DN = `

È (1  É Ê (1 

S) 2 Ø M ¹ 100 and 'D M )3 ÙÚ

C

È (1  S) 2 Ø É 3Ù Ê (1  M ) Ú

2

È1 SØ CÉ 100 . These rounds Ê 1  M ÙÚ

100 and ' M 3

of transactions obviously will continue until creation of additional currency holding of the public, additional bank deposits and additional supply of broad money falls to zero. Thus the total amounts of N, D and M3 that are created will be given by 'N

C

Ë M 100  Ì Í1  M

M (1  S ) M (1  S ) 2 100 100   (1  M ) 2 (1  M ) 3

'D

C

Ë 1 100  Ì Í1  M

(1  S)

(1  S) 2

(1  M )

(1  M )

'M3

Ë

C Ì100  Í

100  2

3

(1  S) (1  S) 2 100  100  (1  M ) (1  M ) 2

100 

"

Û Ü Ý

"

Û Ü Ý

"

C

Û Ü Ý

C C

M 100 SM 1

SM

(1  M ) 100 (S  M )

100

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Macroeconomics

The above example shows how RBI’s creation of additional high power money of ` 100 creates an additional M3 of `

1 M

SM

100 . This explains (4.12). Note that for the process of

generation of M3, which is also referred to as the money multiplier process, to complete, there has to be no dearth of demand for bank credit. If demand for additional bank credit is inadequate, the process of money multiplier will end with the fulfillment of additional demand for bank credit and the creation of M3 will be less than what is implied by (4.12). To illustrate, in the example given above, if there is no excess demand for bank credit, the second round transactions cannot start. So no additional M3 will be created. Since the process of creation of money is extremely important, another example is given to show how M3 is created. This time, however, we shall assume that all the transactions are carried out with bank deposits and the public do not hold any currency at all. More precisely, we assume that l = 0. Given this assumption, Eq. (4.12) reduces to

M3

1

S

H

(4.13)

The example will explain (4.13). It will also bring out the role of the RBI as the clearing house of the banks, i.e. it will show how interbank transactions are settled through the RBI. Let us now focus on the following example. Suppose the RBI lends ` 100 to the government, which has account with the RBI—see RBI’s balance sheet in Table 4.1. The RBI will deposit this amount in the account of the government. The government took the loan obviously to finance purchase of goods and services. The government will pay the sellers with cheques drawn on its account with the RBI. Suppose the sellers bank with Bank 1. They will deposit the cheques with Bank 1. Upon receiving these cheques, Bank 1 will send them to the RBI. The RBI upon receiving the cheques will debit this amount from the account of the government and credit the amount, ` 100, in the account of Bank 1, which Bank 1 holds with the RBI. Bank 1 will then credit this amount in the accounts of the sellers. In the balance sheet of Bank 1, see Table 4.3, therefore the deposits on the liabilities side rise by ` 100 and so do on the assets side its deposits with the RBI, which constitutes its reserves of cash. In the RBI’s balance sheet in Table 4.3, on the assets side net RBI credit to the government will go up by ` 100. On the liabilities side banks’ deposits with the RBI will go up by ` 100. This marks the end of Round 1 transactions. At the end of Round 1 therefore we find that DH = ` 100 and DD = ` 100. In our example currency holding of the public is zero by assumption. This implies that M3 = D. Thus at the end of Round 1 transactions DD = DM3 = ` 100. At the end of Round 1 transactions, Bank 1 is holding the whole of its additional deposit of ` 100 in the form of cash reserves. Obviously, it is not in equilibrium. This starts the second round transactions. Bank 1 will lend out (1 – r) fraction of its additional deposit of ` 100. It will open an account in the name of the borrower and credit the loan amount in this account. The borrower will purchase goods and services with the loan and pay the sellers with cheques drawn on its account with Bank 1. Suppose the sellers bank with Bank 2. The sellers will deposit the cheques in their accounts with Bank 2. Upon receiving these cheques Bank 2 will send them to the RBI. Both Bank 1 and Bank 2 have accounts with the RBI. The RBI, after

Financial Sector, Money Supply and Interest Rates

145

receiving these cheques, will debit the amount, ` (1 – r)100, in the account of Bank 1 and credit the same amount in the account of Bank 2 and send the cheque to Bank 1. Then Bank 1 will debit this amount in the account of the borrower. Bank 2, on the other hand in, its own balance sheet will raise its deposit with the RBI on the assets side and the deposits of the depositors on the liabilities side by ` (1 – r)100. This marks the end of second round transactions. Round 2 therefore does not affect the total amount of liabilities or assets of the RBI. Accordingly, no high powered money is created in Round 2. Let us focus on Bank 1. It is now in equilibrium. Its cash reserves are now down by ` (1 – r)100, while its loans are larger by ` (1 – r)100. Thus it has now allocated its additional deposit of ` 100 optimally between cash reserves and loans and investments. In Bank 2’s balance sheet, however, on the liabilities side deposits of depositors are larger by ` (1 – r)100, while on the assets side its deposits with the RBI are larger by the same amount. Hence it is in disequilibrium. Its response to this disequilibrium situation will start the third round transactions. As a result of the transactions in Round 2, the following changes have occurred: DH = 0, DD = ` (1 – r)100 and DM3 = `(1 – r)100. In the third round, you should be able to work it out yourself, the following changes will occur: DH = 0, DD = ` (1 – r)2100 and DM3 = ` (1 – r)2100. This process of creation of M3 will continue until the additional deposit and money created in each successive round falls eventually to zero. Thus at the end of the money multiplier process the total amount of H and M3 created will be given by the following: DH = 0 and

"

' M3 C [100  (1  S)100  (1  S) 2100  ] C

100

S

'H S

This explains (4.13). In our discussion of money supply we have assumed that the banks hold a fixed fraction, r, of their deposits in the form of reserves of cash. We pointed out earlier that the cash reserves banks hold can be divided into two parts, required reserve and excess reserve. The ratio of the former to the deposits is stipulated by the RBI. It is called the cash reserve ratio (CRR). We shall denote it by r1. The banks determine the latter and we shall denote the ratio of excess reserves to deposits by r2. Then r = r1 + r2 × r1, as it is fixed by the RBI, is a policy parameter of the RBI. r2, on the other hand, is likely to be an increasing function of the rates of interest at which banks can borrow in the short-run to bridge the excess of daily outflow over daily inflow. Banks can borrow from the RBI. The rate at which they can borrow from the RBI is the repo rate (denoted by ir). r2 is therefore likely to be an increasing function of ir. It is also likely to be a decreasing function of the interest rates at which it can lend. The interest rate at which banks can lend to the RBI is the reverse repo rate, which we denote by irr. Let us also denote the average of the interest rates at which banks lend in the market by im. r2 is therefore likely to be a decreasing function of irr and im. Incorporating these in (4.12), we can write it as M3

1 M

È Ø S1  S2 É ir , irr , im Ù  M Ê ( ) ( ) ( ) Ú

H

(4.14)

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Macroeconomics

4.5.1

Regulation of Money Supply

From (4.14), it follows that the RBI can regulate the supply of M3 using a number of instruments such as the supply of high-power money, H, the CRR, r1, and the repo rate and the reverse repo rate, ir and irr. In practice, the RBI uses all these instruments to influence the supply of M3. Explain yourself how a cut in CRR affects the supply of M3. EXERCISE 4.5 (a) Suppose in the market where the US dollar exchanges for rupee there emerges an excess supply of the US $ 100 at the prevailing price of the US dollar in terms of rupee, which is ` 50. The RBI does not want this price to change. What can the RBI do to prevent the price from changing? How will it affect the supplies of H and M3, when both l and r are (1/10)? Explain using the balance sheets of the RBI and banks. (b) Suppose due to proliferation of bank branches and ATMs currency-deposit ratio of the public falls from (1/10) to (1/5), how will it affect the money supply, if r = 1/10? (c) Suppose the Government of France buys Kashmiri carpets worth ` 1 crore for its offices and pays for them by drawing a cheque on its account with the RBI. How will it affect supplies of H and M3, when r = l = 1/10?

4.6

TERM STRUCTURE OF INTEREST RATES

Term structure of interest rates refers to the interrelationship among the interest rates on loans of different maturities. Theories that seek to explain this interrelationship have gained tremendous importance in Indian context following the deregulation of interest rates and the shift in RBI’s monetary policy from controlling growth in money supply to regulating interest rates not by means of administrative fiat but through market interventions. In this scenario, a thorough understanding of the term structure of interest rates is absolutely essential for the successful designing and conduct of monetary policy. There are four major theories of the term structure of interest rates, namely, unbiased expectations theory, liquidity preference theory, market segmentation theory and preferred habitat theory. We shall discuss each of them below.

4.6.1

Unbiased Expectations Theory

This theory states that borrowers and lenders have no preference for loans of any specific maturity. Loans of all the different maturities are equivalent to them. This implies a specific relationship among interest rates on loans of different maturities. To illustrate this point, let us first focus on 1-day and 2-day risk-free loans. Let us denote today’s daily interest rates on these two types of loans by i1 and i2. Focus first on the lenders. They have two options open to them. They can today invest either in a 2-day loan or in a 1-day loan. According to the unbiased expectations theory, they have no bias in favour of either of the two loans. They compare the two loans solely on the basis of how much they expect them to yield in principal and interest. If they invest in the 2-day loan today at the daily interest rate i2, they will earn at the end of

Financial Sector, Money Supply and Interest Rates

147

the two-day period (1 + i2)2 in principal and interest for every rupee invested in the 2-day loan. Alternatively, they can lend out at the interest rate i1 today for 1 day and earn tomorrow (1 + i1) for every rupee invested. However, this sum is not comparable to what the 2-year loan yields two days after today, since the 1-day loan yields (1 + i1) per rupee of investment just one day after today. To compare the income from the one day loan, the lenders have to figure out how much (1 + i1) will yield in principal and interest if it is lent out one day after today again for one day. The problem with this calculation is that today they do not know what the interest rate on 1-day loan will be tomorrow. So they have to work on the basis of what they expect the interest rate on 1-day loan would be tomorrow. Suppose today their expected interest rate on tomorrow’s 1-day loan is i1e2. i1e2 is also alternatively referred to as the expected daily forward rate on 1-day loans on Day 2. Then from the second option of the 1-day loan they expect to earn in principal and interest (1 + i1) (1 + i1e2) for every rupee of investment at the end of the two-day period from today. Note that the investors’ income from the first option of the 2-day loan is certain. But their income from the second option is uncertain. Their actual income from the second option may differ from their expected income, if their expectation goes wrong. Thus the second option is risky. The unbiased expectations theory assumes that the lenders or investors are risk neutral. This means that the investors are indifferent to risk. More specifically, it means that investors, when they compare certain income from an option to the expected income from another option, whose income is uncertain, become indifferent between the two incomes, when the two are equal and prefer the one that is larger. Let us now focus on the investors or lenders in question. If investors or lenders are risk neural, then, according to the unbiased expectations theory, they will be indifferent between the two options if the certain income from the first option is equal to the expected income from the second option, even though the second option is risky. This implies that in equilibrium incomes from the two options mentioned above must be equal, i.e. the following equation must hold in equilibrium: (1 + i1) (1 + i1e2) = (1 + i2)2

(4.15)

Obviously, if the LHS is greater than the RHS, no one will be interested in investing in the 2-day loans, i.e. the whole supply of the loanable funds will go into the one-day loan market today. Let us now focus on the borrowers. According to the unbiased expectations theory borrowers also have no bias in favour of loans of any specific maturity and they are risk neutral. This means that they compare loans of different maturities only on the basis of how much they will have to pay back in principal and interest per rupee borrowed on each of the different types of loans. Consider the example considered here. According to the unbiased expectations theory, the borrowers will compare the 1-day and 2-day loans solely on the basis of how much they will have to pay back per rupee borrowed on each of the two loans. This comparison is complicated because the maturity periods of the two loans are different. They will make the comparison in the following manner. If the borrowers take the 2-day loan today, they will have to pay back at the end of the 2-day period a sum equal to the RHS of (4.15) for every rupee borrowed today. On the other hand, if they take the 1-day loan today, they will have to pay back after one day (1 + i1) per rupee borrowed. However, to compare the loan obligation of the 1-day loan to that

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of the 2-day loan, they will have to figure out how much they will have to pay after the second day, if they again take a 1-day loan of (1 + i1) after the first day to pay back the 1-day loan taken today. If they do this, they will expect that they will have to pay back after 2 days from today the LHS of (4.15) for every rupee borrowed. Since the LHS of (4.15) gives the amount that the borrowers will have to pay back 2 days after today if they take the 1-day loan today, it becomes comparable the RHS of (4.15). Obviously, according to the unbiased expectations theory, given the assumption of lack of bias and risk neutrality, if the LHS of (4.15) is greater than the RHS, borrowers will prefer the 2-day loan to the 1-day loan. In the opposite case they will prefer the 1-day loan. In case the two sides are equal, they are indifferent to both of them. Thus, given the assumptions of the unbiased expectations theory, if the LHS of (4.15) is greater than the RHS, lenders will want to lend only in the 1-day loan market, while the borrowers will want to take only 2-day loans giving rise to excess supply in the 1-day loan market and excess demand in the 2-day loan market. Just the opposite will happen, if the LHS of (4.15) is less than the RHS. This explains why (4.15) will hold in equilibrium. From (4.15) it follows that i2

[(1  i1 ) (1  i1e 2 )]1/2  1

(4.16)

Î! Þ Ñ Ñ Let us explain one important implication of (4.16). It follows from (4.16) that i2 Ï ß i1 Ñ Ñ Ð à ! Î Þ e2 Ñ Ñ when i1 Ï ß i1 . However, a priori it is equally likely for i1e2 to be greater than or less than i1. ÑÑ Ð à

Therefore, it is equally likely for i2 to be greater than or less than i1. However, empirically it has been observed that i2 is usually higher than i1. More generally, it is usually the case that interest rates on loans of longer maturities are higher than those on shorter maturities. The chief shortcoming of the unbiased expectations theory is that it cannot explain this phenomenon. More precisely, it cannot explain why interest rates on loans of longer maturity periods are more likely to be higher than those on loans of shorter maturity periods. Let us now extend our example to incorporate 3-day loans in addition to 1-day and 2-day loans. Suppose the daily interest rate on risk-free 3-day loans is today. Then, under the unbiased expectations theory, as follows from our above discussion, the following equality must hold in equilibrium today (1  i1 ) (1  i1e 2 ) (1  i1e 3 )

(1  i2 ) 2 (1  i1e 3 )

(1  i3 ) 3

(4.17)

where i1e3 º expected daily interest rate on risk-free 1-day loans on the third day or the expected daily forward rate on one-day loans on the third day taking today as the first day. Explain (4.17) yourself. From (4.7) it follows that i3

[(1  i1 )(1  i1e 2 )(1  i1e 3 )]1/3  1

(4.18)

Generalizing from (4.15), (4.16), (4.17) and (4.18), we get in

[(1  i1 )(1  i1e 2 ) (1  i1e 3 )...(1  i1en )]1/ n  1 [(1  in 1 ) n 1 (1  i1en )]1/ n  1

(4.19)

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where in º risk-free daily interest rate on n-day loans today and i 1en º expected risk-free daily forward rate on 1-day loans on the n-th day taking today as the first day. Equation (4.19) states that the daily interest rate on loans of n-day maturity today is determined by the daily interest rate on 1-day loans today and the expected daily forward rates on 1-day loans of all the days starting from tomorrow up to the n-th day. EXERCISE 4.6 Suppose i1 = 0.1 and i1e2 = 0.12, what is the equilibrium value of i2? Why do we not have equilibrium if i2 is higher or less than this value? Given the values of i1 and i1e2, show the state of the 2-day loan market at all the different values of i2 in a graph.

Impact of short-term policies on the term structure of interest rates We can use (4.8) to explain how a policy that is expected to lower or raise interest rates for short periods is likely to affect interest rates on loans of long maturity periods. Suppose, following the adoption of a policy, daily interest rates on 1-day loans are expected to remain depressed for M number of days, where M < n. How will in be affected? Taking logarithm of both sides of (4.19), we get

ln(1  in )

1Ë ln(1  i1 )  n ÌÌÍ

Ç ln(1  i M

ej 1 )

j 1

n M

Ç ln(1  i

Û

e( M h) )Ü 1

h 1

Ü Ý

Taking total differential of both sides, we have iˆN

1 ˈ I n ÌÍ 1

Û iˆ1em  Ç iˆ1em Ü Ç m 1 m M 1 M



n

(4.20)

Ý

d (1  in ) ˆ d (1  i1 ) ˆ em d (1  i1eh ) where iˆN œ , I1 œ , i1 œ ,h 1  in 1  i1 1  i1eh

1, 2, 3, ..., M , M  1, M  2, ..., n .

In (4.20), Iˆ1 › 0, iˆ1em › 0 for m = 1, 2, ..., M and iˆ1em

0 for m = M + 1, M + 2, ..., n.

Suppose, for simplicity, iˆ1em

B and Iˆ1 B ,

then

1 ( MB ) n

iˆN

M B n

(4.21)

It follows from (4.21) that the larger the n relative to M, the less is the change in in relative to the average of the changes in the expected daily forward rates on 1-day loans up to the M-th day. One can easily check using (4.20) that in the case where n £ M iˆN

1 ( nB ) n

B

(4.22)

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From (4.22) it follows that for n £ M the change in in is given more or less by the average of the changes in the expected daily forward rates up to the nth day. The implication of the results reported above is that a policy that is expected to keep short-term interest rates at lower (higher) levels for a short period of time will lower (raise) short-term interest rates, but will produce less depressing impact (exert less upward pressure) on long-term interest rates. The longer the maturity period of a loan relative to the period during which the short-term interest rates are expected to remain depressed (raised), the less will be the impact on its interest rate.

Shortcoming of the unbiased expectations theory It follows from (4.19) that if expected daily forward rates on 1-day loans rise over time, i.e. if i1j 1 ! i1ej  j and the expected daily forward rate on one-day loan tomorrow is higher than the daily interest rate on 1-day loan today, daily interest rates on loans will increase with the maturity periods of loans, i.e. interest rate on a loan of a given maturity period will be less than the interest rate on a loan of a longer maturity period and greater than the interest rates on loans of shorter maturity periods. In the opposite case, interest rates on loans will fall with an increase in the maturity periods of loans. One cannot say a priori how expected daily forward rates on one day loans will behave. All kinds of behaviour are equally likely. So the term structure of interest rates may weave any pattern. The unbiased expectations theory therefore does not imply any specific pattern of the term structure of interest rates. However, as we have already mentioned, the yield curve is usually upward sloping, i.e. interest rate on a loan of longer maturity period is usually higher than the interest rate on a loan of shorter maturity period. Unbiased expectation theory cannot explain why this should be so. This is the reason why this theory no longer finds acceptance. Liquidity preference theory of the term structure of interest rates offers an explanation of why the term structure of interest rates is usually rising. Hence it is accepted as a more satisfactory theory of the term structure of interest rates. We discuss this theory below.

4.6.2

Liquidity Preference Theory

This theory states that liquidity is important to the lenders and they part with liquidity if and only if the incentive is strong enough. Thus, lenders will normally lend short unless the interest rates on longer term loans are high enough. Borrowers, on the other hand, prefer to borrow long and these two disparate preferences together lead to a rising pattern of the term structure of interest rates. In terms of Eq. (4.15), we can put the theory in the following manner. If (4.15) holds, expected income from 1-day loans is the same as that on 2-day loans. This, however, according to the liquidity preference theory, will not induce the lenders to extend 2-day loans. They will be willing to extend 2-day loans if their return is sufficiently higher than the expected return on 1-day loans. Thus, when (4.15) holds, lenders will supply loans only in the 1-day loan market. Borrowers, who prefer to borrow long, on the other hand will be interested in borrowing only 2-day loans when (4.15) holds. There will thus be excess supply in the 1-day loan market and excess demand in the 2-day loan market when (4.15) holds. In equilibrium therefore the RHS of (4.15) has to be sufficiently higher than its LHS, i.e. income in principal and interest

Financial Sector, Money Supply and Interest Rates

151

from 2-day loans has to be sufficiently larger than that from 1-day loans to induce borrowers to take 1-day loans and lenders to supply 2-day loans. The excess of the RHS over the LHS of (4.15) that will obtain in equilibrium is accounted for by the price of liquidity, which we refer to as liquidity premium. Under the liquidity preference theory therefore in equilibrium the following equation must hold (1 + i1) (1 + i1e2) (1 + l2) = (1 + i2)2, where l2 º the liquidity premium > 0

(4.23)

i1e2

From (4.23), it follows that i2 may be greater than i1, even if < i1. Thus the liquidity preference theory makes it more likely that i2 > i1 instead of the other way round. Similarly, (1  i1 ) (1  i1e2 ) (1  l2 ) (1  i1e3 ) (1  l3 )

(1  i2 ) 2 (1  i1e 3 ) (1  l3 )

(1  i3 ) 3

From the above, it follows that

(1  i1 ) (1  i1e 2 ) (1  i1e3 ) ... (1  i1en ) ¹ (1  l2 ) (1  l3 ) ... (1  ln ) (1  in 1 ) n 1 (1  i1en 1 ) (1  ln )

(1  in ) n

(4.24)

From (4.14), it follows that, even if i1en 1  in 1 , in+1 may be larger than in. Hence the liquidity preference theory makes rising term structure of interest rates much more likely than any other pattern of the term structure of interest rates.

Short-term policy and long-term interest rates Let us now focus on our old question in the context of the liquidity preference theory. Suppose, following the adoption of a policy, one-day interest rates are expected to remain depressed (raised) for M number of days, where M < n. How will in be affected? From (4.24), we get (1  in )

[(1  i1 )(1  i1e 2 ) (1  i1e 3 )...(1  i1en ) ¹ (1  l2 ) (1  l3 ) ... (1  ln )]1/ n

(4.25)

Taking logarithm of both sides of (4.25), then taking total differential of both sides assuming the risk premia to be constant, we get back (4.20). Hence, we also get back (4.21) and (4.22) under the same set of assumptions as those made in the context of the unbiased expectations theory. Thus, under the liquidity preference theory also we get back the result that a policy that is expected to keep short-term interest rates at lower (higher) levels for a short period of time will lower (raise) short-term interest rates, but produce much less depressing (stimulating) impact on long-term interest rates.

4.6.3

Market Segmentation Theory

Market segmentation theory states that borrowers and lenders have requirements for loans of specific maturities. This means that demand for and supply of loans of any given maturity are independent of the states of other loan markets in general and interest rates on loans of other maturities in particular. Thus interest rates on loans of different maturities are largely independent

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of one another. According to this theory, therefore, the term structure of interest rates is unlikely to chart out any specific pattern. Hence it also fails to explain why the term structure of interest rates is usually upward rising.

4.6.4 Preferred Habitat Theory This theory admits that borrowers and lenders have preferences for loans of specific maturities. However, unlike market segmentation theory, it states that they can shift from their preferred habitats if interest rates on loans of other maturities are sufficiently high. Even though this theory does not imply complete independence of interest rates on loans of different maturities, it suggests that the interlinkage among interest rates on loans of different maturities is weak. It also cannot explain why the yield curve is usually upward sloping. The liquidity preference theory may be regarded as a specific version of this theory, since it also states that borrowers and lenders have their preferred habitats. However, the liquidity preference theory goes further and specifies which habitats borrowers and lenders prefer. More precisely, it states that lenders prefer to lend short, while borrowers prefer to borrow long. By dint of this specification of the preferred habitats of borrowers and lenders, it is able to explain why the yield curve is likely to be upward sloping.

4.7

MONETARY POLICY AND THE TERM STRUCTURE OF INTEREST RATES

The RBI is the monetary authority of India. It is responsible for maintaining price stability, meeting all legitimate needs for credit and also the stability of the financial sector. The major policy that it adopts to achieve these objectives is the monetary policy. Monetary policy consists of the policy of regulating the determinants of money supply such as the CRR, the supply of high-powered money and the interest rates that are set by the RBI itself with a view to influencing the interest rates. The interest rates that the RBI fixes, as we have already explained, are the repo rate and the reverse repo rate. The RBI gives to the banks short-term loans (overnight to 3 days) at the repo rate. The banks in their turn can lend their excess short term funds to the RBI at the reverse repo rate. The RBI fixes the reverse repo rate. The repo rate is set with reference to the reverse repo rate. At present the repo rate is set 150 basis points (i.e. 1.5 percentage points) above the reverse repo rate. We shall examine below how these policy instruments affect the market interest rates on loans of different maturities. For this purpose we shall develop a very simple model of interest rate determination. We assume for simplicity that only two types of loans are available, 1-day loans and 2-day loans, which we denote by L1 and L2 respectively. Interest rates on these two types of loans are denoted by i1 and i2 respectively. We denote the total demand for loans for both these types of loans together by LD. We assume that LD is a decreasing function of both i1 and i2, i.e. an increase in either of the two interest rates, given the other, or an increase in both the interest rates lowers LD. Thus

LD

LD (i1 , i2 )

˜ LD 0 ˜ i1

and

˜ LD 0 ˜ i2

(4.26)

Financial Sector, Money Supply and Interest Rates

153

Let us now focus on the supply of loans. We assume for the present that the households and firms with surplus funds or saving park them in banks as deposits and the supply of loans to the households and firms in need of loans come only from the banks. The amount of loans the banks plan to supply is closely related to the supply of M3, which is the sum of bank deposits and currency with the public. Banks, on the other hand, keep a part of their deposits as reserves of cash and lend out the rest. The amount of loans the banks plan to supply is therefore equal to M3 minus the sum of currency with the public and the cash reserves the banks plan to hold. Denoting total supply of loan by LS, we can write it as LS

M3  N  SD

È Ê

M3 

M

1 M

Ø Ú

1  S1  S2 É ir , irr , i1 , i2 Ù  

È Ø S1  S2 É ir , irr , i1 , i2 Ù  M Ê   Ú

M3 

S

1M

1 S H SM

M3

È

Ø

H œ L É S1 , ir , irr , i1 , i2 , H Ù Ú Ê     

(4.27)

From (4.23), we get i2, given expectations and the liquidity premium, as a function of i1. Thus

i2

È Ø e2 Ù É i i1 , i1 É  Ù Ê Ú

(4.28)

Using (4.28), we can write the equilibrium condition of the overall loan market as

LD (i1 , i(i1 , i1e 2 ))

L ( S1 , ir , irr , i1 , i(i1 , i1e 2 ), H ) 













(4.29)

Clearly, we can solve (4.29) for the equilibrium value of i1. Again, putting this value of i1 in (4.23) or (4.28), we can solve it for the equilibrium value of i2. The solution is shown in Figure 4.2 where LD and LS schedules in the first quadrant represent the every i1, given i1e2. The latter gives aggregate supply of loans corresponding to every i1, given i1e2 and the policy

Figure 4.2

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Macroeconomics

parameters of the RBI. The equilibrium i1 corresponds to the point of intersection of the two schedules. In the second quadrant, the ii schedule represents (4.23). It gives the equilibrium value of i2 corresponding to every i1, given i1e2 and l2. The value of i2 that corresponds to the equilibrium value of i1 on ii gives the equilibrium value of i2. We are now in a position to examine the impact of a policy induced reduction in CRR or an increase in H on the structure of interest rates with the help of Figure 4.2. Let us for simplicity and for the present purpose interpret L1, i1 and e 1e2 as one-year loan, annual interest rate on one-year loan in the current year and expected annual forward rate on one-year loan in the next year respectively. Similarly, let us suppose L2 and i2 stand for the 2-year loan and annual interest rate on the 2-year loan respectively. If the reduction in CRR and the increase in H are conceived as long-term policy changes, i.e. if people expect CRR and H to remain larger for long periods of time, their expected forward interest rate will fall. However, if the policy changes are expected to be short-run, i.e. if they are expected to be reversed in the second year, i1e2, will remain unaffected. Let us start with the latter case where the policy of monetary expansion is conceived as a short-run measure. In this case the relationship between i1 and i2, as given by (4.23) and represented by ii in Figure 4.2, will remain unaffected. Since i1e2 remains unchanged, the demand schedule, LD, in Figure 4.2 remains the same. The supply of loan, however, will increase at every i1 following the reduction in CRR or the increase in H bringing about a rightward shift in the LS schedule in Figure 4.2. Hence both i1 and i2 will decline. Obviously, in this case, supply of loans in both the markets will be larger in equilibrium. Explain this point yourself. Let us now consider the case where the policy is conceived as a long-term one. In this case i1e2 will decline. The fall in i1e2 will, vide (4.23), reduce i2 corresponding to every given i1 bringing about a leftward swivel of the ii pivoting the origin. Since i2 is less corresponding to every i1, the demand for loan will be larger corresponding to every i1. Hence LD schedule in Figure 4.2 will shift to the right. For the same reason the increase in the supply of loan due to the cut in CRR or the rise in H corresponding to every i1 will be less than that in the earlier case. For both the rightward shift in the loan demand schedule and the smaller amount of rightward shift in the loan supply schedule, the fall in i1 will be less than that in the earlier case. However, the fall in i2, as we shall show below, will be larger in the present case than that in the previous case. To see why, suppose i2 has fallen to the same level in both the cases. i1 in the present case will therefore be higher than that in the earlier case. At this (i1, i2) of the present case, the demand for credit will be less and the supply of loans will be larger than those that obtained at the equilibrium (i1, i2) in the previous case. There will therefore be excess supply in the present case, if, following the reduction in CRR or the increase in H, i2 falls to the same level as that in the previous case. Hence, for equilibrium, i2 and consequently i1 have to fall more raising demand and reducing supply and thereby removing excess supply. From the above it follows that when monetary policy is expected to have long-term impact, long-term interest rates fall more. One can also extend this argument to show that the longer the maturity period of a loan relative to the period during which the new monetary policy is expected to stay, the less will be its change.

Financial Sector, Money Supply and Interest Rates

4.7.1

155

Liquidity Adjustment Facility (LAF), Open Market Operation (OMO) and Monetary Stabilization Scheme (MSS)

LAF, MSS and OMO constitute important planks of RBI’s monetary policy. Through these programmes the RBI seeks to smoothen short-term volatility in interest rates. The LAF constructs an interest rate corridor within which it wants the call rates to remain. It is an intervention in the call money market. The RBI fixes a reverse repo rate (denoted by irr) at which it borrows from the banks as much as loan is supplied. Another interest rate called the repo rate and denoted by ir is set 100/150 basis points or 1/1.5 percentage point above the reverse repo rate. The RBI is prepared to lend as much as is demanded by banks at this rate. These interest rates are interest rates on overnight or one-day loans. Obviously, in the 1-day loan market, banks will not lend below the reverse repo rate, as they can lend as much as they want to the RBI at this rate. Again, in the one-day loan market, banks will not borrow at any rate higher than the repo rate, since they can borrow as much as they want at this rate from the RBI. We shall examine the implications of LAF using Figure 4.3. Let us first explain Figure 4.3. Note that, if corresponding to any given i1, the value of i2 is given by (4.28) or ii, the market for 2-day loans is in equilibrium, since i2 is at its equilibrium value corresponding to the given i1. Thus at any given i1 and the corresponding i2 as given by (4.28), if there is excess supply of (demand for) aggregate loans, 1-day loans will be in excess supply (demand). In Figure 4.3, in the first quadrant, DD and SS represent the demand and supply schedules of 1-day loans respectively in the absence of LAF operations, when corresponding to every i1, the 2-day loan interest rate, i2, is such that (4.28) is satisfied so that the 2-day loan market is in equilibrium. In fact, in the second quadrant we reproduce the ii schedule of Figure 4.2. DD and SS schedules intersect at that i1, which satisfies (4.29). We denote it by i1*. The corresponding equilibrium value of i2 is denoted by i2*. In Figure 4.3, we find that in the absence of LAF operations of the RBI, i1 settles down to i1* and i2 to i2*. The LAF operations will modify the shapes of the demand and supply schedules of 1-day loans. Let us explain. Note first that the 1-day loan market constitutes

Figure 4.3 LAF operations of the RBI.

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a part not only of the call money market but also of the other segments of the money market. The difference between the call money market and the other segments of the money market is that in the former only banks participate, while in the latter not only banks but also other financial institutions and corporations take part. Under LAF, RBI is prepared to borrow from banks as much as they want to lend at irr. Hence banks will obviously not supply any loans in the 1-day loan market at any interest rate below irr. Since banks are important players in these segments, the supply of loans in these markets will shrink drastically at interest rates below irr. Under LAF, therefore, supply of 1-day loans in Figure 4.3 is given by the schedule SS1S2S3. Again, under LAF, the RBI is prepared to lend to the banks as much as they want at the repo rate, ir. Accordingly, the banks will stop demanding loans from these markets at interest rates above ir. Hence demand for loans will decline substantially in these markets at interest rates greater than and equal to ir. The demand for 1-day loans in the presence of LAF is therefore given by DD1D2D3. From Figure 4.3, it is clear that ir and irr act as ceiling and floor respectively to i1 unless demand is very large relative to supply or supply is very large relative to demand. For example, in the absence of LAF, the point S1 of the supply schedule, SS, has to be to the right of the demand schedule DD for the interest rate to go below irr. In the presence of LAF, however, the supply schedule has to be much further to the right for i1 to go below irr. In fact, the point S2 and not S1 of the supply schedule has to be to the right of the demand schedule for i1 to go below irr. Again, in the absence of LAF, the point D1 of the demand schedule, DD, has to be to the right of the supply schedule for i1 to go above ir. However, in the presence of LAF, the demand schedule has to be much farther to the right for i1 to move above ir. In fact, in the presence of LAF, the point D2 of the demand schedule has to be to the right of the supply schedule for i1 to go above ir. From this example, it is clear that the LAF reduces substantially the possibility of i1 going below irr or moving above ir. This is how the LAF seeks to construct an interest rate corridor to reduce the volatility of interest rates on 1-day loans. Let us now focus on how the LAF operations affect interest rates on loans of other maturity periods. This will obviously depend, among others, on people’s expectations regarding the stability of the reverse repo and repo rates. Let us explain. Suppose people expect the RBI to revise these policy rates every T number of days and the LAF operations also keep the interest rates on 1-day loans within the interest rate corridor. Then, expected daily forward rates on 1-day loans during these T days will be subject to these floors and ceilings. Given the liquidity premia, therefore, interest rates on loans up to the maturity period of T days will be subject to some floors and ceilings. It, in fact, follows from (4.24) that for loans up to the maturity period of T-days, the floors and ceilings will be given respectively by (1 + irr) (1 + ln)1/n and (1 + ir) × (1 + ln)1/n for n = 2, 3, 4, ..., T. For loans of longer maturity periods, however, the floors and ceilings will not hold, as expected daily forward rates on 1-day loans will not be subject to any floor or ceiling beyond the period of T days. Explain the above points yourself. Table 4.5 gives data regarding RBI’s LAF operations during the period September 1–September 10, 2009. The RBI under LAF auctions off repos and reverse repos. On 1 September 2009, as we find from Table 4.5, the RBI auctioned 1-day reverse repos at the maximum reverse repo rate of 3.25%. It received 57 bids, which amounted to ` 1,41,840 at the reverse repo rate of 3.25%. It accepted all the bids. This means that the RBI on 1 September 2009 borrowed from banks ` 1,41,840 for 1 day at the rate of 3.25% in the form of reverse repos. On September 1, the RBI auctioned repos also at the minimum repo rate of 4.25%. But it received no bids.

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Table 4.5 LAF Date Sep 09

Repo/ reverse repo period (days)

1

2

1 2 3 4 7 8 9 10

Repo/reverse repo auctions under liquidity adjustment facility Repo (Injection)

Reverse repo (Absorption)

Bids Bids Cut- Bids received Bids accepted received accepted off Number Amount Number Amount rate Number Amount Number Amount 3

4

5

6

7

Net Outinjection standing (+)/Net amount Cut- absorption off (–) of rate liquidity [(6)–(11)]

8

9

10

11

12

13

14

1 1 1 3 1 1 1

57 57 60 56 52 55 56

141840 142060 158290 168570 147765 149240 120235

57 57 60 56 52 55 56

141840 142060 158290 168570 147765 149240 120235

3..25 3..25 3..25 3..25 3..25 3..25 3..25

–141840 –142060 –158290 –168570 –147765 –149240 –120235

141485 141705 157935 168215 148885 119880 131340

1

56

131695

56

131695

3..25

–131695

138370

Source: RBI Monthly Bulletin 2009.

No banks were willing to take loans from the RBI at the pre-specified repo rate on September 1. The last column of Table 4.5 gives the total amount of outstanding debt of the RBI due to its repo and reverse repo operations. On September 1, RBI’s total outstanding debt due to repo and reverse repo operation was ` 1,41,840 crore. If the RBI sells reverse repo of ` 100 crore, its outstanding debt goes up by ` 100. If the RBI sells repo of ` 100 crore, its outstanding debt falls by ` 100 crore. When the RBI pays back the reverse repo loans, its outstanding debt declines. When the RBI gets back its repo loans, its outstanding debt goes up. Let us illustrate these concepts with an example. Suppose on 1 August 2009, RBI’s outstanding loan on account of repo and reverse repo operations was zero. On 2 August, the RBI sells 3-day reverse repo of ` 100 crore and also 3-day repo of ` 50 crore. This means that the RBI takes a loan of ` 100 crore from banks by selling reverse repos and gives a loan of ` 50 crore by selling repos. So, on 2 August as a result of these transactions, total outstanding debt of the RBI becomes ` 50 crore. On 3 August, the RBI sells 2-day reverse repo of `100 crore. After these sales, its outstanding debt rises to ` 150 crore. On 4 August, the RBI again sells 1-day reverse repo of ` 100 crore. These sales again raises RBI’s outstanding debt to ` 250 crore. On 5 August no fresh sales of repo or reverse repo takes place. On 5 August, however, it pays back all its reverse repo loans and gets back all the repo loans. So its outstanding debt at the end of 5 August becomes zero. Explain the other rows and columns of Table 4.5 yourself. It is clear from Table 4.5 that the interest rate on risk-free 1-day loans in the money market during the period covered in Table 4.5 was either equal to or less than the reverse repo rate. Otherwise, the banks would not have lent their excess funds to the RBI.

Open market operations (OMO) of the RBI Even though the RBI creates an interest rate corridor, which is 150 basis points wide, it does not want the interest rate to vary that much. It seeks to keep variations in interest rates within

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a much smaller band. For this purpose it undertakes open market operations (OMO). OMO consists of buying and selling of securities by the RBI. In the event there takes place a surge in demand for one-day loans creating excess demand for such loans at the prevailing interest rates. There will be upward pressure on the interest rate. The RBI can halt the upward movement of interest rates by supplying 1-day loans and thereby removing the excess demand for loans. The RBI supplies loans by buying securities from the 1-day loan market. Similarly, if there emerges excess supply of 1-day loans and interest rates tend to decline, the RBI can arrest the fall in interest rates by borrowing from the 1-day loan market and thereby removing the excess supply. The RBI borrows by selling securities in the 1-day loan market. These operations are referred to as OMO. Table 4.6 gives the data of the RBI’s OMO in the year 2009–10. It shows, for example, that in April 2009–10, the RBI purchased government’s dated securities of ` 21,130 in face value and sold to the state governments and others Government of India dated securities of ` 747.03. In the net, therefore, it purchased Government of India dated securities of ` 20,382.97 in face value. Obviously, net purchase of securities by the RBI through the OMO directly raises the stock of high-powered money and thereby sets the money multiplier process into motion. Just the opposite happens in the event of net sales of securities by the RBI. Table 4.6 Year/ Month Market 1

2

2009–10 April May June July August September

21,130.00 15,374.40 6765.60 7724.37 13,462.09 14,111.64

Open market operations of the RBI

Government of India dated securities—face value Purchase Sale Net purchase (+)/ State governments Market State governments net sales (–) and others and others 3

4

5 747.03 207.91 315.25 2479.71 982.68 243.85

6 20,382.97 15,166.49 6450.35 5244.66 12,479.41 13,867.79

Source: RBI Monthly Bulletin 2009.

EXERCISE 4.7 Explain the implications of OMOs for money supply.

Monetary stabilization scheme (MSS) In the pre-reform era there was a ban on inflow of foreign capital, i.e. foreigners were not allowed to buy Indian financial or physical assets. The post-reform era witnessed substantial relaxation of these restrictions. From 2000 foreign capital started flowing in on a substantial scale. To buy Indian assets, foreigners have to buy first Indian rupee with their own currencies.

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159

Thus capital inflows created excess demand for rupee in exchange for foreign currencies putting upward pressure on the exchange rate. Since the RBI intervenes in the foreign exchange market to keep the exchange rate stable, inflow of foreign capital since 2000 induced the RBI to absorb the excess supply of foreign currencies and thereby to meet the excess demand for rupee at the prevailing exchange rate. Following the purchase of foreign currencies by the RBI, its assets went up by the rupee value of the foreign exchange bought. As the foreigners spent the Indian currency thus acquired to buy domestic assets, they went into the banks and into the hands of the public as additional deposits and currency respectively. Banks held these deposits initially as cash reserves. Thus liabilities of RBI increased too by the amount of the rupee value of the foreign currencies purchased by the RBI. Thus new high-powered money equal to the rupee value of the foreign currencies purchased by the RBI was created. We denote this amount by 'H DH. It follows from (4.7) and (4.8) that banks’ cash reserves and deposits increased by , 1 M M 'H while currency holding of the public went up by . Explain this point yourself. The banks 1M obviously wanted to give more loans. At the time the inflow of foreign capital took place, the interest rate on 1-day loans was equal to irr. Given expectations and the liquidity premia, the given irr fixed the interest rates on loans of all maturities. At this fixed set of interest rates there emerged excess supply of loans as banks’ cash reserves increased. This excess supply was, however, absorbed entirely by the RBI at its reverse repo window in the call money market and not in any other segment of the loan market. The reason may be explained as follows. The given irr, as we mentioned above, fixed the equilibrium interest rates on loans of all maturities. If there emerged excess supply in any segment, the interest rate in that segment would have tended to fall inducing the lenders, given the interest rates in the other segments, to withdraw all their loan supply from the given segment. Hence the interest rate in the given segment would cease to fall. Hence the whole of the excess supply was finally lent to the RBI at its LAF window at irr. Thus the additional cash reserves of the banks went back to the RBI. As the banks lent to the RBI, reserves held by the banks in the form of vault cash and deposits with the RBI, which are on the liabilities side of the RBI, declined. On the assets side, as RBI borrowed from the banks, its net domestic credit to the commercial sector declined neutralizing partly the increase in its stock of foreign exchange assets which occurred on account of the inflow of foreign exchange. Thus LAF neutralized significantly the impetus to money supply given by the acquisition of foreign exchange by the RBI. If we focus on the liabilities of the RBI, at the end of the absorption of the excess supply of loans by the RBI at its reverse repo window, only currency held by the public remained larger by

M 'H , but banks’ deposits with 1M

the RBI and their vault cash went back to their initial level. Banks’ deposits also remained larger by

'H . 1 M

Thus M3 increased only by DH and the money multiplier process could not

work. If the banks could lend out their additional deposits in the market, the money multiplier process would have started working. This neutralization of the impetus to money supply is called sterilization. When there is a sustained inflow of foreign capital, as there was during 2000–2004, sterilization through the LAF’s reverse repo window becomes a problem as the

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stock of government securities with which the RBI absorbs the loans may get exhausted. To tackle this problem, the RBI set up a new scheme called the monetary stabilization scheme (MSS). It has at its disposal a large stock of government securities. The objective of this scheme is to absorb the excess liquidity of the banks at irr, when the increase in banks’ liquidity is due to capital inflows that are less temporary or more permanent in nature. The purpose of this scheme is to reduce LAF’s burden of sterilization (Figure 4.4).

Figure 4.4 Monetary stabilization scheme.

Source: RBI

Monetary policy and LAF From the above it follows that if the RBI adopts expansionary monetary policy, which consists of raising of money supply, by reducing CRR or by raising H through OMO, there will be no impact on money supply or interest rates, when the LAF keeps the 1-day interest rate fixed at a given irr. This is quite obvious. Note that, as we explained above, given expectations and the liquidity premia, the irr set by the RBI fixes the equilibrium levels of all other interest rates. If RBI lowers CRR, the banks will plan to lend more at the set of interest rates fixed by the given policy rate, irr. There will therefore emerge excess supplies in different segments of the loan market. However, given the liquidity premia and the expected forward rates, interest rate in

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161

none of the segment will fall. This is because if it falls in any segment on account of the excess supply, the lenders will consider it optimal to withdraw all their loan supplies from the given segment. Hence, the entire excess supply will be eventually offered to the RBI at its LAF reverse repo window. The stock of high-powered money will therefore go down by the amount of CRR reserves released by the lowering of the CRR. On the liabilities side of the RBI’s balance sheet, banks’ reserves held in the form of deposits with the RBI and vault cash will go down by this amount. On the assets side, net domestic credit of the RBI to the commercial sector will fall by this amount, as the RBI borrows this amount from the banks. Thus the reduction in CRR will produce no impact either on money supply or on the interest rates, when the raising of money supply does not affect expected forward rates on 1-day loans. If it does, the raising of money supply will lower interest rates. If expected forward rates decline following the reduction in CRR, interest rates, given and the liquidity premia will fall raising demand for loans in different segments of the loan market making it possible for the banks to extend some loans in the segments where interest rates go down. Thus if banks’ planned increase in loan supply materializes, the money multiplier process will work fully. However, if banks’ plans are only partly realized, a part of the additional cash reserves released by the cut in CRR will get absorbed at the reverse repo window of the RBI. In such a situation the money multiplier process will work only partly. From the above it follows that, when the RBI as a matter of policy fixes 1-day interest rate at irr, it may be prudent if a reduction in CRR is accompanied by a commensurate lowering of irr so that interest rates in all the different segments of the loan market fall unambiguously and absorb at least partly the additional supplies of loans brought about by the lowering of CRR. In similar circumstances, for similar reasons, a raising of CRR should be accompanied by a hike in irr for the desired impact.

4.8 CONCLUSION Note that the LAF, OMO and MSS have strong implications for money supply. Let us explain. Again, suppose for simplicity that there are two types of loans: 1-day and 2-day loans. Consider the situation where there is excess demand for 1-day loans at ir, when, with i1 = ir, i2 is such that the 2-day loan market is in equilibrium. In terms of Figure 1 the demand curve is so far to the right that the point D2 is to the right of the supply curve and the value of i2 corresponds to ir on ii. Under these circumstances the RBI will lend to the banks at ir to meet the excess demand. As a result, the stock of high-powered money in the economy will increase. The increase in the high-powered money will lead to an increase in credit supply bringing about rightward shifts in the credit supply schedule. This process will continue until the credit supply schedule intersects the credit demand schedule at ir. Similarly, if there emerges excess supply at irr, banks will lend out their deposits to the RBI bringing about a reduction in the stock of high-powered money. The loan supply schedule as a result will shift to the left. This process will continue until the loan supply schedule intersects the loan demand schedule at irr. Again, if the equilibrium value of i1 happens to be in between ir and irr, and if the RBI seeks to lower (raise) it to irr(ir), it will start purchasing (selling) securities through the OMO raising (lowering) the stock of high-powered money. The increase in the stock of high-powered money will start shifting the loan supply schedule to the right (left) and thereby lowering (raising) interest rate. This process will continue until i1 falls (rises) to irr(ir). Thus, if the RBI through LAF, OMO

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and MSS seeks to keep interest rate at any given value, the stock of high-powered money becomes an endogenous variable. It assumes a unique value corresponding to the targeted interest rate. Similarly, if the RBI through the operations mentioned above seeks to keep interest rates within a band, the stock of high-powered money will also have to be within a corresponding range. The RBI cannot control both interest rates and the supply of broad money. EXERCISE 4.8 (a) Suppose there are only two types of loans, 1-day and 2-day loans. Today’s expected daily forward rate on 1-day loans of tomorrow is 5% and the liquidity premium is 2%. What relationship will hold between interest rates on 1-day and 2-day loans today in equilibrium? Show in a graph the state of the 2-day loan market today corresponding to any given value of i1. Suppose demand for and supply of 1-day loans are given by L 1D = 10 – 4i1 and L1S = 6i1 + 2H respectively, when corresponding to every i1 the value of i2 is such that the 2-day loan market is in equilibrium and H = 2.5. (i) Derive the equilibrium values of i1 and i2. Show the equilibrium in a graph. Suppose the total supply of loan is given by 10i1, when i2 corresponding to every i1 is at its equilibrium value. What are the equilibrium quantities of loans in the two loan markets? (ii) Suppose the RBI fixes irr and ir at 4% and 5% respectively. What will be the equilibrium values of i1 and i2? Will H remain unchanged? If not, will H eventually settle down to an equilibrium value? If yes, discuss the process.

REFERENCE Modigliani, F. and Sutch, R. (1966), The Term Structure of Interest Rates, American Economic Review (Papers and Proceedings), May.

5 5.1

IS-LM Model

INTRODUCTION

We shall now extend the simple Keynesian model, which focuses on the real sector or the commodity market alone, by incorporating into it the financial sector. This extended model is referred to as the IS-LM model. Keynes’ ideas regarding the interlinkage between the real sector and the financial sector found its most cogent and enduring interpretation in the IS-LM model developed by Hicks (1937). It formally captures what Keynes thought about how the real and the financial sectors are linked together. Despite some of its major weaknesses, which we shall discuss later, it constitutes one of the most popular and trusted models of monetary economics. It helps us understand in a clear and plausible manner how repercussions in the real sector get transmitted to the financial sector and vice versa and what role money plays in the determination of the real variables such as aggregate real output, employment, etc.

5.2

THE MODEL

The IS-LM model, as we have just noted, focuses on the interlinkages between the real and the financial sectors as envisioned by Keynes. We shall discuss below both these sectors in turn. We first consider the real sector or the commodity market.

5.2.1 The Commodity Market The difference between the SKM and the IS-LM model in the characterization of the commodity market is the following. In the former, aggregate planned consumption demand is a function only of personal disposable income and aggregate planned investment is either exogenously given or a function of GDP/NDP. In the IS-LM model both these components of aggregate planned demand are in addition decreasing functions of interest rates. Both consumption and 163

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investment are partly financed with borrowing and interest rates constitute the cost of borrowing. Obviously, the higher the cost of borrowing, the less is the incentive to borrow to finance consumption and investment. Hence, the higher the interest rates, the less are likely to be the investment and consumption expenditures. This very brief explanation as to why interest rates may influence consumption and investment expenditures will suffice for the present. We shall later discuss the reasons in detail in separate chapters on consumption and investment functions. To keep matters simple, we shall assume that only aggregate planned investment is a decreasing function of the interest rates. We also abstract from the fact that interest rates on different types of loans are different. We assume instead that interest rates on all the different types of loans are the same and denote this common interest rate by i. We also postulate for the present that government’s consumption expenditure is exogenously given, total tax revenue collected by the government is a lump sum and transfers are nil. Finally, the economy considered here is closed. Accordingly, the three different components of aggregate planned final demand in the commodity market in the present case are given by the following equations: Consumption function 0  C„  1

C (Y  T );

C

(5.1)

Investment function I = I(i);

I¢ < 0

(5.2)

Government consumption G

G

(5.3)

where C º aggregate planned private consumption expenditure, Y º GDP, I º aggregate planned gross investment expenditure, T œ aggregate lump sum tax revenue collected by the government and G º government’s consumption expenditure. Just as in the SKM, in the IS-LM model also, there is idle productive resources, producers keep their prices fixed and adjust their output to whatever demand comes forth at the fixed prices. In other words, in the IS-LM model also, prices of goods and services are exogenously given and aggregate output is determined by aggregate planned final demand for goods and services. The commodity market or the real sector is therefore in equilibrium if aggregate output or GDP equals aggregate planned final demand for goods and services. The equilibrium condition of the real sector is thus given by the following equation: Y

C (Y  T )  I (i)  G

(5.4)

where i º the common nominal interest rate. Unlike in the SKM, here the equilibrium condition (5.4) contains two unknowns, i and Y. We can therefore solve (5.4) for the equilibrium value of Y if and only if we specify the value of i. Corresponding to every pre-specified value of i, we shall get a value of Y that satisfies (5.4). In other words, we can solve (5.4) for the value of Y that equilibrates the goods market as a function of i, given the exogenous variables,

G, I , T and the parameters of the consumption and investment functions. Alternatively, we can solve (5.4) for the value of i that equilibrates the goods market as a function of Y, given the exogenous variables, G, I , T and the parameters of the consumption and investment functions. This function gives corresponding to every different value of Y, the value of i that equilibrates the commodity market. From this function, therefore, we shall get an infinitely large number

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165

of combinations of Y and i that keep the commodity market in equilibrium. The set of all these combinations when plotted in the (Y, i) plane in a graph is called the IS curve. Let us illustrate the point made above with an example. Suppose consumption and investment functions are given by C C  c ¹ (Y  T ) and I I  d ¹ i respectively. With government consumption exogenously given at G, the equilibrium condition in the goods market will be given by Y

C  c ¹ (Y  T )  I  d ¹ i  G

(5.5)

(C  cT )  ( I  di)  G 1c

(5.6)

Solving (5.5) for Y, we get Y

Equation (5.6) gives us the value of Y corresponding to every i that equilibrates the goods market, given G, T and the parameters of the consumption and investment functions C , c and d . The inverse of (5.6) is given by i

[C  I  G  cT ]  cY  Y d

(5.7)

Equation (5.7) gives the value of i corresponding to every Y that equilibrates the goods market, given G, T and the parameters of the consumption and investment functions C , c and d . The [C  I  G  cT ] d and its slope is [–(1 – c)Y]. It is quite easy to explain (5.7). The numerator on the RHS gives the amount of excess demand for goods and services at any given Y, when i = 0. The equilibrium value of i corresponding to the given Y is the one which removes the excess demand that obtains at the given Y, with i = 0. From the aggregate demand function given by the RHS of (5.5), we find that a unit increase in i, Y and all other variables remaining unchanged, reduces aggregate demand and therefore excess demand by d. Hence, to reduce aggregate demand and

graph of Eq. (5.7) in the (Y, i) plane is the IS curve. Its vertical intercept is

therefore the excess demand by {[C  I  G  cT ]  cY  Y } , i will have to rise from zero to [C  I  G  cT ]  cY  Y . Therefore, corresponding to any given Y, if i assumes the value d

Ë C  I  G  cT ÛÝ  cY  Y given by Í , the commodity market will be in equilibrium. d

Let us illustrate the point made above with an example. Suppose C T G 10, I 100, c = 0.75 and d = 5. Given this information, the aggregate planned demand and the excess demand at Y = 50, with i = 0 is given by [10 + 0.75(50 – 10)] + 10 + 10 = 60 and 60 – 50 = 10 respectively. From the aggregate demand function, [10 + 0.75(Y – 10)] + [10 – 5i] + 10, it follows that the aggregate demand and therefore the excess demand, given Y, falls by 5 per unit increase in i. Hence, at Y = 50 the excess demand will fall to 0 and therefore the commodity

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market will come to equilibrium if i rises from 0 by such an amount that the excess demand falls by 50. Since, given Y, excess demand falls by 5 per unit increase in i, to reduce excess demand by 50, i will have to rise from 0 to (50/5) = 10 units to 10. Thus, with Y = 50, the goods market will be in equilibrium at i = 10. EXERCISE 5.1 Plot (5.7) in the (Y, i) plane in a graph. What are its vertical intercept and slope? What is the meaning of its vertical intercept? What is the magnitude of its vertical intercept? Can you explain this magnitude? In the IS curve, I and S stand for investment and saving respectively. Let us explain why. We can write the goods market equilibrium condition (5.4) as

Y  C (Y  T )  G

I (i)

(5.8)

The LHS of (5.8) is nothing but aggregate planned saving. Hence, at every (Y, i) on the IS curve aggregate planned saving equals aggregate planned investment. This explains why IS curve is called IS.

Graphical derivation of the IS curve When specific forms of the consumption and investment functions are not known as is the case with (5.4), it is not possible to solve the goods market equilibrium condition, for the goods market equilibrium i is a function of Y, given the parameters. Still it is possible to get some idea about the shape of the IS using graphical techniques. We illustrate this using Figure 5.1 where the AD(i0) schedule gives the level of aggregate planned demand at every Y, when i is fixed at i0. The equation of the AD(i0) schedule is given by AD(i0) = C (Y  T )  I (i0 )  G

Figure 5.1 Graphical derivation of the IS.

(5.9)

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167

At every Y the level of planned aggregate demand as shown by the AD(i0) schedule is equal to the sum of I(i0), G and the aggregate planned consumption demand corresponding to the given Y. The 45° line in Figure 5.1 helps us identify the goods market equilibrium value of Y, when i = i0. Focus on the point of intersection of the AD(i0) schedule and the 45° line. We denote the value of Y that corresponds to the point of intersection by Y0. Obviously, planned aggregate demand corresponding to Y0, as given by the AD(i0) schedule equals Y0. Hence the value of Y that equilibrates the goods market, with i = i0, is Y0. Thus (Y0, i0), as shown in Figure 5.2, is a point on the IS. Now, suppose i is lowered from i0 by di to i1. This raises planned aggregate demand at every Y by (I¢di) > 0 (Q di < 0), and therefore brings about an upward shift in the AD schedule by the same amount. The new AD schedule is shown by the line AD(i1) in Figure 5.1. The vertical distance between AD(i1) schedule and AD(i0) schedule is given by (I¢di) > 0. Clearly, AD(i1) schedule will intersect the 45° line at a higher Y. We denote this Y by Y1. Thus (Y1, i1) is another point on the IS curve as shown in Figure 5.2. Repeating this exercise again and again, we can generate the whole IS.

Figure 5.2 IS curve.

Shape of the IS Figure 5.2 clearly shows that IS is a downward sloping or negatively sloped curve. It means that along the IS curve Y and i move in the opposite directions. More precisely, if we move from one point to another on the IS and if at the new point Y is larger than that at the initial point, i at the new point is less than that at the initial point. It is quite easy to see why. Consider any given point on the IS. Suppose we raise Y from that point by dY keeping i unchanged. The rise in Y raises supply by dY. It also raises disposable income, (Y  T ) by dY. This increase in disposable income in turn raises aggregate planned consumption demand by C¢dY < dY. Since demand increases less than supply, there emerges an excess supply of (1 – c¢) dY at this point.

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If we keep Y at this higher value, in which direction will we have to change i to restore equilibrium in the commodity market? Since planned aggregate demand is a decreasing function of i, we have to lower i to remove the excess supply and thereby to get back to the IS curve. This explains why IS is negatively sloped. The next question is by how much we will have to lower i to reduce excess supply by (1 – c¢) dY to zero. We know that per unit fall in i, given Y and the exogenous variables, aggregate planned demand increases and therefore excess supply falls by (–I¢). Te reduce aggregate demand and excess supply by (1 – c¢) dY, interest rate i will (1  c „) dY (1  c „) dY . Note that gives the absolute value of the fall in interest (  I „) (  I „) rate that is needed to restore equilibrium in the goods market if from any point we raise Y by

have to fall by

(1  c „) dY . C¢ and I¢ in the I„ above expression are obviously evaluated at the initial (Y, i) on the IS. Let us now focus on the slope of the IS. The slope of IS is defined at every point on the IS. The slope of the IS at any of its point gives the amount of change in i that is required to equilibrate the goods market per unit increase in Y when we raise Y from the given point by a small amount dY keeping i unchanged. We know that if from a given point on the IS we raise Y by a small amount, dY, keeping i unchanged, the amount of change in i that is required to dY. The actual required change in i is negative and it is given by

(1  c „) dY . Obviously, if we divide this expression ( I „) by dY, we shall get the amount of change in i that is required to restore equilibrium in the goods market per unit increase in Y, when we raise Y from any point on the IS by a small amount, restore equilibrium in the goods market is

(1  c „) . ( I „) We can derive the slope of the IS mathematically as well. Taking total differential of the goods market equilibrium condition treating all variables other than Y and i as constants, we have dY = C¢dY + I¢di (5.10)

dY, keeping i unchanged. Thus the slope of the IS is given by

The LHS gives the amount of change in aggregate supply as Y changes by dY. The RHS gives the change in aggregate planned demand when Y and i change by dY and di respectively. Clearly, if we start from a point or (Y, i) on the IS and change Y and i by dY and di respectively so that (5.10) is satisfied, then such values of dY and di will keep the goods market in equilibrium. We can therefore get the value of the slope of the IS by dividing both sides of (5.10) by dY and then solving for (di/dY). It is given by di dY

1  C„ I„

(5.11)

EXERCISE 5.2 What is the slope of the IS given by (5.7)? Explain it. What is the value of the slope of the IS given by (5.7) when C

T

G

10, I

100, c

0.75 and d

5? Explain it.

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169

State of the goods market at points off the IS Suppose you are shown just a graph of the IS curve and a point off the IS, curve and you are asked to ascertain the state of the goods market at such a point. How will you do it? You can do it in the following manner. At every point on the IS the goods market is in equilibrium. To ascertain the state of the goods market at any point off the IS, you have to compare the given point to one on the IS, which has either the same Y or the same i. Thus to discern the state of the goods market at a point such as A1 as shown in Figure 5.2, you have to compare it to either A or B. A1 has the same i as A, but a larger amount of Y. Hence there is excess supply of Y at A1, since C¢ < 1. Alternatively, A1 has the same Y as B, but a higher i. Thus at A1 aggregate supply and consumption demand are the same as those at B, but investment demand is less. Therefore at A1 there must be excess supply. Thus at every point to the right of IS there is excess supply. Similarly, one can easily deduce that at every point to the left of the IS there is excess demand in the goods market. (Prove this yourself.) EXERCISE 5.3 Suppose you are given an equation of the IS. Suppose this equation is given by i = 200 – 2Y. Is there any excess demand or excess supply at (Y = 95, i = 12)? Explain your answer. Derive the exact magnitude of disequilibrium, if I¢ = – 2. If I¢ = – 2, what is the value of marginal propensity to consume out of the disposable income? Explain your answer.

Shift in the IS schedule The IS schedule will shift if the parameters of the IS schedule change. The parameters of the IS schedule are T , G and the parameters of the consumption and investment functions. If any one or more of these parameters change, then the IS schedule will shift. Let us illustrate with the example of an increase in G by dG . To find out whether the IS will shift or not, one has to consider any given point on the initial IS and examine whether aggregate supply or aggregate demand corresponding to the given point has changed or not following the increase in G . We find from (5.1) and (5.2) that the determinants of C and I are Y, i and T and not G . Hence at every point on the initial IS aggregate supply, aggregate consumption and investment demand are the same as before, but G is larger by dG . Hence at every point on the initial IS there is now an excess demand of dG . Thus the initial IS no longer gives the combinations of i and Y that keep the goods market in equilibrium. In fact, now at every given i the goods market will be in equilibrium at a larger Y, or at every given Y the goods market will be in equilibrium at a higher i. Thus the new IS curve will be to the right or above the initial IS. Alternatively, following the increase in G by dG , the IS shifts to the right or upward. We can also derive the horizontal or vertical shifts in the IS following the increase in G by dG mathematically as follows. The horizontal shift in the IS following an increase in G by dG is given by the amount of change in Y that keeps the goods market in equilibrium at any given i. Obviously, we get it by taking total differential of (5.4) treating i and all exogenous variables other than G as given. This gives us the following equation: dY

C „dY  dG

(5.12)

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Macroeconomics

The LHS gives the change in aggregate supply as Y changes by dY. The RHS gives the change in aggregate planned demand when Y and G change by dY and dG respectively, while i and all exogenous variables other than G remain unchanged. Therefore the value of dY that satisfies (5.12) will equilibrate the goods market, with i remaining unchanged, following the increase in G by dG . This value of dY therefore gives the horizontal shift in IS. It is given by dY

dG 1  C„

(5.13)

Explanation of (5.13) is quite simple. The numerator on the RHS gives the amount of excess demand that is created at any (Y, i) on the initial IS following the increase in G by dG . Equilibrium will be restored in the goods market, with i remaining unchanged at its initial value, when Y rises to such an extent that the excess demand falls in absolute value by dG to zero. Now, with i remaining unchanged, excess demand falls by (1 – C¢) in absolute terms when Y rises by 1 unit. Therefore excess demand will fall in absolute terms by dG when Y rises by [( dG)/(1  C „)] .

EXERCISE 5.4 (a) Define and derive the vertical shift of the IS in the case considered above. Derive both the vertical and the horizontal shifts of IS following an increase in T by dT . (b) Consider the following equations:

C

C  c ¹ ([1  t ]Y )

I

I  ai

G G Write down the equation of the IS. Plot it in a graph indicating its vertical intercept and slope. Explain their meanings. Consider any point off the IS. Indicate the state of the goods market at that point. Can you measure the exact magnitude of the excess demand/supply at the given point? What are the parameters that determine the position of the IS? Consider any given point on the initial IS and examine the effect of an increase in I by dI on the aggregate demand and the aggregate supply corresponding to that point. Derive the horizontal and the vertical shifts of the IS and explain them. (c) Consider the following equations: C = 0.8(1 – t) Y, t = 0.25, I = 900 – 50i and G 800 . Derive the equation of the IS. What is the value of its slope? Explain its meaning. What are the determinants of the position of the IS. Find out the horizontal and the vertical shifts the of the IS following (i) a change in G by 5 units and (ii) an increase in t by 0.25. Explain these magnitudes.

5.2.2

The Money Market or the Financial Sector

Characterization of the money market in the IS-LM model is based on the theory of liquidity preference. Just as the commodity market, the money market also has a demand and a supply

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side. The theory of liquidity preference regards the supply of money as a policy parameter of the monetary authority (central bank). This happens when, as follows from our previous chapter, excess reserves are a function only of the policy rates. Thus money supply in the IS-LM model is exogenously given. (5.14) M M The demand for money, on the other hand, is defined as the amount of money that the economic agents want to keep in their hands at every point of time on the average. Thus, if I say that my demand for money is ` 200, it means that I want to keep in my possession ` 200 at every point of time on the average. The question that automatically arises is why one should want to hold money, since one cannot earn any additional income in future from such holding. If the money held is lent out or invested in physical capital, it will earn additional interest or profit income in future. The liquidity preference theory states that individuals hold money because of its liquidity. The liquidity of a commodity, as you should be able to recall from our previous chapter, is a measure of how readily the commodity can be exchanged for another commodity without any loss in value. Since money is universally accepted as a medium of exchange in all market transactions, it is the most liquid of all commodities, when prices are stable. One can buy with money any good or service one wants to without any loss of value, when prices are stable. Other commodities such as bonds, shares, land, houses, etc., are much less liquid than money. Consider the situation where one is not holding any money and has kept all one’s wealth in shares, bonds and physical assets such as land, houses, etc. To make any purchase—even to board a bus or have a cup of tea in a tea stall—one has to first sell some of one’s physical or financial assets. Selling physical assets is extremely time-consuming. If one tries to sell land, house or other physical assets quickly, one has to do so at much lower prices than what one would have got had one searched longer. Selling shares, bonds etc. is also quite time-consuming and costly. On has to sell them through brokers who charge hefty commissions. Moreover, the prices of shares, bonds etc., vary a great deal even in the short-run. Hence sales of such assets may involve considerable capital loss. Clearly, it is quite costly to convert physical and non-money financial assets into money not only in terms of brokers’ commissions and capital losses but also in terms of the time and effort one has to spend in the process. Therefore, if one does not hold any money, it becomes very costly to make any purchase. Accordingly, individuals have to hold money because of its liquidity. It should be noted here that individuals hold money not for the sake of holding money per se but for the goods and services it can buy. In other words, individuals want to hold purchasing power over goods and services or the generalized command over goods and services that money represents. Purchasing power or generalized command over goods and services of a given stock of money, M, is given by (M/P), where P denotes the price level or the average price of goods and services. (M/P) is called real balance and individuals’ demand is for real balance and not for nominal money balance. Since the stock of real balance held by an individual can easily be lent out, i.e. held in the form of interest bearing financial assets, the opportunity cost of holding real balance is the amount of interest income foregone. Clearly, therefore, the higher the interest rate the greater will be the incentive on the part of the economic agents to economize on the holding of real balance. Hence the demand for real balance is likely to be a decreasing function of the rate of interest. Again, the greater the value of goods and services that the individuals want to purchase, the more is the necessity for holding real balance. Since demand for goods

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and services is an increasing function of income, demand for real balance should be an increasing function of income too. Hence, according to the theory of liquidity preference L = L(i, Y);

Li < 0, LY > 0

(5.15)

where L denotes planned aggregate demand for real balance. In the IS-LM model, as we have already pointed out, the price level is fixed and the supply of money—see (5.14)—is a policy variable of the central bank. Hence the supply of real balance, denoted by LS, is exogenously given. Thus LS

M P

(5.16)

Clearly, there is equilibrium in the money market if the supply of real balance, ( M / P), is equal to demand for real balance. Money market equilibrium condition is therefore given by M (5.17) L (i, Y ) P Just as the equation of the IS curve, Eq. (5.17) also contains two unknowns, i and Y, since

P and M are exogenously given in this model. Hence, we can solve it for i as a function of Y, given the exogenous and the policy variables. This function gives corresponding to every Y the value of i that equilibrates the money market. The graph of this function in the (Y, i) plane is called the LM curve. How does it look like? Let us examine. Consider a pair (i, Y) that satisfies (5.17). If we now raise Y keeping i unchanged, demand for real balance will rise creating an excess demand for real balance at the given i. Hence to keep the money market in equilibrium at the higher level of Y, i has to be raised. Thus the LM curve is positively sloped. i.e. Y and i move in the same direction along the LM schedule. We shall now derive the LM graphically using Figure 5.3. The vertical line gives the supply of real balance schedule. It shows that the supply of real balance is ( M/ P) whatever be the value of i. The LL(Y0) line gives demand for real balance schedule, when Y is fixed at Y0, i.e., it gives the amount of aggregate planned demand for real balance at every different i, when Y is fixed at Y0. The value of i that keeps the money market in equilibrium, with Y = Y0, corresponds to the point of intersection

Figure 5.3

Graphical derivation of the LM curve.

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of the LL(Y0) and the vertical line. It is denoted by i0. Thus (Y0, i0) is a point on the LM as shown in Figure 5.4.

Figure 5.4 LM curve.

If Y is raised from Y0 to Y1, demand for real balance corresponding to every i rises (by how much?). Hence demand for real balance schedule, as shown in Figure 5.3, shifts from LL(Y0) to the right to LL(Y1). Accordingly, as we see in Figure 5.3, with Y = Y1, a higher i, i1, equilibrates the money market. Thus (Y1, i1) is another point on the LM, as shown in Figure 5.4. Repeating this exercise again and again, we can generate the whole LM. Clearly, it is positively sloped. EXERCISE 5.5 M and kY  li respectively, P when k, l > 0. Derive the equation of the LM and plot it in a graph in the (Y, i) plane. Why is it positively sloped? Explain.

Suppose supply of and demand for real balance are given by

Mathematical derivation of the slope of LM The slope of LM, (di/dY), measures the amount of change in i that will keep the money market in equilibrium per unit increase in Y, when Y is raised from any given point on the LM by a small amount. We can derive the slope mathematically as follows. Taking total differential of the money market equilibrium condition treating all exogenous variables as given, we get 0 = LY dY + Lidi (5.18) The LHS of (5.18) gives the change in the supply of real balance, which is zero. The RHS gives the change in the demand for real balance if Y and i change by dY and di respectively. Clearly, starting from any given point on the LM, if Y and i change by dY and di respectively such that Eq. (5.18) is satisfied, the new values of Y and i will remain on the LM. We can therefore solve (5.18) for the value of di that will keep the money market in equilibrium as a function of dY, if initially Y and i were on the LM. It is given by di

LY dY  Li

(5.19)

Equation (5.19) gives the amount of change in i that will keep the money market in equilibrium, when Y rises by dY from any given point on the LM. Note that LY and Li in (5.19) are evaluated at the given point or the given (Y, i) on the LM.

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Dividing both sides of (5.19) by dY, we get LY di (5.20) dY  Li Equation (5.20) gives the amount of change in i that keeps the money market in equilibrium per unit increase in Y, when Y rises from any given point on the LM by a small amount dY. Let us now explain the value of the slope. If Y rises by dY from a point on the LM, with i remaining unchanged, then aggregate supply of real balance remains unchanged, while aggregate demand for real balance goes up by LY × dY. Hence at the given i there emerges an excess demand of LY × dY. To restore equilibrium in the money market at this larger Y, interest rate i has to be raised so that demand for real balance, L, falls by LY dY in absolute terms. Since L falls in absolute terms by (–Li) when i rises by 1 unit, it will fall by LYdY, when i goes up by [LY dY/(–Li)]. Therefore, we get the amount of change in i that keeps money market in equilibrium per unit increase in Y when Y rises from any given point on the LM by dY by dividing [LY dY/(–Li)] by dY. Hence the slope of the LM is given by (LY /(–Li)). This explains the slope of LM. EXERCISE 5.6 M and kY  li P respectively, when k, l > 0. Derive the slope of the LM implied by them. Explain it. What is the vertical intercept of this LM in the (Y, i) plane? Give the economic meaning of this vertical intercept. (b) Suppose the equation of an LM curve is given by i = –20 + 0.5Y. What is its slope? Explain. What is the state of the money market at (Y = 100, i = 40). Plot the graph of this LM in the (Y, i) plane. Take any point to the left of this LM. What is the state of the money market at such a point? Explain your answer. What is the minimum information you need to know the exact state of the money market at such a point? Explain.

(a) Suppose supply of and demand for real balance are given by

Shift of the LM schedule Position of the LM is determined by the parameters of the equation of the LM. Parameters of the LM schedule are ( M / P) and those of demand for real balance function, L(×). If any one or more of these parameters change, then the LM schedule will shift. Let us illustrate with the example of an increase in ( M / P) by (dM / P) . To find out whether the LM will shift or not, one has to consider any given point on the initial LM and examine whether aggregate supply of real balance or aggregate demand for real balance corresponding to the given point has changed or not following the increase in ( M / P) by (dM / P) . We find from (5.15) that the determinants of L are Y, i and the parameters of L(×) and not ( M / P) , the stock of real balance1. 1

L(×) is the general form of the demand for real balance function and does not explicitly show any parameter determining demand for real balance. However, if we take a specific form of L(×), it must contain some parameters determining demand for real balance besides i and Y. For example, suppose L(×) º lYY + lii; lY > 0, li < 0. Here lY and li are the parameters or constants of the demand for real balance function and they determine the demand for real balance besides i and Y.

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Hence at every point on the initial LM aggregate demand for real balance is the same as before, but ( M / P) is larger by (dM / P) . Therefore at every point on the initial LM there is now an excess supply of (dM / P) . Thus the initial LM no longer gives the combinations of i and Y that keep the money market in equilibrium. In fact, now at every given i the money market will be in equilibrium at a larger Y, or at every given Y the money market will be in equilibrium at a lower i. Thus the new LM curve will be to the right or below the initial LM. Alternatively, following the increase in ( M / P) by (dM / P) , the LM shifts to the right or downward. We can also derive mathematically the horizontal or vertical shifts in the LM following an increase in ( M / P) by (dM / P) as follows. The horizontal shift in the LM following an increase in ( M / P) by (dM / P) is given by the amount of change in Y that keeps the money market in equilibrium following an increase in ( M / P) by (dM / P) , corresponding to any given i. Obviously, we get it by taking total differential of (5.17) treating i and all exogenous variables other than ( M / P) as given. This gives us the following equation: (dM / P )

LY dY

(5.21)

The LHS gives the change in aggregate supply of real balance following an increase in ( M / P) by (dM / P). The RHS gives the change in aggregate planned demand for real balance when Y changes by dY, while i remains unchanged at its initial value. Therefore, the value of dY that satisfies (5.21) will equilibrate the goods market, with i remaining unchanged at its

initial value, following an increase in ( M / P) by (dM / P) . This value of dY therefore gives the horizontal shift in LM. It is given by dY

(dM / P) LY

(5.22)

Explanation of (5.22) is quite simple. The numerator on the RHS gives an amount of excess supply of real balance that is created at any (Y, i) on the initial LM following the increase in ( M / P) by (dM / P ). Hence, with i remaining unchanged at its initial value, equilibrium will be restored in the money market, when Y rises to such an extent that the demand for real balance rises by (dM / P). Now, with i remaining unchanged, demand for real balance rises by LY when Y rises by 1 unit. Therefore demand for real balance, at the given i, will rise by (dM / P) when Y rises by [(dM / P)/ LY ] . Similarly, we can show that the vertical shift in LM will be given by

[(dM/ P)/ Li ] . Show it yourself. EXERCISE 5.7 (a) Define and derive the vertical shift in the LM in the case considered above. (b) Suppose supply of and demand for real balance are given by ( M / P) and L = lY ×Y _ li × i; lY > 0, li < 0 respectively. Derive the equation of the LM. Plot it in a graph in the (Y, i) plane. Derive the slope of the LM and explain it. What factors determine the position of the LM? Derive the horizontal and vertical shifts in the LM following an increase

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in (i) the income sensitivity of the demand for real balance, lY and (ii) the interest sensitivity of the demand for real balance, (–li). Explain these shifts. (Ignore the negative values of i, since they are infeasible. At such interest rates there will be no incentive on the part of the economic agents to part with liquidity. So the supply of loans will fall to zero. Hence there cannot take place any transactions in the loan market at such interest rates. Let us illustrate with an example. Suppose i is –10 per cent. If a lender lends ` 100 at such an interest rate, she will get back after one year only ` 90. Why will she lend out her money then? She will obviously find it profitable to hold her money in the form of money only, when the interest rate is negative. We shall discuss this point in detail later.) (c) Consider the following equations: L = .25Y – 62.5i and M / P = 500. Write down the equation of the LM. Derive its slope and explain its meaning. What are the parameters that determine the position of LM? Derive its vertical and horizontal shifts when (i) the supply of real balance rises by 10, (ii) the income sensitivity of demand for real balance increases by .05 and (iii) the interest sensitivity of demand for real balance increases by .05. Explain their magnitudes.

Relationship between the money market and the rest of the financial sector Here we shall explain how the money market and the rest of the financial sector are related to one another in the IS-LM model. Economic agents hold their wealth in the form of financial and physical assets. Financial assets in turn fall into two categories, money and non-money financial assets. Non-money financial assets are all loans except for equities. The key distinction between money and non-money financial assets in the context of the IS-LM model is that the latter are less liquid than the former. For simplicity, therefore, we shall refer to all non-money financial assets simply as bonds. The physical assets in the form of which economic agents hold their wealth are precious metals (such as gold and silver), land, houses, art objects, etc. These assets are the least liquid. Purchase and sale of such assets involve a long process of deliberation, searching, etc. Hence in the IS-LM model, which considers only the short-run, the stock of physical assets is given. The IS-LM model assumes that in the short-run economic agents can change only their stocks of money and non-money financial assets. They can decide in the short run to reduce their stock of money and increase their stock of non-money financial wealth and vice versa. We denote the total stock of financial wealth in the possession of the public by W. W equals the sum of the average stocks of money and non-money financial wealth in the possession of the public, which we denote by MS and BS respectively. Again, W must equal the sum of the stocks of money and bonds the public want to hold on the average. This is the wealth budget constraint of the public. The stock of money the public want to hold on the average is the aggregate demand for money. We denote it by MD. We refer to the stock of bonds people want to hold by BD. We can therefore write the public’s wealth budget constraint as MS + BS = W = MD + BD

(5.23)

(MS – MD) + (BS – BD) = 0

(5.24)

From (5.23), it follows that

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Equation (5.24) implies that the money market and the market for other financial assets or bonds are mirror images of one another. The excess supply in one market implies an equal amount of excess demend in the other market and vice versa. If there is excess supply of money or real balance, it means that the public have more real balance than they want. Obviously, they want to buy bonds with their excess real balance giving rise to an equal amount of excess demand for bonds and conversely. Thus, if one market is in equilibrium, so must be the other market and vice versa. For these reasons, it is not necessary to consider both the markets explicitly. The IS-LM model accordingly considers explicitly only the money market and ignores the market for loans or other financial assets.

5.2.3 Equilibrium in the IS-LM Model The IS-LM model is given by Eqs. (5.1)–(5.4) and (5.14)–(5.17). The key equations of the model are (5.1), (5.2), (5.4) and (5.17) containing four endogenous variables, namely C, I, Y and i. The system is, therefore, determinate. We can solve the two equilibrium conditions, (5.4) and (5.17), for the equilibrium values of Y and i. Substituting these values of Y and i in (5.1) and (5.2), we get the equilibrium values of C and I respectively. The equilibrium values of these variables are derived graphically in Figure 5.5, where Y and i are measured along the horizontal and the vertical axes of the first quadrant respectively. Positive values of I are measured in the

Figure 5.5 Graphical derivation of the equilibrium values of Y, i, C and I.

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western direction along the horizontal axis of the second quadrant, while positive values of C are measured along the vertical axis of the fourth quadrant in the southern direction. IS and LM schedules are plotted in the first quadrant, while investment and consumption functions are plotted in the second and the fourth quadrant respectively as II and CC. The equilibrium values of Y and i, denoted by Y e and ie respectively, correspond to the point of intersection of the IS and LM. The equilibrium value of C corresponds to the equilibrium value of Y on CC, while equilibrium value of I corresponds to the equilibrium value of i on the II schedule.

Stability of equilibrium We now examine the stability of equilibrium of the IS-LM model. To do that, we have to first specify how the endogenous variables behave in all possible situations. The rules or mechanisms that govern their behaviour are referred to as adjustment rules or adjustment mechanisms. They may be specified as follows. Key endogenous variables of the IS-LM model are C, I, i and Y. Regarding C and Y, we assume that they are always given by the consumption and investment functions respectively. Regarding i it is assumed that it rises, stays unchanged or falls according as demand for real balance exceeds, equals or falls short of the supply of real balance. This rule may be explained as follows. Interest rate is determined in the loan market. It follows from (5.24) that excess supply of real balance implies excess supply for loans and vice versa. In the face of excess supply of loans interest rate tends to decline, while it tends to rise in the event of excess demand for loans. Again, it is in a position of rest when demand for loans and supply of loans are equal. This explains the adjustment rules for i. The adjustment rules regarding Y are the same as that in the SKM. Thus Y rises, falls or stays unchanged according as excess demand for goods and services is positive, negative or zero. Besides the adjustment rules specified above, the IS-LM model also makes an assumption regarding the speeds of adjustment of Y and i. It assumes that interest rate adjusts at a much faster rate than Y so much so that if both the goods and the money market are in disequilibrium, i will adjust and clear the money market before any adjustment can take place in Y. We are now in a position to carry out the stability analysis. We shall, however, do it only graphically. Let us consider any (Y, i) off both the IS and LM as shown by point A in Figure 5.5. At such a point there is excess supply in both the markets. Hence interest rate will fall and clear the money market and this it will do before any adjustment in Y takes place. Thus the economy will move to B on LM as shown in Figure 5.5. At B, there is excess demand in the goods market even though money market is in equilibrium. Y will therefore start rising. As soon as Y rises, there will emerge excess demand in the money market driving up interest rate to B1 on the LM. This is how the adjustment will take place along the LM until the equilibrium is reached at the point of intersection of IS and LM. We are now in a position to carry out a few comparative static exercises. EXERCISE 5.8 Take a point in each of the three remaining zones in Figure 5.5 and show how Y and i adjust from each of the points.

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Fiscal Policy

Fiscal policy refers to the government’s policy of influencing macro variables by changing its budgetary instruments such as government consumption, taxes, transfers and subsidies. The major objective of government’s fiscal policy in the short-run is stabilization, i.e. keeping Y in equilibrium at its full employment level by suitably managing the level of aggregate planned demand for goods and services. We shall illustrate how fiscal policy can do this by considering the case where the government raises G or government consumption and finances it by internal borrowing through sale of bonds or securities in the market. The quantitative effect of an increase in government expenditure on macro variables depends crucially on how it is financed. The government can finance it by selling its dated securities (such as NSC, KVP, etc.) in the market or by borrowing from the central bank (RBI in Indian context). The latter amounts to printing money. The government can also finance its expenditure by collecting additional taxes. The method of financing government expenditure by printing money or borrowing from the central bank is called deficit financing in India. G may be given in nominal or in real terms. If G is given in real terms (which we get by deflating the nominal or money value of G by the average price of goods and services denoted P) and if the government finances dG by deficit financing, the stock of high-powered money goes up by (P×dG). In case G is given in nominal terms, the stock of high-powered money goes up by dG. The money supply accordingly rises by the money-multiplier times the increase in the amount of highpowered money. When additional government expenditure is financed with additional taxes, government consumption and taxes go up by the same quantity. At present, however, we shall focus on the case where the government raises G and finances it by borrowing not from the central bank but from the public or the market.

5.3.1

Increase in Government Expenditure by dG Financed by Internal Market Borrowing

We shall first examine the issue graphically. To derive the impact of the policy graphically, we have to first examine how it affects IS, LM, consumption function CC and investment function II, as shown in Figure 5.6. The policy implies an increase in government expenditure by dG and an increase in the value of stock of government bonds or loans held by the economic agents by dG. The stock of government loans held by the economic agents is not a determinant of any component of aggregate planned demand for goods and services. Hence corresponding to every given i and Y, the values of aggregate planned consumption and investment demand remain unchanged despite the increase in the amount of government loans held by economic agents. CC and II therefore remain unaffected. However, at every given i and Y on the IS the amount of government consumption is now larger bringing about excess demand of dG in the goods market. Accordingly, the goods market will be in equilibrium at a higher i corresponding to every Y or at a larger Y at every i. The IS therefore shifts to the right or upward. More precisely, as you should be able to work out yourself, the increase in government consumption by dG brings about a rightward or upward shift in the IS by the amounts (dG/[1 – C¢]) or [dG/(–Li)], respectively, even though it leaves CC and I I unaffected. The new IS is shown by IS1 in Figure 5.6.

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Figure 5.6

Impact of fiscal policy.

Neither G nor the stock of government loans held by the economic agents is a determinant of the demand for or supply of real balance. Hence values of demand for and supply of real balance corresponding to every (Y, i) on the LM remain unaffected and therefore continue to be equal to one another despite the increases in G and the stock of government loans held by economic agents. Hence the LM remains unaffected. The new equilibrium (Y, i) will correspond to the point of intersection of the new IS, which is to the right or above the initial IS and the initial LM. Thus the policy considered here, as shown clearly in Figure 5.6, will raise Y, i and C and lower I. From this result it follows that, if the economy is in recession with Y less than its full employment level, the government can achieve full employment equilibrium by raising G by a sufficiently large amount and financing it by internal borrowing. However, one important point to note here is that the policy of raising output and employment described above is not costless from the society’s point of view. Here, the increase in government’s consumption demand reduces or crowds out investment and thereby inflicts a cost on the society. Investment means addition to the stock of capital and hence investment in the present period leads to growth in the society’s or economy’s stock of capital in the future period. Productive capacity and therefore the full employment or potential output of an economy in any period is determined by the stocks of natural resources, capital and labour existing in the given period. The stock of natural resources remains invariant over time. Economists and demographers are still far from identifying the factors that determine the rate of population growth, which is an important

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determinant of the rate of growth of labour force. Accordingly, they regard the rate of growth of labour force largely as exogenous. The other major factor that determines the rate of growth of labour force is investment in human capital, which one may include in I. The rate of growth of capital and rate of technological progress depend principally on investments in physical capital and human capital, which constitute I. Hence the most important way the policy makers can influence growth rate of productive capacity and thereby that of full employment or potential output of an economy is through investment. The present policy of raising output and employment in the short-run is costly since it reduces investment and therefore the growth rate of full employment or potential output. If the government is able to stabilize the economy successfully at the full employment level of output in the short-run in every period, the rate of growth of aggregate and therefore that of per capita output or income will be determined, among others, by the level of investment that occurs. Since per capita income is one important index of development and of individuals’ welfare, maximizing the growth rate of per capita income along with short-run stabilization constitutes an important policy objective of the government everywhere. Obviously, the present policy of short-run stabilization is unattractive because of its crowding-out effect. However, there are ways of reducing this effect. We shall discuss later how this can be done. From Figure 5.6 it is clear that the steeper the LM, i.e. the higher the slope of the LM, the larger is the crowding-out of investment and less is the expansion in output and employment following a given increase in G financed by internal borrowing. Therefore the steeper the LM, the less is the attractiveness of this policy as a programme of short-run stabilization. Another problem with this policy is that it adds to government or public debt. Continuous increase in public debt may also turn out to be quite costly in the long-run. However, it is not possible in the present context to dwell on this point any further.

5.3.2

Mathematical Derivation of the Result

We can derive the impact of the fiscal policy considered above on Y and i using Eqs. (5.4) and (5.17). Substituting the equilibrium values of Y and i, denoted by Ye and ie respectively into (5.4) and (5.17) and then taking total differential of the resulting identities treating all exogenous variables other than G as fixed, we get the following equations: dY e

and

C „dY e  I „di e  dG e

0 = LY dY + Lidi

e

(5.25) (5.26)

Let us now explain these two equations. Here, G changes from the initial equilibrium to the new by a given amount dG . Since Y and i are endogenous variables, they are also likely to change from the initial to the new equilibrium following the increase in G and the amounts of their changes are dYe and die. dG is known to us. We have ourselves changed G by a given value dG to examine its impact on the endogenous variables. dYe and die are unknown to us. In fact, the purpose of the present exercise is to determine their values. The LHS of (5.25) gives the amount of change in aggregate supply of goods and services from the initial to the new

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equilibrium as Y changes by dYe. The only determinants of aggregate planned demand for goods and services that have changed from the initial to the new equilibrium are Y, i and G and they have changed by the quantities dYe, die and dG respectively. Hence the RHS of (5.25) gives the change in aggregate planned demand for goods and services from the initial to the new equilibrium. Since aggregate planned demand for goods and services is equal to aggregate supply of goods and services in both the equilibrium situations, the two sides of (5.25) must be equal, i.e. dYe, die and dG must satisfy (5.25). Let us now focus on (5.26). Since supply of real balance from the initial to the new equilibrium is unchanged, the LHS gives the change in the supply of real balance from the initial to the new equilibrium, which is zero. Again, the only determinants of demand for real balance that have changed from the initial to the new equilibrium are Y and i by dYe and die respectively. Hence the RHS gives the change in demand for real balance from the initial to the new equilibrium. Since demand for and supply of real balance are the same in both the equilibrium situations, the two sides of (5.26) must be equal. From the above it follows that both (5.25) and (5.26) must hold when dG , dYe and die represent changes in G, Y and i from the initial equilibrium to the new one. Since dG is known, (5.25) and (5.26) contain only two unknowns, dYe and die. Note that C¢, I¢, LY and Li are all constants and known to us. This is because we know that the consumption, investment and demand for real balance functions and C¢, I¢, LY and Li are all evaluated at the initial values of Y and i, which are also known to us. Hence, C¢, I¢, LY and Li are all constants and known. We can therefore solve these two equations for dYe and die. These solutions are given by dY e

di e

dG !0 LY Û Ë 1  Ì C „  (  I „) (  Li ) ÜÝ Í Ë L Û ¹Ì Y Ü!0 L Û (  Li ) Ý Ë 1  ÌC „  (  I „) Y Ü Í (  Li ) Ý Í dG

(5.27)

(5.28)

We are now in a position to derive the changes in the equilibrium values of C and I, which we denote by dCe and dIe respectively. Taking total differential of (5.1) and (5.2) treating T as fixed and substituting dYe and die for dY and di respectively, we have

and

dCe = C¢ ×  dYe > 0

(5.29)

dIe = I¢ × di e < 0

(5.30)

Let us now explain (5.27). The numerator gives excess demand for goods and services that is created at the initial equilibrium (Y, i) following the increase in G by dG . Given our assumption regarding the behaviour of producers, they will begin to expand production. The economy will achieve a new equilibrium, when the increase in Y reduces this excess demand in absolute value by dG to zero. To derive the amount of increase in Y that will achieve this, we have to find out by how much excess demand falls in absolute value per unit increase in

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Y. We know that, when Y goes up, aggregate demand for goods and services, with i remaining unchanged at its initial equilibrium value, rises by C¢ per unit increase in Y. Hence at the initial equilibrium i excess demand in absolute value will fall by (1 – C¢) per unit increase in Y. However, i will not remain unchanged. It adjusts at a much faster rate than Y. Hence, with the rise in Y from the initial equilibrium (Y, i), i will go up by the value of the slope of the LM, (LY//[–Li]), per unit increase in Y and clear the money market. As a result, investment demand in absolute value will decline by (–I¢)×(LY/[–Li]) per unit increase in Y. This gives the amount of investment demand that is crowded out per unit increase in Y in the present model. Thus per unit increase in Y consumption demand to the tune of C¢ is crowded-in, while (–I¢)×(LY/[–Li]) amount of investment demand is crowded out and the net amount of increase in demand per unit increase in Y is therefore [C¢ – (–I¢) (LY /[–Li])] and not C¢ as in the SKM. Thus excess demand here falls in absolute value by {1–[C¢ – (–I¢) (LY /[–Li])]} per unit increase in Y and this is larger than the corresponding quantity, (1 – C¢), in SKM. Hence in this model excess demand will fall by dG in absolute value, when Y rises by

dG /{1  [C „  ( I „) ( LY /[  Li ])]} Since here excess demand falls in absolute value by a larger quantity per unit increase in Y than in SKM, Y has to rise by a smaller quantity here to reduce the excess demand by dG or any given quantity. Hence the government expenditure multiplier is smaller here than that in the SKM. Since due to per unit increase in Y, interest rate rises by (LY/[–Li]), die must be given by e (dY ).(LY /[–Li]). This explains (5.28).

5.3.3

The Multiplier or the Adjustment Process

We shall now describe the multiplier or the adjustment process under the standard assumption that i adjusts at a much faster rate than Y to clear the money market. Following the increase in G by dG , there emerges an excess demand of dG in the goods market at the initial equilibrium (Y, i). Hence producers will expand Y by dG in the first round. The whole of this increase in Y will accrue as additional factor income in the hands of the people. Since taxes are lumpsum, the whole of this additional factor income will be added to their disposable income and thereby raise their consumption demand by C „dG . However, the rise in Y by dG will create excess demand for money by the amount [( dG) LY ]. Economic agents will therefore try to withdraw funds from the credit market to augment their stock of real balance giving rise to excess demand for credit at the initial equilibrium i. This will start raising i and, given our assumptions regarding the speed of adjustment of i, derive the interest rate up to the money market clearing level at once. Interest rate will rise by (dG) ( LY /  Li ) , since (LY /–Li), the slope of LM, gives the increase in i that equilibrates the money market per unit increase in Y, when Y rises from a situation of money market equilibrium. This rise in interest rate will reduce investment demand by [ I „ ¹ (dG) ¹ ( LY /  Li )] . Thus in the second round aggregate demand for

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goods and services will go up not by C „dG as in SKM, but by a smaller quantity

[C „d G  I „ ¹ (dG)( LY /  Li )] œ R dG and Y in the second round will go up by the same amount. In the third round, for the same reason as in the second round, increase in Y by R dG will raise consumption demand by (C „R dG) and raise interest rate and thereby lower investment demand by (R dG) ¹ ( LY /  Li ) and I „ ¹ (R dG) ¹ ( LY /  Li ) respectively. Therefore, in the third round, aggregate demand will go up by (C „R dG)  I „ ¹ (R dG) ¹ ( LY /  Li ) R 2 dG raising Y by the same quantity. This process will go on until the additional demand that is generated in each successive round eventually falls to zero. When that happens, the economy will achieve a new equilibrium. Thus the total increase in Y is given by

dY e

dG  R dG  R 2 dG  "

1 dG 1R

1 dG Ë È LY Ø Û 1  ÌC „  (  I „) É Ê  Li ÙÚ ÜÝ Í

(5.31)

5.3.4 Note on Crowding-out Effect The amount of investment demand that is crowded out by the policy considered here is given by (5.30). It reduces the expansion in Y by [I¢die/(1 – C¢)], i.e. it gives the reduction in Y from Y2 to Y1 as shown in Figure 5.6. Let us explain. Had i remained the same at its initial equilibrium value, i0, as shown in Figure 5.6, Y would have gone up by [ dG /(1  C „)] to Y2 in Figure 5.6. However, i does not remain unchanged at its initial equilibrium value, but rises by die to i1. This increase in i makes investment demand less by (–I¢×die). Hence at (Y2, i1) there exists an excess supply of (I¢×die). Therefore, at the new equilibrium i, i1, the goods market will be in equilibrium when Y falls from Y2 by [(I¢×die)/(1 – C¢)] in absolute value. Thus [–I¢×die)/(1 – C¢)] gives the distance Y1Y2 in Figure 5.6. One can easily check that [ dG /(1  C „)]  [(  I „ ¹ di e )/(1  C „)] = dYe by using (5.27) and (5.28). EXERCISE 5.9 (a) Explain why an increase in G raises Y by a smaller quantity in the IS-LM than in SKM. (b) Consider the following equations representing an economy: C

0.8(1  t )Y , t

0.25,

I 900  50i, G 800, L 0.25Y  62.5i, M/ P 500. Find out the impact of an increase in G by 10 financed by borrowing from the public on all the endogenous variables and explain.

5.3.5

Efficiency of Fiscal Policy

Efficiency of fiscal policy may be assessed on two grounds, namely how effective it is in influencing output and employment and how much cost it involves. We shall discuss each of

IS-LM Model

185

these two measures in turn. Focus on the first. From Figure 5.6 it is clear that, given other factors, the steeper the LM curve the less effective is the policy considered above in raising output and employment. Again, given other factors, the less is the rightward shift in the IS, the less is the above policy’s impact in raising output and employment. From our above analysis, we find that the smaller the decline in excess demand for goods and services per unit increase in Y, the larger is the increase in GDP brought about by a given increase in G financed by internal borrowing. The analysis also yields that the larger the C¢ and smaller the crowding out effect the smaller is the reduction in excess demand per unit increase in Y. Again, the less the interest sensitivity of investment demand, as measured by (–I¢), and the less the slope of the LM, as given by [LY /(–Li)], i.e. the flatter the LM, the less is the crowding out effect and therefore the greater is the effectiveness of the policy considered above. Explain all the points made above yourself. EXERCISE 5.10 From the point of view of the efficacy of a policy in influencing output and employment, compare the policy considered above to the policy of a tax financed by increase in G. Which of these two policies will you recommend in times of deep recession? Explain. Let us now focus on the second issue. Efficiency of a policy is also measured in terms of the cost it involves. Consider the policy discussed above. Governments use it to raise GDP and employment. But it is not costless. As we have seen above, it crowds out private investment and thereby inflicts a cost on the society. Investment adds to productive capacity of the economy and thereby augments future potential or full employment output. Reduction in investment accordingly curtails economy’s growth potential. If increase in G takes the form of investment in infrastructure such as road building or building of bridges, irrigation facilities, etc., it will not only add to the society’s growth potential but also exert strong stimulating impact on private investment. In the new equilibrium private investment may become larger instead of being smaller. EXERCISE 5.11 (a) Make investment a decreasing function of rate of interest and an increasing function of public investment in infrastructure denoted by Ig. Write down the IS-LM model under this assumption. Suppose the government raises Ig and finances it by borrowing from the public. Under what conditions will this policy raise private investment? Illustrate the situation graphically and explain. Is this policy superior to the other two policies considered above? Explain your answer. (b) One important objective of fiscal policy in the short-run is to keep the economy in equilibrium at the full employment level of output. However, such policies, as we have already pointed out, may not be costless. Suppose the government has to raise Y by a given amount, A, to achieve full employment equilibrium and the government wants to do this either through an internal loan financed by increase in G or through a tax financed by increase in G. By how much the government will have to raise G in each case? Which policy will you prefer and why? (c) Take linear consumption, investment and real balance functions and show that autonomous shifts in the investment function or volatility of investment can cause economic fluctuations or fluctuations in GDP in the IS-LM model. Does there exist any

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condition under which volatility of investment will fail to produce any impact on Y? Discuss your answer in detail. (d) If the output falls, firms suffer losses. This might depress business sentiments leading to a decline in investment. This scenario is captured by making investment not only a decreasing function of i but also an increasing function of Y so that a reduction in Y, given i, brings about a fall in investment and vice versa. Does the explanatory power of the IS-LM model in explaining economic fluctuations in terms of the volatility of investment improve if investment behaves the way suggested above? Explain.

5.3.6

Built-in Stabilizers

SKM and IS-LM model explain fluctuations in GDP, which are also alternatively referred to as economic fluctuations, in terms of exogenous shocks to aggregate final demand. Obviously, the larger the value of the multiplier, the greater is the fluctuations in GDP in response to any given exogenous shock to aggregate demand. The factors that reduce the values of the multipliers dampen fluctuations in GDP due to exogenous demand shocks. These factors are referred to as built-in stabilizers. EXERCISE 5.12 If taxes are an increasing function of Y or transfers are a decreasing function of Y, do they act as built-in stabilizers? Explain your answer. If taxes are an increasing function of GDP and if the government expenditure equals tax collection, will this programme act as a built-in stabilizer? Explain.

5.4 Monetary Policy The policy that seeks to influence the macro variables by changing the supply of money is called monetary policy. The central bank is the monetary authority of a country. It adopts expansionary and contractionary monetary policies by changing the CRR and the repo and reverse repo rates. Expansionary (contractionary) monetary policy consists of raising (lowering) of money supply. Let us first examine the impact of an increase in money supply on aggregate output, consumption and investment graphically with the help of Figure 5.7. The IS and LM are plotted in the first quadrant, investment function is represented by the II schedule in the second quadrant, while the consumption function is represented by CC in the fourth quadrant. We assume that the monetary authority increases money supply by dM . To examine its impact graphically, we have to first find out how it affects II, CC, IS and LM. The value of I corresponding to any given i depends upon the parameters of the investment function only and not on M . An increase in M therefore produces no impact on the value of I corresponding to any given i. Hence the II schedule remains unaffected. For similar reasons CC remains unaffected also.

IS-LM Model

Figure 5.7

187

Impact of monetary policy.

To ascertain the direction of shift in IS, we have to find out how demand for goods and services and supply of goods and services are affected at any given (i, Y) on the IS. Demand for goods and services depends only upon i, Y, the parameters of the consumption and investment function and G , and not on M . Therefore the value of demand for goods and services corresponding to any given (i, Y) on the IS is not affected by an increase in M . The aggregate supply of goods and services corresponding to any given (i, Y) on the IS is obviously the given Y and therefore is not affected by the change in M . Therefore at every (i, Y) on the initial IS values of aggregate planned demand for goods and services and aggregate supply of goods and services remain unaffected and hence continue to be equal. IS therefore remains unaffected. The LM, however, as we have pointed out already will shift to the right by (dM / PLY ) or downward by [  ( dM / PL i )] in absolute value. The new equilibrium (Y, i) corresponds to the point of intersection of the new LM and the IS. Thus equilibrium value of Y will rise and that of i will fall raising both C and I in the new equilibrium, as shown in Figure 5.7. Let us now derive these results mathematically. Substituting the equilibrium values of Y and i, denoted by Ye and ie respectively, into (5.4) and (5.17) and then taking total differential of the resulting identities treating all exogenous variables other than ( M / P ) as fixed, we have dYe = C¢dYe + I¢die and

(dM / P)

LY dY e  Li di e

(5.32) (5.33)

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Macroeconomics

Let us now explain the two equations. Here, M changes from the initial equilibrium to the new one by a given amount dM . Since Y and i are endogenous variables, they are also likely to change from the initial to the new equilibrium following the increase in M and the amounts of their changes are dYe and die, whose values we shall determine. The LHS of (5.32) gives the amount of change in aggregate supply of goods and services from the initial to the new equilibrium as Y changes by dYe. The only determinants of aggregate planned demand for goods and services that have changed from the initial to the new equilibrium are Y and i, and they have changed by the quantities dYe and die respectively. Hence the RHS of (5.32) gives the change in aggregate planned demand for goods and services from the initial to the new equilibrium. Since aggregate planned demand for goods and services is equal to aggregate supply of goods and services in both the equilibrium situations, the two sides of (5.32) must be equal, i.e. dYe and die must satisfy (5.32). Let us now focus on (5.33). Since supply of real balance from the initial to the new equilibrium has changed by (dM / P ) , the LHS gives the change in the supply of real balance from the initial to the new equilibrium. Again, the only determinants of demand for real balance that have changed from the initial to the new equilibrium are Y and i by dYe and die respectively. Hence the RHS gives the change in demand for real balance from the initial to the new equilibrium. Since demand for and supply of real balance are equal in both the equilibrium situations, the two sides must be equal. Thus dYe, die and dM must satisfy (5.33). From the above it follows that dYe and die must satisfy both (5.32) and (5.33). Since dM is known, (5.32) and (5.33) contain only two unknowns, dYe and die. Note that C¢, I¢, LY and Li are evaluated at the initial equilibrium values of Y and i. Hence they are all known and constants. We can therefore solve these two equations for dYe and die. These solutions are given by dY e

di e

[(dM / P ) /( Li )] ¹ I „ !0 LY Û Ë 1  Ì C „  (  I „) (  Li ) ÜÝ Í

dM / P Ë L Û  dY e ¹ Ì Y Ü  0 Li Í (  Li ) Ý

(5.34)

(5.35)

Again, taking total differential of (5.1) and (5.2) treating T as fixed and substituting dYe and die for dY and di respectively, we have dCe = C¢  × dYe > 0 (5.36) e e (5.37) and dI = I¢ × di > 0 e e where dC and dI denote changes in C and I respectively from the initial to the new equilibrium. Let us now explain (5.34). The numerator gives the excess demand for goods and services that is created at the initial equilibrium Y following the increase in M by dM and the consequent decline in i that takes place to clear the money market. Let us explain. Following the increase in the supply of real balance by (dM / P ) , there emerges an excess supply in the money market of the same amount at the initial equilibrium (i, Y). This gives rise to excess supply of loans

IS-LM Model

189

of the same amount. i will accordingly fall and clear the money market and thereby the loan market at the initial equilibrium Y by raising demand for real balance by (dM / P) . Since demand for real balance rises by (–Li) per unit decline in i, demand for real balance rises by (dM / P ) , when i falls by [(dM / P )/(  Li )] in absolute value. This raises investment demand by [( dM / P )/(  Li )] (  I „) œ G , since investment demand rises by (–I¢) per unit decline in i. Thus,

following an increase in ( M / P ) by (dM / P ) , aggregate demand for goods and services at the initial equilibrium Y rises by f, when i adjusts with Y remaining unchanged at its initial equilibrium value to equilibrate the money and the loan market. This explains the numerator. Given our assumption regarding the behaviour of producers, they will begin to expand production to meet this excess demand of f. The economy will achieve a new equilibrium, when the increase in Y reduces this excess demand in absolute value by f to zero. To derive the amount of increase in Y that will achieve this, we have to find out by how much excess demand falls in absolute value per unit increase in Y. We know that, due to per unit increase in Y aggregate demand for goods and services, with i remaining unchanged, rises by C¢. Hence at the given value of i, excess demand for goods and services in absolute value will fall by (1 – C¢) per unit rise in Y . However, i will not remain unchanged. It adjusts at a much faster rate than Y. Hence, with the rise in Y, i will go up per unit increase in Y by the value of the slope of the LM, (LY/[–Li]), and clear the money and the loan market and this will reduce investment demand in absolute value by (–I¢) × (LY/[–Li]). This gives the amount of investment demand that is crowded out per unit increase in Y in the present model. Thus due to per unit increase in Y consumption demand to the tune of C¢ is crowded in, while (–I¢) × (LY/[–Li]) amount of investment demand is crowded out and the net amount of increase in demand per unit increase in Y is therefore [C¢ – (–I¢) (LY/[–Li])] and not C¢ as in the SKM. Thus excess demand here falls in absolute value by {1–[C¢–(–I¢)(LY/[–Li])]} due to per unit increase in Y and this is larger than the corresponding quantity, (1 – C¢), in SKM. Hence in this model excess demand will fall by f in absolute value, when Y rises by f/{1–[C¢–(–I¢) (LY/[–Li])]}. We find from the above that at first i at the initial equilibrium Y falls by [( dM / P )/( Li )] in actual value to clear the money market. Subsequently, as Y increases from its initial equilibrium value by dYe, interest rate rises by (dYe).(LY/[–Li]), since per unit increase in Y interest rate rises by (LY/[–Li]). die is therefore given by (5.35). Since the IS curve is unchanged and Y is larger in the new equilibrium, the new equilibrium value of i has to be less. Otherwise the goods market will not be in equilibrium. Thus on the RHS of (5.35) the absolute value of the first term, which gives the decline in i that takes place at the initial equilibrium Y following the rise in M by dM (fall in i from A to B in Figure 5.7) is larger in absolute value than the value of the second term, which gives the increase in i caused by the rise in Ye by dYe. Since in the new equilibrium Y is larger and i is less, both consumption and investment as given by (5.36) and (5.37) respectively are larger.

5.4.1

The Multiplier and the Adjustment Process

The economics behind the result may be explained in terms of the following multiplier or the adjustment process. We shall describe the multiplier process under the standard assumption that

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i adjusts at a much faster rate than Y to clear the money market. Following the increase in M by dM , there emerges an excess supply of (dM / P) in the money market at the initial equilibrium (Y, i). Economic agents will obviously want to park this excess real balance in interest bearing assets, i.e. they will want to lend out this excess liquidity giving rise to excess supply in the loan market at the initial equilibrium (Y, i). Dissatisfied lenders will offer their loans at a lower i forcing other lenders to make matching offers. This price competition among lenders will drive down interest rate to the level that clears the money and therefore the loan market. In Figure 5.7, i will fall from A to B. This decline in i, as we have already pointed out, will raise planned aggregate demand for goods and services by [( dM / P )/(  Li )] (  I „) œ G generating an excess demand for goods and services at the initial equilibrium Y. Hence producers will expand Y by f in the first round. The economy will thus move from B to a point such as B1 in Figure 5.7. The whole of this increase in Y will accrue as additional factor income in the hands of the people. Since taxes are lumpsum, the whole of this additional factor income will be added to the disposable income of the households and thereby raise their consumption demand by C¢f. However, the rise in Y by f will create excess demand for money, which will, given our assumptions regarding the speed of adjustment of i, drive the interest rate up to the money market clearing level, i.e. to LM corresponding to this higher Y. Interest rate will rise by fÿ× (LY/–Li), since (LY /–Li), the slope of LM, gives the increase in i that equilibrates the money market per unit increase in Y, when Y rises from a situation of money market equilibrium. This rise in interest rate will reduce investment demand by [I¢ × (f)  ×  (LY /–Li)]. Thus in the second round aggregate demand for goods and services will go up not by C¢f as in SKM, but by a smaller quantity [C¢f + I¢ × (f) × (LY /–Li)] º qf and Y in the second round will go up by the same amount. In the third round, for the same reason as in the second round, increase in Y by qf will raise consumption demand by (C¢qf) and raise interest rate and thereby lower investment demand by (qf) × (LY /–Li) and I¢ × (qf) × (LY /–Li) respectively. Therefore, in the third round aggregate demand will go up by (C¢qf) + I¢ × (qf) . (LY /–Li) = q2f raising Y by the same quantity. This process of increase in Y and i will go on along the new LM schedule until the additional demand that is generated in each successive round eventually falls to zero. When that happens, the economy achieves a new equilibrium. Thus the total increase in Y from the initial to the new equilibrium is given by

dY e

G  RG  R 2G  "

1 G 1R

1 Ë È L ØÛ 1  Ì C „  (  I „) É Y Ù Ü Ê  Li Ú Ý Í

¹G

(5.38)

EXERCISE 5.13 (a) Consider the following equations representing an economy: C

I

900  50i, G

800,

L

0.25Y  62.5i, M / P

0.8(1  t )Y , t

500 and P

0.25,

1 . Find out the

impact of an increase in M on all the endogenous variables, illustrate graphically and explain. Describe the process of expansion.

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191

(b) Suppose the government raises G and finances it by borrowing from the central bank. How are the endogenous variables in the IS-LM model affected? Derive the results mathematically, illustrate graphically and explain.

5.5

INTER-LINKAGE BETWEEN THE REAL AND THE FINANCIAL SECTORS IN THE IS-LM MODEL

One important point to be noted in this context is that in the IS-LM model changes in the supply of money or autonomous shifts in demand for real balance function do not directly affect the real sector or the commodity market. They do so only through their impact on the loan market by affecting the interest rate. The linkage is therefore quite fragile and will break down if investment or, more generally, aggregate planned demand for goods and services is insensitive to interest rate. (How will the IS look like in this case? Will exogenous disturbances on the demand or on the supply side in the monetary sector, which lead to shifts in the LM, affect output and employment in this case?) The inter-linkage will also collapse if interest rates are very low or near zero so that economic agents do not have any incentive to part with liquidity or real balance. You should be able to recall that the Keynesian theory of interest, which is, as we have already mentioned, alternatively referred to as the liquidity theory of interest, states that money is the most liquid of all assets and people value liquidity. They do not part with money or real balance unless interest rates on loans are sufficiently high. Thus, when interest rates are low, following an increase in money supply, economic agents will have no urge to lend out their excess money balances. They will prefer to hold this additional real balance as real balance only. Thus the increase in money supply will have no repercussions in the loan market and therefore will leave interest rates unaffected. Obviously, monetary policy will fail to produce any impact on output and employment in this case. This situation is referred to as liquidity trap. When the economy is in liquidity trap, individuals want to hold all the real balance they have in their possession in the form of real balance only. If there takes place any increase in the stock of real balance, they will willingly add the additional supply to their stock of real balance leaving the loan market undisturbed. Hence in the liquidity trap economic agents are likely to hold much larger amount of real balance than what they optimally plan to hold. A contraction in money supply, i.e. a contractionary monetary programme may not therefore make it necessary for the economic agents to withdraw funds from the loan market to carry out transactions. The stock of real balance that they are left with may exceed their optimal holding even after the contraction in money supply has taken place and this excess or idle real balance might be sufficient to enable them to carry out their additional transactions with ease. Hence in the liquidity trap a contractionary monetary policy may also fail to affect the loan market or the interest rate and therefore leave the commodity market, output and employment undisturbed. Thus, when the economy is in a liquidity trap, expansionary or contractionary monetary policy may be completely ineffective in influencing the output and employment. Japan went into a recession in the 1990s and expansionary monetary policy adopted by the Japanese monetary authority failed to lift the economy out of the recession. Paul Krugman, an authority in international economics, who won Nobel Prize in economics in 2008, attributed this failure of the monetary policy to liquidity trap (Krugman, 1999). In Japan, at that time the short-

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term interest rate was almost zero and medium and long-term interest rates were also very low. This prompted Krugman to hypothesize that in the nineties Japan was in a liquidity trap. Shortterm interest rates are almost zero in Japan even now.

5.5.1 LM Schedule in the Liquidity Trap Suppose in an economy there exists liquidity trap at i0, i.e. at interest rates equal to or less than i0, economic agents have no incentive to part with liquidity. We know that Y and i fall together along the LM. Let us go on reducing i and Y along LM. Suppose the money market comes to equilibrium at i0, when Y falls to Y0 (see Figure 5.8). If Y is reduced further from Y0, demand for real balance will fall and economic agents will have excess real balance in their hands. However, at this low interest rate they have no incentive to part with liquidity. So they will want to hold this excess real balance in the form of real balance itself. Therefore the money market or the loan market will remain in equilibrium at i0 even with this lower Y. Thus, even if Y is reduced from Y0, money market will remain in equilibrium at the same interest rate, i0. Hence the LM is horizontal in the liquidity trap zone as shown in Figure 5.8.

Figure 5.8 LM and the liquidity trap.

It should be noted that at every point on the horizontal stretch of the LM except at (i0, Y0) economic agents hold more real balance than what they optimally plan to. This excess real balance is referred to as idle balance. If money supply and therefore supply of real balance go up, there emerges idle balance even at (i0, Y0). Hence, if, following such an increase in money supply, Y rises from Y0, with i remaining unchanged at i0, economic agents will have no necessity to withdraw funds from the loan market to finance additional requirement of real balance to carry out larger volume of transactions. They will simply use the idle balance in their hands for this purpose. Therefore, even if Y rises from Y0, with i remaining unchanged at i0, loan market and the money market will remain in equilibrium until the idle balance in the hands of the economic agents gets completely exhausted. Thus, following an increase in money supply, the horizontal stretch of the LM will get extended as shown in Figure 5.8. LM¢ is the new LM

IS-LM Model

193

corresponding to the larger supply of real balance. Let us illustrate the concept of liquidity trap with an example. Suppose P = 1 and demand for real balance, denoted by L, is given by L = lY ×Y + li ×i, with lY > 0 and li < 0. Suppose there exists liquidity trap at i0 so that at every i £ i0 there is no incentive on the part of the economic agents to part with liquidity. At (Y0, i0) the optimum amount of demand for real balance, i.e. the amount of real balance which economic agents optimally plan to hold, is given by (lY ×Y0 + li×i0) and suppose this is equal to the aggregate supply of real balance. Thus Y0 is the maximum value of Y that can keep the money market in equilibrium with i = i0. Per unit reduction in Y from Y0, with i remaining unchanged at i0, the amount of idle real balance that accumulates in the hands of the economic agents is lY. (How much idle real and money balances are there in the hands of the economic agents when Y falls to zero?) If money supply goes up by dM, it accumulates as idle real balance in the hands of the economic agents at (Y0, i0). Per unit increase in Y from Y0, with i remaining unchanged at i0, the optimum quantity of real balance economic agents want to hold goes up by lY and therefore the amount of idle real balance in the hands of the economic agents declines by lY. As long as there is idle balance in the hands of the economic agents, they use it to finance the increase in the amount of real balance required for transactions due to the rise in Y. Hence the loan market and therefore the money market remain in equilibrium at i0 despite the increase in Y from Y0 following the increase in money supply as long as the idle real balance in their hands does not get exhausted. The idle balance is exhausted when Y rises by ( dM / lY ) . Thus the horizontal stretch gets extended by ( dM / lY ) at i = i0 following the increase in M by dM . The economy is in the liquidity trap if it is in equilibrium at i0, i.e. if IS intersects the LM at its horizontal stretch as shown in Figure 5.8. The economy is in recession if it is in equilibrium in the liquidity trap, since both Y and i are very low. As we have already explained and as is clear from Figure 5.8 also, in this situation monetary policy is completely ineffective. Fiscal policy is, however, fully effective here, i.e. it is as effective as in the SKM, since interest rate remains unchanged despite the increase in Y and therefore the crowding out effect does not operate. The horizontal stretch of the LM is also referred to as the Keynesian zone. EXERCISE 5.14 Suppose the economy is caught in a liquidity trap. Illustrate the situation in a graph. Discuss the impact of fiscal and monetary policies in such a situation. Derive the results mathematically as well. Explain why monetary policy is completely ineffective, while fiscal policy is fully effective in the liquidity trap region.

5.5.2

The Classical Zone of the LM

The LM schedule may also have a vertical stretch. This portion is referred to as the classical zone. Let us elaborate. Rate of interest represents the cost of holding real balance. The higher the interest rate the greater is the incentive for economizing on the holding of real balance. Hence, if the interest rate is sufficiently high, the holding of real balance may be reduced to the maximum possible extent and further cuts in the holding of real balance following a rise in i may be very difficult or impossible. Hence at high levels of interest rates, the demand for

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real balance may be highly or completely interest inelastic. Consider a point on LM at which interest rate is so high that demand for real balance is completely interest insensitive. A unique Y corresponds to the given i. At this given (i, Y) on LM, the demand for real balance and the supply of real balance are equal. If i is raised further, keeping Y unchanged from this point, demand for real balance will remain unchanged and therefore will remain equal to supply of real balance. Thus at this higher i also the money market will remain in equilibrium at the initial Y. Hence, LM may become vertical for sufficiently high values of i. The situation is illustrated in Figure 5.9 where LM is vertical at i ³ ih.

Figure 5.9

The classical zone and the LM.

The vertical stretch of the LM is referred to as the classical zone. In this zone, as shown in Figure 5.9, an increase in public expenditure financed by market borrowing or reduction in taxes, which brings about rightward shifts in the IS will produce little impact on Y, but raise i significantly. In fact, in this zone, an increase in government expenditure financed by market borrowing will fully crowd out private investment, i.e. the increase in i will reduce private investment by the same amount as the increase in G. Similarly, an increase in consumption induced by a tax cut in this zone will reduce investment by an equal amount so that aggregate final demand remains unchanged. Prove these points yourself. However, monetary policy will be fully effective in this case. Let us explain. When the economy achieves equilibrium at the vertical portion of the LM, the level of aggregate output is constrained by the stock of money supply and not by anything else. At such high interest rates demand for real balance is completely insensitive to interest rate. Hence demand for real balance is a function of Y alone and the money market accordingly is in equilibrium at a unique Y at all such high levels of i. Money market cannot be in equilibrium at any higher level of Y, given the stock of money supply, at such high levels of i. As long as demand for real balance is a decreasing function of interest rate, a given stock of real balance can support larger and

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larger levels of aggregate output. When Y and as a result demand for real balance rise, people withdraw funds from the loan market to meet the additional demand for real balance. There emerges excess demand for loans at the initial interest rate. Interest rate therefore starts rising. The excess demand for loans and the rise in interest rate persist until the latter removes the excess demand for real balance at the higher level of Y. Thus, as long as demand for real balance is a decreasing function of interest rate, the money market can be in equilibrium at higher and higher levels of Y, with a given stock of real balance. In such a situation equilibrium value of the income velocity of circulation of money defined as the ratio of (PY) to M rises with an increase in Y. However, at sufficiently high levels of interest rates at which demand for real balance ceases to be interest sensitive, equilibrium in the money market occurs at a unique level of Y. At higher levels of Y there is excess demand in the money market and money market is in disequilibrium. In this situation people will withdraw funds from the loan market to meet the excess demand creating excess demand for loans at the initial interest rate and thereby exerting an upward pressure on the interest rate. But this rise in interest rate, unlike in the normal situation, cannot remove the excess demand since demand for real balance is completely insensitive to interest rate. Hence, when i is sufficiently high, money market can be in equilibrium at a unique Y. At such levels of i, it cannot be in equilibrium at any higher level of Y. The situation can be illustrated with the example depicted in Figure 5.9 where the initial equilibrium takes place at the vertical portion of the LM and the government undertakes an expansionary fiscal policy shifting the IS to the right. Following such a change, as shown in Figure 5.9, the economy moves from A to B so that Y remains unchanged, while only i rises. Let us now explain how this happens. There first emerges an excess demand for goods and services at the initial equilibrium (i, Y) and Y begins to rise generating excess demand for real balance, which, as we have just explained, starts raising i. However, in this case, the increase in i cannot remove excess demand for real balance directly. It does so only through its impact on the goods market. The increase in i reduces investment demand and equilibrium is restored in the economy when the rise in i reduces aggregate demand for goods and services to its initial level so that Y falls back to its initial level too. In this case equilibrium value of private investment falls exactly by the same amount as the increase in G. Hence in this case there takes place full crowding out of private investment. EXERCISE 5.15 Consider the case where the equilibrium occurs in the classical zone of the LM. How will the monetary policy work in this case? Illustrate graphically and explain your answer. Derive mathematically the amount of increase in Y. Is the increase in Y in this case following a given increase in money supply larger than that in the normal situation? Derive and explain your answer.

5.6

SHORT-RUN ECONOMIC FLUCTUATIONS AND THE IS-LM MODEL

In the IS-LM model, as follows from the above discussion, economic fluctuations or fluctuations in GDP may be caused not only by autonomous shifts in investment or aggregate demand function as in SKM but also by changes in money supply and shifts in the demand for real balance function. Thus depression or recession may be due to depressed business sentiments

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leading to extremely low levels of investment or due to low levels of money supply or both. Keynesians put greater emphasis on the volatility of investment demand as the principal cause of short-run economic fluctuations. There is, however, a school of thought referred to as the monetarists, who downplay the role of investment volatility as a cause of short run economic fluctuations. They consider money to be all-important and identify changes in money supply as the main cause of short-run fluctuations in GDP. Friedman and Schwartz (1963), two leading monetarists, in their epic study, Monetary History of the United States of America, attributed the Great Depression to a substantial reduction in money supply. Orthodox Keynesians, on the other hand, hold depressed business sentiments of the investors as a principal factor responsible for recession in an economy. They do not recognize the importance of money supply as a cause of economic fluctuations. Differences in the positions of the orthodox monetarists and the orthodox Keynesians can be attributed to the differences in their assumptions regarding the slopes of the IS and LM schedules. If the LM curve, for example, is very steep or vertical, volatility of investment or autonomous shifts in the aggregate demand function, which cause displacements in the IS schedule and leave LM unaffected, produce little or no impact on aggregate output and employment. On the other hand, changes in money supply, which bring about displacements in the LM, but leave IS unaffected, cause substantial fluctuations in output and employment. (Prove this proposition identifying the condition under which the LM is steep or vertical. Show that, when the LM is vertical, an increase in G financed by market borrowing leads to full crowding out of private investment.) On the other hand, if IS is very steep or vertical, changes in money supply or shifts in demand for real balance function, which lead to shifts in the LM alone, cannot produce much of an impact on aggregate output and employment. But volatility of investment or autonomous shifts in the aggregate demand function produce substantial fluctuations in real variables. (Prove this proposition identifying the condition under which the IS is steep or vertical.) Actually, Keynesians think that aggregate demand for goods and services displays little sensitivity to interest rates (vertical or steep IS) particularly in times of recession when business sentiments are depressed, while monetarists assume demand for real balance to have little interest elasticity (vertical or steep LM). The controversy is clearly empirical and has to be settled through more rigorous empirical exercises.

5.6.1

Money and Economic Fluctuations

The central bank of a country may adopt contractionary monetary programmes and thereby bring about a downturn in economic activities. However, a reduction in money supply may also be induced by deterioration in banks’ expectations. In times of recession, sales, output and employment fall to low levels. Firms incur heavy losses. Many of them may fail to repay their debts or pay interest on their debts. If banks’ borrowers default on a large scale, banks may also in turn become bankrupt and fail to meet depositors’ claims. In such a situation banks lose credibility with the public and have to move out of business. Hence, if banks apprehend that a recession is imminent, they allow for a significant increase in the default rate in future and raise substantially the amount of excess reserves. This brings about a large autonomous decrease

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in money supply generating, as we have already seen, a strong recessionary pressure. If investment is sensitive to interest rate and the economy is not in liquidity trap, deterioration in bankers’ expectations will be self-fulfilling further aggravating the situation. See in this context Blinder (1981). Firms’ profit in general is an increasing function of GDP. When the economy is buoyant and GDP rises, firms’ profit goes up making it easier for them to service their debt. Default rate as a result goes down inducing banks to reduce their excess reserves. Hence banks’ excess reserves and therefore money supply may be, among others, a decreasing function of GDP. In this situation, even if a recession is initiated by an autonomous decline in investment demand, the fall in output and employment will also lower money supply, which, in turn, will strengthen the contractionary forces and deepen the recession thereby. Thus both real and monetary factors may interact and reinforce each other in generating economic fluctuations. This is the idea of financial accelerator as propounded by Bernanke et al. (1981). EXERCISE 5.16 When money supply has the form specified above, an autonomous reduction in investment or money supply leads to a larger fall in output and employment compared to the situation where money supply has an autonomous component only. Explain.

5.7 COMPARISON OF FISCAL AND MONETARY POLICY 5.7.1

Monetary and Fiscal Policy Mix

Sometimes the government has more than one target. As we have already pointed out, besides stabilization the government may have growth or investment target. When the government has two target variables, it usually has to use both fiscal and monetary policies to achieve its goal. The point may be illustrated with the help of the situation presented in Figure 5.10 where

Figure 5.10

Monetary and fiscal policy mix.

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equilibrium Y is less than its potential level, denoted Yf, by, say, a. Besides raising Y to its full employment or potential level, the government may also want to increase investment by a given amount, say, b. To raise investment by b the government has to lower i by a given amount, (b/(I¢)) (Explain this amount). The target levels of Y and i, which correspond to A are shown in Figure 5.10. To achieve this target the government has to adopt policies so that the IS and LM both shift and intersect each other at A. Since fiscal policy affects the IS alone, while monetary policy shifts only the LM schedule, the government has to adopt both the policies to achieve its target. If, accidentally, the targeted point is on the IS (LM), fiscal policy (monetary policy) alone will be sufficient. Of course, if the target is to raise investment along with GDP, the targeted point cannot be on the LM. Let us first examine by how much the monetary authority has to change money supply so that the new LM passes through A. For the LM to pass through A the supply of money should be such that it is equal to the demand for money at A. Compared to the initial equilibrium point, B, at A the level of income, Y, is larger by a, while the level of interest rate is less by (b/I¢)). Hence demand for money at A is larger than that at B by the amount {P×{LY ×a + Li(b/I¢)]}. Accordingly, money market will be in equilibrium at A if the supply of money is raised from its initial value by {P×{LY ×a + Li(b/I¢)]}. The LM corresponding to this larger supply of money will pass through A. Let us now focus on the IS. By how much G or T or both have to be changed so that the IS passes through A? At A, GDP and investment demand are larger than those at B by a and b respectively. The larger level of Y at A makes aggregate demand at A larger by (C¢×a). Thus at A aggregate final demand is larger by [C¢×a) + b] than that at B. If, by accident, a equals [(C¢×a) + b], the goods market is in equilibrium at A. In this case A must be on the initial IS passing through B since changes in demand and supply from A to B are due to changes in i and Y only. At the same values of parameters determining the position of the IS passing through B, the goods market will be in equilibrium at A. If a and [(C¢×a) + b] are different, A is not on the initial IS and G and T have to be changed so that the change in demand from B to A equals a and therefore the goods market is in equilibrium at A. If G and T change by dG and dT respectively, demand for Y, with i and Y remaining unchanged, will change by (dG – C¢dT). Thus, if dG and dT change by such values that a = [(C¢×a) + b] + (dG – C¢dT)

(5.39)

then the goods market will be in equilibrium at A, i.e. the IS corresponding to these new values of G and T will pass through A. All the combinations of dG and dT that satisfy (5.39) will make the IS pass through A. We can work out the same exercise mathematically also. Taking total differential of the equations of IS and LM, we get

dY e

C „ ¹ (dY e  dT )  I „ ¹ di e  dG

dM

P ¹ ( LY ¹ dY e  Li ¹ di e )

Substituting into the above equations the targeted values of dYe and die, we have a

and

dM

C „ ¹ (a  dT )  b  dG P ¹ ( LY ¹ a  Li ¹ [ b / I „])

(5.40) (5.41)

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Note that (5.40) is the same as (5.39) and we also pointed out above that to achieve the targets the government has to raise the money supply by the RHS of (5.41). Let us now explain (5.40) and (5.41). The LHS of (5.40) gives the change in aggregate supply when Y changes by the targeted quantity. The RHS gives the change in aggregate demand when Y and i change by their respective targeted quantities and G and T change dG by dT respectively. Thus, if dG and dT satisfy (5.40), then corresponding to such values of dG and dT the goods market will be in equilibrium with Y and i changed by their respective targeted quantities. In other words, the IS curve corresponding to each such combination of dG and dT will pass through the targeted pair of i and Y. Similarly, consider Eq. (5.41). The LHS gives the change in money supply from its value at initial equilibrium. The RHS gives the change in demand for money when Y and i change from their initial equilibrium values by their respective targeted quantities. Clearly, if the monetary authority changes money supply by an amount that satisfies (5.41), the money market will be in equilibrium when Y and i change by their respective targeted quantities. From the above it follows that if the government and the monetary authority change G, T and M by such quantities that satisfy (5.40) and (5.41), the goods and the money markets will be in equilibrium at the targeted values of Y and i. From (5.40) it is also clear that, if a = [(C¢×a) + b], (5.40) is satisfied even when government leaves its fiscal instruments unaffected. In this case the targeted values of i and Y keep the goods market in equilibrium even when all the parameters of the goods market equilibrium condition remain unchanged. Clearly, targeted quantities of Y and i in this case lie on the initial IS only. This is obviously a very special case and in this case fiscal policy is not necessary to achieve the target. Similarly, if the targeted changes in Y and i are such that the RHS of (5.41) is zero, no change in money supply is needed, i.e. monetary policy is unnecessary to keep the money market in equilibrium when Y and i change by their respective targeted quantities. In this case the targeted values of Y and i lie on the initial LM. This case is, however, not possible here since the targeted change in i is negative. EXERCISE 5.17 (a) As a programme of expansion, monetary policy is superior to fiscal policy, if growth is a target variable along with stabilization. If the government wants to raise output by a stipulated amount, the level of investment will be larger when the instrument used to achieve the target is the monetary policy. If fiscal policy is used instead, the level of investment will decline due to crowding out effect. Do you agree with the above statement? Explain your answer. (b) Represent (5.40) and (5.41) in a graph. What information do they give? Explain their vertical intercepts and slopes. Indicate their solutions. (c) As a policy of contraction, however, fiscal policy is preferable to monetary policy from the point of view of investment. Explain. Figure 5.10 represents a situation which needs expansionary policies. We shall now focus on a situation where contractionary programmes are needed. The case is illustrated in Figure 5.11 where the IS and the LM intersect at a level of Y that is greater than the full employment GDP.

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Figure 5.11

Contractionary policies in IS-LM model.

We assume that i adjusts instantaneously to clear the money and the loan markets, while Y adjusts sluggishly. The implication of this assumption is that the economy will be on the LM at every instant (explain why). The value of i corresponding to Yf on LM is i0. There is excess demand in the goods market at (Yf, i0) and also at every point on the LM to the left of (Yf, i0). So producers will produce Yf and the interest rate will settle down to the money market clearing level, i0, corresponding to Yf. The situation is obviously one of disequilibrium. There is excess demand for goods and it will generate strong inflationary pressures in the system. Dissatisfied buyers will offer higher prices to bid away scarce goods from other buyers. The latter will therefore be forced to raise their offers too. Thus a price competition among the buyers will break out, which will lead to a price-spiral or inflation. Inflation is costly to the society for several reasons. It mainly hurts the weaker sections of the people whose nominal or money income usually do not rise in steps with prices in times of inflation. Hence every government everywhere considers inflation to be undesirable. With the rise in prices or inflation, LM will start shifting leftward (explain why) and eventually intersect the IS at Yf and thereby restore equilibrium in the system. However, no government will allow this process of equilibration to operate since inflation is undesirable. As soon as the government realizes that inflationary pressures are building up in the system, it will adopt fiscal or monetary policy to restore equilibrium at Yf and thereby diffuse the inflationary pressure. If the government wants to have a high level of investment, it will obviously adopt fiscal policy, which shifts the IS and leaves LM unchanged, to stabilize the economy, since investment at Q is larger than that at H. By how much the government will have to change G or T or both to stabilize the economy at Q? The level of aggregate demand at (Yf, i0) is given by C (Y f  T )  I (i0 )  G œ AD(Y f , i0 ), where G amd T are the initial values of G and T respectively. To achieve the equilibrium at (Yf, i0), the government will have to change G and T in such a manner that the level of aggregate demand at (Yf, i0) falls in absolute value by the amount of excess demand existing at (Yf, i0) at the initial values of G and T, i.e. the required change in aggregate demand at (Yf, i0) is negative of the amount of the excess demand existing at (Yf, i0) at the initial values of G and T. The change in aggregate planned demand, with (Y, i) remaining unchanged at (Yf, i0), as G and T change by dG and dT respectively is given by [ dG  C „(Y f  T ) dT ]. We get this

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expression by taking total differential of the aggregate demand function and setting Y equal to Yf and dY and di equal to zero. Again, the excess demand existing at (Yf, i0) at the initial values of G and T is given by [AD(Yf, i0) – Yf]. Therefore, we get the required values of dG and dT by solving the following equations: [AD(Y f , i0 )  Y f ]

Þ

dG

Y f  AD(Y f , i0 )

[ dG  C „(Y f  T ) dT ]

[Y f  AD(Y f , i0 )]  C „(Y f  T ) dT

(5.42)

Equation (5.42) is represented by the GT schedule in Figure 5.12. The GT schedule gives corresponding to every dT the value of dG that satisfies (5.42). Equation (5.42) may be explained as follows. It states that, if dT = 0, i.e. if the government leaves tax collection unchanged, it will have to set dG = Yf – AD(Yf, i0). Let us explain. Yf – AD(Yf, i0) gives the amount of excess supply at Q at the initial values of G and T as in Figure 5.11. Obviously, the goods market will be in equilibrium at Q if, T remaining unchanged, G is raised by the amount of this excess supply, i.e. if dG is equal to Yf – AD(Yf, i0). This explains the vertical intercept of GT.

Figure 5.12 Fiscal policy.

Let us now focus on the slope of (5.42). The slope of (5.42) is C „(Y f  T ) . It measures the amount by which dG has to be changed to keep goods market in equilibrium at Q per unit increase in dT from a combination of dG and dT that satisfies (5.42). If from such a combination dT is raised, keeping dG unchanged, per unit increase in dT aggregate demand at Q(Yf, i0) will fall by C „(Y f  T ) creating an excess supply of the same amount. To keep the commodity

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market in equilibrium at Q(Yf, i0), the government therefore has to raise dG by C „(Y f  T ) . This explains the slope. Of course, to adopt the kind of policy specified above, the government has to know all the relevant equations for the economy. There are ways of estimating these equations. In the heydays of Keynesianism (1940–1970), economists used to suggest policies on the basis of such equations. EXERCISE 5.18 Derive the value of the horizontal intercept of the GT schedule in Figure 5.12 and explain it.

5.8 CONCLUSION IS-LM model constitutes a theory of short-run fluctuations in GDP. In reality periods of recession or low growth during which GDP falls far short of its potential level and those of high growth and inflation during which GDP is close to its full employment level alternate over time. The government adopts fiscal and monetary policies to contain recession and inflation. These stabilization policies are therefore essentially short-run in nature. IS-LM model shows that monetary policy and repercussions in the financial sector affect real variables through their impact on interest rates. However, it abstracts from term structure of interest rates and assumes that interest rates on loans of all the different maturity periods are equal. In the previous chapter on the term structure of interest rates we have shown that short-run monetary policies will affect short-term interest rates much more than long-term interest rates. Short-term loans mainly finance consumption loans. Investment requires long-term loans. The main impact of monetary policies is therefore principally on consumption demand. This is, however, inappropriate in countries like India that are poorly endowed with infrastructure. Infrastructure is built mainly by the government and governments in countries like India are subject to severe resource constraints. They should, therefore, regard recessions as opportunities to make large-scale investment in infrastructure, since they can finance such investments in times of recessions with money creation. This will have strong positive impact on depressed business sentiments, make complementary private investment profitable and lift the economy quickly out of recession. Large-scale public investment in infrastructure financed with money creation is by far the best and most sensible way of tackling recession in countries like India. The IS-LM model is based on the liquidity preference theory of interest rates, which regards the money market and the market for loans (or market for non-money financial assets) as the exact images of one another. Excess supply in one implies excess supply of an equal amount in the other and vice versa. Interest rate, which is the price of the service rendered by loans, is determined in the loan market through the interaction of the forces of demand for and supply of loans. However, in the liquidity preference theory, equilibrium in the loan market implies equilibrium in the money market and vice versa. Hence to characterize equilibrium it is not necessary to consider explicitly both the loan and the money markets. The liquidity preference theory accordingly focuses only on the money market, derives the equilibrium value of the interest rate from the money market equilibrium condition alone and relegates the loan market to the background.

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The neglect of the loan market is responsible for some of the major weaknesses of the IS-LM model. It does not show, for example, how final expenditures are financed. More precisely, it cannot show how levels of final expenditure and supplies of loans are related to one another. We have also seen in the previous chapter, which discusses the process of generation of money, how intimately the supply of money and that of credit are connected to one another. They are in fact outcomes of the same process. The IS-LM model, however, does not take into account the process of creation of money. It cannot therefore show how monetary authority can change money supply or how the money that is created gets into the hands of the economic agents. For all these reasons it seems the IS-LM model needs to be improved upon to remove these deficiencies.

PROBLEMS 1. (a) In an IS-LM model, the planned investment is a function of interest rate, i, alone and [dI/di] = –50. An increase in demand for real balance is found to shift the LM by –(1/.25) units and (1/62.5) respectively. Now, following a shift in the import function, Y in equilibrium is found to have increased by 500 units. Compute the change in the planned level of investment from the initial to the new equilibrium. (b) Suppose that the government takes an additional loan of ` 100 from the central bank. Explain how this will lead to an increase in the stock of high-powered money by the same amount, assuming CRR to be unity. Show how people will come to hold an additional amount of money of the same amount at the end of the first round transactions of the money multiplier process when high-powered money goes up by ` 100. 2. How does an increase in government expenditure financed by taxation affect GDP and investment in the IS-LM model? Explain. 3. Suppose following an autonomous increase in the supply of money by 2 units, the LM schedule shifts vertically by – .2 unit and horizontally by 10 units. Also assume that P = 1. Derive the interest sensitivity and income sensitivity of the nominal value of excess supply of money and explain your answer. Derive also the equation of the LM schedule under the assumption that M 100 . Plot the LM schedule in a diagram. If, other things remaining the same, the vertical shift in the LM schedule were –.1 instead of –2, how would the LM be affected? Would the effectiveness of fiscal policy be affected? If yes, then would it be solely due to the difference in the magnitudes of the crowding out effect? Derive this difference and explain your answer. M 900; L .25Y  62.5i . At Y = 100, with money P market in equilibrium, excess demand for goods and services is 10. At Y = 150, with money market in equilibrium, aggregate demand for goods and services is 119 and interest sensitivity of aggregate demand for goods and services is 5. Derive the excess demand for goods and services as a function of Y when i is always such that the money market is in equilibrium at every point of time. Derive also the equilibrium value of Y.

4. Consider the following equations:

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Show them in a graph. Can you explain the equilibrium value of Y in terms of the parameters of the excess demand function? Can you break up the co-efficient of Y in the aggregate demand function obtained from the excess demand function derived earlier into two components: one giving the crowding in effect and the other the crowding out effect of a unit increase in Y? Explain your answer. 5. Suppose the government controls G in such a manner that the amount of budget deficit remains unaffected. By how much will the aggregate private saving be affected following an autonomous increase in the exogenously given investment in the simple Keynesian model? Explain your answer. M 900 and L = .25Y – 62.5i. Suppose the interest P sensitivity of demand for real balance falls from 62.5 to 60. How will it affect the state of the money market at any point on the original LM? By how much will (i) Y has to be changed, given r and (ii) r has to be changed, given Y to restore the equilibrium in the money market? Indicate the horizontal and vertical shifts in the LM. Does Y and r really change by the aforesaid amounts? Explain.

6. Consider the following equations:

7. In the IS-LM model for a closed economy, following an increase in government consumption by b, equilibrium interest rate rises by a. The slope of the IS is c. In the new equilibrium, investment, which is an increasing function of income and a decreasing function of interest rate, remains unchanged. Derive the investment function, which is linear and which does not contain any autonomous component, when marginal propensity to consume is m.

REFERENCES Bernanke, B.S. (1981), Bankruptcy, liquidity and recession, American Economic Review. Friedman, M. and Schwartz, A.J. (1963), The Great Contraction, Princeton University Press, Princeton. Hicks, John R. (1937), ‘“Mr. Keynes and the Classics’: A suggested interpretation.” Econometrica. Reprinted in J.R. Hicks, Critical Essays in Monetary Theory, Oxford University Press, 1967. Krugman, P. (1999), Thinking about the Liquidity Trap, Paul Krugman’s Official Website.

6 6.1

Classical Theory

INTRODUCTION

Keynes (1936) put together the major macroeconomic ideas of his predecessors in the framework of a single model and referred to it as the classical model. One major result of the classical model is Say’s law, which states that supply creates its own demand. It implies that whatever be the level of aggregate production, a market economy contains a mechanism that automatically generates a level of aggregate demand that equals the given level of aggregate supply. In the classical theory, therefore, there is no possibility of excess supply (over-production) or excess demand (under-production) of goods and services at the economy-wide level. Another important feature of the classical theory is that it assumes that markets of all the produced goods and factor services are perfectly competitive and all the prices are perfectly flexible and market clearing. This assumption rules out the possibility of involuntary unemployment (excess supply) of labour or capital. If at any wage rate, for example, there emerges excess supply of labour, i.e. if at the given wage rate workers are willing to sell more labour than what the firms want to hire, the wage rate will go on falling making it profitable for the firms to employ more until the excess supply disappears. Obviously, this model cannot explain persistence of involuntary unemployment of labour or capital in market economies. However, a market economy does not behave the way the classical theory says it does. Involuntary unemployment of both labour and capital is the most daunting feature of a market economy. In every market economy, in every period, one finds quite a large segment of the labour force jobless even though they are willing to work at the prevailing wage rate. Similarly, producers also find themselves saddled with unutilized productive capacity. A market economy goes through alternating periods of recession and boom. In times of recession both involuntary unemployment of labour and unutilized productive capacity of the installed capital go up significantly, while they go down sharply in times of boom. The objective of macroeconomics is to explain these phenomena. Involuntary unemployment of labour and capital reached an all time high during the Great Depression of the thirties. In the 1930s the Great Depression in the 205

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USA made millions of workers involuntarily jobless, and hundreds and thousands of firms bankrupt for six long years. Obviously, it dealt a severe blow to the classical macroeconomic beliefs and led to their collapse. Keynes (1936) developed a model capable of explaining why involuntary unemployment of labour and capital occur in market economies and why they experience alternating phases of recession and boom. However, before discussing the Keynesian theory, it is advisable to present the classical model to identify the key differences between the two theories that make one’s predictions inconsistent with the behaviour of a market economy and make the other’s consistent.

6.2

SAY’S LAW: MARKETS FOR GOODS AND CREDIT

Let us first focus on the market for produced goods and services in the classical model. For simplicity, we abstract from government’s economic activities. We know that the goods market is in equilibrium when aggregate planned saving and aggregate planned investment are equal. In the classical theory, as we pointed out above, Say’s law holds. This means that in the classical theory aggregate planned saving (denoted S) is always equal to aggregate planned investment (denoted I). Usually, saving and investment are made by different groups of economic agents. The bulk of the former comes from the households, while the major part of the latter is made by firms. Moreover, saving and investment are driven by different factors. The former is driven by people’s need to provide for old age, illness, etc., while the latter is undertaken to earn future income. There is thus a priori no reason why they should always be equal. However, despite this, classical theory shows that they remain equal more or less always in market economies. Classical theory assumes that savers use their saving to extend loans, as loans yield interest income. Thus saving in classical theory constitutes supply of new loans. It further assumes that saving is an increasing function of interest rate. This is because interest rate constitutes the reward of saving. Hence, the higher the interest rate, the greater is the incentive to save. People can also hold their saving in the form of money. But they do not do so, since money, according to classical writers, does not yield any income. It is a barren asset. It further assumes that demand for new loans comes only from the investors. Investors need credit to finance their investment. Interest rate constitutes the cost of borrowing. Hence, the higher the interest rate the less is the incentive to invest. In the classical theory therefore aggregate planned investment is a decreasing function of the interest rate. Thus saving and investment functions, which are identical respectively with the supply of loans and demand for loans functions in the classical theory, are given by (6.1) and (6.2). S = S(r) S¢ > 0

(6.1)

I = I(r) I¢ > 0

(6.2)

Loan market in the classical model is perfectly competitive and the interest rate is perfectly flexible and market clearing. The loan market is in equilibrium when demand for loans, I(r), equals supply of loans, S(r). Thus, the loan market is in equilibrium when the following condition is satisfied: I(r) = S(r) (6.3)

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207

One can solve (6.3) for the equilibrium rate of interest. The solution of (6.3) is shown in Figure 6.1, where saving and investment schedules are represented by S and I respectively. The equilibrium rate of interest rate corresponds to the point of intersection of these two schedules. It is referred to as the natural rate of interest by the famous Swedish economist Wicksell. It is denoted by rn in Figure 6.1. The interest rate by assumption adjusts instantaneously to clear the loan market. Given the perfect flexibility of interest rate, r always equals rn and, accordingly, demand for loans and supply of loans are always equal. Let us explain. If r is above (below) rn, there is excess supply (excess demand) in the loan market and the interest rate falls (rises) until saving and investment become equal. The adjustment in interest rate occurs instantaneously. Therefore, both the goods market and the loan market are always in equilibrium. This ensures Say’s law.

Figure 6.1

6.3

Equilibrium in the goods market and the loan market.

AGGREGATE SUPPLY: AGGREGATE PRODUCTION AND LABOUR MARKET

From Say’s law it follows that in the classical theory whatever be the level of aggregate output produced by the producers, it will create an equal amount of demand. How much will then the producers produce? They will, in this scenario, obviously produce the level of output that maximizes their profit. In what follows we shall derive the profit maximizing level of output of the firms, when producers can sell whatever they produce. In the classical model, all the markets are perfectly competitive. There are thus a large number of firms. They produce goods and services using capital and labour. However, the focus here is on the short-run. Hence the stock of capital of every firm is given. Markets for both produced goods and labour are perfectly competitive. Hence firms are price takers in both the markets. The production function of the firms is given by Y = F(L, K );

FL > 0

and

FLL < 0

(6.4)

where L denotes labour and K the fixed stock of capital. The production function states that the marginal productivity of labour is positive and it diminishes with an increase in employment. Profit-maximizing exercise of the firms is given by max 3 L

PF ( L, K )  WL  A

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where P º profit, P º price level, i.e. the average price of produced goods and services. W º the money wage rate and A º the fixed cost consisting of fixed interest charges on past loans and depreciation. In the above profit maximization exercise, P, W, K and A are all given to the firms. Therefore, they choose only L to maximize their profit. Carrying out the above maximization exercise, we get the following first-order condition for profit-maximization: ˜3 ˜L

PFL ( L, K )  W

0

(6.5)

The first-order condition states that, if there exists an L, say L*, such that the firm’s profit is maximized at that L, then (¶P/¶L) corresponding to that L is zero. If (¶P/¶L) > ( 0) as L is raised (lowered) from its lower (higher) to the initial value. (Note that when L is lowered from its higher to the initial value, dL < 0.) Two points emerge clearly from the above discussion. First, if at any given L marginal productivity of labour is different from the real wage rate, profit can be raised by changing the level of L. Therefore, at such a level of L, profit cannot be at its maximum level. Hence, at the level of L at which profit is maximum, marginal productivity of labour should be equal to the real wage rate. Second, if at a level of L at which marginal productivity of labour equals the real wage rate, profit need not necessarily be at its maximum level. It may be at its minimum level as well. (Prove this point yourself.) If at such a level of L marginal productivity diminishes with an increase in L, firm’s profit is maximized locally (i.e. in a very small neighbourhood of the given L) at the given L. On the other hand, if at a level of L at which marginal productivity of labour equals the real wage rate, marginal productivity of labour rises with an increase in L (i.e. if (¶2F/¶L2) < 0), profit at such a level of L is at its local minimum. (Explain this point yourself.) This explains why firm’s profit achieves a local maximum at the value of L at which both the first and second order conditions are satisfied. If there is a unique L at which the first order condition is satisfied and if the second order condition is satisfied at every L, i.e. if (¶2F/¶L2) < 0 at every L, then firm’s profit achieves a global maximum at the L at which the first order condition is satisfied. This condition may be explained with the help of Figure 6.2 where values of F¢(L) and (W/P) are plotted against L. The F¢(L) schedule gives the value of F¢(L) corresponding to every L, while the horizontal line gives the value of the given real wage rate corresponding to every L. The first order condition is satisfied at a unique L labelled L*, which corresponds to the point of intersection of the two schedules. When the second order condition is satisfied at every L, the F¢ ( L , K ) schedule is negatively sloped throughout at every L as shown in Figure 6.2. It implies that at every L less (higher) than L*, marginal productivity of labour, F¢ ( L , K ) , is greater (smaller) than the marginal cost of hiring one unit of labour, (W/P). If L is raised (lowered) from such a level by 1 unit, firm’s revenue in real terms goes up (falls) by (¶F/¶L), while its cost in real terms rises (declines) by a smaller (larger) quantity, (W/P). Hence its profit

Figure 6.2

Derivation of labour demand.

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will go up by [(¶F/¶L) – (W/P)] > 0 ([(W/P) – (¶F/¶L)] > 0). Thus, at every level of employment less (higher) than its profit-maximizing level, the firm will be able to raise its profit by hiring more (less) labour. This explains our proposition. We can solve (6.5) for the profit-maximizing level of employment or labour demand, LD, as a function of real wage rate, given K and the production function. It is given by LD = LD(w) LD¢ < 0 (6.7) The labour demand function is shown in Figure 6.3.

Figure 6.3 Labour demand schedule.

Let us now explain why LD¢ < 0. This follows straightway from Figure 6.2, which shows that the higher the real wage rate, the less is the profit-maximizing level of employment. We can derive this result mathematically also. Denoting the profit-maximizing level of employment by LD and putting it into (6.5), we get the following identity

FL ( LD , K ) œ

W P

Taking total differential of the above identity, we get FLL dLD

ÈW Ø dÉ Ù Ê PÚ

(6.8)

It is quite easy to explain the above equation. Following a given change in the real wage rate, there is a new optimum. In the initial optimum situation, the marginal productivity of labour is equal to the initial real wage rate. In the new optimum situation, the marginal productivity of labour is equal to the new real wage rate. Therefore, the change in the marginal productivity of labour from the initial optimum situation to the new optimum situation is equal to the change in the real wage rate from the initial optimum situation to the new optimum situation. The marginal productivity of labour changes from the initial optimum situation to the new optimum situation solely because of the change in the level of employment from the initial optimum situation to the new optimum situation. The change in the level of employment from the initial optimum situation to the new optimum situation is given by dLD. Hence, the LHS of (6.8) gives the change in the marginal productivity of labour from the initial optimum situation to the new

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optimum situation. The RHS of (6.8) gives the change in the real wage rate from the initial equilibrium situation to the new one. This explains why the two sides of (6.8) are equal. Equation (6.8) contains only one unknown, dLD, since d(W/P) is known by hypothesis and FLL(L, K ) is also known and constant for the following reason. We know the production function and FLL(L, K ) is evaluated at the initial values of L and K , which are known. Hence FLL(L, K ) is known and constant. We therefore get the value of dLD by solving (6.8). Solving (6.8), we get 1 ÈW Ø dLD d FLL ÉÊ P ÙÚ dLD ÈW Ø dÉ Ù Ê PÚ

1 0 FLL

(6.9)

EXERCISE 6.1 Explain the RHS of (6.9), i.e. explain why the RHS of (6.9) gives the value of

dLD . ÈW Ø dÉ Ù Ê PÚ

6.3.1 Supply of Labour In any given period of time (a day, week, or month, etc.), an individual has a fixed amount of time or labour at his disposal. A rational individual is assumed to divide his/her fixed time or labour endowment optimally between labour supply and leisure so that his/her utility is maximized. Hence supply of labour of an individual is derived from the following optimization exercise:

max U ( y, l) y, l

Subject to y

X ¹ ( L  l)

where U(×) represents the utility function of the individual and y, w, L and l denote respectively the real income of the individual, real wage rate, the given endowment of labour of the individual and the amount of leisure consumed by the individual. Since all the markets are perfectly competitive, individuals are price takers in the markets of both produced goods and labour. Hence w is given to the individuals. Note that the constraint gives the budget of the individual. It gives corresponding to every l consumed by the individual the amount of real income he earns by selling the rest of his labour endowment in the market at the real wage rate w. This budget is represented by the straight line BB in the (l, y) plane in Figure 6.4. The above constrained optimization exercise may be written as the following unconstrained one: max U (X [ L  l ], l) l

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Figure 6.4

Decomposition of the price effect into substitution and income effects.

In the above unconstrained exercise, l is the only choice variable of the individual. Note that U (X [ L  l ], l) gives the amount of utility the individual derives from every (l, y) in his budget, i.e. from every point on his budget line BB in Figure 6.4. The first-order condition (FOC) is given by dU dl

U y (¹).( X )  U l (¹)

0 À [U l (¹)/ U y (¹)]

X

(6.10)

and the second-order condition (SOC) is given by

d 2U dl 2

0

(6.11)

dU measures the amount of change in U per unit dL increase in l when l rises from a point on the budget line by a very small amount along the budget line (i.e. when the increase is l is accompanied by a commensurate fall in y so that the individual remains on the budget line. The first-order condition states that, if there exists on the budget line an l at which individual’s utility is maximized, then at that l, say l*, the value of (dU/dl) = 0. It is quite easy to explain the condition. If at l* the value of (dU/dl) > ( (( wl*. Therefore, according to Slutsky, the individual’s real income at w¢ remains the same as before if (w¢l* – wl*) (º T) amount of income is taken away from him. In such a situation, if he choose the initial optimum level of l, l*, his post-tax income will be wl*, the initial optimum level of y. Thus, according

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to Slutsky, the individual’s real income at the budget line defined by the equation

215

w¢ is the same as its initial level if he chooses from

y=

w¢l – T

(6.13)

where, as we just said, T º w¢l* – wl*. Substituting the value of T and l* respectively for T and l in (6.13), we will find that (l*, y = wl*) which satisfies (6.13). Thus the budget line (6.13) passes through the initially optimum point (l*, wl*) and have the slope w¢. This budget line is labelled SS in Figure 6.4. The new real income is obviously given by the new budget line, S1B, corresponding to w¢. Let us now derive the substitution effect using Slutsky’s definition of real income. It is given by the change in the individual’s optimum choice due to the rise in w to w¢, when his real income at w¢ is the same as before, i.e. when he chooses from SS in Figure 6.4. The consumer chooses from the budget line, SS, and not from below it because SS gives the largest and therefore, given the axiom of non-satiety, the best of the bundles available to him, when his budget is given by (6.13). At the initially chosen bundle the MRSly is now less than w¢. Hence, if he substitutes income for leisure along the budget line SS, i.e. if he moves upward along SS, he will be better-off. Let us explain. If he reduces l, then per unit reduction in l the compensation that he will require to be on the same indifferences curve (IC) is MRSly amount of additional income, which is less than the extra income, w¢, that he will earn. This excess income of (w¢ – MRSly) will move him over to a higher IC. Thus as long as w¢ – MRSly, the consumer benefits by reducing l and raising y along SS. He attains the highest IC remaining on SS at the point at which w¢ = MRSly. This point is labelled A1 in Figure 6.4. One can easily figure out that if at any point on SS w¢ < MRSly, the individual gains by raising l and thereby reducing y along SS. From the above it follows that substitution effect induces the individual to substitute y for leisure, which has become more expensive in terms of y following the rise in w. Hence due to substitution effect the optimum l falls raising labour supply. The change in the individual’s choice due to the change in the individual’s real income alone, is called the income effect. In Figure 6.4, budget lines SS and S1B, as per Slutsky, represent respectively the individual’s initial and new levels of real income when the real wage rate is w¢. This implies that when the individual moves from SS to S1B, his real income alone increases as he faces the same real wage rate on both SS and S1B. Thus we can derive the income effect by examining the change in consumer’s optimum choice as he moves from SS to S1B. If both y and l are normal goods, demand for both will increase and hence the optimum point on S1B will lie in between B1 and B2. Thus, income effect will raise demand for both when they are normal goods. In Figure 6.4, the optimum point is labelled A*. In Figure 6.4, the reduction in l from l0 to l2 is due to the substitution effect, while the increase in l from l2 to l1 is due to the income effect. Thus the whole change in l is accounted for by the substitution and income effects. Here the income effect is weaker than the substitution effect and hence the optimum l falls and therefore labour supply rises following the rise in w. However, the income effect could be stronger than the substitution effect also in which case l would rise and labour supply would fall with the rise in w. However, usually the substitution effect is regarded as stronger than the income effect and the labour supply is assumed to be an increasing function of w.

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EXERCISE 6.2 Decompose the total change in the optimum quantity of leisure following the rise in the real wage rate using the Hicksian definition of real income.

6.3.2

Equilibrium in the Labour Market

The labour market is in equilibrium when labour demand and labour supply are equal, i.e. when the following equation is satisfied LD(w) = LS(w)

(6.14)

We can solve (6.14) for the equilibrium value of w, which is referred to as the full employment real wage rate. Putting this value of the equilibrium real wage rate either in the labour demand function, (6.7), or in the labour supply function, (6.12), we get the equilibrium level of employment. This equilibrium level of employment is called the full employment level of employment. Full employment real wage rate and employment are denoted by wf and Lf respectively. Substituting the equilibrium level of employment in the production function, (6.4), we shall get the equilibrium level of aggregate output or GDP. It is referred to as the full employment level of GDP and is denoted by Yf. It should be noted that utility functions or tastes and preferences of the workers are the parameters of the labour supply function. Accordingly, they determine its position. Similarly, the given stocks of capital and natural resources along with the parameters of the production function or the technology determine the position of the labour demand schedule. Given these parameters of the labour demand and labour supply schedules, Yf and Lf give the maximum levels of output and employment possible in a market economy, where economic agents participate in economic activities on their own volition. Let us explain. As there is no coercion or application of force, firms and workers respectively demand and supply only those quantities of labour, which maximize their profits and utilities. These quantities are determined, as we have shown earlier, only by the real wage rate, given the parameters noted above. In the full employment situation the level of real wage rate that prevails is the full employment real wage rate, wf. In this situation firms and workers demand and supply the same quantity of labour Lf and therefore there is equilibrium in the labour market. Firms produce the corresponding level of output, Yf. The situation is shown in Figure 6.5 where in the lower panel LDLD and LSLS represent respectively the labour demand and labour supply functions. Lf and wf correspond to the point of intersection of these schedules. In the upper panel, the schedule labelled F(×) represents the production function. Yf corresponds to Lf on this production function. From Figure 6.5 it is clear that, if w falls below wf, labour supply will fall, while labour demand will rise. Employment at this lower w will obviously be determined by the amount of labour supply. Hence both output and employment will go down below Yf and Lf respectively. For similar reasons if w rises above w f, employment and output will again fall below Yf. This establishes our proposition. Let us now sum up our findings so far. From the characterization of the goods and the credit market it follows that the rate of interest remains equal to the natural rate always keeping saving and investment equal. The goods market therefore remains in equilibrium all the time, whatever be the level of aggregate output. Producers accordingly produce the level of output that maximize

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Figure 6.5

217

Labour market equilibrium.

their profit when output is not subject to any demand constraint. Given technology and the stocks of land and capital, this profit maximizing level of output is determined by the real wage rate, which, in turn, is determined in the labour market. If at the real wage rate faced by the producers, there is excess supply of (excess demand for) labour, money wage rate falls (rises) instantaneously by assumption pulling down (up) the real wage rate to the market clearing level. Thus the real wage rate more or less remains always at the market clearing level inducing the producers to employ the full employment amount of labour and supply the full employment level of output. In the classical theory, therefore, there cannot emerge unemployment of labour except in very short periods of time. Thus, in the classical model, producers always produce the full employment level of output, whatever be the level of P. Let us explain. Given the assumptions of the classical model, whatever be the level of P, money wage rate adjusts instantaneously to such a level that the real wage rate at the given P equals the full employment real wage rate

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inducing the workers to supply and the producers to employ the full employment amount of labour and thereby produce the full employment level of output. Thus, aggregate supply in the classical model is independent of P. Accordingly, the classical aggregate supply schedule is vertical in the (Y , P) plane as shown in Figure 6.6. It is labelled AS.

Figure 6.6 Aggregate supply schedule of the classical model.

The goods market, credit market and the labour market constitute the real sector of the economy in the classical model. Formally, Eqs. (6.1), (6.2), and (6.3) comprising the goods and the credit markets together with (6.4), (6.7), (6.12) and (6.14) characterizing the labour market constitute the real sector of the model. These equations together determine all the endogenous variables contained in them, namely S, I, r, Y, w, LD and LS. These are the real variables of the classical model. The real sector of the classical model is therefore a self-contained independent system capable of determining all its endogenous variables without any reference to the monetary sector. This phenomenon is referred to as the classical dichotomy. In modern economies, prices and wages are quoted in terms of money. Thus a model is not complete unless it shows how money wage rate and money prices are determined. In the classical theory, these nominal variables are determined in the monetary sector. In what follows we shall present the monetary sector of the classical model.

6.4 MONEY MARKET Monetary sector in the classical model consists of the money market. The money market, like every other market, has two sides, a demand side and a supply side. We describe them below. The supply of money, denoted by MS, in the classical model is exogenously given. Thus MS

M

(6.15)

Classical theory recognizes only one motive for holding money: the transaction motive. People hold money only to carry out transactions. In the classical model, it is assumed to be a proportional

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function of nominal GDP given by PY, where P denotes price level and Y denotes real GDP. Denoting demand for money by MD, we have (6.16) MD = kPY where k is a parameter. It gives the reciprocal of the income velocity of circulation of money. PY . It gives us the Let us explain. Income velocity of circulation of money is defined as MS number of times every unit of money changes hands on the average to generate the nominal GDP. Suppose nominal GDP is ` 100, while the total money supply in the economy is ` 10. Then income velocity of circulation of money is 10. This means that on the average every rupee changes hands ten times to generate the nominal GDP of ` 100. Let us explain this point a little further. To produce goods and services, producers have to hire factor services and pay for them. When they produce goods and services of ` 100, they have to pay ` 100 for factor services. If money supply in the economy is ` 10, at any given instant of time producers can at the most have ` 10. How do they make the payment of ` 100 then? They cannot obviously do it in one go. On the average they have to make the payment in ten instalments of ` 10 each during the period under consideration. After making one installment of payment, they have to wait for the ` 10 to come back to them. ` 10 goes back to them as factor owners purchase produced goods and services. This example illustrates the concept of income velocity of circulation of money of the classical writers. The money market is in equilibrium when demand for and supply of money are equal, i.e. when the following equation is satisfied (6.17) M kPY Equation (6.17) is referred to as the quantity theory of money. The equilibrium value of Y, Yf, as we have seen above, is determined in the real sector. Substituting Yf for Y in (6.17), we can solve it for the equilibrium value of P. The quantity theory of money therefore determines the M money price of goods and services. It is given by . Multiplying the equilibrium value of kY f the real wage rate, wf, yielded by (6.14), by the equilibrium value of P, we get the equilibrium value of the money wage rate. The money market in the classical theory therefore determines the nominal variables, viz., the money price and the money wage rate. The determination of the money price and the money wage rate is shown in Figure 6.7, where the AD schedule in the first quadrant shows all the combinations of P and Y that satisfy (6.17). The vertical AS schedule of Figure 6.6 is superimposed on the AD schedule in Figure 6.7. The point of intersection

Figure 6.7 Determination of equilibrium values of P and W.

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of the AD and AS schedules in Figure 6.7 gives the equilibrium value of P, labelled P*. In the second quadrant, the WW line gives all the combinations of W and P such that at each such (W, P), the ratio of W to P equals the equilibrium value of the real wage rate, wf. The equilibrium value of W, labelled W*, corresponds to the equilibrium value of P on the line WW.

6.4.1

Neutrality of Money

What effect does an increase in the money supply produce in the classical model? This is the question the quantity theory of money deals with. We shall now focus on this issue. Suppose the money supply goes up by dM . How will it affect the endogenous variables of the classical model? Note that money supply does not figure anywhere in the equations of the real sector. Accordingly, as we pointed out earlier, the equilibrium values of the real variables are independent of money supply. Graphically, all the schedules in Figures 6.1–6.6 remain unchanged despite the increase in money supply and, hence, equilibrium values of all the real variables remain unchanged. The equilibrium value of Y therefore remains at Yf. It therefore follows from (6.17) that the increase in money supply will only lead to a change in the price level, P, whose value M . Thus an increase in money supply will only lead to an equiproportionate is given by kY f increase in the price level and leave the equilibrium values of all the real variables unchanged. If money wage rate doubles, so will the price level. The money wage rate whose equilibrium M value is given by PX f X will also increase in the same proportion as the price level kY f f and the money supply. A change in the money supply in the classical model, as follows from the above, does not produce any real effect, i.e. it leaves the equilibrium values of the real variables unaffected. It only brings about equiproportionate changes in the nominal variables, namely the money price and the money wage rate. This result is referred to as the neutrality of money. This is an important result yielded by the classical theory or the quantity theory of money. This result may be derived graphically as follows. Following a change in money supply, as we pointed out earlier, all the schedules in Figures 6.1–6.6 remain unaffected. Therefore the AS schedule in Figure 6.7 remains unchanged. Let us now examine how the AD schedule in ÈMØ Figure 6.7 is affected. We can rewrite (6.17) as É Ù ÊPÚ

kY . Following an increase in M , this

È Ø equation is satisfied, given Y, if P rises in the same proportion as M so that É M Ù remains ÊPÚ unchanged. The AD schedule in Figure 6.7 therefore shifts upward in the same proportion as money supply. Hence, the equilibrium P given by the point of intersection of the AD and AS rises in the same proportion as money supply. Let us now examine how different economic agents respond to an increase in money supply to produce the result noted above. Following an increase in money supply, people find that they have more money in their hands than they want to hold to carry out their transactions. They will use this excess money balance to purchase goods and services creating excess demand in the

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goods market. This will start raising the price level. The rise in the price level will lower the real wage rate below its market clearing level generating excess demand for labour. The money wage rate will rise instantaneously to keep the labour market in equilibrium. Thus, with the rise in the price level, the money wage rate will also start increasing in the same proportion keeping the real wage rate at the market clearing level. Hence, producers will continue to produce the full employment level of output. This process of increase in the price level and the money wage rate will continue until through the rise in the price level transaction demand for money goes up and becomes equal to the new higher money supply absorbing all the excess money balance in the hands of the people in their transaction balance. When this happens, excess demand for goods and services also disappears as people cease to have any excess money balance to spend against goods and services. This explains why a change in money supply brings about an equiproportionate increase in the price level and the money wage rate leaving all the real variables unaffected. EXERCISE 6.3 (a) Examine the impact of a decline in the income velocity of circulation of money in the classical model. (b) Suppose people become thriftier. How will it affect the endogenous variables in the classical model? (c) Incorporate government expenditure and taxes in the classical model. Suppose government expenditure is financed partly by taxes and partly by borrowing. What will be its impact in the classical model? (d) How will the classical model behave if saving and investment are independent of the rate of interest, r?

6.5 PROBLEMS WITH THE CLASSICAL THEORY The classical theory paints a fairy-tale picture of a market economy. The assumptions are tailored to derive the results that suit the interests of the champions of market economies. Obviously, between the assumptions and the reality falls the shadow. In what follows we shall seek to assess the major assumptions of the classical model one by one. Let us start with the Say’s law. Naturally, the sharpest and most enduring attack on classical assumptions came from Keynes himself. Keynes regarded Say’s law as implausible and questioned the way classical theory derived it. Keynes pointed out that saving and investment are unlikely to be interest elastic. Focus on saving first. We have found in the chapter on consumption function that the substitution and income effects produced by a change in interest rate pulls saving in opposite directions. Hence, theoretically, the impact of a change in interest rate on saving is likely to be weak. Empirically also evidences do not support the position that saving is interest elastic. Investment may also be highly interest inelastic in times of recession when business sentiments are depressed. If both saving and investment schedules are interest inelastic, they will not intersect each other at any positive interest rate. The classical theory in such a situation will fail to determine the interest rate and therefore will be indeterminate. Keynes also pointed out that money is liquid and liquidity is desirable to people. So, unless the interest rate on loans is

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sufficiently high, economic agents will not consider it optimal to part with liquidity. This means that at interest rates not sufficiently high, savers will hold their savings in the form of money instead of lending them out. At such interest rates, therefore, supply of loans will be zero. This implies that at such interest rates there can only be excess demand for loans. Hence, interest rate in a market economy will never fall to such low levels. Therefore, for classical theory to be able to determine interest rate, saving and investment schedules will have to intersect at sufficiently high interest rates. For that, interest elasticity of saving and investment schedules will have to be sufficiently high, a condition, which is unlikely to be met in reality. Show the situation in a graph measuring S and I on the horizontal axis and interest rate on the vertical axis. Label the saving and investment schedules SS and I I respectively. They do not intersect at any feasible interest rate. To get out of the problem, as pointed out by Keynes, Pigou incorporated the stock of real balance in the possession of the private sector, usually denoted by ( M / P), as a determinant of private saving. The stock of real balance refers to the real value of the stock of government money (currency and coins and deposits with the central bank) and government debt in the possession of the private sector. Why is real balance a determinant of private saving? Pigou’s answer to this question runs as follows. Pigou argues that people save for two reasons: to earn interest income and to provide for old age, illness, etc. This means that even if interest rate falls to zero, people will save for the second motive. He said that the larger the amount of wealth in the possession of the households, the more secure they feel against contingencies such as old age, illness, etc., and hence the weaker is the second motive for saving. Thus the larger the amount of wealth in the possession of the private sector, the less is likely to be its saving. Obviously, when we consider the private sector as a whole, its wealth consists of the stocks of physical capital and the real value of the stocks of government money and government debt in its possession. The most important feature of the stock of real balance in the possession of the private sector is that its real value is a decreasing function of the price level, P. Pigou thus writes the classical saving function as S

È MØ S É r, Ù Ê PÚ

Sr ! 0

and

Sm  0

(6.18)

˜S and Sm œ ˜ S / ˜( M / P) . In (6.18), for simplicity, the whole of the money supply, ˜r M , is assumed to consist of high-powered money. We have also ignored government debt here. Let us now examine how the saving function proposed by Pigou solves the problem pointed out by Keynes. For this purpose focus on the graph you have been asked to draw above where the saving and investment schedules labelled SS and I I respectively fail to intersect at any feasible rate of interest. Given the assumptions of perfectly competitive labour and goods markets and perfectly flexible wage rate, producers will produce the full employment level of output, but will fail to sell the whole of it as saving remains greater than investment at every feasible interest rate. In this situation, the price level will go on falling raising the real balance. The rising real balance will start reducing saving, i.e. it will start shifting the SS schedule in the graph you have been asked to draw above leftward and this deflationary process will continue until the SS schedule intersects the I I schedule at the minimum of the feasible rates of intersect.

where Sr œ

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This is how, Pigou shows, the incorporation of the real balance in the saving function resolves the problem pointed out by Keynes. In Figure 6.8, the minimum of the feasible interest rates is labelled i0. The process of deflation will continue until the SS schedule intersects the II schedule at i0. The effect that a change in the real balance has on saving is referred to as the real balance effect. Real balance effect is, however, extremely weak theoretically. People save for the future. Their incentive to save may be less if they have reasons to believe that the real value of their future wealth is higher. Obviously, a reduction in current prices raises the value of the real balance in the current period. It does not raise the real balance of the future periods. A reduction in current prices is likely to be regarded as a transient phenomenon. A fall in current prices cannot prevent future prices to be 100 times or 1000 times higher. There is no reason why a fall in the current prices will induce people to expect a fall in future prices as well. There are, on the contrary, several channels through which a fall in current prices may widen excess supply instead of reducing it. If, for example, a fall in current prices generates deflationary expectations, i.e. if it induces individuals to expect further fall in prices, they will consider it optimal to postpone their purchases and thereby engender further fall in prices fulfilling their expectations. Again, if prices fall, firms’ income in terms of money goes down, but their debt servicing charges in terms of money remain unchanged. So, if the fall in prices is substantial, firms may go bankrupt defaulting on their loan obligations. This may bring about a collapse in the confidence of the financial institutions and other lenders in the borrowers generating a credit crunch. Moreover, a large-scale default on the part of the firms may lead to bankruptcy of banks and other financial institutions engendering a collapse of the entire financial system. This will clearly bring about severe shortage in credit supply implying drastic shrinkage in aggregate demand for goods and services. Thus, a fall in prices may severely exacerbate an excess supply situation instead of correcting it. It follows that the Pigovian defence against Keynes’ attack on Say’s law is extremely weak and unconvincing. All these arguments against Pigou’s real balance effect was developed by Keynes himself. See in this context Keynes (1936), Chapter 19, pp. 257–271. Let us now focus on the assumptions of perfectly competitive goods and labour market and perfectly flexible wages and prices. These assumptions fly in the face of reality. In developed market economies there are just a handful of giant firms in every industry. Thus the market structure in every industry is oligopolistic. Hence, a la kinked demand curve oligopoly model of Sweezy, prices of produced goods and services are likely to be highly rigid. This is true of the labour market as well. A firm while deciding on what wage rate to pay bases its decision on what other firms are paying to similar workers. Since labour is not auctioned and since firms and workers take buying and selling decisions independently in an uncoordinated manner, none of them has any inking as to what the market clearing wage rate is. For all these reasons wage rate may be highly rigid or inertial in market economics. Workers also, while deciding on whether to sell their labour to a particular firm take into account what other workers working in similar positions are getting in other firms. If a firm offers a lower wage rate than others, workers will not accept such a wage rate as they will expect vacancies to be available at wage rate prevailing in the market. They may also regard such a gesture on the part of a firm unfair and may form a bad opinion about the firm. Work environments also differ markedly across firms. So a firm offering a higher wage rate may arouses the suspicion that it is worker

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unfriendly. Workers having the same kind of skill differ a great deal in their attitude to work, ability, intelligence, morality, etc. There should be a market clearing wage rate for each of these types of workers having the same academic qualification. It is therefore impossible to know the market clearing wage rate. If a firm decides to pay less than what the others are paying, there is a high chance that it will end up with the worst of the workers available and thereby lose out in competition. Similarly, if a firm seeks to pay more than the others, he might start a wage war, which will hurt all of them. So, even if workers are not unionized, in market economies money wages may be fairly rigid. Keynes pointed out that in matured market economies, money wage rate in a firm is set through negotiations between the owners of the firm and trade unions. Trade unions bargain to ensure that they get at least what workers in similar positions are getting in other firms. He also points out that the wage that is agreed upon remains unaltered for a long period so that in the short-run money wage is fairly rigid. If we incorporate price rigidity in the classical system, it will become indeterminate. Let us incorporate money wage rigidity first. Let us assume, following on the argument of Keynes, that workers are willing to supply their labour at the average money wage rate prevailing in the market, which may be regarded as fixed in the short-run. The implication of this assumption is that labour supply is perfectly elastic at the average money wage rate prevailing in the economy, which we denote by W . This labour supply function is given by

W

W

(6.19)

Equation (6.19) states that the supply price of labour is W . If we replace classical labour supply function, (6.12), with (6.19), all the major classical results will be gone. We elaborate it below. Labour demand function is derived from the first-order condition for profit maximization, (6.5). We rewrite it as follows: (6.20) W PFL ( L , K ) (6.20) gives the demand price of labour corresponding to every L. This means that corresponding to every L (6.20) gives, the money wage rate at which the given L maximizes profit and is therefore demanded. The labour market is in equilibrium, when demand price of labour and supply price of labour are equal. Labour market equilibrium is therefore given by (6.21) W PFL ( L , K ) Let us explain (6.21). If at any given L the demand price of labour equals its supply price, W , producers’ profit at W is maximized at the given L and therefore their demand for labour exactly equals the given L. Hence the labour market is in equilibrium at the given L. If we fix the value of P, we can solve (6.21) for L, i.e. we can solve (6.21) for the labour market equilibrium value of L as a function of P, given W and K . Thus, we have L

L  P; W L P ! 0

(6.22)

The solution of (6.21) or derivation of (6.22) is shown in the lower panel of Figure 6.8 where the equilibrium value of L corresponds to the point of intersection of the inverse labour demand schedule, P0 FL ( L , K ) , which corresponds to a given P, P0, and the labour supply schedule, LSLS,

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which is horizontal at W . The equilibrium value of L, which corresponds to the point of the intersection of the P0 FL ( L, K ) schedule and the inverse supply schedule is labelled L0. At any other L, say, L  L0 ( L ! L0 ) demand price of labour, P0 FL ( L , K ) ! ()W . If L is raised (lowered) from L , per unit increase (decrease) in L value of output or total revenue will rise (fall) by P0 FL ( L , K ) , while cost will increase (decrease) by W . Since P0 FL ( L , K ) ! () W , per unit increase (decrease) in L profit will go up by P0 FL ( L , K )  W (W  P0 FL ( L , K )) . Hence producers will gain by raising (lowering) L from L . If P goes up from P0 to, say, P1, the value of marginal productivity of labour will be higher at every L. So P1 FL ( L, K ) schedule will, as shown in the lower panel of Figure 6.8 will lie above the P0 FL ( L, K ) schedule. Hence the labour market equilibrium value of L will rise. The labour market equilibrium value of L is thus an increasing function of P. This explains the sign of the derivative of (6.22). Substituting (6.22) into the production function, we get aggregate output planned by the producers or aggregate supply of goods and services as an increasing function of P. This is the aggregate supply function, as you will see in the next chapter, of the Keynesian model. It is given by

and

Y

Y S ( P; W )

Y

Yf

YPS ! 0 for P  P „

for P • P

Figure 6.8

Labour market equilibrium.

(6.23)

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The derivation of (6.23) from (6.22) is illustrated in Figure 6.8, where in the upper panel the schedule labelled F(×) represents the production function. The labour market equilibrium value of Y or the aggregate supply on the production function corresponds to the labour market equilibrium L as derived in the lower panel. Thus at P = P0 the labour market equilibrium value of L, as shown in the lower panel, is L0 and, accordingly, the labour market equilibrium Y is the one that corresponds to L0 on the production function in the upper panel. This Y is labelled Y0. Similarly, at P = P1 the labour market equilibrium values of L and Y are labelled L1 and Y1 respectively in Figure 6.8. The labour market equilibrium values of L and Y accordingly rise with the increase in P. When P rises sufficiently high the labour market equilibrium values of L and Y become equal to their respective full employment values. At the minimum of such PS labelled P in Figure 6.8 the labour demand schedule intersects the horizontal stretch of the labour supply schedule at the full employment amount of labour. This labour demand schedule is labelled PFL ( L, K ) in the lower panel of Figure 6.8. Obviously, for all P • P , the labour market is in equilibrium with full employment levels of L and Y. The aggregate supply curve is therefore vertical at the full employment level of Y for P • P . Thus, the aggregate supply schedule given by (6.23) is upward sloping for P  P and vertical at Y = Yf for P • P . The aggregate supply schedule representing (6.23) is labelled AS as shown in Figure 6.9. Equation (6.23) gives the value of Y which the producers consider optimal to produce, hiring labour at the fixed supply price of labour, W .

Figure 6.9

Aggregate supply function.

We rewrite the money market equilibrium condition (6.17) as M (6.24) kP Equation (6.24) gives the value of Y corresponding to every P that equilibrates the money market. Given Say’s law in the classical model ensured by sufficiently high interest elasticities Y

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of investment and saving functions and perfect flexibility of interest rates, whatever Y the producers produce will be demanded. Thus, if corresponding to any P producers produce the Y that satisfies (6.24), the money market will be in equilibrium and so will be the goods market. Hence, (6.24) may be regarded as the aggregate demand function of the classical model. Obviously, the classical model will be in equilibrium, when aggregate demand and aggregate supply are equal, i.e. when the following equation is satisfied M kP

Y S ( P)

(6.25)

Let us explain (6.25). At the P that satisfies (6.25), the Y that producers consider optimal to produce is also the one that equilibrates the money market. The goods market will also be in equilibrium at this Y. Hence the solution of (6.25) gives the equilibrium value of P. Substituting it in either the aggregate supply function, (6.23), or in the aggregate demand function, we shall get the equilibrium value of Y. Equation (6.3) gives the equilibrium value or r that keeps the goods market in equilibrium whatever be the value of Y. Solution of (6.25) is shown in the upper panel of Figure 6.10 where the AD schedule represents (6.24) and the AS represents (6.23). The equilibrium values of Y and P correspond to the point of intersection of the AD and AS schedules. They are labelled Y* and P* respectively. The lower panel shows the solution of (6.3). Let us now derive the major modifications that we have to make in the results of the classical model following the incorporation of money wage rigidity. It is clear from Figure 6.10 that if, given other factors, money supply is sufficiently small, the AD will intersect the AS at a Y < Yf . This means that in this situation the classical model is in equilibrium with less than full employment level of output. Since in this equilibrium firms employ less than the full employment amount of labour, the real wage rate that they face in equilibrium, (W / P*) ! X f . Clearly, at this real wage rate the amount of labour the workers plan to supply as given by the classical labour supply function, (6.12), is larger than what the firms have purchased. Hence there is excess supply of labour or involuntary unemployment in the labour market. Despite this, the labour market is in equilibrium because of the assumption of money wage rigidity. In this situation, in the classical model money wage rate falls removing excess supply of labour. But this mechanism fails to work here. Thus, once we introduce money wage rigidity, the classical model fails to keep a market economy in full employment equilibrium all the time. It may get caught in an equilibrium with involuntary unemployment. So, the most important result of the classical model that a market economy contains mechanisms that ensure full employment of capital and labour all the time becomes invalid. It is clear from (6.23) that the AS schedule in Figure 6.10 is independent of money supply. However, (6.24) shows that the AD schedule in Figure 6.10 shifts with changes in money supply. So changes in money supply in this modified classical model will lead to changes in equilibrium levels of output and employment making money non-neutral. So the other important result of the classical model that money is neutral is also gone. If in keeping with reality we incorporate price rigidity, the classical model will be indeterminate or inconsistent. Let us explain. Suppose P P . Then from (6.17) we find that the money market will be in equilibrium at a unique Y

M / kP . Again from (6.5), (6.7), (6.12)

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Figure 6.10

Money wage rigidity in the classical model.

and (6.14) it follows that in equilibrium producers will produce a unique Y, Yf. Clearly, if ( M / kP ) › Y f , which should normally be the case, no equilibrium will exist in the classical model. It will thus become inconsistent or indeterminate. We may sum up the findings of this section as follows. The classical theory fails to explain involuntary unemployment of labour and capital and their fluctuations in the course of a trade cycle is no surprise. Assumptions of perfect competition, perfect flexibility of wages, prices, etc., are so far removed from reality that the classical results hardly merit serious attention. If we incorporate some of the major features of reality such as interest insensitivity of saving and investment functions, oligopolistic market structures leading to rigidities in prices, lack of information, coordination etc. engendering rigidities in money wages, the classical theory either becomes inconsistent or yields equilibrium with involuntary unemployment and non-neutrality of money.

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6.6 CONCLUSION Classical theory shows that a market economy contains mechanisms that ensure full employment of labour and capital all the time. If ever unemployment occurs, it will be extremely short lived. It also yields that money is neutral, i.e. a change in money supply does not produce any impact on the real variables. It only leads to equiproportionate changes in money prices and money wage rates so that relative prices and real wage rates remain unaffected. It is in fact an ode to the efficacy of a market economy in bringing about full-utilization of productive resources. The classical theory, however, has one lacuna. Even though it shows that a market economy engenders full employment of productive resources, it cannot say anything regarding its efficiency in allocating productive resources across different lines of production and distributing produced goods among different final users of the produced goods. To remove this deficiency, Patinkin (1965) recast the classical model in the framework of a Walrasian general equilibrium model where every demand and supply functions are derived from explicit optimizing behaviour of buyers and sellers. This reformulated classical model throws light not only on whether a market economy brings about full employment of resources, but also on how efficiently it allocates them across different uses. Needless to say, given the assumptions, this model gives full marks to market economy on both counts. There is, however, a gulf of difference between myth and reality. The performance of every real market economy leaves much to be desired. Mild to severe recessions with large-scale involuntary unemployment of labour and capital lasting from two to six years occur regularly in every one of them. Periods of high rates of growth or boom with spiraling inflation also occur frequently. In the face of this hard reality, classical theory’s description of a market economy seems like a fairy tale. Its inconsistency with reality is so vivid that no one seriously researching into how a market economy functions will consider it worthwhile to pay any attention to it. The severest blow to the classical beliefs was dealt by the Great Depression of the thirties and the recent severe economic meltdown in the US. The Great Depression of the thirties induced Keynes (1936) to develop a theory capable of explaining why involuntary unemployment of labour and capital occurs and why recessions and booms alternate in market economies. It is still the best and the most reliable theory of unemployment and short-run cyclical fluctuations in market economies. We shall discuss it at length in the next chapter.

REFERENCES Keynes, J.M. (1936), The General Theory of Employment, Interest and Money, Macmillan, London. Patinkin, D. (1965), Money, Interest and Price, The MIT Press, New York.

7 7.1

Complete Keynesian Model

INTRODUCTION

Keynesian theory of determination of aggregate output and employment finds its fullest form in the complete Keynesian model (CKM). It is by far the most reliable theory even today for comprehending why GDP fluctuates cyclically in the short-run and what policies the government can adopt in situations where a market economy is in the grips of recessionary or inflationary forces. That economics still gets some respect in societies today is all on account of the Keynesian theory. Keynesian measures are still the only recourse in market economies plagued with macroeconomic instability. Nowhere is it better exemplified than in the USA and Europe still grappling with recessionary forces using large-scale fiscal and monetary policy measures. Ironically, it is in these countries that the Keynesian theory, as we have explained in Part II of this book, received its shabbiest and most dishonest treatment. It will be quite clear from Part II of this book that the powers that be in these countries instead of unravelling and facing the truth boldly are bent on distorting the truth to their own peril as the recent macroeconomic catastrophe in their own turf amply demonstrates. CKM has two sides: a demand side and a supply side. We shall discuss both of them in turn. Sections 7.2 and 7.3 will focus on the demand side and the supply side respectively. Section 7.4 will bring the two sides together and present the full CKM and explain its working. Section 7.5 will contain the concluding remarks.

7.2 COMPLETE KEYNESIAN MODEL: AGGREGATE DEMAND IS-LM model captures only a part of the Keynesian theory of income determination. It represents only its demand side and yields the aggregate demand function. Let us illustrate. The equations of the IS and LM are given by Y

C (Y  T )  I (i)  G 230

(7.1)

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231

M (7.2) k (Y )  m(i) P In this chapter, we denote the interest sensitive component of the demand for real balance function by m(i), since L denotes labour here. We can solve (7.1) and (7.2) for the equilibrium values of i and Y as functions of P, given

and

the exogenous variables such as T , G, M and the parameters of the consumption, investment and money demand functions. These functions are given by Y

and

i

Y D ( P; G, T , M )

i(P; G, T , M )

(7.3) (7.4)

Equations (7.3) and (7.4) give respectively the values of Y and i that keep both the goods and the money markets in equilibrium corresponding to every P, given the exogenous variables of the IS-LM model. Equation (7.3) is referred to as the aggregate demand function. Let us explain. It is assumed in the IS-LM model that i is highly flexible and it instantaneously clears the money market. This implies that, corresponding to any given (P, Y), the interest rate, i, will immediately settle down to the level that clears the money market at the given (P, Y). Thus, if, at any given P producers produce the level of Y that is yielded by (7.3) corresponding to the given P, the interest rate, i, will immediately settle down to the level yielded by (7.4) corresponding to the given P. At the given (P, i) both the goods market and the money market will be in equilibrium. Therefore the produced Y will exactly meet the aggregate demand for goods and services equilibrating the goods market. This explains why (7.3) is called the aggregate demand function. Since, specific forms of the consumption, investment and money demand functions are not known, we cannot solve (7.1) and (7.2) explicitly for the equilibrium values of Y and i. However, we can illustrate the solution graphically. This we shall do with the help of Figure 7.1. Consider the IS and LM(P0) schedules in the upper panel of Figure 7.1. LM(P0) is the LM that corresponds to a given P, P0. They intersect at (Y0, i0). Thus (Y0, P0) is a point on the aggregate demand schedule labelled AD in the first quadrant in the lower panel of Figure 7.1. It represents (7.3). In the second quadrant iP schedule represents (7.4). Thus (i0, P0) is a point on the iP schedule in the lower panel of Figure 7.1. Let us now consider a reduction in P by dP. At every (i, Y) it will reduce demand for money by [k(Y) + m(i)]dP < 0 (since dP < 0) and thereby generate excess supply of money of –[k(Y) + m(i)]dP > 0. Corresponding to any given i, aggregate output, Y, therefore has to be raised so that demand for money goes up by the amount of the excess supply and thereby equilibrates the money market. The LM therefore shifts horizontally to the right. The amount of the horizontal shift can be derived quite easily. The demand for money, given i, goes up by k¢ per unit increase in Y. Therefore, to raise demand for money by –[k(Y) + m(i)] dP > 0, Y has to be raised by {–[k(Y) + (m(i)] dP/k¢} > 0. At (Y0, i0), for example, the amount of the horizontal shift of the LM is given by {–[k(Y0) + m(i0)] dP/k¢(Y0)} > 0. The IS curve, however, remains unaffected following the given reduction in P. Explain it yourself. A reduction in P therefore lowers the equilibrium level of i and raises the equilibrium value of Y. The aggregate demand (AD) schedule is therefore downward sloping, while the iP schedule is positively sloped as shown in the lower panel of Figure 7.1. Following this reduction in P by dP to, say, P1, the equilibrium values of Y and i become Y1 and i1 respectively. (Y1, P1) is therefore another point on AD and (i1, P1) is another point on iP. The horizontal stretch of the

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Figure 7.1 Derivation of the aggregate demand function.

LM corresponding to i2 too gets extended following a reduction in P. The amount by which it gets extended following a reduction in P from P0 to P1 is given by {–[k(Y–1) + m(i2)] dP/k¢(Y–1)} > 0. When P falls to P2, the horizontal stretch of the LM gets extended to such an extent that the given IS intersects the LM corresponding to P2, labelled LM(P2) in Figure 7.1, just at the right-hand end of its horizontal stretch represented by the point (i2, Y2). (Y2, P2) is obviously a point on the AD in the lower panel of Figure 7.1. If P is lowered further, the horizontal stretch will get extended again. Thus if P is lowered below P2, the (i, Y) given by the point of intersection of the IS and the LM corresponding to the new P lower than P2 will remain the same as the one that equilibrates the goods market and the money market at P2. Thus, for every P £ P2 the goods market and the money market will be in equilibrium at (i2, Y2). At such values of P therefore both the AD and the iP schedules in the lower panel of Figure 7.1 will be vertical at Y2 and i2 respectively. EXERCISE 7.1 (a) Consider the following equations C = 0.8(1 – t)Y, t = 0.25, I = 900 – 50i, G = 800, L = 0.25Y – 62.5i, M = 500. Derive the aggregate demand function. Explain it and plot it in a graph. (b) Derive the slope of the AD schedule mathematically and explain it.

Complete Keynesian Model

7.2.1

233

Shifts in AD

The position of the aggregate demand function depends upon the parameters of the consumption, investment and demand for real balance functions and also upon the government’s policy parameters, G, T and M . Changes in any of these parameters will produce shifts in the aggregate demand function. Consider, for example, an exogenous increase in money supply. How will it affect AD and iP schedules? Following an increase in M by, say dM , there emerges an excess supply of money of dM at every (i, Y) on the upward sloping stretch of the initial LM. The money market will therefore be in equilibrium if, given i, Y is raised to such an extent that demand for money goes up by dM . This happens when, corresponding to every i aggregate output, Y, goes up by (dM/ k„) . Thus the upward sloping part of the LM shifts to the right by (dM / k „) . Let us now focus on the horizontal stretch of the initial LM. At every (i, Y) on the horizontal stretch people now hold an extra money balance of dM and they do so willingly. So the money market remains in equilibrium at every such point. So the horizontal stretch of the initial LM becomes a part of the new LM as well. Let us now focus on the (i, Y) at the righthand end of the horizontal stretch of the initial LM. Let us denote it by (i2, Y2). Initially, people did not have any ideal money balance at (i2, Y2). But now they have idle money balance of dM . So, now, if Y rises from Y2, with i remaining unchanged at i2, the rise in demand for money that the increase in GDP gives rise to will be met from the idle money balance at the same i. So the money market will continue to remain in equilibrium at i2 despite the increase in Y as long as there exists idle money balance. The idle money balance will be fully absorbed when Y rises from Y2 by (dM / k „(Y2 )) . The horizontal stretch in the new LM will therefore get extended to the right by this amount and correspond as before to i2. At the right-hand end of dM the horizontal stretch of the new LM values of i and Y will be i2 and Y2  respectively. k „(Y2 ) The situation is shown in the upper panel of Figure 7.2, where the initial LM corresponding to P0 is labelled LM(P0), while the LM labelled LM(P0, dM) is the new LM corresponding to P0 and the new larger money supply. The IS now cuts LM(P0, dM) at a larger Y and a lower i. The downward portion of the AD schedule presented in the first quadrant of the lower panel of Figure 7.2 therefore shifts to the right following the increase in money supply. But the upward sloping portion of the iP schedule shown in the second quadrant of the lower panel of Figure 7.2 shifts inward. Let us now focus on the vertical portions of the AD and iP schedules. The IS in the upper panel of Figure 7.2 cuts the LM(P2), the LM corresponding to P2 in the initial situation, at the right-hand end point of its horizontal stretch. So both initial AD and initial iP were vertical for P £ P2. The new LM corresponding to P2 is labelled LM(P2, dM) in the upper panel in Figure 7.2. It has a larger horizontal stretch corresponding to i2. Hence the given IS cuts it inside its horizontal stretch at (Y2, i2). At (Y2, i2) both the goods market and the money market are in equilibrium. Hence (Y2, P2) is a point on the vertical portion of the new AD as well. So is (i2, P2) on the vertical portion of the new iP schedule. It is clear from the point of intersection of the IS and LM(P2, dM) in the upper panel of Figure 7.2 that the given IS will intersect the LM in the new situation of larger money supply at the right-hand end

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Figure 7.2 Derivation of the aggregate demand function.

point of its horizontal stretch at a P > P2. This P is labelled P3. Thus the vertical segments of both the new AD and the new iP labelled AD1 and iP1 respectively will be larger as shown in the lower panel of Figure 7.2. Find out the magnitude of (P3 – P2). EXERCISE 7.2 Derive the magnitudes of horizontal shifts in the AD and iP schedules mathematically and graphically following an increase in (i) G and (ii) T .

7.3

COMPLETE KEYNESIAN MODEL: AGGREGATE SUPPLY

Assume for simplicity that there are a large number of firms producing goods and services using capital and labour. However, the focus here is on the short-run. Hence the stock of capital of every firm is given. Markets for both the produced goods and services and labour are perfectly

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competitive. Hence they are price takers in both the markets. The production function of the firms is given by (7.5) Y = F(L, K ) FL > 0 and FLL < 0 where L denotes labour and K the fixed stock of capital. The production function states that the marginal productivity of labour is positive and it diminishes with an increase in employment. Firms are profit maximisers. Their profit is given by P = PF(L, K ) – WL – A where P º profit, W º the money wage rate and A º the fixed cost consisting of fixed interest charges on past loans and depreciation. In the profit function, P and W are given to the firms since they are price takers in all markets. K and L are also given. Firms therefore choose only L to maximize profit. There profit-maximizing exercise is formally written as max 3 L

PF ( L, K )  WL  A

Carrying out the above maximization exercise, we get the following first-order condition for profit-maximization: ˜3 (7.6) PFL ( L, K )  W 0 ˜L The first-order condition states that, if there exists a L, say L*, such that the firm’s profit is maximized at that L, then (¶P/¶L) corresponding to that L is zero. If (¶P/¶L) > ( 0) as L is raised (lowered) from its lower (higher) value to the initial value. (Note that when L is lowered from its higher value to the initial value, dL < 0). Two points emerge clearly from the above discussion. First, if at any given L marginal productivity of labour is different from the real wage rate, profit can be raised by changing the level of L. Therefore, at such a level of L, profit cannot be at its maximum level. Hence, at the level of L at which profit is maximum, the marginal productivity of labour should be equal to the real wage rate. Second, if at a level of L at which the marginal productivity of labour equals the real wage rate, profit need not necessarily be at its maximum level. It may be at its minimum level as well. (Prove this point yourself.) If at such a level of L the marginal productivity of labour diminishes with an increase in L, firms’ profit is maximized at the given L. On the other hand, if at a level of L at which the marginal productivity of labour equals the real wage rate, the marginal productivity of

˜2 F

! 0 ), profit at such a level of L is at its minimum. ˜ L2 (Explain this point yourself.) This explains why firm’s profit achieves a local maximum at the value of L at which both the first-order and the second-order conditions are satisfied. If there is a unique L at which the first-order condition is satisfied and if the second-order condition is satisfied at every L, i.e. if (¶2F/¶L2) < 0 at every L, then firm’s profit achieves a global maximum at the L at which the first-order condition is satisfied. This condition may be explained with the help of Figure 7.3 where values of F¢(L) and (W/P) are plotted against L. The F¢(L) schedule gives the value of F¢(L) corresponding to every L, while the horizontal line gives the value of the given real wage rate corresponding to every L. The first-order condition is satisfied at a unique L labelled L*, which corresponds to the point of intersection of the two schedules. When the second-order condition is satisfied at every L, the F „( L , K ) schedule is negatively sloped throughout as shown in Figure 7.3. It implies that at every L less (higher) than L* the marginal productivity of labour, F „( L , K ) , is greater (smaller) than the marginal cost of hiring one unit of labour, (W/P). If L is raised (lowered) from such a level by 1 unit, firm’s revenue in real terms goes up (falls) by (¶F/¶L), while its cost in real terms rises (declines) by a smaller (larger) quantity, (W/P). Hence its profit will go up by [(¶F/¶L) – (W/P)] > 0 ([(W/P) – (¶F/¶L)] > 0). Thus, at every level of employment less (higher) than its profit-maximizing level, the firm will be able to raise its profit by hiring more (less) labour. This explains our proposition. We can solve (7.6) for the profit-maximizing level of employment or labour demand, LD, as a function of real wage rate, given K and the production function. It is given by LD = LD(w); LD ¢ < 0 (7.8)

labour rises with an increase in L (i.e. if

where

w º real wage rate. The labour demand function is shown in Figure 7.4.

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Figure 7.3 Derivation of the profit-maximizing level of employment.

Figure 7.4

Labour demand schedule.

Let us now explain why LD¢ < 0. This follows straightway from Figure 7.3, which shows that the higher the real wage rate, the less is the profit-maximizing level of employment. We can derive this result mathematically also. Denoting the profit-maximizing level of employment by LD and putting it into (7.6), we get the following identity:

W P Taking total differential of the above identity, we get FL ( LD , K ) œ

FLL dLD

ÈW Ø dÉ Ù Ê PÚ

(7.9)

It is quite easy to explain the above equation. Following a given change in the real wage rate, there is a new optimum. In the initial optimum situation, the marginal productivity of labour is

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equal to the initial real wage rate. In the new optimum situation, the marginal productivity of labour is equal to the new real wage rate. Therefore, the change in the marginal productivity of labour from the initial optimum situation to the new optimum situation is equal to the change in the real wage rate from the initial optimum situation to the new optimum situation. The marginal productivity of labour changes from the initial optimum situation to the new optimum situation solely because of the change in the level of employment from the initial optimum situation to the new optimum situation. The change in the level of employment from the initial optimum situation to the new optimum situation is given by dLD. Hence, the LHS of (7.9) gives the change in the marginal productivity of labour from the initial optimum situation to the new optimum situation. The RHS of (7.9) gives the change in the real wage rate from the initial equilibrium situation to the new one. This explains why the two sides of (7.9) are equal. Equation (7.9) contains only one unknown, dLD, since d(W/P) is known by hypothesis and FLL ( L, K ) is also known and constant for the following reason. We know the production function and FLL ( L, K ) are evaluated at the initial value of L and K , which are also known. Hence FLL ( L, K ) is known and constant. We therefore get the value of dLD by solving (7.9). Solving (7.9), we get 1 ÈW Ø dLD d FLL ÉÊ P ÙÚ Þ

dLD ÈW Ø dÉ Ù Ê PÚ

1 0 FLL

(7.10)

EXERCISE 7.3 Explain the RHS of (7.10), i.e. explain why the RHS of (7.9) gives the value of

dLD . ÈW Ø dÉ Ù Ê PÚ

However, for analytical convenience, we shall not work with (7.8). We shall rewrite (7.8) in the following manner to suit our purpose. We shall first rewrite the first-order condition, (7.6), as (7.11) W PFL ( L , K ) Equation (7.11) gives the demand price of labour in terms of money. More precisely, it gives corresponding to every L, given P, the value of the money wage rate W at which the given L maximizes producers’ profit and is therefore demanded. In Figure 7.5, P0 FL ( L , K ) schedule represents (7.11) in the (L, W) plane where L is measured on the horizontal axis and W and the value of marginal productivity of labour are measured on the vertical axis. It gives corresponding to every L the value of the marginal productivity of labour evaluated at the given value of P, P0. It therefore shows corresponding to every L the value of the money wage rate at which the given L maximizes profit and is therefore demanded, when P is fixed at P0. Following a given increase in P from P0, the value of marginal productivity of labour schedule shifts upward.

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239

Figure 7.5 Demand price of labour.

EXERCISE 7.4 Suppose the production function is given by LB K 1B . Derive the value of marginal productivity of labour schedule when K 10 and P = 1. Plot it in a graph. Explain why it gives corresponding to every L its demand price. What happens to this schedule, when P is raised from 1 to 2?

7.3.1

Supply Price of Labour

Keynes accepted the classical labour supply function given by (6.12) in the previous chapter, but he regarded it as a notional supply curve, which the workers want to attain, but they normally cannot. This means that in a market economy in normal circumstances, the real wage rate that prevails is higher than the full employment real wage rate so that workers cannot sell as much labour as they want to giving rise to excess supply of labour or involuntary unemployment. In classical theory, the real wage rate cannot stay above the full employment real wage rate because of the assumption of perfect flexibility of money wage rate. In the face of excess supply of labour, in the classical theory, money wage rate falls reducing the real wage rate to the full employment level instantaneously. This does not happen in the Keynesian theory because Keynes assumes that money wage rate is rigid or at least inflexible downward so that the equilibrating mechanism that works in the classical model does not work in Keynes’ and the Keynesian system as a result can be in equilibrium with excess supply or involuntary unemployment in the labour market. In the developed market economies, Keynes pointed out, the labour market is not perfectly competitive and money wage rates are determined through negotiations between trade unions and employers. These negations take place in different firms separately and independently. The wage contracts the two parties agree on are usually long period contracts of two to three years. The money wage rate fixed by the contracts cannot be revised until the contracts expire. As a result, if in any given short period, there emerges excess supply of labour, the money wage rates, as they are fixed by long period contracts, cannot fall to clear the labour market. This prevents the workers in the short run in normal circumstances in developed market economies from operating on their planned labour supply schedule. Thus in the Keynesian theory, money wage rate is taken to be rigid as given by

W

W

for

L £ Lf

(7.12)

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In (7.12) Lf denotes the full employment level of employment, which corresponds to the point of intersection of the classical labour demand and classical labour supply schedules. Note that the classical labour demand function and the Keynesian labour demand function are identical. Keynes accepted the classical full employment level of employment and the classical full employment level of output as respectively the maximum levels of employment and output possible in market economies. However, he showed that, usually, in the market economies levels of output and employment get stuck below their respective full employment levels. Let us now see how he demonstrates that. However, before going into that, let us explain (7.12). It states that the workers are willing to supply as much labour as is demanded up to the full employment level at the fixed wage rate W . In other words, the labour supply function is perfectly elastic at the fixed money wage rate as long as L £ Lf. LSLS, in Figure 7.6, represents the Keynesian labour supply function, (7.12).

Figure 7.6

Keynesian labour supply function.

Obviously, the labour market in the CKM is in equilibrium when demand price of labour given by (7.11) equals the supply price of labour given by (7.12). Labour market equilibrium is therefore given by (7.13) W PFL ( L , K ) Let us explain (7.13). If at any given L the demand price of labour equals its supply price, W , producers’ profit at W is maximized at the given L and therefore their demand for labour exactly equals the given L. Hence the labour market is in equilibrium at the given L. If we fix the value of P, we can solve (7.13) for L, i.e. we can solve (7.13) for the labour market equilibrium value of L as a function of P, given W and K . Thus, we have L

L ( P; W )

LP ! 0

(7.14)

The solution of (7.13) or derivation of (7.14) is shown in the lower panel of Figure 7.7 where the equilibrium value of L at a given P, P0, corresponds to the point of intersection of the inverse labour demand schedule, P0 FL ( L, K ) and the inverse labour supply schedule, LSLS.

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241

The equilibrium value of is L labelled L(P0). At any other L, say L0 < L(P0) (L0 > L(P0)) demand price of labour, P0 FL ( L0 , K ) ! ()W . If L is raised (lowered) from L0, per unit increase (decrease) in L value of output or total revenue will rise (fall) by P0 FL ( L , K ) , while cost will increase (decrease) by W . Since P0 FL ( L0 , K ) ! () W , per unit increase (decrease) in L profit will go up by P0 FL ( L0 , K )  W (W  P0 FL ( L0 , K )) . Hence producers will gain by raising (lowering) L from L0. If P goes up from P0 to, say, P1, the value of marginal productivity of labour will be higher at every L. So P1 FL ( L, K ) schedule will, as shown in the lower panel of Figure 7.7 will lie above the P0 FL ( L, K ) schedule. Hence the labour market equilibrium value of L will rise. Thus the labour market equilibrium value of L is an increasing function of P. This explains the sign of the derivative of (7.14). Substituting (7.14) into the production function, we get aggregate planned output of the producers or aggregate supply of goods and services as an increasing function of P. This is the aggregate supply function of the Keynesian model. It is given by Y

Y S ( P; W )

Figure 7.7

YPS ! 0 „

(7.15)

Labour market equilibrium.

Derivation of (7.15) from (7.14) can be illustrated using Figure 7.7, where in the upper panel the schedule labelled F(×) represents the production function. The labour market equilibrium value of Y or the aggregate supply on the production function corresponds to the labour market equilibrium L as derived in the lower panel. Thus at P = P0, the labour market equilibrium value of L, as shown in the lower panel, is L(P0) and, accordingly, the labour market equilibrium Y

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is the one that corresponds to L(P0) on the production function in the upper panel. This Y is labelled Y(P0). Similarly, at P = P1 the labour market equilibrium values of Y and P are labelled L(P1) and Y(P1) respectively in Figure 7.7. The labour market equilibrium values of L and Y rise with the increase in P. When P rises sufficiently high the labour market equilibrium values of L and Y become equal to their respective full employment values. At such P labelled P in Figure 7.7 the inverse labour demand schedule PFL ( L , K ) intersects the horizontal stretch of the labour supply schedule at its right-hand end point. At every P higher than P the inverse labour demand schedule will intersect the labour supply schedule at its vertical portion. Thus, the aggregate supply schedule given by (7.15) will be upward sloping for 0 … P … P and vertical for P ! P . The aggregate supply schedule representing (7.15) and labelled AS is shown in Figure 7.8.

Figure 7.8

Aggregate supply function.

7.4 EQUILIBRIUM IN THE COMPLETE KEYNESIAN MODEL Obviously, the Keynesian model is in equilibrium when aggregate demand and aggregate supply are equal, i.e. when the following equation is satisfied: Y D ( P; G, T , M )

Y S ( P; W )

(7.16)

We can solve (7.16) for the equilibrium value of P. Corresponding to this P, the Y the producers produce equilibrates not only the labour market but also the goods and the money markets. Substituting this equilibrium value of P either in the aggregate demand function, (7.3), or in the aggregate supply function, (7.15), we get the equilibrium value of Y. Again, substituting this equilibrium value of Y in (7.4) and in the production function, (7.5), we shall get respectively the equilibrium values of L and i. Substituting the equilibrium values of i and Y in the consumption and investment functions, we get the equilibrium values of consumption and investment. The solution of the equilibrium values of the endogenous variables of the CKM is shown in Figure 7.9, where in Panel A in the first quadrant AD and AS intersect at (Y0, P0). In the second quadrant, the equilibrium value of i labelled i0 corresponds to P0 on the iP schedule. In Panel B, the LM corresponding to the equilibrium P, P0, intersects the IS at (Y0, i0). In the lower part of Panel C,

Complete Keynesian Model

Figure 7.9

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Equilibrium in CKM.

the inverse labour demand function, P0 FL ( L, K ), that obtains in equilibrium intersects the horizontal labour supply function at L0. Y0 corresponds to L0 on the production function labelled F(×) in the upper portion.

7.4.1

Equilibrium with Involuntary Unemployment

Let us now focus on the most important feature of Keynesian equilibrium. The real wage rate that prevails in the equilibrium depicted in Figure 7.9 is (W / P0 ) . Note that the labour demand

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functions are identical in the classical and Keynesian models. The levels of real wage rate, employment and output that correspond to the point of intersection of the classical (which is also Keynesian) labour demand function and the classical labour supply function are respectively referred to as full employment levels of real wage rate, output and employment in both the classical and Keynesian models and they are denoted by wf, Lf and Yf. In Figure 7.9, at the equilibrium real wage rate, (W / P0 ) , the amount of labour demanded is L0 < Lf. Clearly then, (W / P0 ) >

wf and there is excess supply in the labour market. The workers are unable to sell as

much labour as they want to at the prevailing real wage rate. Hence there is involuntary unemployment in equilibrium. The amount of involuntary unemployment in Keynesian theory is measured by the shortfall of the equilibrium level of employment from the maximum level of employment a market economy can achieve. This maximum attainable level of employment is obviously Lf. Hence the amount of involuntary unemployment that exists at the equilibrium depicted in Figure 7.9 is (Lf – L0). The model is in equilibrium despite the existence of excess supply of labour because of the assumption that the money wage rate is rigid at W . This is the reason why money wage rate does not fall despite the existence of excess supply of labour. If it was not rigid by assumption, it would have fallen and thereby pulled down the real wage rate to the market clearing level. Note that the involuntary unemployment that normally exists in equilibrium in the CKM can be removed by raising the level of aggregate demand to a sufficiently high level. Suppose, for example, the aggregate demand schedule in Figure 7.9 is given not by AD but by AD¢ that cuts the AS at, say (Yf, P5), located on its vertical portion. In this context, we must mention an important assumption of Keynes. He assumed that money wage rate is rigid as long as the level of employment is less than the full employment level. However, once the level of employment attains the full employment level, the workers attain their planned or notional labour supply schedule. This happens when the real wage rate, given by

W becomes equal to its full P

W below wf, there emerges excess demand P for labour. In such situations, Keynes argued, firms compete with one another for scarce labour and the money wage rate becomes fully flexible. It rises until the real wage rate equals wf. From Figures 7.7, 7.8 and 7.9, it is clear that the inverse labour demand schedule corresponding to

employment level,

wf . If P rises further lowering

P intersects the Keynesian labour supply schedule at the right-hand end of its horizontal stretch. This implies that (W / P ) X f . It is clear from Figure 7.9 that P5 > P . Hence,

(W / P5 )  X f . At this real wage rate, obviously, producers will want to employ more labour than Lf, while the supply of labour will be less than Lf creating excess demand for labour. Money wage rate in this situation, according to Keynes, will rise to pull up the real wage rate to its full employment level. From the above it follows that the involuntary unemployment in CKM can be removed by raising aggregate demand for goods and services. In other words, the involuntary unemployment arises in equilibrium in the CKM on account of inadequacy of aggregate demand.

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245

EXERCISE 7.5 Derive the demand for labour function when production function of firms is given by Y = K 0.5 L0.5. Suppose the classical labour supply function is given by LS = 2w. Derive the values of Lf, Yf and wf. Suppose the money wage rate is fixed at W = ` 10. Derive the aggregate supply function. Suppose the aggregate demand function is given by Y = 100 – P. Derive the equilibrium values of Y, P, i and L. What is the real wage rate? Derive the value of the autonomous component of the aggregate demand function for which the real wage rate at W = ` 10 is the full employment real wage rate. If the value of the autonomous component of aggregate demand function goes up further, how will W and P behave? More precisely, derive W and P as functions of the value of the autonomous component of aggregate demand when it is so large that there is full employment equilibrium.

7.5

WORKING OF THE CKM: COMPARATIVE STATIC EXERCISES

We shall now explain the working of the CKM by carrying out a couple of comparative static exercises. Let us first examine how an increase in government expenditure financed by internal borrowing affects the endogenous variables in the CKM. Internal borrowing here means borrowing by selling bonds in the domestic market to the public.

7.5.1

Effect of an Increase in Government Consumption Financed by Internal Borrowing

We shall first work out graphically and then derive the results mathematically. For graphical analysis first we have to focus on how AD and AS schedules are affected by an increase in government expenditure financed by internal borrowing. Consider the AD schedule first. It is derived from the IS-LM diagram. An increase in government expenditure financed by internal borrowing does not have any impact on the LM schedule. This is for the following reason. The position of the LM schedule is determined by the price level, P, supply of money, M and parameters of the money demand function. Sale of bonds by the government in the market leaves these variables unaffected. So LM remains undisturbed. The increase in G, however, affects the IS. Suppose G goes up by dG. It will create an excess demand for goods and services by the amount dG at every (Y, i) on the initial IS. At every i therefore the goods market will be in equilibrium at a larger Y. Accordingly, the IS will shift rightward. Hence at every P the goods and the money markets will be in equilibrium at a higher levels of Y and i. The situation is shown in Figure 7.10, where the LM schedule corresponding to a given P, P0, labelled LM(P0) intersects the initial IS at (Y0, i0) and the new IS, labelled IS1, which is to the right of the initial IS, at a larger (Y, i), labelled (Y1, i1). Thus, at P0 the level of Y on the initial AD, labelled AD0 in Figure 7.10, is Y0, while it is Y1 on the new AD, labelled AD1 in Figure 7.10. Similarly, at P0 the levels of i on the initial and the new iP schedules, labelled iP0 and iP1 in Figure 7.10, are i0 and i1 respectively. Let us now focus on the vertical portion of the AD schedule. We find from Figure 7.10 that the initial IS cuts the LM(P1) at the right-hand end point of its horizontal stretch. Therefore for P £ P1, the initial AD is vertical. (Explain this point

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Figure 7.10

Effect of an increase in G financed by internal borrowing.

yourself.) However, the new IS, as it lies to the right of the initial IS, cuts LM(P1) at its upward sloping part. It will obviously cut an LM corresponding to a lower P at the right hand end point of its horizontal stretch. This LM corresponds to P2 < P1 in Figure 7.10 and is labelled LM(P2). The value of Y that equilibrates the goods and the money markets at P2 following the increase in government expenditure is Y2, which is larger than the value of Y that equilibrates the goods and the money markets at P1 in the initial situation. Thus, the vertical portion of the new AD corresponds to a lower P, P2, and a higher Y, Y2, as shown in Figure 7.10. Let us now focus on the AS schedule, which is derived from (7.5) and (7.13). Its position is determined by W , K and the parameters of the production function. As government expenditure or the stock of bonds held by the public does not figure anywhere in the production function or the labour demand and the labour supply functions, they have no role to play in determining the position or shape of the AS. Thus, the increase in government expenditure financed by internal borrowing leaves the AS schedule undisturbed. Since AD shifts to the right and AS remains unaffected, in the new equilibrium values of both Y and P will be larger. The situation is shown in Figure 7.10 where the new AD, AD1 intersects AS at (Y3, P3) > (Y0, P0). The state

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247

of the goods market and the money market in the new equilibrium is given by the point of intersection of the LM corresponding to P3 labelled LM(P3) intersects the new IS, IS1, at (Y3, i3). i3 is clearly the new equilibrium i. It is necessarily higher than the initial equilibrium i on account of being given by the point of intersection of a higher IS and a higher LM. Figure 7.11 captures the state of the labour market in the initial and the new equilibrium situations. In the new equilibrium P3 F ( L, K ) schedule intersects the horizontal labour supply schedule, LSLS, at L3, which corresponds to Y3 on the production function, labelled F(×). The result yielded by the graphical analysis is that, following an increase in government expenditure financed by internal borrowing, GDP, employment, price level and interest rate go up. We shall now derive this result mathematically.

Figure 7.11

Effect of an increase in G financed by internal borrowing on labour market.

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Mathematical derivation of the result The key equations of the CKM are given by the goods market equilibrium condition, (7.1), the money market equilibrium condition, (7.2), the production function, (7.5), and the labour market equilibrium condition, (7.13). These four equations contain the four key endogenous variables of the CKM, namely Y, i, P and L. We shall use these four key equations to derive the impact of an increase in G financed by internal borrowing on the four key endogenous variables of the CKM mentioned above. We do this in the following steps. First, denoting their equilibrium values of the four key endogenous variables by Y*, i*, P* and L* and substituting them into (7.1), (7.2), (7.5) and (7.13), we convert them into the following identities: Y * œ C (Y *  T )  I (i*)  G

(7.17)

M œ P*[ k (Y *)  m (i*)]

(7.18)

Y * œ F ( L*, K ); FL ! 0

and

FLL  0

W œ P* FL ( L*, K )

(7.19) (7.20)

Next, taking total differential of these four identities treating all exogenous variables other than G as fixed, we have

dY * œ C „dY *  I „di*  dG 0 = P*k¢dY* + P*m¢di* + [k(Y*) + m(i*)] dP* dY* = FLdL* 0 = P*FLLdL* + FLdP*

(7.21) (7.22) (7.23) (7.24)

Let us now explain Eqs. (7.21), (7.22), (7.23) and (7.24). Following an increase in G by dG financed by internal borrowing, the four endogenous variables, Y, i, P and L change from the initial equilibrium to the new equilibrium by dY*, di*, dP* and dL* respectively. These quantities must satisfy Eqs. (7.21)–(7.24). Let us explain. First, focus on (7.21). The goods market should be in equilibrium in both the initial equilibrium and the new equilibrium. Therefore, the change in Y* from the initial equilibrium to the new equilibrium, given by dY*, must be equal to the change in aggregate demand for goods and services from the initial equilibrium to the new equilibrium. Aggregate demand for goods and services changes from the initial equilibrium to the new equilibrium because of the changes in G , Y* and i* by dG , dY* and di* respectively. The RHS of (7.21), therefore, gives the change in aggregate demand for goods and services from the initial equilibrium to the new equilibrium. Clearly, it should be equal to dY*. This explains (7.21). Note that (7.21) contains only two unknowns, namely dY* and di*. This is because dG is given. We have ourselves fixed the value of dG to examine how this given increase in G affects the endogenous variables of CKM. C¢ and I¢ are evaluated at the initial equilibrium values of the disposable income and interest rate. Hence they are constant and known. Similarly, the money market must also be in equilibrium in both the initial and the new equilibrium situations. Therefore, the change in money supply from the intial equilibrium to the new equilibrium, which is zero, should be equal to the change in demand for money from the

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249

initial equilibrium to the new equilibrium. Demand for money changes from the initial equilibrium to the new equilibrium on account of changes in Y*, i* and P* from the initial equilibrium to the new equilibrium by dY*, di* and dP* respectively. Hence, the expression on the RHS of (7.22) gives the change in demand for money from the initial equilibrium to the new equilibrium. This explains why the two sides of (7.22) must be equal. Equation (7.22) also contains only three unknowns, viz., dY*, di* and dP*. Explain this point yourself. The production function must also be satisfied in both the equilibrium situations. Producers change aggregate production or GDP from the initial equilibrium to the new equilibrium by dY*. They do so by changing the employment of labour alone by dL*. Hence dY* should be equal to the marginal productivity of labour evaluated at the initial ( L*, K ) times dL*. This explains (7.23). Finally, labour market is also in equilibrium in both the equilibrium situations. Hence the change in the supply price of labour from the initial equilibrium to the new equilibrium, which is zero, must be equal to the change in the demand price of labour from the initial equilibrium to the new equilibrium. The latter changes on account of changes in P* and L* by dP* and dL* respectively. Hence the expression on the RHS of (7.24) gives the change in the demand price of labour from the initial equilibrium to the new equilibrium. This explains (7.24), which contains only two unknowns, namely dL* and dP*. Explain this point yourself. We can therefore solve Eqs. (7.21)–(7.24) for the four unknowns, dY*, di*, dP* and dL*. We shall solve them in the following manner. Solving (7.23) for dL* in terms of dY* and substituting in (7.24), we rewrite it as 0

P*

FLL dY *  FL dP* FL

(7.25)

We can now solve (7.21), (7.22) and (7.25) for dY*, di* and dP*. Solving them and rearranging terms, we get

dY *

dG Ë Û Ì Ü 1 Ì Ü 1  ÌC „  I „ Ü ÎÑ  F ÞÑ Ü Ì (  mi „ ) Ï k „  (k  m) LL ß Ì FL2 àÑ ÜÝ ÐÑ Í

(7.26)

Let us explain the RHS of (7.26). The numerator, dG, gives the amount of excess demand for goods and services that emerges in the initial equilibrium situation, i.e. at the initial equilibrium (Y, i, L, P), following the increase in G by dG. In response to that, P starts rising, which in turn induces producers to expand production. This process of increase in P and Y continue until the excess demand of dG is removed through the rise in Y. The denominator gives the reduction in excess demand for goods and services per unit increase in Y. With per unit increase in Y, supply goes up by unity. But at the same time demand goes up too. Consumption demand rises directly by C¢. To induce producers to raise Y by unity, P has to rise by

FL2 . Let us explain  FLL P*

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this point. To raise Y by unity, as we find from the production function, (7.5), L has to increase

1 Ø È by (1/FL). This will lower the value of the marginal productivity of labour by É  P* FLL Ù F Ê LÚ in absolute terms. (Work it out yourself.) Since value of the marginal productivity of labour falls below W by the aforementioned quantity, producers will not be interested to raise employment by (1/FL). To induce them to do so, P has to rise to make the value of the marginal productivity of labour equal to W at this higher level of employment. In other words, to induce producers to raise employment by one unit, P has to rise to such an extent that the value of the marginal 1 Ø È productivity of labour at this higher level of employment rises by É  P* FLL Ù . Since the F Ê LÚ value of the marginal productivity of labour is given by P*FL, per unit increase in P*, the value of marginal productivity of labour, given the level of employment, rises by FL. To raise the value of marginal productivity of labour by

1 Ø È ÉÊ  P* FLL F ÙÚ , P has to rise by L

1 È 1 Ø È 1 Ø  P* FLL  P* FLL 2 Ù . As Y rises accompanied by the rise in P needed to make É Ù É FL Ê FL Ú Ê FL Ú the increase in Y profitable, the demand for money goes up on account of the increase in both Y and P. The demand for money goes up due to both the unit increase in Y and the rise in P Ë  FLL Û by Ì k „  (k  m) Ü , creating this much of excess demand for money. This in turn will FL2 ÝÜ ÍÌ induce i to rise to the market clearing level. Let us now compute by how much i will rise. The demand for money falls in absolute value by m¢ per unit increase in i. To reduce money demand

Ë  FLL Û  FLL Û 1 Ë by Ì k „  (k  m) , therefore, i has to rise by k „  (k  m) Ì Ü . This will reduce 2 Ü m „ ÍÌ FL ÜÝ FL2 ÝÜ ÍÌ  FLL Û I„ Ë investment demand by Ì k „  (k  m) Ü . Thus, per unit increase in Y, aggregate supply „ m ÌÍ FL2 ÜÝ goes up by unity, but aggregate demand also goes up in the net by

 FLL Û ÑÞ I„ Ë ÑÎ Ü ß . Therefore, per unit increase in Y as P and i adjust along with ÏC „  m „ Ì k „  (k  m) FL2 ÝÜ àÑ ÍÌ ÐÑ the rise in Y to keep the labour market and the money market in equilibrium, excess demand Ë ÎÑ  FLL Û ÞÑ Û I„ Ë k „  ( k  m) for Y falls by Ì1  ÏC „  Ì Ü ß Ü . Hence excess demand falls by dG , when m „ ÌÍ FL2 ÜÝ Ñà ÜÝ ÌÍ ÑÐ Ë ÎÑ  FLL Û ÞÑ Û I„ Ë k „  (k  m) Y rises by dG Ì1  ÏC „  Ì Ü ß Ü . This explains (7.26). m „ ÍÌ FL2 ÝÜ àÑ ÜÝ ÌÍ ÐÑ

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Intuitive explanation of the result How does the economy move from the initial equilibrium to the new equilibrium? Following the increase in G financed by internal borrowing, there emerges excess demand for goods and services. Dissatisfied buyers then start bidding up prices to get of the scarce goods. The rise in the price level removes excess demand in two ways. First, it makes it optimal for the producers to produce more. Second, the rise in P and the consequent increase in Y generate excess demand for money driving up interest rate and thereby reducing aggregate demand for goods and services. In both these ways the excess demand gets met through the increase in P. The multiplier process that sets into motion by the increase in G by dG may be described as follows. There emerges first dG amount of excess demand for goods and services putting È 1 Ø upward pressure on prices. When P, as you should be able to derive, rises by É  P* FLL 2 Ù dG , FL Ú Ê producers find it optimal to raise Y by dG and thereby meet the excess demand for goods and È 1 Ø services. Let us denote É  P* FLL 2 Ù by f. f gives the amount of increase in P needed to FL Ú Ê

induce producers to raise Y by unity. In the first round therefore Y rises by dG . The expansionary process, however, does not stop here. The increase in Y by dG accrues as factor income in the hands of the people. Since the tax is lumpsum, the whole of this increase in real income adds to their disposable income and induces them to raise their consumption demand by (C „ ¹ dG ) . The rise È 1 Ø in Y by dG and the increase in P by É  P* FLL 2 Ù dG in the first round creates excess FL Ú Ê

È Ø demand for money by the amount P * k „(C „ ¹ dG)  (k  m)  P* FLL 1 dG œ R dG , where É 2Ù FL Ú Ê È 1 Ø R œ P* k „C „  (k  m) É  P* FLL 2 Ù . (q gives the amount of increase in money demand per FL Ú Ê unit increase in Y allowing for the increase in P needed to make the unit increase in Y profitable.) The excess demand for money induces economic agents to withdraw funds from the loan market to meet their excess demand for money. This creates excess demand of an equal amount in the loan market putting upward pressure on i, which rises instantaneously and clears the loan market and thereby the money market. Consequently, i rises by [R dG /(  m „)] to clears the money market. This lowers investment demand by I „ ¹ [R dG /(  m „)] . Thus, in the second round, aggregate demand for goods and services goes up by {C „  I „ [R /(  m „)]}dG . Price accordingly rises and

when it rises by G{C „  I „[R /( m „)]} dG , producers raise Y by {C „  I „[R /(  m „)]}dG and meets the excess demand. This increase in Y raises people’s disposable income by the same amount. So consumption demand in the third round goes up by C „{C „  I „[R /( m „)]} dG . The second

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round increase in Y and P raises money demand by R{C „  I „[R /(  m „)]} dG , which in turn R raises interest rate and thereby lowers the investment demand by I „ {C „  I „[R /(  m „)]} dG . (  m „) Thus, in the third round aggregate demand and GDP will rise by C „{C „  I „[R /(  m „)]} dG +

R {C „  I „[R /(  m „)]} dG {C „  I „[R /(  m „)]}2 dG . This process of expansion will (  m „) continue until the increase in output that takes place in each round eventually drops to zero. When that happens, the economy achieves its new equilibrium. Thus, the total increase in Y from the initial equilibrium to the new one denoted by dY* is given by I„

dY *

dG  {C „  I „[R /(  m „)]} dG  {C „  I „[R /(  m „)]}2 dG  {C „  I „[R /(  m „)]}3 dG  "

dG 1  {C „  I „[R /( m „)]}

(7.27)

The values of dY*, given by (7.26) and (7.27), are the same. EXERCISE 7.6 (a) Derive the values of di*, dL* and dP* and explain them. (b) How does an increase in government consumption financed by taxation affect the endogenous variables in the CKM? Explain.

7.5.2

Effect of an Increase in Money Supply

Let us now examine the effect of an increase in M by dM brought about by the central bank in the CKM. We shall work out the results first graphically and then mathematically. We have to first focus on the AD and AS schedules. Since money supply does not figure anywhere in the production function or labour demand or labour supply functions, AS is not affected by an increase in M . Develop this argument in detail yourself. Consider now the AD schedule. Following an increase in M , the LM schedule corresponding to every given P shifts rightward, but the IS remains unaffected. Hence, corresponding to any given P the goods markets and the money market come to equilibrium with a larger Y and a lower i. Hence AD shifts to the right. The vertical portion of AD will now correspond to the same Y as before, but now it will be longer. Explain why yourself. In Figure 7.12, initial and new AD schedules are labelled AD and AD1 respectively. The AS schedule is the same as before. It is clear from Figure 7.12 that following an increase in M both Y and P go up. In Figure 7.12, the new and the initial equilibrium (Y, P) are labelled (Y0, P0) and (Y1, P1) respectively. The state of the goods market and money market is shown in Panel B of Figure 7.12, while the state of the labour market is shown in Panel C of Figure 7.12. The initial and the new LM are labelled LM(P0) and LM ( P1 , dM ) and they intersect the given IS at (Y0, i0) and (Y1, i1). Since both the initial equilibrium and the new equilibrium are located on the same IS and since Y1 > Y0, interest rate

Complete Keynesian Model

Figure 7.12

Effect of an increase in money supply.

253

254

Macroeconomics

in the new equilibrium, i1, is less than the interest rate in the initial equilibrium, i0. In Panel C, the new labour demand schedule, P1FL, is above the initial labour demand schedule, P0FL, and cuts the labour supply schedule at a higher L, L1, which corresponds to Y1 on the production function labelled F(×). Our graphical analysis yields that, following an increase in money supply, GDP, employment and price level go up and the interest rate goes down. These results are derived mathematically as follows. First, denoting the equilibrium values of the four key endogenous variables, viz. Y, i, P and L by Y*, i*, P* and L* respectively and substituting them into (7.1), (7.2), (7.5) and (7.13), we convert them into the following identities: Y * œ C (Y *  T )  I (i*)  G

(7.28)

M

P*[ k (Y *)  m(i*)]

(7.29)

Y*

F ( L*, K ); FL ! 0

W

P* FL ( L*, K )

and

FLL  0

(7.30) (7.31)

Next, taking total differential of these four identities treating all exogenous variables other than M as fixed, we have dY * œ C „dY *  I „di*  dG (7.32) dM

P* k „dY *  P* m „ di*  [ k (Y *)  m (i*)] dP*

dY* = FLdL*

(7.33) (7.34)

0 = P* FLLdL* + FLdP*

(7.35)

Explain why we shall get the values of changes in GDP, interest rate, price level and employment from the initial equilibrium to the new equilibrium following the change in money supply by solving (7.32)–(7.35). Solving these equations, we get

dY *

I „(dM / m „) Ë Û Ì Ü 1 Ì Ü 1  ÌC „  I „ Ü  F ÑÞ Ü ÑÎ Ì (  m „) Ï k „  ( k  L ) LL ß Ì FL2 àÑ ÜÝ ÐÑ Í

!0

(7.36)

Let us now explain the expression on the RHS of (7.36). First focus on the numerator. It gives us the amount of excess demand for goods and services that emerges following the rise in M by dM at the initial equilibrium Y, L and P, when i adjusts and clears the money market. Let us explain. The increase in M by dM creates an excess supply of money dM . Hence interest rate falls to raise demand for money by dM to equilibrate the money market. Per unit fall in interest rate cause demand for money to go up by (–Li). Hence demand for money goes up by

dM , when interest rate falls in absolute terms by dM (  Li ) . This raises investment demand by

Complete Keynesian Model

255

[( dM / Li ) I „] , since per unit fall in interest rate investment demand goes up by (–I¢). Thus there emerges an excess demand of the above-mentioned amount at the initial equilibrium Y, L and P. This excess demand will start driving up the price level and thereby induce the producers to raise Y. This process will continue until the excess demand is removed. The denominator, as we have already explained, gives the decline in excess demand per unit increase in Y, when i and P adjust along with the unit increase in P to keep the labour market and the money market in equilibrium. Hence, (7.36) gives the increase in the equilibrium value of Y from the initial equilibrium to the new equilibrium following the increase in M by dM . Let us now explain how the economy moves from the initial equilibrium to the new one. Following the increase in M by dM , there emerges an excess supply of money in the initial equilibrium situation driving down interest rate to the market clearing level. This raises investment demand leading to excess demand for goods and services at the initial equilibrium Y, L and P. This will start raising the price. The increase in the price level will remove the excess demand in the following manner. On the one hand, it will induce producers to raise Y. On the other hand, the rise in P and Y will also raise interest rate and thereby reduce investment demand. In both these ways, the rise in P removes the excess demand and thereby equilibrates the system. Describe the multiplier process yourself.

EXERCISE 7.7 (a) Suppose aggregate demand for goods and services is interest inelastic. Under this condition, how many markets do you have to consider in the CKM to explain why aggregate output and employment fluctuate in market economies. Explain your answer, (b) Suppose the aggregate production function in the CKM is Y = L. Will the values of the multipliers in this case in the CKM be less than those in the IS-LM? Derive mathematically. Also illustrate graphically. Explain the intuition of your answer. (c) In India, the objective of monetary policy is to keep the interest rates stable through the open market operations. How will you modify CKM to explain the behaviour of the economy, when RBI follows the policy mentioned above. In these circumstances, if the RBI cuts down CRR, how will it affect the endogenous variables of the model? Explain your answer. (d) Suppose the supplies of government provided crucial infrastructural inputs such as power, roads, etc., becomes scarcer. How will you capture its impact in the CKM? Explain. (e) Suppose the government adopts an expansionary policy. If it thinks that the economy behaves in accordance with the CKM, will it expect with a reduction in unemployment, inflation as well? Explain. (f) CKM explains short-run fluctuations in GDP in terms of volatility of investment. Can CKM really explain cyclical fluctuations in GDP in terms of volatility of investment? Suppose market structures of produced goods and services are oligopolistic. And it is not possible for the producers to maximize profit in any precise manner by equating the marginal returns from variable inputs to their respective prices, as they cannot perceive these marginal returns. Instead, they simply add a mark-up to the average variable cost of production to set their prices. Will the CKM’s explanatory power increase if the producers behave the way suggested above? Explain.

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Macroeconomics

7.6 CONCLUSION The CKM is a serious and true attempt at capturing the working of a market economy where lack of information, absence of coordination among individual players, dominance of a few people in the ownership of resources, workers’ efforts at organizing themselves to gain in bargaining strength, etc., severely impede the price adjustment process. Every industry in mature market economies is in the grips of a few giant firms making the assumption of perfect competition a myth. Keynes, however, made only those changes in classical assumptions, which he considered minimum to explain why phenomena such as Great Depression can occur in market economies. He made two major changes. He got rid of the loanable funds theory of interest, which yields Say’s law. He did not believe in interest elasticity of saving and investment. Moreover, he also held that there is a floor below which interest rate cannot fall on account of people’s preference for liquidity. For these reasons he did not regard the loanable fund theory of interest as capable of determining interest rate. He therefore developed an alternative theory, the theory of liquidity preference, for determining interest rates. He obliterated the direct link between the goods and the loan market posited in the loanable fund theory and forged a link between the loan market and money market instead through the wealth budget constraints of the individuals. He showed that, as you should be able to recall, loan market and money market are mirror images of one another. This renders it unnecessary to consider both the loan market and the money market, when the focus is on the determination of interest rate in equilibrium. If the money market is in equilibrium at a given interest rate, it must also equilibrate the loan market and vice versa. Accordingly, Keynes relegated the loan market to the background and considered only the money market in his liquidity preference theory of interest. This buried Say’s law once and for all. The other major change was his incorporation of money wage rigidity or at least downward flexibility of money wage rate. This was necessary to generate underemployment equilibrium (i.e. equilibrium with involuntary unemployment or excess supply of labour). You cannot have excess supply of labour in equilibrium if money wage rate is perfectly flexible. In such a situation, in the face of excess supply of labour, money wage rate will go on falling so that you will not get any equilibrium, when there is excess supply of labour. Money wage rigidity is an important feature of reality. Money wage rigidity is an important feature of reality not only because of money wage rate, as pointed out by Keynes, which is set through long period wage contracts but also because of other factors. Even when workers are not unionized, money wage rates tend to be rigid. When a worker agrees to work for a firm, he does so for a money wage rate that he agrees to accept and that the firm agrees to pay. This agreement is arrived at independently by the firm and the worker in an uncoordinated manner. Since labour in not auctioned by a centralized authority, neither an individual firm nor an individual worker has any clue as to what the market clearing wage rate is. Moreover, workers of the same academic qualification vary substantially in skill levels, ability, attitude towards work, morality, loyalty, attitude towards others, political inclinations, affiliations, etc. There should be a market clearing wage rate for each of these different types of workers of the same educational qualification. This applies to work environments in different firms engaged in the same line of production as well. This tremendous variety makes the scenario extremely complicated. When a worker agrees upon a wage rate, on what basis does he do so? He, as Keynes pointed out, takes into account what the other firms are paying for the same kind of work. He is unlikely to accept a wage rate

Complete Keynesian Model

257

that is less than what other firms are paying. Since he is unlikely to have any clue as regards the state of the labour market, he will hope to get a job at the wage rate that he finds workers of the same kind are getting. It therefore seems sensible to assume that every worker will be willing to sell his labour at the wage rate that he finds his kind of workers are getting in the market. This kind of argument applies to the firms as well. Since both employed and unemployed workers respond to advertisements and given the mind boggling variety among workers of apparently the same level of skill, individual firms are unlikely to have any clue as to the state of the market of any specific kind of labour. Hence, a firm when it agrees to pay a money wage rate to a worker, it does so on the basis of what other firms are paying for the same kind of workers. It is unlikely to offer a lower money wage rate, as that might attract only the unemployables. Even if it succeeds initially in roping in good workers, he runs the risk of eventually ending up only with the wrong kind of workers. It is unlikely to offer a higher wage rate either, as it will generate excess supply making such an offer unnecessary and non-optimal. Thus individual workers’ supply price and individual firms’ demand price are likely to be equal to the wage rate that they think is prevailing in the market. This kind of behaviour tends to build a high degree of inertia in the wage adjustment process and tends to make the money wage rate rigid. Since individual workers and firms have no influence over the price level and regard it as independent of their behaviour and since the money wage rate a firm agrees to pay and a worker agrees to accept has no impact on the price level, a higher money wage rate is considered better by individual workers and worse by the individual firms. In the organized sector in India and also in many other countries, the wage contracts include escalation clauses, which link the money wage rate to the cost of living index of the workers. That kind of clause tends to make even the real wage rate rigid, even though no one knows whether the given real wage rate is market clearing or not. In the absence of a trustworthy centralized authority grading firms and workers and auctioning them off, the notion of the market clearing wage rate remains elusive. Given the staggering variety of labour and firms of apparently the same kind, it becomes risky for a firm to offer a lower wage rate than what it thinks the market is paying. Similarly, it becomes risky for a firm to employ a worker offering his service at a wage rate that is less than what the firm thinks similar kind of workers are getting in the market. For the same kind of reason, it becomes risky for a worker to offer his service at a wage rate less than what he thinks the market wage rate is. It is also risky for a worker to accept an offer by a firm that pays more than what he thinks other firms are paying. All these factors tend to make the money wage rate persistent and slow to adjust. In times of deep recession characterized by large-scale bankruptcy and closures, involuntary unemployment becomes all too evident to everyone. However, even in times of such recession firms, which are still afloat, may not consider it optimal to downsize or to cut money wages. These firms at such times will be engaged in fierce competition with one another to increase their shares in a rapidly shrinking market. In such circumstances any anti-labour move taken by a firm unilaterally may threaten all its employees and may induce the most efficient of them to move out and join its rivals and thereby make it lose out in competition. So, oligopolistic interdependence may keep the money wage rate rigid even in times of deep recession. However, in times of boom or high growth, there may arise acute scarcity of labour. In such circumstances buoyed by rosy future, business prospects firms may engage with one another in wage competion to attract scarce labour. In such situations money wage rate will, of course, rise. Thus, Keynesian assumption that the money wage rates in market economies are inflexible downward makes perfect sense to us.

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Macroeconomics

Replacement of the loanable funds theory of interest with the liquidity preference theory of interest to destroy Say’s law and the incorporation of money wage rigidity were the changes that Keynes considered minimum necessary for developing a theory capable of explaining recessions in market economies. He did not make any other significant change. The assumption that saving and investment are functions of aggregate income rather than that of interest rate constituted a major plank of his attack on the loanable funds theory of interest. The assumption, however, also yielded the multipliers. The upward sloping supply curve of the CKM is particularly suitable for India, where outputs of some of the crucial sectors supplying the rest of the economy with crucial infrastructural inputs such as power, roads, transport, etc., are subject to capacity constraints. Agricultural output is also capacity constrained in the short-run, as the output of a crop cannot be changed during the period that elapses between one sowing season to the next. For these reasons, as output expands, the supply bottlenecks tighten raising the marginal cost of production. Producers, for example, may have to use power from more expensive captive sources, when power from large scale production units becomes scarce. With increased congestion on roads, scarcity of rail transport, etc., the cost of transport goes up with increase in production. Agricultural goods become dearer as demand increases. For all these reasons the upward sloping supply curve of the CKM is particularly suitable for India. Even though CKM is a good starting point for developing models to capture the behaviour of market economies, it may be improved upon in certain areas to make it more realistic and more applicable to India and elsewhere. One major weakness of the CKM is of course the financial sector, which it conceives in terms of stocks of supply of money and demand for money. The real sector, however, is characterized in terms of flows. Flows refer to a period of time. Thus the real sector determines output per unit of time such as daily output, weekly output, monthly output or annual output. Stocks, on the other hand, are defined at every instant of time. At every instant of time there is a stock of supply of money and a stock of demand for money and these determine an interest rate at every instant of time. This obviously raises a problem of interpretation. Suppose the flows in the real sector are quarterly. The real sector thus determines quarterly output, quarterly consumption, etc. Stocks of demand for money and supply of money should determine interest rate at every instant. Note that, even if stock of money supply remains the same at every instant during a given period, the money holding of the public will vary from one instant to the other. Thus interest rates of different instants during the given period are likely to be different. In the IS-LM and CKM, demand for money refers to the average of these instantaneous money holdings during the given period. What does the stock of demand for money defined in the above sense and the stock of supply of money determine in the CKM or in the IS-LM? Do they determine the average of these instantaneous interest rates? Will the average of the interest rates of all the instants during the given period really be equal to the interest rate that the demand for money and supply of money in the IS-LM or CKM determine? These issues are obviously unresolved. Even if we ignore this problem, there are other more serious problems that the characterization of the financial sector in the CKM gives rise to. Quite a large part of private and public consumption and investment expenditures are financed with credit. Thus the process of generation of credit and that of demand should be closely related to one another. Again, we know that the process of generation of money and that of bank credit occur simultaneously. Thus they are also

Complete Keynesian Model

259

intimately linked. Again, savers lend out quite a large part of their saving to the financial intermediaries such as banks, insurance companies, etc., and also to the government. Thus the process of generation of saving and that of credit are also intimately connected. To sum up, the processes of generation of saving, credit, money, expenditure and income are actually very closely interrelated. In other words, the multiplier process that takes place in the real sector in CKM and the money multiplier process must occur together. However, the IS-LM and CKM fail to capture these interrelationships. In the final chapter of our book, we shall develop a model that seeks to redress this problem. One important, perhaps by far the most important, macroeconomic phenomenon of India is the extreme inequality in its distribution of income. India’s organized sector, which contributes about 65 per cent of its GDP employs only 5 per cent of its labour force, the unorganized sector accounts for the rest of the GDP and employs the remaining part of the labour force. The other alarming feature is that the rate of growth of employment in the organized sector is negative, while its output is growing at a much faster rate than that of the unorganized sector. In sum, roughly, at the present 65 per cent of India’s GDP accrues as income to just about 5 per cent of India’s population, while the rest of the population gets only 35 per cent of its GDP as income. Moreover, with the passage of time, larger and larger proportion of India’s GDP will accrue as income to smaller and smaller proportion of the population. To focus on this issue, which is absolutely essential in Indian context, one has to construct a disaggregated model that divides the economy into organized and unorganized sectors to capture their interactions and the mechanism that is widening the inequality in income distribution. The model should also suggest ways of putting a stop to the growing inequality or of reversing it. We take up this challenge as our future research agenda.

REFERENCE Keynes, J.M. (1936), The General Theory of Employment, Interest and Money, Macmillan, London.

8 8.1

The Real Sector and the Financial Sector

INTRODUCTION

One major weakness of the CKM is of course the financial sector, which it conceives in terms of stocks of supply of money and demand for money. The real sector, however, is characterized in terms of flows. Flows refer to a period of time. Thus the real sector determines output per unit of time such as daily output, weekly output, monthly output or annual output. Stocks, on the other hand, are defined at every instant of time. At every instant of time there is a stock of supply of money and a stock of demand for money and these determine an interest rate at every instant of time. This obviously raises a problem of interpretation. Suppose the flows in the real sector are quarterly. The real sector thus determines quarterly output, quarterly consumption, etc. Stocks of demand for money and supply of money should determine interest rate at every instant. Note that, even if stock of money supply remains the same at every instant during a given period, money holding of the public will vary from one instant to the other. Thus interest rates of different instants during the given period are likely to be different. In the IS-LM and CKM, the demand for money refers to the average of these instantaneous money holdings during the given period. What does the stock of demand for money defined in the above sense and the stock of supply of money determine in the CKM or in the IS-LM? Do they determine the average of these instantaneous interest rates? Will the average of the interest rates of all the instants during the given period really be equal to the interest rate that the demand for money and supply of money in the IS-LM or CKM determine? These issues are obviously unresolved. Even if we ignore this problem, there are other more serious problems that the characterisation of the financial sector in the CKM gives rise to. Quite a large part of private and public consumption and investment expenditures are financed with credit. Thus the process of generation of credit and that of demand should be closely related to one another. Again, we know that process of generation of money and that of bank credit occur simultaneously. Thus they are also intimately linked. 260

The Real Sector and the Financial Sector

261

Again, savers lend out quite a large part of their saving to the financial intermediaries such as banks, insurance companies, etc. and also to the government. Thus the process of generation of saving and that of credit are also intimately connected. To sum up, the processes of generation of saving, credit, money, expenditure and income are actually very closely interrelated. In other words, the multiplier process that takes place in the real sector in CKM and the money multiplier process must occur together. However, the IS-LM and CKM fail to capture these interrelationships. In this chapter, we shall develop a model that seeks to redress the problems noted above.

8.2 The Model We shall develop first a very simple model that completely resolves the problems noted above. This model is derived from Rakshit (1993). We can easily extend this model to more general cases whenever needed. The model divides the economy into two sectors, namely the real sector and the financial sector. We shall characterize the financial sector first.

8.2.1

The Financial Sector

The economy consists of the government, Central Bank, commercial banks, firms and households. The government takes loans only from the Central Bank and the Central Bank in its turn lends only to the government. Only firms take loans from the commercial banks and the commercial banks receive deposits only from the households who hold their entire wealth or savings in the form of bank deposits. Households are the ultimate lenders and do not take any loans. These assumptions can be easily generalized without any change in the results drawn. The asset– liability structure of the economic agents, given the simplifying assumptions specified above, is presented in Table 8.1. It is assumed in Table 8.1 that the government takes loans from the RBI only to acquire physical assets. Households, government and firms carry out their transactions only with bank deposits. Accordingly, they do not hold any currency. Let us now focus on the supply of loans in this economy. Table 8.1 Assets and liabilities of economic agents

Government Central Bank Commercial banks Firms Households

Asset

Liability

Vg Lgc Lf +H Vf D

Lgc H D Lf W

W º households’ wealth and Vg º government’s physical assets, Lgc º government’s loans from the Central Bank, H º stock of high-powered money, H º reserves of the commercial banks, Lf º loans of the firms from banks, D º aggregate deposits of the commercial banks, Vf º physical assets of the firms. Banks do not hold any excess reserves and the required reserve ratio is r. It is also clear from the asset–liability structure that non-bank economic agents, who are referred to as the public, do not hold any currency and carry out all their transactions with bank deposits only.

262

Macroeconomics

Supply of loans Let us first consider the Central Bank. It extends loans only to the government. Its total outstanding loan to the government is denoted by Lgc in Table 8.1. It should be equal to its total outstanding liability, which is the total stock of high-powered money in the economy and it is denoted by H. Suppose the Central Bank gives a loan of ` 1 to the government who spends it to buy goods. How will this ` 1 come back to the Central Bank and create high-powered money of ` 1? Explain it yourself. Given our assumptions, the whole of this stock of high-powered money will be held by the banks as reserve or deposits with the Central Bank, since, by assumption, banks do not hold any vault cash. Assuming that banks do not want to hold any excess reserves and denoting the CRR by r, the total amount of outstanding bank loans is given H H by (1  S) . Note that gives the total amount of bank deposits and also the total supply

S

S

of broad money, M3. Explain these points yourself. Let us now consider a given period. Suppose in the given period government takes a loan of DLgc from the Central Bank. The government uses it to finance its consumption expenditure of G in the given period. The supply of high-powered money in the given period as a result will rise by DLgc = DH, which will end up as additional reserves of the commercial banks. (Explain the reason yourself.) The commercial banks as a result will be able to and therefore plan to extend new loans of (DH/r) in the given period. Denoting the amount of new loans that the commercial banks plan to supply in the given period by DLB, we have

'LB

(1  S )

'H

(8.1)

S

DH = DLgc

and

(8.2)

Equations (8.1) and (8.2) give respectively the planned supply of loans by the commercial banks in the given period and the supply of loans to the government by the Central Bank.

8.2.2 The Real Sector We assume that in the real sector aggregate output is determined by aggregate final demand for goods and services. The price level is fixed and it is taken to be unity. The aggregate planned consumption demand is given by C = a + bY

a>0

and

00

(8.4)

where i º nominal interest rate. We assume, again for simplicity, that investment is financed entirely with loans. Government consumption, G, is also, as we have already mentioned, financed with loans from the central bank. Thus, G = DLgc = DH (8.5)

263

The Real Sector and the Financial Sector

The goods market is in equilibrium when Y = a + bY + A – iB + G

8.3

(8.6)

INTERACTION BETWEEN THE REAL AND THE FINANCIAL SECTORS

Both government consumption and investment expenditure are financed entirely with loans. The demand for commercial banks loans comes only from the investors. The demand for new bank loans in the given period is therefore given by (8.4). The supply of new bank loans in the given period is given by (8.1). We can work under two alternative assumptions. We can assume that the credit market is competitive and the interest rate clears the market for bank credit. Alternatively, we can assume that the banking sector is oligopolistic so that oligopolistic interdependence as captured in the kinked oligopoly demand curve model makes interest rates charged by banks rigid at a level at which there is excess demand for credit. In the former case where interest rate clears credit market, the credit market is in equilibrium when demand for loans and supply of loans are equal, i.e. when the following condition is satisfied:

(1  S )

'H

A  iB

S

(8.7)

In the latter case, as there is excess demand for credit at the fixed interest rate, investment is determined by the supply of credit. In equilibrium, therefore, investment will be given by the supply of new loans in the given period. Thus

(1  S)

I

'H

(8.8)

S

Let us take up the former case first. In this case, the equilibrium of the economy is given by (8.6) and (8.7), which contain two endogenous variables, Y and i. We may solve (8.6) and (8.7) as follows. Solving (8.7) for i, we get 'H A  (1  S) S (8.9) i B Substituting (8.5) and (8.9) into (8.6), we get

Y

a  bY  (1  S)

'H

S

 ' L gc

Solving the above equation for Y, we get a  (1  S) Y

'H

S

1b

 'H

1 'H a  1b 1b S

(8.10)

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Macroeconomics

Equations (8.9) and (8.10) give the equilibrium values of i and Y respectively. Let us now describe the process through which the equilibrium is reached. This will bring out clearly the close interaction between the real and the financial sectors. Let us now explain the process through which aggregate output and interest rate are determined in the economy in the given period. At the beginning of the period government borrows DLgc from the Central Bank and spends it on goods and services. Households also draw down their deposits by a and spend it for consumption purposes. This will create the familiar a  ' L gc . The whole of this multiplier process in the real sector raising aggregate output by 1b will accrue as factor income to the households and they will save (1 – b) fraction of this income. They will, therefore, save (a + DLgc) and hold it in the form of bank deposits. Household deposits with banks thus go up by DLgc. The a amount of deposit made by the households restore their deposits to their initial level. So banks get new deposits of DLgc only. The commercial banks initially will hold these deposits in the form of deposits with the Central Bank, i.e. in the form of reserves. (Describe the details of this process yourself.) Thus the loan to the government adds to the stock of high-powered money in the given period. This is where the first round of a  ' Lgc a  ' H expansion ends. In the first round therefore Y expands by , the deposits of 1b 1b commercial banks and therefore the supply of broad money and also the stock of high-powered money rise by DH. Now the second round of expansion starts, as the banks find themselves in disequilibrium. They have additional reserve of DH = DLgc and they will plan to increase their supply of credit by (1 – r)DH = (1 – r) DLgc. There will thus emerge an excess supply of credit. To induce the investors to borrow this amount, the interest rate will settle down to the level at which investment A  (1  S ) ' H demand equals the supply of credit. This interest rate is given by . Investment b demand in the second round will therefore go up by (1 – r)DH, which in turn will lead to a (1  S ) ' H multiple expansion in Y by . Households will receive this as additional factor income 1b and save out of it (1 – r)DH, which they will hold in the form of bank deposits. Therefore, households’ bank deposits and deposits of commercial banks go up by (1 – r)DH. The commercial banks hold these additional deposits in the form of reserves with the central bank. This marks the end of the second round of expansion. Similarly, in the third round, commercial banks will extend additional loans of (1 – r)2DH and the interest rate will fall to raise investment demand (1  S ) 2 ' H . Consequently, saving and bank 1b deposits will go up by (1 – r)2DH. This process of expansion will continue until the increase in demand that occurs in every round eventually drops to zero. Thus the total amount of Y that will be produced in the given period is given by

by this quantity. As a result, Y will go up by

'Y

a  ' H (1  S) ' H (1  S) 2 ' H   " 1 b 1b 1 b

a 'H  1  b (1  b)S

(8.11)

The Real Sector and the Financial Sector

265

Equation (8.11) shows that the value of Y at the end of the expansionary process is the same as that given by (8.10). The total amount of saving and investment and therefore the total increase in the deposits of commercial banks or in the supply of broad money in the given period is given by

S

I G

'D

'M3

' H  (1  S )' H  (1  S )2 ' H  "

'H

S

(8.12)

We can derive the equilibrium value of S by subtracting (8.3) from (8.10). Doing that we find that 1 'H Û 'H Ë a (8.13)  S Y  a  bY (1  b) Ì Üa 1 1   b b S S Í Ý (8.13) shows that (8.12) gives the equilibrium value of S. EXERCISE 8.1 (a) Derive the equilibrium values of the endogenous variables of this model under the assumption that the interest rate is fixed. Describe also the multiplier processes that generate these equilibrium values. (b) Derive the equilibrium values of the endogenous variables of this model when government consumption is zero and consumption and investment expenditures are not financed with loans but with the consumers and investors own wealth and income. Assume in this case that investment demand is a function not of interest rate but of income. Describe the multiplier processes that yield these equilibrium values. (c) Instead of assuming P to be unity, bring it explicitly into the equations and derive its impact on the endogenous variables and thereby derive the aggregate demand function. (d) Can liquidity trap kind of situation arise in this model? (e) Suppose firms raise funds not only by borrowing from banks but also by selling corporate securities directly to the households. Households also hold their wealth not only in the form of bank deposits but also in the form of corporate securities. Extend the model to this case.

8.4

CONCLUSION: EVALUATION OF THE MODEL

This simple model redresses all the problems mentioned in the introduction regarding the deficiencies of the characterization of the financial sector in the IS-LM and therefore in the CKM. The model brings out clearly the interrelationships that exist among processes that generate income, saving, new credit and expenditure. It shows that the multiplier process that occurs in the real sector and the money or credit multiplier process that occurs in the financial sector take place simultaneously reinforcing each other. It brings to the fore the process through which savings are used by the financial intermediaries to extend credit. It also makes the classical loanable funds theory of interest stand on its head by showing how government consumption and investment expenditures financed by borrowing generate through the income

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Macroeconomics

and the money-credit multiplier processes an equal amount of saving making the Keynesian precept that demand creates its own supply true. Had all the expenditures been financed with the spenders’ own wealth, only the multiplier process in the real sector would have worked. Let us now focus on the issue of demand for money. Here people hold their entire wealth in the form of deposits of the commercial banks, i.e. in the form of money. The stock demand for money of the households is their entire wealth. The flow demand for money is their saving. This is, obviously, a special case. We can easily generalize this model to the situation where households hold their wealth and saving in the form of not only bank deposits but also government and corporate securities and currency. Unlike the IS-LM and the CKM, which cannot handle the situation where interest rates are rigid, this model can handle the situation where the interest rates are flexible as well as the one where interest rates are fixed. Here we have kept P unchanged and assumed it to be unity. We can easily drop this assumption, consider P explicitly and examine its impact to derive the aggregate demand schedule of the CKM. Fuller development of this model and its extension to the case of an open economy is our future research agenda.

REFERENCE Rakshit, M. (1993), “Money, Credit and Monetary Policy”, in Majumdar, T. (Ed.) Nature, Man and the Indian Economyt, Oxford University Press, Delhi.

9 9.1

Consumption Function

INTRODUCTION

Keynes believed in a stable consumption function. In fact, it was the fulcrum on the basis of which he developed his theory. However, he did not develop any theory of aggregate consumption. He merely posited aggregate planned real consumption expenditure/demand of the households as an increasing function of their aggregate real income in the short run and specified some properties of this consumption function. It yielded the famous multiplier result, which opened up the opportunities for stabilizing the economy using fiscal and monetary programmes. Obviously, those who did not want the government to meddle with economic matters, as it raises the bogey of high taxes, confiscation of properties, curtailment of economic freedom due to regulatory policies, etc., trained their guns against Keynesian consumption function. They tried to develop alternative theories of consumption to weaken the Keynesian multiplier result and thereby the efficacies of fiscal and monetary policies. Even though short-run data of income and consumption lent superb empirical validity to the Keynesian consumption function, its detractors got an excellent opportunity to dismantle it as data revealed, a la Kuznets, a discrepancy between the short-run income–consumption relationship and its long-run counterpart. It was felt necessary to develop theories to explain these discrepancies. Taking advantage of this revelation, economists opposed to Keynes tried to formulate theories whose principal objective was to undermine Keynesian consumption function and the multiplier result that it implies in the garb of explaining the discrepancy mentioned above. Two such major theories that hold sway in the mainstream macroeconomics today are the life cycle theory of consumption developed by Ando and Modigliani (1963) and the permanent income hypothesis of consumption of Friedman (1957). We shall present in this chapter the Keynesian consumption function and also the two alternative theories of consumption mentioned above. We shall make a critical assessment of the two alternative theories and show 267

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Macroeconomics

that they are unacceptable as satisfactory theories of consumption. We shall discuss another theory of consumption called the relative income hypothesis of consumption developed by Duesenberry and argue that it is a much better theory of consumption than those of Ando and Modigliani, and Friedman.

9.2

KEYNESIAN CONSUMPTION FUNCTION

As already mentioned, Keynes did not develop a theory of consumption. He simply posited a consumption function, which, he claimed, captures a fundamental psychological law that governs individuals’ consumption behaviour. He pointed out that individuals’ aggregate real planned consumption expenditure is an increasing function of their aggregate real disposable income. However, he also asserted that, though an increase in aggregate real disposable income induces individuals to increase their real aggregate consumption expenditure, the increase in the latter is usually less than that of the former. In other words, individuals use the increase in their aggregate real disposable income not only to add to their aggregate real consumption expenditure but also to increase their saving. He also specified that the proportion or fraction of aggregate real disposable income households spend on consumption, which is referred to average propensity to consume (APC), falls as aggregate real disposable income rises. Denoting aggregate real consumption expenditure by C and aggregate real disposable income by YD, we can write the Keynesian consumption function as follows: È

C

C (YD)

0



dC dYD

C Ø Ù Ê YD Ú dYD

dÉ 1

and



0

(9.1)

dC is referred to as marginal propensity to consume (MPC). It gives the amount of increase dYD in aggregate real consumption expenditure per unit increase in aggregate real disposable income, when the latter rises by a very small amount. According to Keynes MPC is greater than zero, but less than unity. Again, (C/YD) gives the fraction or proportion of aggregate real income spent on consumption. This is, as we have already mentioned, referred to as average propensity to consume (APC). According to Keynes, APC falls as aggregate real disposable income goes up. This implies that [d(C/YD)/dYD] < 0. This explains (9.1). A linear consumption function with an autonomous component, defined as that part of aggregate real consumption expenditure that is independent of aggregate real disposable income and an induced component, which refers to that part of aggregate real consumption expenditure that depends upon the aggregate real disposable income, satisfies both the properties of the consumption function specified by Keynes. Such a consumption function is specified below:

C = A + bYD

A > 0, 0 < b < 1

(9.2)

The short-run data on aggregate real disposable income of the households and aggregate real consumption expenditure lend tremendous support to the consumption function posited by Keynes. In what follows, for simplicity, we shall ignore taxes and government.

Consumption Function

9.3

269

DISCREPANCY BETWEEN THE SHORT-RUN AND LONG-RUN CONSUMPTION–INCOME RELATIONSHIP

Kuznets showed that the relationship between aggregate real consumption and aggregate real income in the short run, as revealed by data, matches the Keynesian consumption function, but in the long run the APC instead of falling with a rise in aggregate real income becomes a constant. In other words, the long-run data of aggregate real consumption expenditure and aggregate real income show that the relationship between the two is a proportional one so that the ratio of the two is a constant. Let us explain this point a bit further. The short run is defined as a period not longer than a year. If we take daily or weekly or fortnightly data of aggregate real consumption expenditure and aggregate real income of the households for a year and plot them in a graph in the consumption–income (Y–C) plane, then the equation of the line that best fits the scatter of aggregate real consumption expenditure and aggregate real income of the households gives the short-run consumption function. According to Keynes, a short-run consumption function in the (Y–C) plane is upward sloping and its slope at every point, which is nothing but the marginal propensity to consume (MPC) at the given point, is less than unity. Moreover, the APC along such a consumption function falls as aggregate real income of the households rises. A short-run consumption function is shown in Figure 9.1. It is labelled CC. The APC at any given point on CC is given by the slope of the straight line joining the given point and the origin. On the other hand, the long-run is defined as a long period of fifty years or more. If you plot annual data of aggregate real consumption expenditure and aggregate real income of the households for a long period of time spanning, say fifty years or more in a graph, the equation of the line or the curve that best fits the scatter of annual aggregate real consumption expenditure and aggregate real income of the households gives the long-run consumption function. The ratio of the aggregate real consumption expenditure and aggregate real income of the households, i.e. the APC, is constant along a long-run consumption function. The graph of a long-run consumption function is shown in Figure 9.2. It is labelled LC. The question that therefore emerges is how to reconcile the short-run income–consumption relationship with the long-run one. We shall discuss two major attempts in that direction in the next two sections. It is clear that had aggregate real consumption been a function of aggregate real income of the households alone, the relationship between the two would have been the

Figure 9.1 Short-run Keynesian consumption function.

Figure 9.2 Long-run consumption function.

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Macroeconomics

same in both the short run and the long run. The relationship between the two can change from the short run to the long run if and only if aggregate real consumption expenditure depends not only upon aggregate real income of the households but also on some other variable/variables whose values do not change in the short run but vary in the long run. In such a scenario, obviously, the short-run consumption function will shift from one short period to the next making the long-run relationship between C and Y differ from its short-run counterpart. One obvious determinant of C is aggregate stock of physical and financial wealth of the households, which does not change much in the short run, but varies substantially in the long run. If aggregate real consumption expenditure were made a function of both aggregate real income of the households and aggregate stock of wealth of the households, it would have fitted both the short-run and the long-run data of income and consumption quite well. However, such a consumption function would have left the Keynesian consumption function and the multiplier result that it implies perfectly intact. So they adopted a different route. They used a theory of household consumption developed by Fisher, which makes aggregate real income of a household a function of the present value of the expected lifetime real income of the household, as the basis. Fisher’s theory implies that aggregate real consumption expenditure of the households instead of being a function of their aggregate real current income is a function of the present value of their expected aggregate lifetime real income. This theory, as we shall show later, seriously undermines the multiplier effects of the Keynesian short-run stabilization policies. The theories that were developed to explain the discrepancy between the short-run and the long-run consumption–income relationship built on the theory of Fisher mentioned above. We shall present two of the most famous of such theories, namely the life cycle hypothesis of Ando and Modigliani and the permanent income hypothesis of Friedman. However, before going into them, we shall present the theory of household consumption developed by Fisher. It is popularly referred to as Fisher’s model of intertemporal choice.

9.3.1 Fisher’s Model of Intertemporal Choice Both the life cycle and permanent income theories of consumption, as we just mentioned, are based on Fisher’s model of intertemporal choice where he shows how an individual takes his consumption and saving decisions. We therefore first present this model here. It assumes that an individual has two-period life and the individual has no uncertainty regarding his life span or his future real income. The two periods of his life are denoted by Period 1 and Period 2 and his real incomes in Periods 1 and 2 are denoted by Y1 and Y2 respectively. The individual in Period 1 knows Y2 with certainty. The individual is free to borrow or lend as much as he can afford to in Period 1 at a given interest rate, r. The individual exhausts his lifetime income on his lifetime consumption. This implies that the present value of his lifetime consumption in Period 1 discounted at the rate of interest, r, equals in Period 1 the present value of his lifetime income discounted at the interest rate, r. In other words, the following equation holds: C2 Y Y1  2 ( œ W ) 1r 1r The utility function of the individual is given by C1 

U = U(C1, C2)

(9.3)

(9.4)

Consumption Function

271

The individual has to decide on how much to consume in Period 1 and how much to save, i.e. the individual has to choose C1 and C2, given his certain knowledge about his present and future income and the rate of interest at which he can borrow and lend. He makes this choice maximizing his utility given by (9.4) subject to his budget constraint given by (9.3). Formally, the optimization exercise he carries out is the following:

Max U (C1 , C2 ) C1 , C2

s.t. C2 Y Y1  2 ( œ W ) 1r 1r Since the specific form of the utility function is not given, we cannot carry out the optimization exercise and derive the optimum values of C1 and C2. C1 

EXERCISE Suppose the utility function is given by U = 0.8 log C1 + 0.2 log C2. Derive now the optimum values of C1 and C2. We, however, illustrate the solution of the optimization exercise graphically in Figure 9.3 and thereby identify the variables that determine the optimum values of C1 and C2. In Figure 9.3, BB represents the budget line given by (9.3). I1, I2, etc., represent the indifference curves

Figure 9.3

Impact of an increase in the rate of interest on current and future consumption.

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Macroeconomics

showing the utility function or tastes and preferences of the individual. From the budget line the individual chooses the point at which one of the indifference curves of the individual is tangent to the budget line so that at the chosen point the slope of the budget line equals that of the indifference curve. This point is labelled A in Figure 9.3. This is the optimum point on the budget line as it lies on the highest indifference curve attainable from the budget line. The position of the budget line is determined by its vertical intercept, which is given by the value of C2 that we get from (9.3) by putting C1 = 0, and its slope. The vertical intercept of the budget line, as we derive from (9.3), is given by W(1 + r). The absolute value of the slope of the budget line, the equation of which may be rewritten as C2 = W(1 + r) – (1 + r)C1 is (1 + r). Corresponding to every (W, r), therefore there is a unique budget line. Given the tastes and preferences of the individual, corresponding to every (W, r), there is a unique budget line and a unique optimum (C1, C2) on the given budget line. Thus optimum values of C1 and C2 are functions of W and r. They are written as follows: C1 = C1(W, r) and

C2 = C2(W, r)

(9.5)

Let us now examine how C1 and C2 are likely to respond to changes in W and r. A change in W alone will bring about parallel shifts in the budget line. Hence it will produce only pure income effect. If C1 and C2 are normal goods, an increase in W will lead to an increase in both. The effect of a change in r alone is, however, much more complex. An increase in r alone, for example, will increase the vertical intercept and reduce the horizontal intercept of the budget line making it steeper. It will thus produce both an income effect and a substitution effect. Let us elaborate. (1 + r) gives the amount by which the consumer, given his budget, has to reduce C2 if he raises C1 by 1 unit. It thus gives the marginal cost of raising C1 in terms of C2 or the price of C1 in terms of C2. The absolute value of the slope of an indifference curve, which gives the marginal rate of substitution of C1 for C2 and denoted by MRSC1,C2, on the other hand, gives the amount by which the consumer has to lower C2 following a unit increase in C1 from a point on an indifference curve to remain on the same indifference curve. It thus gives the marginal benefit of raising C1 in terms of C2. At the optimum point on any given budget line, the marginal benefit of raising C1 in terms of C2 is equal to its marginal benefit—as given by point A on BB in Figure 9.3. You can easily check that at every point on the budget line to the left of the optimum point marginal benefit of raising C1 is higher than its marginal cost. Hence if the individual from such a point raises C1 by unity, he will have to, given his budget, lower C2 by the marginal cost, (1 + r), which is, however, less than the amount by which he will have to lower C2 to remain on the same indifference curve. Thus, by raising C1 from such a point by unity and lowering C2 along the budget line, the individual will move over to a higher indifference curve. Similarly, you can argue that starting from any point on the budget line to the left of the optimum point, the individual will gain by reducing C1 and raising C2 along the budget line. Now focus on the initial optimum point, A, in Figure 9.3. At this point, following the rise in r, marginal cost of raising C1 in terms of C2 exceeds its marginal benefit. A, therefore, no longer represents the point of individual’s choice on the given indifference curve. If the consumer has to choose a point from the given indifference curve at this higher r, he will gain if he substitutes C2 for C1 along the given indifference curve. Let us explain. Suppose from the given point the individual lowers C1 by 1 unit. Then, given his budget, he will be able to raise C2 by

Consumption Function

273

the marginal cost of raising C1, which is (1 + r1), when r1 is the new higher interest rate so that r1 > r. This new marginal cost of raising C1 in terms of C2 is larger than the marginal benefit of raising C1 in terms of C2 at point A, which is nothing but the amount by which he will have to raise C2 to remain on the given indifference curve following a unit reduction in C1 from point A. Thus, if from the initial optimum point, A, the individual lowers C1 by unity and raises C2 by what his budget at the higher r, r1, permits, he moves over to a higher indifference curve. Thus, to remain on the given indifference curve, he need to raise C2 by a smaller amount than what his budget permits. Thus the cost of attaining the given indifference curve declines if he lowers C1 by unity from A and rises C2 by such an amount that he remains on the initial indifference curve, I1, in Figure 9.3. Thus, if, following a given increase in r, the consumer has to make his choice from the indifference curve on which he was in the initial optimum situation, he will be able to save on the cost of remaining on the given indifference curve by lowering C1 and raising C2 along the given indifference curve as long as (1 + r1) exceeds MRSC1, C2. The cost of attaining the given indifference curve will be minimized by substituting C2 for C1 along the given indifference curve, he reaches the point where (1 + r1) equals MRSC1, C2. The individual will obviously choose this point. The point chosen by the individual following the increase in r to r1 from the initially attained indifference curve, I1, is labelled A1 in Figure 9.3. The changes in the optimum values of C1 and C2 following a given increase in r, when the individual makes the choice at the new higher interest rate from the indifference curve he attained in the initial optimum situation give the substitution effect of the given increase in r. The movement from A to A1 on the initially attained indifference curve, I1, is therefore due to the substitution effect produced by the given increase in r. Thus, following an increase in the rate of interest, current consumption, C1, falls and therefore current saving defined as (Y1 – C1), rises as a result of substitution effect. The income effect produced by the given increase in r is, however, ambiguous. Following the increase in r, the vertical intercept of the budget line becomes larger, while its horizontal intercept declines making the budget line steeper and giving rise to two possibilities. The new budget line may be below the initial optimum point, A, or it may be above it. The new budget line in the former case is labelled B1B1 in Figure 9.3. It is labelled B2B2 in the latter case in Figure 9.3. If the initial optimum point, A in Figure 9.3, is unattainable from the new budget line, the real income of the individual is less following the increase in r. This is the case when the budget line is B1B1 in Figure 9.3. This decline in real income will reduce optimum values of C1 and C2, as indicated by the point A2 on B1B1 in Figure 9.3, if they are normal goods raising current saving. The movement from A1 to A2 is due to the income effect. In this case, the substitution effect and income effect produced on current saving by an increase in r reinforce each other and tend to make it larger. In the other case, where the new budget line is above the initial optimum point, as exemplified by B2B2 in Fugure 9.3, the increase in r makes the individual’s real income larger. In this case both C1 and C2 will rise on account of the income effect tending to lower current saving. The movement from A1 to A3 on B2B2 in Figure 9.3 is due to income effect here. In this case, therefore, the income effect and substitution effect produced by an increase in r on current saving work in opposite directions and the current saving will go down if the income effect is stronger. Thus the effect of an increase in interest rate on current consumption and current saving is ambiguous.

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Macroeconomics

EXERCISE 9.1 (a) Suppose the utility function of an individual is given by U C10.5C20.5 . Also suppose that W = 200 and r = 0.5. Derive the optimum values of C1 and C2. Illustrate the solution graphically. Consider the point on the budget line corresponding to C1 = 80. Will the consumer gain, if he substitutes C1 for C2, from such a point? If yes, compute the gain to the consumer per unit increase in C1 and the commensurate reduction in C2, when C1 is raised by a small amount. Suppose the interest rate rises to 0.15. By how much will C1 and C2 change? Decompose these changes into substitution and income effects. (b) Take the individual of Problem (a). Suppose he can lend at the interest rate of 10 per cent, but he can borrow only at a higher interest rate of 15 per cent. What is the minimum value of Y1 for which the optimum choice of the consumer remains unaffected? Explain your answer and illustrate graphically. What happens if Y1 is less than this minimum value? Take a numerical value of Y1 and illustrate both mathematically and graphically. Now suppose the individual can lend at the rate of interest of 15 per cent, but he cannot borrow. Also suppose Y1 = 50. What is the optimum choice of the individual in this case? How will a unit increase in Y1 affect this optimum choice? Explain your answer.

9.4

LIFE CYCLE HYPOTHESIS OF CONSUMPTION

Life cycle hypothesis of consumption (LCH) starts from where Fisher leaves off. We found in the last section that current consumption of an individual depends upon the present value of his lifetime income. It depends on current interest rate as well. However, a change in interest rate may exert two opposite effects on current consumption. Hence the impact of a change in interest rate on current consumption is likely to be quite weak. Following on these lines, the life cycle hypothesis assumes that the current consumption of an individual is a function of the present value of his expected lifetime income. It goes further and assumes that the current consumption of an individual is a proportional function of the present value of the expected lifetime income of the individual and what fraction of the present value of the expected lifetime income the individual will spend on current consumption depends upon his age. LCH postulates that this fraction is high for the young and the old people and low for the middle aged people. Formally, denoting the consumption of the ith individual of age T in the current period, period t, by CtiT, the present value of his expected lifetime income by WtiT and the fraction of WtiT that he spends on current consumption by aiT, we can write his consumption function as CtiT =

a iTWtiT

(9.6)

LCH distinguishes between the present value of expected lifetime property income and the present value of expected lifetime non-property income. The former is nothing but the value of the property or assets of the individual in the current period, period t. It is denoted by AtiT. Let us illustrate this point with an example. Suppose an individual has a house, which, if rented out, yields rental income. What is the market value of the house in the current period? It should be the present value of the expected rental incomes of the house over its lifetime. Let us explain why. Suppose its current price is higher. Then no one will be interested in purchasing it.

Consumption Function

275

Everyone will consider it profitable to rent in the given house or a similar house instead of purchasing the given house. So the price of the house will fall. If the price is less, then everyone will consider it profitable to purchase it instead of renting it or a similar house. This kind of argument holds for every asset, physical and financial. You must be able to recall how the price of a bond is determined from Chapter 4. WtiT can then be written as

AtiT 

WtiT

N T

ytiT j

j 0

(1  r ) j

Ç

(9.7)

where N denotes the last period of the individual’s life so that (N – T) gives the total number of remaining periods in his life. Let us denote the average lifetime non-property income of the individual by ytiTNe defined as

ytiTNe

1

N T

N T

j 0

ytiT j

Ç (1  r)

(9.8)

j

Using (9.8), we can rewrite (9.7) as AtiT  ( N  T ) ytiTNe

WtiT

(9.9)

Substituting (9.9) into (9.6), we rewrite it as CtiT

B iT [ AtiT  ( N  T ) ytiTNe ]

(9.10)

Suppose, for simplicity, that all individuals of age T has the same value of a and the same number of remaining periods in life. Let us denote this common a by aT. Then summing (9.10) over all the individuals of age T, we have

B T [ AtT  (N  T ) ytTNe ]

CtT

(9.11)

where Ct º aggregate consumption in period t of all individuals of age T, º aggregate stock TNe º aggregate of the average of physical and financial assets of all individuals of age T and yt expected non-property incomes of all the individuals of age T. Aggregating (9.11) over all Ts, i.e. over all age groups, we can derive the aggregate consumption function. Just to illustrate how this aggregation is done, suppose there is just another age group T ¢, with the same life span, N. Suppose their aggregate consumption function is given by T

AtT

CtT

„

B T [ AtT „

„



(N



T „) ytT Ne ] „

(9.12)

Adding (9.11) and (9.12), we have Ct

where Ct º t,

CtT

+

CtT ¢

(9.13)

aggregate real consumption expenditure of the economy in period

B œ [B tT R  B tT (1  R )] , „

B At  C ytNe

where R œ

AtT and At At

AtT  AtT œ aggregate stock of physical „

and financial assets of the individuals in the economy, C

œ

(N



T )G



(N



T „)(1  G ),

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Macroeconomics

ytNe œ ytTNe  ytT Ne and G œ „

ytTNe ytNe

. One can easily generalize and incorporate as many age

groups as one wants. Still one will get an aggregate consumption function such as (9.13). Finally, LCH assumes that the aggregate average expected non-property income is a proportional function of current aggregate income of the individuals, which we denote by Yt. Hence Yt Ne

E Yt

(9.14)

Substituting (9.14) into (9.13), we rewrite it as Ct = aAt + rYT

r º bd

(9.15)

LCH thus yields the consumption function (9.15). It estimated (9.15), i.e. it estimated the values of the coefficients, a and r, using the data of the US economy. Equation (9.15) is capable of reconciling the short-run and long-run income–consumption relationships. In the short run At is more or less fixed, but Yt varies. Moreover, the estimated values of the coefficients are both positive and less than unity. So, in the short run, (9.15) reduces to the Keynesian consumption function as given by (9.2). In the long run, however, both At and Yt vary and they vary proportionately with one another so that their ratio, (At/Yt), is a constant. In other words, the recorded values of At and Yt in different years in the long run are such that their ratio is a constant. Dividing both sides of (9.15) by Yt, we get Ct Yt

B

At S Yt

(9.16)

From (9.16), it follows that in the short run as Yt rises (At/Yt) falls. This means that the APC falls as Yt rises in the short run. Hence the short-run income–consumption relationship as implied by (9.15) or (9.16) satisfied the postulate made by Keynes. In the long run, however, both At and Yt increase proportionately, so that (At/Yt) becomes a constant. Hence the APC, as follows from (9.15) or (9.16), becomes a constant in the long run. This is how LCH reconciles the short-run and the long-run income–consumption relationships. The next task for LCH is to explain the income–consumption relationship yielded by the cross section budget studies. Cross section budget studies show that richer households have lower APC than their poorer counterparts. LCH explains it in terms of differences in age structures of households in higher and lower income classes. It assumes that young and old individuals are poorer than the middle aged people and the APCs of young and old individuals are higher than that of the middle aged people. LCH argues that the proportion of middle aged people in the people belonging to richer income classes is higher leading to lower APC of the people belonging to richer classes. Let us explain this point. Suppose there are M number of people in an income class, with income Yt, of which m proportion of individuals belong to the middle age, with an APC of h and the rest (1 – m) proportion are either old or young with a higher APC of g. Let us now compute the APC of the people of this income class of M number of individuals. The aggregate income of these individuals is MYi. The number of middle aged people in this income class is mM and their total income is mMYi. Their total consumption expenditure is hmMYi. Similarly, total income and consumption expenditure of the young and

Consumption Function

277

old people of the given income class is given by (1 – m)MYi and g(1 – m)MYi. The APC of the people of this income class is therefore given by [hmMYi + g(1 –m)MYi]/MYi = hm + g(1 – m). Since h < g, the higher the m the less is the APC of the people belonging to the income class. Let us elaborate. Suppose m increases by dm. Then, given h and g, the first term, hm, increases by h×dm, while the second term, g(1 – m), decreases by – gdm. Hence the APC changes by (h – g)dm < 0. Thus, given the APCs of people belonging to different age groups, the APC of the people belonging to any given income class is a decreasing function of m. The LCH postulates that the richer an income class, the greater is the value of m in that class, and hence the less is the APC of the people of the income class.

9.4.1 Implication of the LCH for the Keynesian Multiplier The objective of the LCH is to weaken the effectiveness of stabilization policies. According to LCH, consumption is a proportional function of the aggregate lifetime income of the individual. It follows therefore that any policy that has a temporary impact on people’s income are unlikely to affect the present value of their lifetime income and therefore their consumption much. Stabilization policies are adopted to tackle temporary upswings and downswings of GDP. Hence they are essentially temporary in nature. Such policies, according to LCH, are unlikely to be effective in influencing aggregate income. Let us illustrate with the example of an increase in G made by the government to tackle a recession. The policy is temporary as it will be withdrawn once the economy recovers. People know that. Hence they will regard the increase in G and the expansion in aggregate income that it brings about as transient. Hence they will not expect much of an increase in present value of their lifetime income. Accordingly, they may not bother to increase their consumption. Hence the increase in G will fail to produce much of a multiplier effect. The multiplier effects of stabilization programmes, if LCH is true, will be either non-existent or very weak. Mainstream macroeconomics hails LCH, as, mainstream macroeconomists claim, it has microfoundation, i.e. its basic postulate that real consumption expenditure of an individual depends upon the present value of his expected real lifetime income is derived from explicit optimizing behaviour of a consumer. Scant attention is paid to the possibility that the behaviour of consumers in the real world may drastically differ from the behaviour pattern evinced by the consumer in Fisher’s intertemporal choice model.

9.4.2 Evaluation of LCH Neither Fisher’s model of intertemporal choice nor LCH seems satisfactory as a theory of consumer behaviour. The reasons are the following. Let us start first with LCH’s explanation of the income–consumption relationship yielded by the cross section budget studies. It makes the stunningly absurd assumption that the the proportion of middle aged people is higher in a population belonging to a higher income class. It is one thing to say that an individual’s income earning capacity reaches its peak when he is middle aged and another to claim that the proportion of middle aged people in a higher income class is larger. The latter makes sense if one assumes that all individuals are identical except for their ages. An individual’s income depends upon a

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Macroeconomics

host of factors and almost all of them are much more important than his age. These are the level and quality of skill acquired by an individual, inheritance, innate ability of an individual, attitude towards work, earning money, etc. In sports and also in entertainment, income earning capacity of the young individuals is the highest. In politics, in India, the old individuals hold sway. A middle aged agricultural labourer earns less than 90 per cent of what a fresh engineering graduate earns. In sum, people belonging to low income classes are people with low levels of skill. If proportion of people with higher levels of skill and larger inheritance and not of middle aged people rises with income, LCH cannot explain why APC of a richer class of individuals is less. Consider a middle aged agricultural labourer and a middle aged engineer. Obviously, the APC of the former will be unity or very close to unity, while that of latter will be much less than unity. The LCH has no clue as to why the APCs of these two individuals are different. The LCH obviously cannot explain the income–consumption relationship yielded by cross section budget studies. Hence, it cannot be accepted as a satisfactory theory of consumption of individuals or of aggregate consumption function. Let us now focus on the Fisher’s model of intertemporal choice. An individual does not have the knowledge, even if he is the best medical expert in the world, to make a guess regarding his life span or to have a probability distribution over different possible life spans. This holds also for future real incomes. No rational individual will waste time making guesses regarding them or depend on those guesses in taking consumption–saving decisions. There are simply no rational means of making such guesses. People desperate to wriggle out of difficult situations can at the best consult astrologers. In such a scenario, obviously, the model developed by Fisher is laughably absurd. No one takes consumption–saving decision the way suggested by the model. Even though economics can hardly boast of any single even roughly accurate forecast, mainstream macroeconomics seems to set great store by the predictive power of economics and other sciences. Not even simpletons find such stances convincing. Given the dominance of babas (godmen), astrologers, temples and deities, it is quite clear how much strength today’s sciences give to the individuals. EXERCISE 9.2 (a) How will an increase in the retirement age affect the aggregate consumption function? (b) How will an increase in the proportion of old people affect the aggregate consumption function? (c) Compare the effects of the stabilization policy of reducing the tax rate in the following two situations: in one the consumption function follows the LCH and in the other the aggregate consumption function is Keynesian.

9.5

PERMANENT INCOME HYPOTHESIS

Permanent income hypothesis (PIH) was developed by Friedman (1957). It also built on the result yielded by Fisher’s intertemporal choice model. However, instead of making aggregate real consumption expenditure of individuals a function of the present value of their aggregate expected lifetime income, Friedman introduced the concept of permanent income, which he defined as the fixed level of aggregate real expenditure that the individuals can sustain indefinitely

Consumption Function

279

on the basis of their aggregate expected real lifetime income. The permanent income (denoted by Yp) may therefore be formally defined as follows:

W Þ

Yp 

Yp Yp   (1  r ) (1  r ) 2

"

Yp r

Yp = rW

(9.17)

Instead of making aggregate real consumption expenditure of the individuals (C) a function directly of W, Friedman made C a proportional function of Yp, which is directly a function of W. The microfoundation of PIH therefore also stems from Fisher’s theory of intertemporal choice. However, Friedman introduced a concept of permanent consumption, denoted by Cp which he defined as aggregate planned or aggregate expected real consumption expenditure. PIH thus postulates the following aggregate consumption function C = mYp

0 0, and Cp = mYp and (ii) Y = Yp, when Y = Y0. Again, for Y > Y0, YT = (1 + a)Yp and for Y < Y0, YT = –aYp.

9.6 CONCLUSION Keynes proposed a short-run aggregate consumption function which, he claimed, captures a fundamental psychological law of individuals. He regarded the proposed consumption function to be quite stable in the short run. The chief characteristic of the Keynesian consumption function is that MPC is positive but less than unity and APC is a decreasing function of aggregate income. Data on income and consumption lent solid support to the Keynesian consumption function. The results of cross section budget studies also satisfy Keynesian precept. They show that the APC of households of a higher income class is less than the APC of households of a lower income class. In India also the relationship between income and consumption satisfies Keynesian postulates not only in the short run but also in the long run. Long-run data on consumption and income show that the APC declined steadily from one decade to the next right from the fifties till the present, while aggregate real income also increased steadily all through the period under consideration. Kuznets’ finding in the context of the US economy, however, muddied the placid scenario regarding the income–consumption relationship. They showed that, even though income and consumption behave in accordance with the Keynesian postulates in the short run, the APC is constant in the long run. This finding, as you should be able to recall, is not borne out by Indian

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Macroeconomics

data which reveal a steadily declining APC with a steadily increasing aggregate real income in the long-run. Therefore, the efforts that were made to reconcile the short-run and long-run income–consumption relationship seem irrelevant in Indian context. We therefore choose not to waste much efforts at reconciliation of the short-run and long-run income–consumption relationships. They are relevant in the context of the US economy. However, we critically assessed two major efforts made at reconciling the short-run and long-run income–consumption relationships. These are the LCH and the PCH. We find both of these theories to be severely wanting as theories of individuals’ consumption behaviour.

REFERENCES Ando, A. (1963) and Modigliani, F. (1963), The Life Cycle Hypothesis of Saving: Aggregate Implications and Tests, American Economic Review. Friedman, M. (1957), The Permanent Income Hypothesis: A Theory of Consumption Function, Chapter 3, Princeton University Press.

10

Investment Function

Keynesian Theory of Investment in Fixed Capital

10.1

INTRODUCTION

Investment in fixed capital is at the core of the Keynesian explanation of trade cycles. Keynes regarded it as highly volatile and explained trade cycle in terms of its volatility. Keynes attributed the instability of investment to the uncertainty surrounding its future yields and the irrational optimism or pessimism that drives investment behaviour in such circumstances. According to Keynes, investment is the only component of final demand through which people’s expectation regarding the future affect the present. The classical or the neoclassical theory of investment does not put any emphasis on the uncertainty associated with the future yields from investment, which is obviously the most vital feature of investment. Hence these theories do not merit serious considerations. Therefore, in what follows, we shall ignore the classical and the neoclassical theories of investment and present only the Keynesian theory of investment in fixed capital.

10.2

INVESTMENT IN FIXED CAPITAL

Stock of fixed capital refers to the stock of machinery and equipment and construction. Investment in fixed capital means addition to the stock of machinery and equipment and construction. How do the entrepreneurs decide whether to add and by how much to add to the stock of fixed capital? To answer this question, let us start with an example. Suppose an investor wants to set up a factory. How does he decide whether it is worthwhile or not? He takes the decision on the basis of his expectation regarding the future income from the factory. Suppose he expects the factory to be in use for T periods. Suppose his expected profits inclusive of interest from 287

288

Macroeconomics

this factory during its T-period lifetime are given by Y1, Y2, Y3, …, YT. Suppose the marginal cost (MC) of constructing this factory is C. Also suppose r is the rate of discount, which, if applied to the expected income stream from the factory, makes the present value of the expected income stream from the factory equal to C so that

C

Y1 Y2   1  S (1  S )2

"  (1 Y S) T

T

(10.1)

r is called the internal rate of return of the factory. In any given period a large number of investment projects are available to the investors. Factories of various types can be set up, buildings of different types can be constructed and so on. Consider any given value of r, say, r0. Suppose the real value of the aggregate marginal cost of investment projects whose internal rate of return exceeds or equals r0 is denoted by I0. We can carry out this exercise for every given value of r and derive the aggregate level of investment (which is nothing but the aggregate marginal cost of making the given investment) as a function of r. Let us denote it by I(r). Corresponding to every r, I(r) gives the aggregate real marginal cost of constructing the investment projects whose internal rate of return exceeds or equals the given value of r. It is assumed that the law of diminishing marginal return holds. This means that the marginal cost of constructing an investment project goes up as the number of investment projects rises. Moreover, expected profits from investment projects also fall as the number of investment projects rises. For both these reasons, a lower rÿ is associated with a higher value of I and vice versa. Let us illustrate these points with an example. Suppose a factory is constructed. Its cost of construction is ` 100 and its internal rate of return is 20 per cent. Now suppose another similar factory is constructed. Because of diminishing returns its cost of construction will be higher than ` 100 and its expected future yields will be less than those of the first factory and for both these reasons its internal rate of return will be less than 20 per cent. Suppose it is 19 per cent and its cost of construction is ` 110. Assuming that there are no other investment projects available in the economy, I(r = 20%) = ` 100 and I(r = 19%) = ` 210. If we plot I(r) in the (I, r) plane, we get what Keynes calls the marginal efficiency of capital (MEC) schedule. This schedule gives corresponding to every I the internal rate of return of the last or the marginal unit of investment. If K0 is the amount of capital stock existing at the beginning of the period then the marginal efficiency of capital schedule gives corresponding to every given capital stock, K0 + I, the internal rate of return of the last or marginal unit of capital, which is the marginal efficiency of capital of the given capital stock. Suppose the value of r corresponding to a given level of investment, I0, is r0. Then r0 is the marginal efficiency of capital of the given stock of capital, K0 + I0. The marginal efficiency of capital schedule is shown in Figure 10.1. Let us now derive the relationship between the rate of interest and the optimum level of investment. Suppose the interest rate prevailing in the market is 10 per cent. Consider an investment project whose internal rate of return and cost of construction are 15 per cent and ` 100 respectively. This means that if ` 100 is taken as loan at the point of time under consideration at the rate of interest of 15 per cent, the expected profits from the project are just sufficient to service the debt. Obviously, it is profitable to undertake the investment project by taking a loan at any interest rate less than 15 per cent. From the above it follows that if the rate of interest is i0, then all investment projects whose internal rates of return exceed i0 are profitable

Investment Function: Keynesian Theory of Investment in Fixed Capital

289

Figure 10.1 Marginal efficiency of capital.

and all investment projects whose internal rate of return equals i0 will yield zero expected profit. All investment projects whose interval rates of return are less than i0 are unprofitable. Thus we get the optimum level of investment by setting r = i in the I(r) function. Thus, if i = i0, the optimum level of investment is given by I(r = i0). The situation is shown in Figure 10.2 where the optimum levels of investment and capital stock at the interest rate of i0 are labelled I and K respectively. Clearly, given expectations, the higher the rate of interest rate, the lower are the optimum levels of capital stock and investment. In other words, given expectations, investment is a decreasing function of the rate of interest.

Figure 10.2 Marginal efficiency of capital and investment.

10.3 CONCLUSION: VOLATILITY OF INVESTMENT Keynes regarded investment as extremely volatile. Its volatility stems from the lack of any rational basis for estimating future profit from any investment project. There is no way one can

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Macroeconomics

predict how much an investment project will yield 4 years or 8 years later. Keynes pointed out that in their investment behaviour investors are driven by some kind of optimism, which does not have any rational basis. To quote Keynes (1936), “it is important to understand the dependence of the marginal efficiency of capital of a given stock of capital on changes in expectation, because it is chiefly this dependence which renders the marginal efficiency of capital subject to somewhat violent fluctuations which are the spontaneous explanation of the trade cycle.”1 Again, in another place emphasizing on the volatility of investment, he states, “there is instability due to the characteristic of human nature that a large proportion of our positive activities depend on spontaneous optimism rather than on a mathematical expectation, whether moral or hedonistic or economic. Most, probably, of our decisions to do something positive, the full consequences of which will be drawn out over many days to come, can only be taken as a result of animal spirits—of a spontaneous urge to action rather than inaction, and not as the outcome of a weighted average of quantitative benefits multiplied by quantitative probabilities, … . Thus if the animal spirits are dimmed and the spontaneous optimism falters, leaving us to depend upon nothing but mathematical expectation, enterprise will fade or die—though fears of loss may have a basis no more reasonable than hopes of profit had before … . In estimating the prospects of investment, we must have regard, therefore, to the nerves and hysteria and even the digestion and reactions to the weather of those upon whose spontaneous activity it largely depends.”2

REFERENCE Keynes, J. M. (1936), The General Theory of Employment, Interest and Money, Macmillan, London, 1947.

1

Keynes, J.M., The General Theory of Employment, Interest and Money, Chapter 11, Marginal Efficiency of Capital, p. 144, Macmillan and Co. Limited, St. Martin’s Street, London, 1947. 2 Keynes, J.M., The General Theory of Employment, Interest and Money, Chapter 12, Long-term Expectation, pp. 161–162, Macmillan and Co. Limited, St. Martin’s Street, London, 1947.

11 11.1

Demand for Money

INTRODUCTION

Demand for money is crucially important in the determination of interest rate in the Keynesian theory, as the liquidity preference theory developed by Keynes determines interest rate not in the credit market but in the money market through the interaction of the forces of demand for and supply of money. In the Keynesian theory, repercussions in the real sector affect the monetary sector through their impact on demand for money. Changes in GDP engender changes in demand for money, which in turn affect the interest rate. The changes in interest rate reach back to the real sector through its impact on aggregate demand for goods and services exerting pressure on GDP. Thus, in the Keynesian theory, the demand for money plays a vital role in forging the link between the real and the financial sectors. In what follows we shall first define the concept of demand for money, specify the sources of demand for money and finally, present the theories of demand for money, which identify the factors that determine demand for money.

11.2 DEMAND FOR MONEY: DEFINITION AND SOURCES Economic variables are of two types, namely stocks and flows. A flow variable has a time dimension. It is expressed as a quantity per unit of time. Income, consumption, saving, etc., are all flows. If I say that my income is ` 1000, it does not make any sense. I have to specify whether ` 1000 is my daily income or monthly income or annual income, etc. Thus income has to be expressed as a quantity per unit of time. This is true for saving, investment, production, etc. A stock, in contrast, does not have a time dimension. It is simply expressed as a quantity at a given point of time. The supply of money, for example, is a stock. If I say that at the present moment supply of M3 in India is ` 100 crore, it makes perfect sense. It means that at the present moment total amount of currency and bank deposits in the possession of the public in India is ` 100 crore. 291

292

Macroeconomics

Demand for money is defined as the amount of money individuals want to hold on the average at every point of time. If I say that my demand for money at present is ` 200, it makes perfect sense. It means that at present I want or plan to hold ` 200 on the average at every point of time. Why should individuals want to hold money instead of spending them? If an individual spends immediately whenever any money comes his way, he does not want to hold any money and therefore his demand for money is zero. However, most individuals do not spend immediately whenever they get hold of some money. They keep some money in their hands most of the time. The question is why do they do that. Classical theorists identified only one source of or motive for holding money. They referred to it as the transactions motive. Keynes pointed to two more motives for holding money, namely precautionary and speculative. In what follows we shall dwell on them at length. EXERCISE 11.1 (a) What do I mean when I say that my demand for monry is ` 50. Is it a stock? (b) Consider a flour milling firm, which produces flour from wheat. Is its output a flow? Explain. (c) Is the allowance you get from your father to meet your expenses a flow? Explain.

11.3

TRANSACTION DEMAND FOR MONEY

Let us first focus on the transaction motive for holding money. This gives rise to transaction demand for money, which is defined as the amount of money that people want to hold on the average at every point of time to carry out their transactions. Transaction demand for money is for M1. Why should people hold M1 to carry out their transactions? They do so for two reasons. First, timings of people’s receipts of income and those of their expenses or purchases usually do not match. Second, it is costly to convert non-M1 assets into M1. Let us illustrate the two points with an example. Take the case of a salaried person. He gets his salary on the first day of every month, but normally his monthly purchases are not concentrated on the first day of every month. They are usually spread all over the month. It is quite possible for the person to put all his income in the form of non-M1 assets such as bonds, shares, etc., as soon as he gets his income, but he has to first convert them into M1 to make purchases and such conversions involve cost. To convert bonds into M1, the person has to contact his broker and ask him to sell some of his bonds. He has to pay a commission to the broker. The broker in turn has to find out a buyer to sell the bond. It involves time. These costs of converting nonM1 assets into M1 are referred to as brokerage fee in the literature of demand for money. Let us illustrate the predicament of not holding narrow money with a simple example. Suppose you have put all your income in bonds. Then everyday to make your daily purchases you have to first contact your broker and get some of your bonds sold for narrow money. Obviously, such behaviour is not optimal. Hence, for the two reasons specified above, people hold narrow money to carry out their transactions. What factors determine transaction demand for money (M1). We shall present the model developed by Baumol (1952) to identify these factors.

Demand for Money

293

EXERCISE 11.2 (a) Suppose an individual gets ` 100 daily and also spends ` 100 daily. What is his demand for money? (b) Will there be any transaction demand for money in an economy where it is costless to convert financial assets into currency? How do you define broad money in such a scenario? Explain your answer using the concept of liquidity.

11.4

BAUMOL’S THEORY OF TRANSACTION DEMAND FOR MONEY

The model developed by Baumol (1952) shows how an individual’s transaction demand for money is determined. It considers a given period of time and assumes that the individual whose transaction demand for money it focuses on plans to make purchases of a given value, denoted by T, in the given period of time. At the beginning of the period individual’s entire income is held in the form of non-money financial assets. Henceforth in the context of transaction demand for money, by money we shall mean only narrow money or M1. The individual decides to convert m amount of non-money financial assets into money at regular intervals during the given period to make the planned purchases. This means that he will have to make this conversion of non-money assets into money (T/m) number of times during the given period. Suppose the interest income yielded by the non-money assets he holds over the given period per rupee invested in such assets is r. Every time the individual converts his non-money assets into money he has to pay a fixed brokerage fee of ` B. The individual’s purchases or expenditures are uniformly spread over the given period. This means that, at every point of time during the given period, the amount of planned expenditure or the value of planned purchases of the individual is the same. The implication of the last assumption is that, if the individual withdraws m amount of money at the beginning of a given interval from his stock of non-money financial assets and uses it to finance his purchases, the amount of his money holding will decline uniformly (i.e. at a constant rate) during the interval and become zero at the end of the interval. The situation is shown in Figure 11.1 where the length of the first interval is given by the length of the line OA1 on the horizontal line OA. OA gives the length of the given period. At the beginning of each interval m amount of money is withdrawn. It is given by the length of the line OH. At the beginning of each interval the amount of money balance in the hands of the individuals is m or OH. It declines uniformly along the straight line HA1 until the money balance falls to zero at the end of the first interval. If we add up the money balance in the hands of the individual at every point of time during the given interval, the total will be given by the area of the triangle

Figure 11.1

Transaction balance.

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Macroeconomics

OHA1. The area of this triangle is [OH×OA1]/2 = m×OA1/2. The average money balance of the individual during the given interval is therefore given by [m×OA1/OA1]/2 = m/2. This is the average money balance of the individual not only in the first interval but also in every other interval during the given period. The average money balance of the individual during the given period is therefore m/ 2. We are now in a position to compute the cost the individual has to incur to make his planned purchases of the given period by withdrawing m amount of money at regular intervals. He has to make (T/m) number of withdrawals or conversions during the given period. Every time he makes the conversion, he has to incur a fixed brokerage cost of B. So his total brokerage cost in the given period will be B(T/m). Since his average money holding during the given period is (m/2), his stock of non-money assets is also less on the average by (m/2) during the given period. If his stock of non-money assets is less by ` 1, he loses, as we pointed out above, r amount of interest income during the given period. Therefore, if his stock of non-money assets is less by ` (m/2), he will lose ` (m/2)r of interest income during the given period. Thus the total cost of making his planned purchases during the given period by withdrawing m amount of money at regular intervals, denoted by C, is given by C = B(T/m) + (m/2)r

(11.1)

Obviously, the individual will choose m in such a way that C is minimized. Thus the individual will choose m by carrying out the following minimization exercise: min C m

B(T / m)  ( m /2) r

The FOC for maximization is given by

dC dm

r BT  2 m2

0

(11.2) d 2C

BT

! 0 is satisfied. We can dm m3 therefore solve (11.2) for the value of m that minimises C. Let us now explain (11.2). An increase in m exerts two opposite forces on C. A unit increase in C reduces the number of times non-money assets are to be converted into money, given by (T/m), by (T/m2), which in turn reduces brokerage cost by (BT/m2). It therefore gives the marginal benefit of raising m, which we shall henceforth denote by MBm. A unit increase in m, on the other hand, raises the average money balance held by the individuals in the given period, (m/2), by (1/2). This raises the amount of interest income foregone by (r/2). This is clearly the marginal cost of raising m. We shall denote it by MCm. At the optimum m, as follows from (11.2), MCm and MBm are equal. We plot MBm and MCm against m in Figure 11.2. They are given by MBm and MCm schedules respectively. The optimum m corresponds to the point of intersection of these two schedules. It is labelled m*. MBm schedule is a downward sloping convex curve that approaches ¥ as m tends to zero and approaches 0 as m tends to ¥. The MCm schedule, on the other hand, is horizontal at (r/2). At every m < (>) m*, MBm > ( rnmax, everyone’s speculative demand for money is zero and so is the aggregate speculative demand for money. At every r < rnmax, all the individuals whose normal interest rates are above the given r will consider it optimal to hold all their wealth in the form of money, making speculative demand for money positive. The less the r below rnmax, the larger is the number of individuals wanting to hold their wealth in the form of money, making the speculative demand for money larger. The speculative demand for money function for the economy as a whole is therefore downward sloping. At any r less than r nmin whatever be the level of aggregate wealth in the economy, the whole of it will be held in the form of money. The aggregate speculative demand for money function is shown in Figure 11.4.

Figure 11.4

11.8

Aggregate speculative demand for money.

TOBIN’S REFORMULATION OF THE KEYNESIAN THEORY OF SPECULATIVE DEMAND FOR MONEY

Tobin (1958) was not satisfied with the Keynesian theory of speculative demand for money. He interpreted the normal rate of interest of an individual as his expected rate of interest and pointed out that in Keynesian theory individual’s expected rate of interest is unique. Hence, he argues, the individual holds on to his expectation with certainty in Keynesian analysis. Accordingly, in Tobin’s view, Keynesian theory fails to capture uncertainty. Tobin also points out that, normally, an individual has a diversified portfolio, i.e. an individual usually allocates his wealth between money and bonds. Keynesian theory, according to Tobin, fails to explain why an individual has a diversified portfolio. To redress these shortcomings, Tobin reformulated

Demand for Money

299

Keynesian theory to assume that re takes many values and he assigns a subjective probability to each of these possible values of re. By dint of this assumption Tobin is able to show that a risk-averse individual usually diversifies. We shall assess Tobin’s work vis-à-vis Keynes’ later. Tobin’s model is based on the following assumptions. It considers an individual having a given amount of wealth, which is assumed to be unity for simplicity. The individual can hold her wealth in the form of either bond or money. Proportions of wealth held in the form of the bond and money are denoted by A1 and A2 respectively. Obviously, A1 + A2 = 1. The bond in Tobin’s model is a consol or perpetuity, which yields a fixed annual coupon, denoted by A, indefinitely. The current market rate of interest is denoted by r. The current price of a consol or perpetual bond considered here is therefore the present value of this indefinite stream of the fixed annual coupon discounted at the market rate of interest, r. Denoting the current price of bond by P, we have A A A (11.4) P   (1  r ) (1  r ) 2 r

"

The expected income of an individual thinking of buying the consol now after one year is given by the sum of the interest income from the consol, rP = A, and the expected capital gain from A A the consol given by ( P e  P)  , where re denotes the expected rate of interest that will e r r prevail one year from now. Therefore expected return from the consol, i.e. the income from every rupee invested in the consol denoted by m is given by A

N where g œ

rP P  P  P P e

r

e

P 1 P

e r  r 1 A r

Èr Ø 1 Ê r e ÙÚ

r É

rg

(11.5)

r

1. re Tobin assumes, as we have already mentioned, that the individual’s expected interest rate, re, and therefore this expected capital gain, g, can assume many values and he has a subjective probability distribution over these values of g. Tobin further assumes that the mathematical expectation of g denoted by N g

Çpg n

i i

0 , where pi is the probability assigned to the ith

i 1

value of g, which can assume n values. Standard deviation of g denoted by

T

pi (gi  N g )2 Ç i 1 n

is assumed to be a constant. Since, as follows from (11.5), every rupee invested in the bond yields an income of r + g, A1 amount of wealth invested in bonds and the rest in money yields an income of A1r + A1g, since income from money is zero. Mathematical expectation of income when the individual invests A1 amount of his wealth in bond and the rest in money, denoted by R, is given by

R

E ( A1r  A1 g)

A1r  E( A1 g)

A1r 

Ç p (A g ) n

i

i 1

1 i

A1r  A1 N g

A1r

(11.6)

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Tobin assumes that the risk of investing A1 amount of his wealth in bond and the rest in money is given by the standard deviation of the income from the portfolio given by A1r + A1g. Denoting the standard deviation of this income by r, we have

S

E ( A1r  A1 g  E ( A1r  A1 g)) 2 E ( A1r  A1 g  A1r ) 2 A1 ( g  E ( g)) 2

E ( A1r  A1 g  A1r  A1 E (g)) 2

E ( A1 g) 2

' E ( g)

E ( A1 g  E ( A1 g)) 2

E ( A1 g)

0

From the above it follows that

r = A1 s

(11.7)

From (11.6) and (11.7), it is clear that the individual can assume different amounts of risk and return by choosing different values of A1. Solving (11.7) for A1 and putting this value in (11.6), we get r R S (11.8)

T

Equation (11.8) gives all possible combinations of R and r that the individual can assume by varying the value of A1 from 0 to 1. Let us explain. First focus on the slope of (11.8), r/s, which gives the amount of increase in R that occurs following a unit increase in r. From (11.7), it follows that a unit increase in A1 will raise r by s. Therefore, if A1 rises by 1/s, r will go up by unity. However, if A1 rises by 1/s, R, as follows from (11.6), will increase by r/s. Let us start from the portfolio where A1 = 0 and A2 = 1. The values of R and r corresponding to this portfolio are both zero. If now the individual raises A1 by 1/s and therefore reduces A2 by 1/s, r will go up to unity from zero and R will rise to r/s from zero. If A1 is raised further by 1/ s and therefore A2 reduced further by 1/s, r will go up by unity from 1 to 2 and R will rise by r/s to 2r/s from r/s. This explains (11.8). It gives all combinations of risk and return the individual can assume by varying the values of A1 and A2. Hence it may be regarded as the individual’s budget constraint involving risk and return. We plot it in Figure 11.5. It is represented by the line BB, which is a ray through the origin, with the slope (r/s). Indifference curves of the individual in risk and return are superimposed on the budget constraint in Figure 11.5. Individuals are assumed to be risk-averse. Hence they willingly take more risk if and only if they get more expected return. Hence indifference curves are upward sloping. The amount of increase in R that compensates for a unit increase in r is assumed to rise with an increase in r. Hence indifference curves are convex downward. The individual is better off, if R is higher corresponding to any given r. Hence a higher indifference curve represents a higher level of utility to the individual. Obviously, an individual will choose from her budget line that point, which is on the highest indifference curve. This is clearly the one at which an indifference curve is tangent to the budget line. The indifference curve I0 in Figure 11.5 is tangent to BB. Hence it is the highest indifference curve attainable from BB. The point of tangency, H, is therefore the optimum point. Let us explain the individual’s optimum choice a little more. The slope of the budget line gives the amount of increase in return following a unit increase in risk. It is therefore the marginal reward of risk taking in terms of

Demand for Money

Figure 11.5

301

Choice of optimum portfolio.

return. The slope of the indifference curve at any point, on the other hand, gives the increase in return required to remain on the same indifference following a unit increase in risk from the given point. The slope of an indifference curve at any point therefore gives marginal required reward of risk taking. At the point of optimum choice on the individual’s budget line marginal reward of risk taking is equal to its marginal required reward. At every point on the budget line to the left of the chosen point marginal reward of risk taking is greater than the its marginal required reward. Hence the individual can go to a higher indifference curve by taking more risk, i.e. by moving right along his budget line. Similarly at any point on the budget line to the right of the chosen point, marginal required reward of risk taking is larger than marginal reward of risk taking. So from such a point the individual will gain by taking less risk, as his reward will fall less than what is required to keep him on the same indifference curve. Equation (11.7) gives the value of r corresponding to every A1. The inverse of (11.7) therefore gives the value of A1 corresponding to every r. In the fourth quadrant in Figure 11.5 the line A1s represents the inverse of (11.7), which indicates the values of A1 corresponding to different values of s. The value of A1 that corresponds to the optimum point, H, on the budget line, as read off from A1s, is A10. It gives the individual’s speculative demand for money at the interest rate, r0, which corresponds to the budget line BB in Figure 11.5. Let us now examine how a reduction in r affects the individual’s speculative demand for money. Following a decline in r, the slope of the budget line becomes less. Hence the budget line becomes a flatter ray through the origin. It is labelled BB1 in Figure 11.5. The point chosen

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by the individual from this new budget line is labelled H2. Let us now decompose the changes in R and r from H to H2 into substitution and income effects. Suppose, following the reduction in r and the consequent decline in R the individual’s income is compensated in such a manner that his budget line shifts upward remaining parallel to BB1 and becomes tangent to the original indifference curve, I0. This point of tangency is labelled H1. Following a decrease in r, marginal reward of risk taking falls. To derive the substitution effect of the decrease in r, we have to identify from the initially attained indifference curve, I0, the point that allows the individual to attain the given indifference curve at the lowest cost at the new lower marginal reward of risk taking. Consider a point on I0 at which marginal reward of risk taking is greater (less) than the marginal required reward of risk taking. If from such a point he raises (lowers) risk by unity, he will, as argued above, move over to a higher indifference curve. This means that by raising (lowering) risk by unity, he will be able to give away some of his income as tax remaining on the same indifference curve, i.e. by so doing he will be able to lower the cost of attaining the given indifference curve. Thus on I0 the point that minimizes the cost of attaining the given indifference curve at the new marginal reward of risk taking is the one at which marginal reward of risk taking equals its marginal required return. This point is labelled H1. Following the reduction in r, marginal reward of risk taking becomes less than the marginal required reward of risk taking. So the cost of attaining the initially attained indifference curve can be reduced by lowering the amount of risk taking. Thus, the substitution effect produced by a decline in r induces the individual to take less risk as it lowers marginal reward of risk taking. The individual takes less risk by switching his wealth from bonds to money. Thus the substitution effect rises by a decrease in the interest rate, raises speculative demand for money. Let us now focus on the income effect. A decrease in the interest rate reduces expected return corresponding to every given risk. It, therefore, lowers the real income of the individual. The decline in the rate of interest reduces the real income of the individual from I0 to I1 in Figure 11.5. The movement from H1 to H2 is due to change in the real income of the individual alone from I0 to I1 as marginal reward of risk taking is the same at both H1 and H2. The decline in r reduces expected return and thereby real income corresponding to the risk associated with H1. This will induce the individual to take more risk to raise expected return. Thus income effect induces the individual to take more risk by investing more in the risky asset, bond. Thus substitution and income effects work in the opposite directions. The former tends to raise speculative demand for money, while the latter tends to reduce it. Clearly, the speculative demand for money will vary inversely with r if substitution effect dominates the income effect. If substitution effect of changes in r dominates over the income effect, the aggregate speculative demand for money will also be a decreasing function of r. Tobin thus succeeds in showing that instead of putting all their wealth either in the form of risky assets or in the form of money, as happens in the Keynesian theory, individuals diversify their portfolio. EXERCISE 11.4 (a) Suppose in an economy individuals have only three different normal rates of interest. Derive the aggregate speculative demand for money schedule for such an economy. (b) Suppose in an economy the current rate of interest is equal to the minimum normal rate of interest of the economy. Suppose money supply in this economy goes up. In what

Demand for Money

(c) (d) (e) (f)

(g)

(h)

11.9

303

form will the economic agents hold this additional money as it gets into their hands? Explain. What will be an economy’s speculative demand for money, if people are certain about their future expenditures? Explain. How will speculative demand for money be affected, if standard deviation of g rises? How will speculative demand for money be affected, if reliable insurance policies covering different types of risk increase significantly? Explain. If, following an opening up of capital account, the chances of financial collapse in people’s perception go up, how will the speculative demand for money be affected? Explain. If an employee of an organization becomes a member of his organization’s employee’s credit society which makes cheap loans available in times of emergency, how will his speculative demand for money be affected? Consider a risk lover. How will his indifference curve look like in the risk-return plane? How will he allocate his wealth between money and perpetuity in Tobin’s model? Explain.

CONCLUSION

Evaluation of Tobin’s theory of speculative demand for money vis-à-vis Keynes’ Tobin’s assumption that individuals have subjective probability distributions over different possible values of expected capital gains is the precursor to the rational expectations theory of expectation formation. Given the multiplicity of financial assets and therefore that of interest rates, it is not possible to calculate the relative frequency of occurrence of any given value of the interest rate with any degree of accuracy. There may be various instruments for taking loans of a given maturity. They may be issued by different organizations. They may vary in their riskiness. The riskiness of an asset may vary from one economic agent to another. So, at any given point of time there usually exists large number of interest rates on loans of any given maturity. Given the mind boggling complexity and variety of the financial world and given the limited resources, time and knowledge available to the economic agents, they can hardly assign reliable values to the chances of occurrence of different possible values of interest rates. In fact, within a short period of time, the period of time considered in Keynesian theory, there may not occur any repetition of any value of the interest rate on any given asset. However, an individual may discern a central tendency of interest rates around which he observes the interest rates to vary and this central tendency may give rise to his notion of a normal level of the rate of interest to which he expects the interest rate to gravitate. To generate a notion of probability distribution, some specific values of the interest rate must recur systematically over some reasonably long period of time. However, such recurrences may not occur at all. Even if such recurrences happen, given the staggering multiplicity of interest rates on loans of any given maturity, it is extremely difficult to notice them.

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Let us illustrate the point with a simple example. Suppose husband of a housewife comes back home from office every evening. If his arrival time has a central tendency, his wife will notice it. If you ask her the time when her husband comes back home in the evening, she will be able to give an answer. She will say that he comes back at around 8 pm. If you then ask her, what is the probability that he will come back at 8.20 today, she is unlikely to be able to give any answer, which she can seriously rely on. It may be that in the last couple of months, her husband’s arrival time varied from 7 pm to 9.30 pm without any single repetition. Housewife’s calculation of the central tendency is also rough and may vary substantially from the actual mean calculated from the actual arrival times of her husband over the last couple of months. The central tendency discerned by the housewife is therefore subjective. Economic agents are intuitively keenly aware of the complexity of the economic world, the instability of the different factors impinging on different economic variables, the extreme inadequacy of their knowledge about how the economy works, the severe constraints operating on their time, resources, ability, accuracy and availability of data. Hence they are aware of the folly of making very precise calculations such as specifying probabilities of occurrences of different possible values of an economic variable. They consider it to be much more reasonable to act on the basis of the central tendency they discern in the values assumed by an economic variable. When we make an estimate of our family expenditure in the coming month, we go by the central tendency that we discern in all the different items of monthly expenditures of our family in the past months. We do not make the estimate by calculating mathematical expectation of different values of our monthly family expenditure after assigning each of them a probability of occurrence. Even if we look at the scenario objectively and assess it rationally, we do not find any rational basis for an individual attempting to assign probabilities of occurrences of different possible values of an economic variable. Economic mechanisms governing different economic variables do not remain unchanged over time. They are subject to change. Given their instability, the data thrown up by the period of time that we consider relevant for forming expectation may be too inadequate for calculating reliable estimates of relative frequencies. Let us go back to the example of the housewife and her husband. Suppose her husband changes office every year. The time relevant for forming an expectation of his arrival time in the current period is the time he spent in his current office and this period is at the most one year long. The data thrown up by this period may not contain even a single repetition and may be too inadequate to estimate relative frequency. However, had he spent twenty years in his current office, the data would have thrown up some specific pattern of relative frequencies. However, the time needed for the relative frequencies generated by a mechanism to be perceptible may be too long to allow the mechanism to remain unchanged. To go back to our example, had the husband’s office and everything else remained unchanged, the relative frequencies would have been observable after twenty years. However, twenty years may be too long for every thing to remain unchanged. Within the twenty years, even if husband’s office remains unchanged, its ownership and/or management may change, husband’s habits may change, transportation system may change, the couple may have bought a new house in a different location and so on and so forth. Moreover, a mechanism determining a variable may not ever throw up a specific relative frequency distribution of the variable it determines. In such a case the relative frequencies thrown up by the data will go on changing over time. Thus, even objectively, there does not seem to be any rational basis for trying to assign probabilities of occurrence to different possible values of an economic variable. Hence,

Demand for Money

305

Keynesian description of how an economic agent behaves seems far more rational than Tobin’s. The ubiquitous practice in economics of assigning probabilities to all possible values of economic variables does not stand up to close scrutiny. The other claim made by Tobin that economic agents have a diversified portfolio for speculative reasons cannot be verified empirically. People hold money for both speculative reasons and also for carrying out transactions. Thus, if we find that an economic agent is maintaining a diversified portfolio, it does not mean that he is doing so for speculative reasons. It may well be that he is holding risky assets only for speculative reasons and money only for carrying out transactions. Empirically, it is not possible to distinguish between transaction and speculative holdings of money. One important point should be made in this context. This will throw more light on the issue of diversification of portfolio. Most of the time the risk associated with bond holding stems from the uncertainty over whether the individual will be able to hold the bonds to their maturity. If the individuals are able to hold the bonds to their maturity, they are completely riskless. However, people may have to sell off the bonds before they mature to meet unforeseen contingencies and these unforeseen lumpy expenditures are what make bond holding risky. However, in most cases this uncertainty does not apply to the entire investable wealth of an individual. Every individual has some notion as to how much money he may keep ready to meet unforeseen contingencies. Availability of different types of insurance policies has also greatly reduced the necessity for holding large amounts of money for meeting contingencies such as accidents, illness, death, destruction of property due to natural calamities, etc. Hence the part of the wealth that the individuals do not consider it necessary to draw upon in case they have to make unforeseen lumpy expenses, they can safely hold in the form of government bonds or corporate bonds of repute, which are hundred per cent safe. The speculative demand for money becomes relevant only in the context of the remaining part of the wealth. If people are apprehensive of capital losses, they may choose to hold the entire remaining part of the wealth in the form of money. Thus, even if individuals hold only money for speculative reasons, we shall find them having a diversified portfolio.

REFERENCES Baumol, W.J. (1952), The Transactions Demand for Cash: An Inventory Theoretic Approach, Quarterly Journal of Economics. Keynes, J.M. (1936 & 1947), The General Theory of Employment, Interest and Money, Macmillan, 1947, London. Tobin, J. (1958), Liquidity Preference as Behaviour Towards Risk, Review of Economic Studies.

Part

II

Macroeconomics Gone Astray

12 12.1

New Classical and New Keynesian Theories

INTRODUCTION

New classical theories do not represent one school of thought. All the theories that came up since the beginning of the seventies challenging the Keynesian theory, the dominant paradigm in macroeconomics till the beginning of the seventies, are referred to as new classical theories. The distinguishing feature of this set of theories is that they subscribe to the view that prices in market economies clear markets even in the short run. They do not recognize market imperfections and the rigidities in prices as important in explaining macro behaviour of market economies. New Keynesian theory, on the other hand, subscribes to the Keynesian view that uncertainties, market imperfections, etc., and the rigidities they imply are central in shedding light on the macro behaviour of a market economy in the short run. The agenda of this theory is to strengthen the theoretical underpinnings of the Keynesian assumptions of price rigidities. They regard Keynesian explanations of such rigidities as inadequate. However, not much should be read in the difference between the new Keynesian and the new classical theories. The difference is only skin deep. Both these sets of theories repose unflinching faith in the efficacies of market economies and regard government interventions as harmful. The new Keynesians are of the view that market imperfections and rigidities are important only in the short run. They are transient phenomena. They reluctantly concede some ground to the Keynesian theory because recessions with large-scale unemployment of labour and capital heaping untold miseries on workers and capitalists alike occur regularly in market economies. They are of the view that, even if in the short run, exogenous demand shocks push a market economy into recession or into an inflationary situation, such an economy contains mechanisms that automatically restore the economy to full employment equilibrium. Therefore, in their vision, market economies behave in accordance with the classical theory except in the short run. In this chapter we shall 309

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give an overview of these theories, point to their similarities and differences and make a thorough evaluation of their positions.

12.2

STAGFLATION AND DEMISE OF THE KEYNESIAN ORTHODOXY

All the oil importing countries in the world in the seventies experienced surges in inflation along with rise in unemployment. The phenomenon is referred to as stagflation. The proponents of both the new Keynesian and the new classical theories regarded this phenomenon as being inconsistent with the Keynesian theory. They argue that Keynesian theory explains inflation in terms of inflationary gap, which is defined as an excess of aggregate planned final demand for goods and services over full employment output. Obviously, if this position is correct, inflation in Keynesian theory can occur only in situations of full employment. Accordingly, they found Keynesian theory inadequate in explaining stagflation. This led them to a search for a new paradigm that could provide insight into the mechanism of stagflation. The Keynesian theory, to quote Mankiw (1985), “could not adequately cope the rising inflation and unemployment experienced during the 1970s.” This inadequacy, it is claimed, induced the advent of the new classical and the new Keynesian theories. Before going into them, let us examine whether there is any merit in the claim that the Keynesian theory was too limited to explain stagflation. Petroleum exporting countries formed a cartel, organization of petroleum exporting countries (OPEC), in the 1960s. During the 1970s OPEC brought about a steep increase in the prices of petroleum and petroleum products. These prices quadrupled during the 1970s generating a tremendous cost push in oil importing countries where oil constituted an extremely important intermediate input in production. What kind of impact is it likely to produce in the CKM? Let us elaborate on this point with a simple example. Suppose aggregate output, denoted by Y, is produced with labour and an imported input using a fixed coefficient production function. Suppose l amount of labour and m amount of the imported input are needed per unit of output of Y. The wage rate and the price of the imported input are fixed at W and Pm respectively. Therefore the minimum price at which the producers will be willing to supply Y, i.e. the supply price of Y, is W l + Pmm. Hence the aggregate supply curve is horizontal up to the full employment level of output. Regarding the demand side we assume that there is no capital mobility and the exchange rate is fully flexible so that the trade balance is always zero. Under these conditions M L (Y , i) . P So we have the usual downward sloping aggregate demand (AD) schedule. The equilibrium (Y, P) corresponds to the point of intersection of the AD and the aggregate supply (AS) schedules as shown in Figure 12.1. If now Pm rises, say to P¢m, the AS schedule, as shown in Figure 12.1, will shift up. AD schedule will remain unaffected. Hence, there will occur, as is clear from Figure 12.1, a contraction in Y and a rise in P. Thus, following a hike in import prices, unemployment and prices will start rising generating stagflation. Oil shock therefore leads to stagflation in CKM. One can easily show that oil shock generates stagflation in CKM under much more general conditions. In any demand–supply model, an adverse supply shock that

the IS is given by Y

C (Y  T )  I (i)  G . The equation of the LM is given by

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311

Figure 12.1 Stagflation in CKM.

produces a cost push will generate stagflationary situations. Before the formation of OPEC, supply shocks were rare. Hence, Phillips curve was stable, and Keynes and the Keynesian theory emphasized on demand side factors to explain recession and inflationary situations. But the CKM is quite adequate to cope stagflation due to adverse supply shocks. The dismissal of the Keynesian theory on account of stagflation in the 1970s can hardly be vindicated on logical grounds. The motivation was surely political. EXERCISE 12.1 (a) Let us now dynamise the CKM presented above. Focus on the dynamics of price first. The price level is given by P* = Wl + Pmm. Now suppose there takes place an increase in Pm to Pm¢ m. Following this, the price level rises to P¢* = Wl + Pm¢ m. However, the price level will not rise to its new level at once. The price level will increase only gradually over time to its new level. Had there been just one good in the economy, the increase in the price level from P* to P¢* would have been instantaneous. However, as there are many goods in the economy and as most of these goods enter as intermediate inputs into the production of most other goods, P may take long to rise from P* to P¢*. Suppose Pm rises. It will first raise the prices of those goods into whose production the imported input enters as an intermediate input. These goods, in turn, enter into the production of some other goods as intermediate inputs. In the second round, therefore, prices of those other goods will go up. They also may be used as intermediate inputs in the production of some goods. Hence, there will be another round of increase in prices and this process will go on until the price level reaches its new equilibrium level, P¢*. There will thus be several rounds of increase in prices spread over quite a long period of time before the price level reaches its new equilibrium level. Let us illustrate the process with a simple example. Suppose in an economy only two goods,

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X1 and X2, are produced. Each of these goods enters into the production of the other as an intermediate input. Besides, the imported input is also used as an intermediate input in the production of both the goods. Labour is also used in their production. Suppose the amounts of labour, imported input and the jth good needed per unit of output of Xi are denoted by li, mi and xji, respectively, where i = 1, 2, j = 1, 2 and j ¹ i. We also assume for simplicity that 0 < x12 = x21 = x < 1. Given these assumptions, supply prices of X1 and X2, denoted by P1 and P2, respectively, are given by P1 = l1W + m1Pm + xP2 and P2 = l2W + m2Pm + xP1. Suppose both the goods are equally important in the country’s GDP so that the price level is given by the simple arithmetic mean of the two prices. Thus, P = (1/2)(P1 + P2) = (1/2) [(l1 + l2)W + (m1 + m2)Pm + x(P1 + P2)] = lW + mPm + xP. Solving for P, we get P = [l/(1 – x)]W + [m/(1 – x)]Pm. If now Pm rises by dPm, the price level P will go up by [m/(1 – x)]dPm. Let us see how P will increase by this given amount. In the first round P1 and P2 will go up by m1dPm and m2dPm respectively. In the next round, producers of both X1 and X2 will have to purchase the other good at a higher price. Hence their marginal and average costs of production and therefore their supply prices will go up. In the second round, prices of X1 and X2 will go up by xm2dPm and xm1dPm, respectively. At the beginning of the third round, therefore, X1 and X2 are dearer by xm2dPm and xm1dPm, respectively. So there prices will rise again by x(xm2dPm) = x2m2dPm and x(xm1dPm) = x2m1dPm, respectively at the end of the third round. This process will go on indefinitely until the increments in the prices of the two goods fall to zero. Thus the total increases in the two prices are given by x dP1 m1 dPm  xm2 dPm  x 2 m2 dPm  x 3 m2 dPm  m1 dPm  m dP 1 x 2 m x and dP2 m2 dPm  xm1 dPm  x 2 m1 dPm  x 3 m1dPm  m2 dPm  m dP 1 x 1 m Therefore

"

"

dP

dP1  dP2 2

m1  m2 x È m1  m2 Ø dPm  dP 2 1  x ÉÊ 2 ÙÚ m

mdPm 

x mdPm 1 x

1 dP 1 x m

The above example shows how gradually P reaches its equilibrium level over time. Denoting the equilibrium value of P = lW + mPm by P*, we can capture this gradual process of adjustment of P formally as follows dP a ¹ ( P *  Pt ) 0  a 1 (i) dt Suppose the aggregate demand function of the CKM is given by A – bPt. Since the aggregate supply curve is perfectly elastic in the CKM presented here as long as GDP is less than its full employment level, corresponding to every Pt producers produce the level of output demanded at the given price. So assume that corresponding to every Pt aggregate output is given by A – bPt. Given these assumptions, derive the time paths of P and Y and plot them in graphs under the condition that the initial value of P, P0 = P0* = lW + mPm and the equilibrium value of P = P1* = lW = mP¢m, where Pm¢ > Pm. Do you get stagflation here?

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313

(b) Adjustment in Y is also time-consuming. Generalize the dynamics of the case presented above by incorporating sluggish adjustments in output to demand corresponding to any given P. This may be formally captured by (dYt/dt) = ¶×([A – bPt] – Yt), where 0 < ¶ < 1. In this case also present the time paths of P and Y graphically. Check whether you get stagflation.

12.3 THE PHILLIPS CURVE In 1958, A.W. Phillips, a professor of London School of Economics, published a paper, which revealed an inverse relationship between the rate of wage inflation and the rate of unemployment during the period 1861–1957. Figure 12.2 reproduces the graph of the Phillips curve from the original article of Phillips. It is a study spanning a period of almost fifty years. Obviously, the inverse relationship between the rate of wage inflation and that of unemployment captured by Phillips is a long run one. From the scatter it is also clear that even if we had divided this long period into several short periods, say decades, we would have obtained almost the same relationship in every decade. In other words, the scatter does not suggest any marked difference in the relationship between the rate of wage inflation and the rate of unemployment in the short run and that in the long run. Since the rate of wage inflation and the rate of price inflation are very close to one another everywhere, Phillips curve later came to connote an inverse relationship between the rate of price inflation and the rate of unemployment. The Phillips curve, signifying an inverse relationship between the rate of price inflation and the rate of unemployment, was found to exist over much shorter periods also. Figure 12.3 depicts the Phillips curve showing an inverse relationship between the rate of price inflation denoted by p and the rate of

Figure 12.2 Original Phillips curve.

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Figure 12.3 Phillips curve in the US economy.

unemployment denoted by u in the 1960s in the US economy. In fact, “during the period 1900– 1960 in the United States, a low unemployment rate was typically associated with a high inflation rate and a high unemployment rate was typically associated with a low or negative inflation rate”. Thus, a stable inverse relationship between inflation and unemployment existed both in the short run and in the long run prior to the 1970s in both the UK and the US economy. The Phillips curve was also markedly stable in both the economies in the sense that there was no evidence of any marked change in the relationship from the short period to the long period. In other words, there was no evidence of any distinct shift in the relationship from one short period, say a decade, to another. It is quite easy to explain the Phillips curve within the Keynesian framework. In a market economy, individuals decide to invest in human and physical capital in an uncoordinated manner. Hence in any given period, the capacities created in different lines of production and the supplies of different kinds of labour seldom match. In this scenario, as GDP rises and approaches its potential level, shortages of various kinds of goods and services crop up putting upward pressure on prices. The closer the GDP gets to its potential level, the greater are the shortages and the more intense is the upward pressure on prices and consequently the steeper is the increase in prices per unit of time. The Phillips curve captures this phenomenon. We shall now extend the CKM a little to show how it can generate Phillips curve. To start with, for simplicity, assume that aggregate planned demand for goods and services, i.e. both aggregate planned investment demand and aggregate planned consumption demand, are insensitive to interest rate so that aggregate demand schedule, labelled AD in Figure 12.4, in the (Y, P) plane is vertical. Regarding the supply side we assume that as Y rises towards it potential or full employment level, scarcities of various types of labour develop forcing firms to compete with one another for scarce labour and thereby putting upward pressure on the wage rate. The closer the Y to its full employment level, the more will be the competition to hire scarce labour among firms and therefore the higher is the rate of wage increase per unit of time. The following equation captures this relationship formally: È dW / dt Ø Wˆ É œ W ÙÚ Ê

R Yf  Y Yf

R

!

0

(12.1)

New Classical and New Keynesian Theories

Figure 12.4

315

CKM and Phillips curve.

Again, for simplicity, we assume that goods and services are produced only with labour using a fixed coefficient production function. Let the labour requirement per unit of output be l. The supply price is therefore Wl. The supply function, labelled AS in Figure 12.4, is horizontal in the (Y, P) plane. The equilibrium occurs at the point of intersection of AD and AS schedules. The equilibrium Y is Y0. With Y at Y0, both W and P will rise, as follows from (12.1) at the rate

R

Y f  Y0 Yf

. If now the demand schedule shifts to the right and becomes vertical at Y1 > Y0, the

equililibrium will occur at Y1 and money wage rate and money price will grow in the new equilibrium at the rate

R

Y f  Y1 Yf

two equilibrium levels of Y are

!

R

Y f  Y0 Yf

. The rates of unemployment corresponding to the

lY f  lY0 lY f

Y f  Y0 Y  Y1 and f respectively. Thus a slight Yf Yf

extension of the CKM generates the Phillips curve. The result derived here will hold even if aggregate demand function is downward sloping and aggregate supply function is upward sloping. We explain it below. You should be able to recall that in the CKM aggregate supply function is derived from the production function Y F (K , L) and the labour market equilibrium condition given by PFL ( K , L )

W . We solve the labour market equilibrium condition for the labour market

equilibrium value of L as a function of P, given W and K . Substituting this value of L in the production function, we get Y as a function of P, given W and K . This is the aggregate supply

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function. We show the solution of the labour market equilibrium condition in Figure 12.5, where the horizontal line at W labelled LS gives the supply price of labour and the downward sloping schedule labelled LD gives the demand price of labour, when P is fixed at P0.

Figure 12.5 CKM with upward sloping AD and downward sloping AS.

New Classical and New Keynesian Theories

317

The equilibrium L, labelled L0, corresponds to the point of intersection of the LS and LD schedules. The level of Y produced with L0 is Y0. (Y0, P0) is a point on the aggregate supply schedule labelled AS in Figure 12.5. The equilibrium occurs also at (Y0, P0) in Figure 12.5 at the point of intersection of the AS and the aggregate demand schedule labelled AD. However, wage is not stationary. It rises at the rate

R . The rise in wage rate brings about upward Y f  Y0 Yf

shift in the AS schedule. This means that the procedures will supply the same Y at a higher P. It implies that there will now be excess demand at P0. So P will start rising along with Y. For the equilibrium to remain at Y0 and therefore at the rate of unemployment of

Y f  Y0 , the Yf

money supply will have to rise so the AD shifts upward too and intersects the new AS at Y0. It thus follows that if in an economy the unemployment rate is sustained at of price and wage inflation will be

Y f  Y0 , the rates Yf

R . Similarly, it can be shown that, if the economy Y f  Y0 Yf

sustains a lower rate of unemployment, it will have to bear with a higher rate of wage and price inflation. A simple extension of the CKM therefore generates the Phillips curve.

12.3.1 Oil Shock and Phillips Curve Since the beginning of the 1970s, the oil prices began to rise steeply. This obviously led to substantial escalation in costs and thereby in inflation rates, whatever was the rate of unemployment. Oil shock thus brought about upward shifts in the Phillips curve. We shall here examine what the impact of oil shock is on the Phillips curve using the framework of the CKM developed above. For simplicity, we assume that producers produce the output with labour and an imported input using a fixed coefficient production function. Suppose the amounts of labour and the imported input required per unit of output are l and m respectively so that the supply price of output is given by lW + mPm, where Pm denotes the price of the imported input. Whatever be the shape of the aggregate demand schedule, the equilibrium price level in the economy, denoted by P, is given by P = lW + mPm. Differentiating it with respect to time, denoted by t, we have dP dt

Þ

dP 1 dt Pt

l

dW dP dP 1 m m À ¹ dt dt dt P

l

dW 1 dP 1 m m dt P dt P

dP 1 1 dW m m l dt Wl  Pm m dt Wl  Pm m

l

dP dW m m mPm lW dt dt  lW Wl  Pm m mPm Wl  Pm m

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Pˆ

Þ

R Wˆ  (1  R )Pˆm

(12.2)

where

Pˆ

ˆ ˆ (dPt / dt )/ Pt , R œ lW/[ lW  mPm ], W œ l (dW/ dt )/[lW ], Pm œ [ d (mPm )/ dt ]/ mPm 

ˆ From (12.2) it follows that the rate of price inflation is an increasing function of W and Pm . Substituting (12.1) into (12.2), we can rewrite it as Pˆ

where

R

R  (1  R ) Pˆm Yf  Y Yf uœ

L f  L lY f  lY œ Lf lY f

R

R  (1  R ) Pˆm u

(12.3)

Yf  Y Yf

From (12.3) it is clear that the rate of price inflation is a decreasing function of u and an increasing function of the rate of oil price inflation. Obviously, if in any given period, given the rate of unemployment, W rises by 10 per cent and Pm increases by 5 per cent or 20 per cent, the rate of price inflation in the given period will be higher than what would have obtained had oil prices remained unchanged. Taking the numerical values of l, m, W and Pm, verify the above proposition yourself.

12.4 NEW CLASSICAL THEORY The advent of the new classical theory can be traced to Friedman (1968). The discomfiture of the theorists with classical leanings can be well understood, since the classical theory is inconsistent not only with the short-run cyclical fluctuation in GDP but also with the Phillips curve, which shows that the rate of unemployment can assume a large number of values, while classical theory predicts only zero rate of unemployment in market economies. The challenge before those who were opposed to the Keynesian ideas was to modify the classical theory to explain cyclical fluctuations in GDP and the Phillips curve retaining the key classical assumptions of perfectly competitive markets and market clearing prices. It was Friedman who took up the challenge and sought to meet it in a dubious way. Since he found himself incapable of reconciling the classical theory with the inverse relationship between the rate of unemployment and the rate of wage inflation discovered by Phillips, he claimed without any evidence that the relationship discovered by Phillips is only partial or incomplete. He posited that the rate of wage inflation depends not only on the rate of unemployment but also on economic agents’ expected rate of inflation. The problem with this assertion is that expected rate of inflation cannot be perceived. Hence the hypothesis cannot be empirically verified. The other problem is that Phillips considered a fairly long period of time, almost a century, during which both the rate of unemployment and the rate of wage inflation varied widely. Had the rate of wage inflation depended on any factor other than the rate of unemployment, this other factor was unlikely to have remained unchanged

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over such a long period of time in the face of such wide variations in the rate of unemployment and the rate of wage inflation. The expected rate of inflation was particularly likely to respond to such large variations in both the rates of unemployment and wage inflation. Hence, if there were any other factors influencing the rate of wage inflation, it would have changed widely too during such a long period. Hence, we would have found evidences of marked shifts in the relationship between the rate of wage inflation and the rate of unemployment and these shifts might even have obfuscated the clear inverse relationship between the rate of wage inflation and the rate of unemployment. However, in the data cited by Phillips, we do not find any evidence of any marked shift in the relationship between the rate of wage inflation and the rate of unemployment. The relationship seems very stable and clear—refer to Figures 12.2 and 12.3. There was no room for the suspicion that there might be another variable impinging on the relationship between the rate of wage inflation and the rate of unemployment. There was also no basis for Friedman’s (1968) claim that the period covered by Phillips was a period of stable rate of inflation, as during the long period covered by Phillips both the rate of unemployment and the rate of wage inflation varied considerably. Despite all the telltale evidences, to the contrary, Friedman went on to rewrite the equation of the Phillips curve to make the rate of wage inflation depend not only on the rate of unemployment but also on the expected rate of inflation. This modified version of the Phillips curve is referred to as the expectation augmented Phillips curve. We shall discuss it in detail below.

12.4.1

Expectation Augmented Phillips Curve

In the late 1960s Friedman and Phelps famously predicted that the Phillips curve would shift. Their predictions dramatically came true in the 1970s in the midst of much fanfare and both of them won Nobel Prize in economics. However, it needed no genius to make the prediction made by Friedman and Phelps. It did not involve any deep economics. The petroleum exporting countries formed a cartel, OPEC, in the mid 1960s to eliminate competition among themselves. It was clear that OPEC was planning a steep hike in oil prices. Since oil constituted an essential intermediate input in production, any substantial increase in oil prices was bound to generate a tremendous cost-push effect bringing about a steep increase in the rate of inflation, whatever might have been the rate of unemployment. This obviously meant a marked upward shift in the Phillips curve. It was clear that the rate of inflation in oil importing countries depended not only on the rate of unemployment but also on the world oil prices. Phillips relation, as we have done in the previous subsection, clearly needed a reformulation to include world oil prices besides unemployment as a determinant of inflation rate. Amazingly, Friedman and Phelps and their followers identified expectations regarding future rate of inflation as the main determinant of inflation rate besides unemployment and relegated oil prices to the background. In their view the shift in the Phillips curve was mainly due to the changes in people’s expectations regarding future rate of inflation and they incorporated expected rate of inflation in the Phillips relation and renamed it expectation augmented Phillips curve. To quote Friedman (1968) “Phillips’ analysis of the relation between unemployment and wage change is deservedly celebrated as an important and original contribution. But, unfortunately, it contains a basic defect—the failure to distinguish between nominal and real wage rates. Implicitly, Phillips wrote his article for a world in which everyone anticipated that nominal prices would be stable and in which that

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anticipation remained unshaken and immutable whatever happened to actual prices and wages. Suppose, by contrast, that everyone anticipates that prices will rise at a rate more than seventy five per cent a year … . Then wages must rise at that rate simply to keep real wages unchanged”. Thus, Friedman suggests that corresponding to any given rate of unemployment, the rate of inflation that will obtain in the economy is determined by the economic agents’ anticipated or expected rate of inflation. Since Phillips curve remained stable prior to the 1970s and became unstable thereafter, the implication of Friedman–Phelps hypothesis is that people’s expectation regarding future rate of inflation remained stable in the former period and became volatile in the latter period. Obviously, it is not clear why people’s expectations should behave in this manner. Moreover, whether actual rate of inflation depends upon expected rate of inflation or not is not verifiable empirically. The motivation for inclusion of expected rate of inflation is clearly a suspect. It reeks of politics. The next section will confirm this suspicion. (Only one American textbook, that of Ackley, attributed the upward shift in the Phillips curve to the oil shock alone and not to an increase in the expected rate of inflation. The text has since then gone out of circulation.) We may criticize Friedman’s hypothesis from another angle also. The above quotation from Friedman (1968) implies that, what economic agents consider important is the rate of growth of real wage rate and not the rate of growth of nominal wage rate. There is no doubt that the variable that is important to the firms and the workers is not the nominal wage rate but the real wage rate. However, the question is whether people can have any expected rate of inflation or whether it is possible for the economic agents to take decisions on the basis of their expected rate of inflation. Note that there is no way of knowing what the rate of inflation is going to be in, say the next two years. Even policymakers in the government cannot make reasonably accurate prediction of the future rate of inflation. This is because economics is as yet far from developing models capable of even roughly accurate predictions of any economic variable. Models in economics enable us to identify the major forces that influence any given economic variable. They also help us make policy prescriptions to tackle inflation, recession, etc. Even there we have a sharply divided house. Inflation in India depends upon a large number of factors such as the state of weather, international oil prices, economic condition of the rest of the world, our government’s fiscal and monetary policies, etc., and these are only broad categories. There is no way to predict how these variables will behave in future. Economic agents are intelligent enough to know all this and obviously do not take any trouble hazarding a guess regarding the future values of the rate of inflation. In such circumstances, whatever be the future course of prices, an increase in the nominal wage rate makes the workers feel better off compared to the situation where there is no increase and the higher the rate of increase in the money wage rate the greater is the rate of increase the real wage rate that the workers and firms expect. One may argue at this point that an increase in wage rate is likely to exert an upward pressure on future prices and hence an increase in nominal wage rate may not make the workers feel better off. We can counter this with the following arguments. First, money wages are raised not by all firms together in one go. They are raised by individual firms acting independently of one another in an uncoordinated manner. An increase in the nominal wage rate by a single firm is unlikely to produce any impact on the future price level. So workers who receive higher wage rate from the firm they work in or about to join have no reason to expect a rise in the future price level on account of the higher money wage rate they have received. Moreover, besides money wage rate, there is a whole host of factors that influence the price level. Hence no clear relationship between

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changes in the current money wage rates and the future price level may be discernible. Finally, even if workers think rightly or wrongly that an increase in the current money wage rate will raise the future price level, they accept raises in their pay by their own firms, as they cannot prevent workers in other firms from accepting such hikes. Clearly, if wages go up in all firms except in one, workers working in the firm where wages have not gone up will be worse off relative to the workers working in the other firms. The implication of the above discussion is that, to individual worker the future course of the average price of goods and services they consume is independent of the money wage rate he is receiving or bargaining for. Hence, an increase in the money wage rate he receives makes him feel better off. Thus, when there emerges shortages of labour, firms compete with one another by offering higher nominal wages and workers accept jobs offering higher nominal wage rates. Keynes was of the view that workers have no means of controlling either the economy-wide average wage rate or the price level. Nor do they have any sensible means of forming reliable expectations of the future rate of inflation. Hence, they, while deciding on whether to accept a job or to quit or to demand a raise, compare the money wage rate being offered to or being received by them by the firm they work in or are thinking of joining to the wage rate being paid to similar workers in other firms. In other words, Keynes was of the view that workers while deciding on whether to demand a raise or quit a firm to join another, etc., are guided not by the real wage rate, which is changing all the time. They take these decisions on the basis of what money wage rate they are getting in relation to what similar workers in other firms are getting. To drive home this point Keynes pointed to an asymmetry in the behaviour of workers. He pointed out that when a firm seeks to cut money wages of its workers, workers resist as much as possible. However, they remain passive when the price level goes up, even though the rise in the price level has the same impact on the real wage rate as that of a cut in the money wage rate. In sum, as workers have no means of ensuring for themselves any given real wage rate, they take decisions on the basis of the money wage rate only. No wonder Phillips derived a clear and stable inverse relationship between the rate of unemployment and the rate of inflation even in the long run. There was no expected rate of inflation at the root of the observed relationship between the rate of unemployment and the rate of inflation. EXERCISE 12.2 (a) When your mother hires a domestic help, how does she determine her pay? (b) Suppose you hire workers to build a house, how will you determine their money wage rates? Will you be happy, if they ask for wage rates higher than those that similar workers engaged in building other houses are getting? Will they be unhappy if you offer them the wage rates prevailing for similar workers in the market? Do you think that the expected rate of inflation of yours or that of workers for the period of construction of the house have anything to do with the determination of the wage rates of the workers you engage? (c) Suppose you work in a firm and your job is to determine the wage rates of different categories of workers working in your firm. Do you not think that the most important information that you need to do your job is how much similar workers engaged in other firms are getting? Is not this also true of your workers, while they decide on whether they should remain in your firm or quit? Does the expected rate of inflation figure anywhere in these calculations?

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(d) Suppose you get a job in the campus placement organized by your university/institute. What factors do you take into account to decide whether you have got the job you deserve? Does expected rate of inflation play any role here?

12.4.2

Expectation Augmented Phillips Curve, Aggregate Supply and Natural Rate Hypothesis

Before introducing Friedman’s expectation augmented Phillips curve, we shall have to first briefly introduce the concept of natural rate of unemployment and natural rate of output. They are both related to the full employment situation. The full employment situation has never been evidenced anywhere, i.e. no one has ever observed an economy where there are no vacancies or unemployment. Vacancies and unemployment always exist in every economy. This has led the new classical economists to postulate that even in the full employment situation, where labour demand and labour supply are equal, there exists some unemployment matched by an equal number of vacancies. The rate of unemployment that exists in the full employment situation is called, a la Friedman (1968) who extended Wicksell’s natural rate of interest to unemployment, the natural rate of unemployment. The output that the firms produce in the full employment situation, given the natural rate of unemployment, is called the natural rate of output and is denoted by Yn (see Figure 12.6).

Figure 12.6

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The expectation augmented Phillips curve is given by the following equation

Q Q e  a ¹ (un  u) a!0 (12.4) where p º actual rate of inflation, pe º expected rate of inflation, u º actual rate of unemployment

and un º natural rate of unemployment. Using Okun’s law, which posits a one-to-one relationship between (un – u) and (Y – Yn), where Yn denotes the natural rate of output, the above equation is rewritten as

Q

Q e  b ¹ (Y  Yn ) b ! 0 (12.5) e Equation (12.5) states that, when Y = Yn, p = p and the higher (less) the Y relative to Yn, the greater (less) is p relative to pe. Friedman and his descendants interpreted (12.5) as the aggregate supply curve. For this they rewrote it in the following manner. We dPt know that d log Pt (# log Pt  log Pt 1 ) . Hence we can write ln Pt  ln Pt 1 # Q t Pt and ln Pte  ln Pt 1 # Q te . Denoting ln Pt , ln Pt 1 and ln Pte by pt , pt 1 and pte respectively, we rewrite the equation of the expectation-augmented Phillips curve as pt

pte  b ¹ (Yt  Yn )

(12.6)

The model of aggregate output (GDP) and the price level has been developed on the basis of (12.6). Equation (12.6) is interpreted as the aggregate supply curve. Since pt and Pt have a one-to-one relationship with one another and since the same is true of pte and Pte, (12.6) is rewitten as Pt Pte  b ¹ (Yt  Yn ) b!0 (12.7) Pt in (12.7) gives the supply price of Yt. Equation (12.7) states that, when Yt = Yn, Pt = Pte and the higher the Yt relative to Yn, the greater is Pt relative to Pte. We shall explain later how we get (12.7) as the aggregate supply curve. For the time being accept it as the aggregate supply curve. The aggregate demand function is derived from the IS-LM model. It is given by Pt = A – BYt (12.8) There is equilibrium in this model when demand price and supply price are equal. There are two concepts of equilibrium here, namely the short-run equilibrium and the long-run equilibrium. The short run is defined as a period of time during which expectations remain unchanged. The long run, on the other hand, is defined as a period of time long enough to allow the expected price to change and also to be realized. The short-run equilibrium is therefore the equilibrium that obtains when demand price and supply price are equal and the expected price is given. The short-run equilibrium is therefore given by the following equation, where Pte is given: (12.9) Pte + b×(Yt – Yn) = A – BYt The model in the short run is given by (12.7), (12.8) and (12.9). They contain three endogenous variables, viz. Yt and demand price and supply price of goods and services, the latter two are, however, equal in equilibrium. We can solve the system as follows. Solving (12.9), we get the equilibrium value of Yt. Putting the equilibrium value of Yt in (12.7) and (12.8), we get respectively the equilibrium values of demand price and supply price, which are equal. Thus, putting the

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equilibrium value of Yt in either (12.7) or (12.8), we get the equilibrium value of Pt. The solution of these equations is shown in Figure 12.7 where the AD schedule represents the aggregate demand function (12.8) and SAS(Pte) represents the short-run aggregate supply function (12.7) for a given expected price Pte. Clearly, the short-run equilibrium values of Pt and Yt correspond to the point of intersection of the SAS(Pte) and AD and they are denoted by Yt0 and Pt0 respectively.

Figure 12.7 Short-run equilibrium.

Equilibrium in the long run The economy, as follows from the definition of the long run, is in long-run equilibrium if expectations are realized, i.e. if Pt = Pte (12.10) and demand price and supply price are equal. The long-run equilibrium is therefore given by (12.7), (12.8), (12.9) and (12.10). They contain four endogenous variables—demand price and supply price (which are both equal in equilibrium), Pte and Yt. Let us now see how we can solve (12.7), (12.8), (12.9) and (12.10) for the long-run equilibrium values of the endogenous variables. From the aggregate supply function, (12.7), it follows that, when (12.10) holds, the producers produce Yn. Thus in equilibrium in the long run, aggregate output settles down to its natural rate, i.e. Yt = Yn

(12.11)

Substituting (12.11) into (12.9), we get the equilibrium value of Pte, as given by Pte = A – BY n

(12.12)

Putting it in (12.10), we get the equilibrium value of Pt, which is the equilibrium value of both of the demand price and the supply price. The equilibrium value of Pt is thus given by Pt = Pte = A – BYn

(12.13)

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Let us explain the solution given by (12.11), (12.12) and (12.13). From (12.7) it follows that in the long-run equilibrium, producers will produce Yn, whatever be the value of the supply price and the expected price, as long as the two prices are equal. Putting the equilibrium value of Yt in the aggregate demand function, we get the equilibrium value of the demand price, the price at which aggregate demand exactly equals Yn. If producers produce Yn, the price in the market will settle down to the level of the demand price corresponding to Yn. If the market price differs from the demand price corresponding to Y = Yn, there will be either excess demand or excess supply depending upon whether the market price is below or above the demand price corresponding to Yn. In the long-run equilibrium, producers plan to supply Yn at any given supply price as long as the supply price and the expected price are equal. In the long-run equilibrium therefore the supply price and the expected price should be equal to the demand price corresponding to Yn. Thus equilibrium values of the demand price, supply price and the expected price and therefore those of Pt and Pte in the long run are given by (12.13). The solution of the long-run equilibrium is shown in Figure 12.8 where the vertical line LAS gives the long-run aggregate supply function representing (12.11). (12.11) states that in the long run producers produce Yn whatever be the value of Pt. Thus the long-run aggregate supply function, (12.11), is vertical in the (Y, P) plane at Yn. AD represents the aggregate demand function, (12.8). The equilibrium values of Pt and Pte correspond to the point of intersection of AD and the LAS in Figure 12.8.

Figure 12.8 Long-run equilibrium.

The motivation for incorporating expectations in the Phillips curve and interpreting the expectation-augmented Phillips curve as the aggregate supply curve is now quite clear. The model shows that in the long run GDP settles down to its natural rate, even though it may deviate from its natural rate in the short run. The result that the GDP will settle down to its natural rate in the long run obviously follows from the definition of the long-run equilibrium and the specific form given to the aggregate supply function. It is undeniable that there occurs booms and busts in the short run in a market economy invalidating the classical theory. To accommodate these short run cyclical fluctuations in GDP, the model presented above allows

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GDP to deviate from its natural rate in the short run. But the model establishes the efficacy of a market economy by showing that even if GDP may deviate from its natural rate in the short run, it settles down to its natural rate in the long run, i.e. there can never occur unemployment of labour and capital in excess of their respective natural rates in the long run. The motivation for incorporating the expected rate of inflation in the Phillips curve in the way it has been incorporated and its interpretation as the aggregate supply function is therefore to show that even if GDP in a market economy may deviate from its natural rate in the short run, it can never do so in the long run. In fact, we shall show later that if we change the form of the expectationaugmented Phillips curve only slightly to write it as Q t

MQ te  b(un  u), where 0  M  1, so

that the equation of the aggregate supply function becomes Pt M Pte  b(Y  Yn ) with 0  M  1 , the result reported above will no longer hold. GDP in such a situation will, except accidentally, deviate from its natural rate even in the long run. Let us now see how Friedman gives a theoretical foundation to the aggregate supply function, (12.7), i.e. how he explains why aggregate supply should behave in accordance with the aggregate supply function specified by him.

Theoretical foundation of the aggregate supply function The challenge before the new classical theorists led by Friedman (1968), who subscribed to the classical view that all the markets are perfectly competitive and prices clear markets all the time, was to show how GDP can fluctuate creating cycles of booms and busts under such conditions. To meet this challenge, the first step that Friedman took was to incorporate inflation expectation in the equation of the Phillips curve and to interpret it as the aggregate supply curve. (It is strange that the aggregate supply function, (12.7), with just the additional feature of a serially uncorrelated disturbance term attached to it, is referred to as Lucas supply curve. It should have been named after Friedman. Following the innovations by Friedman, it became a cakewalk for his descendants, namely, Lucas and his associates, to build on from where Friedman had left off and to, to quote a phrase often used by Friedman and as we shall show shortly, do too much.) The next step he took was to give an explanation of the proposed aggregate supply curve without deviating from the classical assumptions that all the markets are perfectly competitive and all the prices clear markets all the time. In other words, the next step for Friedman was to provide an explanation of the aggregate supply curve he proposed making as little changes as possible to the classical model retaining the assumptions of perfectly competitive markets and the market clearing prices. We present his explanation below. Friedman developed his explanation of the aggregate supply function, (12.7), on the basis of the perfectly competitive labour market of the classical theory, where, as you should be able to recall, labour demand is a decreasing function of the real wage rate, while labour supply is an increasing function of the real wage rate. The labour market is in equilibrium when demand for and supply of labour are equal. The equilibrium in the labour market is referred to as the full employment situation. The levels of output and employment that occur in this situation are called the full employment or potential levels of output and employment and are denoted by Yf and Lf respectively. This situation is shown in Figure 12.9, where real wage rate, denoted by w, is plotted on the vertical axis in the lower panel and labour demand and labour supply, denoted by LD and LS respectively, are measured on the horizontal axis in the lower panel. LDLD and LSLS represent the labour demand and labour supply schedules respectively in the lower

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panel. L denotes employment. In the upper panel L and Y are measured on the horizontal and vertical axes respectively. In the upper panel the concave line labelled F(×) is the production function. You should be able to recall that labour supply function is derived from the utility maximizing behaviour of the workers and labour demand function is derived from the profit maximizing behaviour of the firms. Hence parameters of the utility functions of the workers are the parameters of the labour supply function. They therefore determine its position and shape. Similarly, the given stocks of capital and natural resources along with the parameters of the production function or the technology determine the position and shape of the labour demand schedule. Given these parameters of the labour demand and labour supply schedule, Yf and Lf give the maximum levels of output and employment possible in a market economy, where economic agents participate in economic activities on their own volition. There is no coercion or application of force. Hence firms and workers demand and supply only those quantities of labour, which maximize their profits and utilities respectively and are determined, as we have shown earlier, only by the real wage rate, given the parameters noted above. In the full employment situation, the level of real wage rate that prevails is the full employment real wage rate and is denoted by wf (see Figure 12.9). In this situation firms and workers demand and

Figure 12.9 The labour market in the classical model.

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supply the same quantity of labour, Lf, and therefore there is equilibrium in the labour market (see Figure 12.9). Firms produce the corresponding level of output, Yf (see Figure 12.9). If w falls below wf, labour supply will fall, while labour demand will rise. Employment at this lower w will obviously be determined by the amount of labour supply. Hence both output and employment will go down below Yf and Lf respectively. For similar reasons, if w rises above wf, employment and output will again fall below Yf . However, the full employment situation has never been evidenced anywhere, i.e. no one has ever observed an economy where there are no vacancies or unemployment. Vacancies and unemployment always exist in every economy. This has led the new classical economists to postulate that even in the full employment situation, where labour demand and labour supply are equal, there exists some unemployment matched by an equal number of vacancies. The rate of unemployment that exists in the full employment situation is called, a la Friedman (1968) who extended Wicksell’s natural rate of interest to unemployment, the natural rate of unemployment. The output that the firms produce in the full employment situation, given the natural rate of unemployment, is called the natural rate of output and is denoted by Yn (see Figure 12.6). Economists have identified two major factors responsible for the natural rate of unemployment, namely (i) imperfect information and (ii) imperfect mobility of labour across space and occupations. To quote Friedman (1968) “the natural rate of unemployment, in other words, is the level that would be ground out by the Walrasian system of general equilibrium equations, provided there is imbedded in them the actual structural characteristics of the labour and commodity markets, including market imperfections, stochastic variability in demands and supplies, the cost of gathering information about job vacancies and labour availabilities, the costs of mobility and so on.” Because of the first factor, imperfect information, some persons may remain unemployed despite matching number of vacancies. They take some time and searching to be aware of the existence of suitable vacancies. Similarly, firms may also take some time to be aware of the existence of suitable candidates. By the time the existing vacancies are filled up and the existing unemployed workers find employment, some new vacancies may be created through retirement of employees and inflow of new workers into the job market. Thus unemployment may persist because of imperfect information even in the full employment situation. Again, some vacancies may remain unfilled and some persons may remain unemployed because the skills of the unemployed may not match the skill-requirements of the vacancies. Thus the requirement may be for the doctors, while the unemployed may be engineers. This kind of mismatch to a certain extent may persist always in a market economy, giving rise to some unemployment even in the full employment situation. Again, the spatial distribution of unemployment and that of vacancies may not match and hence, if labour is not perfectly mobile over different parts of a country, there will exist some unemployment even in the situation of full employment. In a market economy, where economic activities are not coordinated by any central authority, the kind of mismatches referred to above is likely to exist to some extent all the time. This explains the natural rate of unemployment. However, we have argued later in the Chapter 13 on modern theories of growth that the concept of natural rate of unemployment is likely to be fundamentally flawed. Let us now focus on how Friedman derives the aggregate supply function from the labour market of the classical model. The aggregate supply curve that we get from the labour market of the classical theory, as you must be able to recall, is vertical. However, Friedman managed to get an upward sloping aggregate supply curve from the same labour market by dint of one

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single assumption. The assumption that did the trick was that the workers cannot perceive a change in the average price level immediately. They take some time to do so. The assumption is justified on the ground that workers do not buy all the goods and services at every point of time. At any given point of time they buy only a few of the goods and services they use. Thus they take some time to realize that prices of not just a few but of more or less all goods have changed. They are aware of this problem, and therefore, while taking decisions regarding labour supply, calculate the real wage rate on the basis of some expected price level, which they expect to prevail in the economy. Regarding money wage rates, however, workers do not have any misperception as they receive them directly. Firms, on the other hand, perceive perfectly the price level and the money wage rate prevailing in the economy since they themselves produce and sell all the goods and services and make the wage payments. The assumption is clearly quite weak and we shall dwell on its weaknesses at length later. Let us now present Friedman’s model formally. First consider the situation where there is no misperception on the part of either workers or firms. Both these groups of economic agents perceive the price level, the money wage rate and therefore the real wage rate actually prevailing in the economy. The labour market in this situation is characterized by the following equations: LD = LD(w); LD¢ < 0 (12.14) LS = LS(w);

LS¢ > 0

L (w) = L (w) D

and

S

(12.15) (12.16)

where w denotes the real wage rate actually prevailing in the economy and perceived by both the firms and trade unions. The equilibrium in the labour market in this situation represents full employment and the real wage rate yielded by the equilibrium condition is the full employment real wage rate, which we denote by wf. Therefore, when there is no misperception, producers will employ L , the natural rate of employment and produce Yn, the natural rate of output. Friedman’s model differs from the one presented above in that, even though workers and firms perceive the money wage rate prevailing in the economy, the workers, unlike the firms, cannot perceive the price level and calculate the real wage rate, while deciding on how much labour to supply, on the basis of an expected price, which they expect to be prevailing in the economy. Let us now denote this expected price level by Pe. Accordingly, the real wage rate they expect to prevail and on the basis of which they take their labour supply decision is given by (W/Pe), where W denotes the actual money wage rate of the economy. (W/Pe) may differ from the actual real wage rate, (W/P), P being the actual money price. Hence the labour supply function in Friedman’s model is given by LS = LS(W/Pe) (12.17) Since firms do not have any misperception, the labour demand is given by (12.18) LD = LD(W/P) Equilibrium in the labour market may therefore be written as (12.19) LD(W/Pe) = LS(W/P) Finally, the production function is given by Y

F ( K , L );

FL ! 0 and FLL  0

(12.20)

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This model yields the amount of output firms will produce at every P, given Pe. This model in fact consists of four equations, (12.17)–(12.20). We can solve these four equations for W, LD, LS and Y, given P and Pe. In other words, we can solve these four equations to determine firms’ labour market equilibrium levels of output and employment and the labour market equilibrium money wage rate corresponding to every P, given the value of Pe. Graphical solution of these equations is shown in Figure 12.10 where the upper panel shows the production function, while the lower panel shows the labour demand and labour supply schedules, labelled LD and LS respectively, against money wage rate corresponding to some given values of P and Pe. The LD is drawn for a given value of P, while the LS corresponds to a given value of Pe. The labour market equilibrium values of W and employment correspond to the point of intersection of the LD and LS schedules. The labour market equilibrium level of Y is given by the point that corresponds to the equilibrium level of employment on the production function. Clearly, if W is above its equilibrium value, there is excess supply of labour and hence it will fall and vice versa.

Figure 12.10 Derivation of aggregate supply function in Friedman’s model.

Now suppose P = Pe. In this situation, the workers’ expected price and the actual price prevailing in the economy are equal. Hence both firms and workers perceive the actual real

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wage rate prevailing in the economy. Under these conditions the labour market equilibrium money wage rate deflated by the actual price level prevailing in the economy should yield the full employment real wage rate, which refers to the real wage rate that equilibrates the labour market when there is no misperception. Otherwise, the labour market cannot be in equilibrium. Let us explain. If at the equilibrium W and the given price level the real wage rate is above (below) the full employment real wage rate, both workers and firms in the present case will correctly perceive it, since P = Pe. Hence there will be excess supply (excess demand) in the labour market. Thus, when P = Pe, full employment real wage rate will prevail in the economy and accordingly firms will produce the natural rate of output, Yn. Let us now consider an increase in P, with Pe remaining unchanged. Every W now corresponds to a lower actual real wage rate and the firms perceive it correctly. Their demand for labour therefore increases at every W. Hence the labour demand schedule shifts to the right in Figure 12.10 following the given increase in P. The new labour demand schedule is labelled LD(P¢) in Figure 12.10. Workers, however, cannot perceive the increase in P and continue to calculate the real wage rate on the basis of their Pe, which remains unchanged. Hence the labour supply schedule remains unaffected. At the initial equilibrium money wage rate, labelled W0 in Figure 12.10, therefore there will emerge excess demand for labour, as shown in Figure 12.10. The equilibrium money wage rate will therefore rise through competition among producers for scarce labour. The rise in W will raise the real wage rate as perceived by the workers inducing them to supply more labour. W and labour supply will thus rise together along the labour supply schedule LS(Pe). As the real wage rate rises through the increase in W, labour demand will fall. W will rise and labour demand will fall along the new labour demand schedule, LD(P¢). Through the increase in W that raises labour supply and lowers labour demand, the excess demand for labour created at the initial equilibrium money wage rate will be removed and the labour market will come to equilibrium with a higher W and larger employment and output. As shown in Figure 12.10, the equilibrium occurs at B with a higher W and larger levels of output and employment. The actual real wage rate will, however, be less in the new equilibrium. Otherwise, the demand for labour and therefore the level of employment would not have been larger. From the above it follows that, if P = Pe, producers will produce Yn. If P rises (falls) from e P , producers will raise (lower) Y from Yn. The higher (lower) the P relative to Pe, the greater is the rightward (leftward) shift of LD and therefore the larger (smaller) is

Behaviour of the economy when aggregate supply is derived from Friedman’s model We shall here illustrate the behaviour of the aggregate demand–aggregate supply model given by Eqs. (12.7), (12.8), (12.9) and (12.10), when the aggregate supply function (12.7), is derived from Friedman’s model. This we shall do by examining the impact of an increase in money supply that gets manifested in an increase in A in the aggregate demand function, (12.8). Suppose the economy was initially in a situation of both short-run and long-run equilibrium as shown in Figure 12.11 at (Yn, P0) corresponding to the point of intersection of the aggregate demand schedule labelled AD, the long-run aggregate supply schedule labelled LAS and the short-run aggregate supply schedule labelled SAS(Pe = P0). The states of the goods and labour markets corresponding to this situation are shown in Figures 12.11 and 12.12 respectively.

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Figure 12.11

Figure 12.12

Behaviour of the new classical AD–AS model.

The states of the goods, money and labour markets.

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Following an increase in money supply, denoted by M, the LM in Figure 12.12 shifts to the right, given P. The IS, however, remains unaffected. Hence goods market and money market will be in equilibrium at a larger Y corresponding to every P. Therefore the AD schedule shifts to the right in Figure 12.11. The new AD is labelled AD1. Since M is not a parameter of the aggregate supply function, the short-run aggregate supply schedule, SAS(Pe = P0) and the longrun aggregate supply schedule LAS are not affected by the changes in M. Hence in the short run, as follows from Figure 12.11, both P and Y will increase. The new higher values of P and Y are labelled P1 and Y1 respectively in Figure 12.11. Let us now see how P and Y rise to their new short-run equilibrium values from their initial equilibrium values, (Yn, P0). First, there emerges an excess demand for goods and services at the initial equilibrium P and Y. Since the goods market is perfectly competitive, dissatisfied buyers begin to bid up prices. Firms perceive the increase in prices, but workers do not. Firms therefore perceive the decline in the real wage rate and raise their demand for labour at the initial equilibrium money wage rate. Workers, however, do not perceive any change in the real wage rate and hence continue to supply the same amount of labour as before at the initial equilibrium money wage rate. There thus emerges an excess demand for labour at the initial equilibrium money wage rate and it begins to rise as a result. Since workers have not perceived any change in the price level, the increase in money wage rate to them means an increase in the real wage rate. Hence they increase their supply of labour bringing about an increase in employment and output. The point can be explained easily with the help of Figure 12.12, where the initial labour demand and labour supply schedule plotted against the money wage rate, W, are labelled LD(P0) and LS(Pe = P0) respectively. Following any given amount of rise in P, which is perceived by the firms and not by the workers, the labour demand schedule shifts to the right, as shown by the dotted line, while the labour supply schedule stays unchanged. This is because corresponding to every W the real wage rate to the firms is now less, but to the workers is the same. Hence W starts rising, raising the real wage rate, and this is perceived by both workers and firms. Hence labour demand falls along the new dotted labour demand schedule and labour supply rises along the LS(Pe = P0) and the labour market achieves equilibrium at higher levels of W, L and Y at B following the given amount of increase in P. Thus, with the rise in P, there takes place an increase in Y. Moreover, P and Y rise along the initial SAS, SAS(Pe = P0), in the short run—refer to Figure 12.11. When P and Y rise to P1 and Y1 respectively, see Figure 12.11, aggregate demand and aggregate supply become equal and the economy achieves the short-run equilibrium. This happens in the period, say, period zero. In course of time, as they purchase more and more goods, workers perceive the rise in the P from P0 to P1. Once they perceive the new price level, they revise upward their expected price in the next period, say Period 1. Here for simplicity we assume that they revise upward their P fully from P0 to P1. Let us explain its implications below. Workers now expect a lower real wage rate to prevail corresponding to every given money wage rate. More precisely, corresponding to every money wage rate the real wage rate expected by the workers is now (W/P1), while it was (W/P0) previously. Hence at every W, workers now supply less labour than previously bringing about a leftward shift in the labour supply schedule in Figure 12.12 in Period 1. Since P1 prevails in the economy, firms perceive it and as a result both the firms and the workers perceive the same real wage rate corresponding to every money wage rate. When workers and firms perceive the same real wage rate corresponding to every W, labour market, as we have already pointed out, will be in equilibrium at the full employment real wage rate. Hence, at P1 the labour market will be in equilibrium at the full employment

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real wage rate, with the full employment amount of labour being demanded and supplied. Hence at P1 firms will supply in Period 1 the natural rate of output, Yn. Hence the SAS will shift upward and cut the LAS at the new expected price, P1, in Period 1. The SAS in Period 1 is therefore given by SAS(Pe = P1) in Figure 12.11. At P1 therefore, with the revision of the expected price from P0 to P1, Y will fall from Y1 to Yn in Period 1 creating a situation of excess demand. Through an adjustment process the same as the earlier one P and Y will rise along the new short-run aggregate supply schedule, SAS(Pe = P1), until Y equals aggregate demand in Period 1. This short-run equilibrium (Y, P) is given by A2 in Figure 12.11. The actual price will therefore exceed the expected price again bringing about a further leftward or upward shift in the short-run aggregate supply schedule in the next period. This process will be repeated until the short-run aggregate supply schedule intersects the new aggregate demand schedule, AD1, at Yn. In Figure 12.11 this happens when the expected price, Pe, rises to P* and the corresponding short-run aggregate supply schedule labelled SAS(Pe = P*) intersects AD at P*. In this case, the actual equilibrium price and the expected price become equal so that there is no reason for the workers to revise their expected price. Hence this equilibrium will be replicated period after period. This is the long-run equilibrium situation. This model therefore establishes the result that exogenous shocks to demand lead to deviations of GDP from its natural level, but in the long run it settles down to its natural level. The model thus successfully explains short-run cyclical fluctuations in GDP in terms of exogenous shifts in aggregate demand retaining the classical assumptions of perfectly competitive markets and market clearing prices and at the same time shows that GDP settles down to its natural rate in the long run. This yields the famous natural rate hypothesis (NRH), which states that in a market economy in the short run exogenous shifts in demand conditions bring about deviations of GDP from its natural rate generating business cycles of booms and busts. But in the long run, GDP settles down to its natural rate. This implies that in the short run a market economy behaves in accordance with the Keynesian theory, but the classical theory best describes its behaviour in the long run. Let us now subject Friedman’s theory to close scrutiny. He derived the aggregate supply curve from the assumption that workers perceive changes in the price level only with a lag. The assumption is untenable for the following reasons. Note that workers, while taking decisions regarding labour supply, calculate the real wage rate not on the basis of the prices of all the goods and services produced in the economy. They are concerned with prices only of those goods, which they consume. Even though they receive their wages and salaries monthly or weekly, they buy the goods and services they need daily. They go to the market daily to buy vegetables, groceries and other items of food. They have to pay transport charges every day commuting to their places of work from home and back. They have to pay rents for their rented houses regularly. They have to pay doctors’ fees and buy medicine quite often for the ill and the elderly members of their families. They also pay fees to the schools and colleges of their children. If prices of these items change, they will come to know of them immediately. In many cases, take the case of house rents or educational charges, for example, they will be informed of the changes in prices immediately. It is true that workers are likely to buy consumer durables infrequently, but their prices are advertised daily in the media. Thus the assumption that the workers will come to know of the changes in the average price of the goods and services they consume with a delay, does not make much sense. Needless to say, the theoretical foundation Friedman developed in support of the aggregate supply function he proposed is extremely weak. No sensible theory of business cycles can be built on such a weak foundation.

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Another crucial problem with the NRH is that its validity depends crucially on the form of the aggregate supply function. If its form changes even slightly, the NRH ceases to hold. Suppose the aggregate supply function has the following form P = kPe + q × (Y – Yn)

00

(12.23)

P = nlPe + nf × (Y – Yn) Þ P = kPe + q × (Y – Yn)

(12.24)

W = lPe + f × (Y – Yn)

0 0 and

= Yn + g × (Pt – Pt ) e

B>0

g>0

(12.29) (12.30)

where Ytd º aggregate demand for goods and services, Yts º aggregate supply of goods and services, Yn º natural rate of output and Pte º expected price in period t. Friedman’s new classical descendants failed to give any plausible theoretical explanation of (12.30). So, in what follows we shall stick to Friedman’s explanation of (12.30) for purposes of illustration of our arguments, despite obvious weaknesses in Friedman’s theoretical construct. The economy is in equilibrium when aggregate demand for goods and services is equal to aggregate supply of goods and services. The equilibrium condition is therefore given by A – BPt = Yn + g × (Pt – Pte)

(12.31)

Pte

When the theory underlying (12.31) is that of Friedman, denotes workers’ expected price. Pt is not perceived by and therefore known to the workers. They are uncertain regarding its value. However, when they have rational expectations, they know that (12.31) determines Pt. If they substitute Pt for Pte in (12.31) and solve it for Pt, they will get the Pt, which, if expected, will be realized. They will set Pte equal to that Pt. The equilibrium value of Pt and Pte is therefore given by A  Yn Pt Pte (12.32) B Substituting the equilibrium value of Pt and Pte in (12.30) or substituting the equilibrium value of Pt in (12.29), we get the equilibrium value of Y, which is given by Yt = Yn

(12.33)

Workers will therefore expect the price as given by (12.32). Here not only workers but also all other economic agents have rational expectations. So all other economic agents also know the model and their expected price and output are also given by (12.32) and (12.33). Producers will accordingly produce the natural rate of output. This model shows that when economic agents have rational expectations, a market economy remains in full employment equilibrium always. Thus the model cannot explain recessions or business cycle. Rational expectation theorists call this a model of perfect foresight. Note that this is a misnomer since workers in this model do not have perfect foresight. They cannot perceive the price level. However, they form accurate expectation of the price level on the basis of the model presented above. Rational expectations theorists were not content with this model, since it cannot explain recession. They wanted to reconcile two incompatible goals. On the one hand, they wanted to show that a market economy has a strong mechanism that tends to keep it in full employment equilibrium all the time. At the same time, they wanted to explain recessions, which last for two to six years or more. Without realizing the contradiction inherent in the two positions, they set about their task in the following manner. They incorporated a serially uncorrelated error term, et, in the supply function. et has zero mean. This kind of an error term can be incorporated in the aggregate demand function as well. However, here for simplicity we incorporate it in the aggregate supply function only. The aggregate supply function is therefore rewritten as Yts = Yn + g . (Pt – Pte) + et

g > 0

(12.34)

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The aggregate supply function, (12.34), states that producers do not have complete control over supply. Aggregate supply can deviate from what is planned by the producers because of the random disturbance term, et. Similar disturbance terms can be incorporated in the aggregate demand function as well. We shall do it later. Rational expectation theorists think that the incorporation of et is sufficient to explain recessions or cyclical fluctuations in GDP. Let us now see why they think so. Rational expectations theory claims that the random disturbance term incorporates uncertainty in the model and interprets Pte as the mathematical expectation of Pt. Thus Pte

E ( Pt )

(12.35)

In equilibrium A  BPt

Yn  H ¹ ( Pt  Pte )  F t

(12.36)

The model is now given by (12.29), (12.34), (12.35) and (12.36). Let us now see how this model is solved. As before people know that the equilibrium Pt is given by (12.36). Solving (12.36) for Pt, we have

A  Yn  H Pte  F t (B  H )

Pt

(12.37)

Workers with rational expectations will calculate mathematical expectation of Pt using (12.37). Thus E (Pt )

E( A)  E (Yn )  H E( Pte )  E (F t ) (B  H )

A  Yn  H E( Pte ) BH

' E(F ) t

0 by assumption (12.38)

Since E(Pt) º Pte, we rewrite (12.38) as

A  Yn  H Pte B H

Pte Solving for Pte, we have

A  Yn B Equation (12.39) gives the expected price of the workers. Substituting (12.39) into (12.37), we have Pte

Pt

A  Yn  H Pte  F t (B  H )

(H  B) A  (H  B)Yn  BF t B( B  H )

(12.39)

(12.40)

Subtracting (12.39) from (12.40), we have Pt  Pte



Ft

BH

(12.41)

Substituting (12.41) into (12.34), we have Yt  Yn

BF t B H

(12.42)

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Equation (12.42) states that Yt exceeds Yn and the economy experiences boom, when the random disturbance term et is positive. Again, Yt falls short of Yn and the economy enters into recession, when the random disturbance et term turns negative. Thus, new classical rational expectation theorists explain booms and busts in terms of random shocks.

Policy irrelevance proposition New classical rational expectations theory suggests that, as we have already discussed, government policies, unless they are completely random, will be anticipated by the economic agents. They will factor them in while forming their expectations and thereby render government policies impotent and irrelevant in influencing output and employment. We shall first formally establish this policy irrelevance proposition and then subject it to close critical scrutiny. To derive the proposition in a simple framework we first incorporate a government’s policy instrument in the aggregate demand function (12.29) and rewrite it as Ytd = Agt – BPt

(12.43)

where gt º the policy instrument. gt may be interpreted as government expenditure, or money supply in period t. Rational expectation theorists claim that if government’s policy is not random—and it cannot be random if the government uses it for some purpose, for example, for the purpose of stabilizing the economy—economic agents from their past observations will perceive the mechanism that determines government’s policies. The assumption is not surprising. If economic agents can perceive the mechanisms that determine the values of all the economic variables, they should also be able to discover the mechanism that determines the values of government’s policy instruments. Let us establish the policy irrelevance proposition using a very simple policy rule. Interpret gt as money supply. Suppose the amount of increase in money supply is an increasing function of the shortfall of actual output from its potential level, Yn, and the excess of targeted price, P*, from its actual level. Here we assume that the government wants to stabilize the price level to P* and Y to Yn. Suppose the mechanism that determines gt is given by gt  gt 1

S ¹ (Yn  Yt 1 )  G ¹ ( P *  Pt 1 )  O t

S ! 0 and G ! 0

(12.44)

where nt is a random disturbance term. People perceive this rule and anticipate the value of the government’s policy instrument. In equilibrium the aggregate demand and the aggregate supply, as given by (12.43) and (12.34) respectively, are equal. The equilibrium condition is therefore given by Agt  BPt

Yn  H ¹ ( Pt  Pte )  F t

(12.45)

The model is thus given by (12.34), (12.35), (12.43), (12.44) and (12.45) in five endogenous variables, Ytd, Yts, Pt, Pte and gt. The system is therefore determinate. We can solve these equations for the five endogenous variables. We solve this system as follows. Solving (12.45) for Pt, we get

Pt

Agt  Yn  H Pte  F t (B  H )

(12.46)

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We can derive mathematical expectation of Pt from (12.46). Thus, as follows from (12.35),

E ( Pt )

Pte

AE ( gt )  E (Yn )  H E ( Pte )  E (F t ) (B  H )

AE ( gt )  H Pte  Yn (B  H )

(12.47)

Solving (12.47) for Pte, we have Pte

AE ( gt )  Yn B

(12.48)

Substituting (12.48) into (12.46), we get Pt

H AE ( gt )  (H

 B)Yn  BF t  ABgt B( B  H )

(12.49)

Subtracting (12.48) from (12.49), we have Pt  Pte

H AE ( gt )  (H

 B)Yn  BF t  ABgt AE (gt )  Yn  B( B  H ) B

BAE ( gt )  BF t  ABgt B( B  H )

A[ E ( gt )  gt ]  F t (B  H )

We can calculate E(gt) from (12.44). E ( gt )

gt 1  S ¹ (Yn  Yt 1 )  G ¹ ( P *  Pt 1 )

' E (vt )

(12.50)

0

(12.51)

Subtracting (12.44) from (12.51), we get E(gt) – gt = –vt

(12.52)

Substituting (12.52) into (12.50), we have Pt  Pte

 Avt  F t (B  H )

(12.53)

Equation (12.53) gives the equilibrium value of Pt – Pte. Therefore, substituting (12.53) into (12.34), we get the equilibrium value of Yt , since in equilibrium Yt = Ytd = Yts. Yt

Þ

Yt  Yn

Yn 

H (  Avt

 Ft )

(B  H )

BF t  H Avt (B  H )

 Ft (12.54)

From (12.54), it follows that equilibrium Yt can deviate from its natural level only because of the random disturbance terms et and vt. Thus, even after incorporating government’s policy, we find that the deviation of aggregate output from its natural rate can be explained only in terms of random factors. This highlights starkly the contradiction of the assumption of rational expectations and the stabilization measures adopted by the policymakers without any exception to tackle every crisis that an economy gets afflicted with.

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EXERCISE 12.6 (a) Suppose aggregate demand and aggregate supply functions of India are given respectively by Pt = Mt – 0.2Yt and Pt Pte  0.5(Yt  Yn ) . Suppose Mt = 20 and Yn = 50. If Indians have rational expectations, what values will Yt, Pt and Pte assume? How long is the Indian economy likely to take to achieve this equilibrium? Illustrate the equilibrium graphically and explain. Is there any room for cyclical fluctuations in GDP in this model? Explain. Suppose M t M  O t , where vt denotes a random error term, with mean zero. Derive now the equilibrium values of the endogenous variables of the model? Is there now any scope for cyclical fluctuations of GDP in India? If your answer is yes, what is the source of these cyclical fluctuations? Illustrate graphically with an example and explain. Suppose vt in Period 1 is 10 and it is zero in every subsequent period. What are the equilibrium values of the endogenous variables in Period 1? What are the equilibrium values of the endogenous variables in Period 2 and in Period 3, when (i) economic agents have rational expectations and (ii) economic agents do not have rational expectations? Assume that the economic agents behave in accordance with Friedman’s model in both the cases except for the fact that in (i) they have rational expectations.

12.5.2 Evaluation of the New Classical Rational Expectation Theory Let us first summarize the results of the new classical rational expectation theory presented above. It states that in the absence of random shocks, a market economy remains always in full employment equilibrium with natural rates of output and unemployment. In a market economy the short-run cyclical fluctuations in GDP and employment are produced by unidentifiable random shocks either to demand or to supply or to both. Governments’ stabilization programmes are also completely unnecessary, ineffective and therefore irrelevant. What are the factors driving the result reported above? From the above it is clear that the results follow from the assumption of rational expectation, and the specific form of the aggregate supply curve. The form of the aggregate supply function is such that, when expected price equals the actual price, producers produce the natural rate of output. When individuals have rational expectations, they know the model and therefore the equilibrium price, which, if expected, will be realized. This is the long-run equilibrium price at which aggregate demand exactly equals the natural rate of aggregate output. Individuals with rational expectations also know that, when expected price equals the actual price, it is optimal to produce the natural rate of output. They will therefore straight away produce the natural rate of output and charge their expected price, which is the price at which aggregate demand exactly equals the natural rate of aggregate output establishing the long-run equilibrium in the short run itself. It is difficult to find an assumption more absurd than that of rational expectation even in economics. Despite its laughable absurdity, it constitutes the basis of all the major macroeconomic theories today. It constitutes the basis of the new Keynesian theory as well. It is sheer waste of time and effort to mount a critique of this assumption. Even Friedman who innovated NRH

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never ever made such claims. His views were, in fact, just the opposite. To quote Friedman (1968) “the Great Contraction might not have occurred at all, and if it had, it would have been far less severe, if the monetary authority had avoided mistakes or if monetary arrangements had been those of an earlier time when there was no central authority with the power to make the kind of mistakes that the Federal Reserve System made. The past few years, to come closer to home, would have been steadier and more productive of economic well-being if the Federal Reserve avoided drastic and erratic changes of direction, first expanding the money supply at an unduly rapid pace, then, in early 1966, stepping on the brake too hard, then, at the end of 1966, reversing itself and resuming expansion until at least November, 1967, at a more rapid pace than can long be maintained without appreciable inflation … . I believe that potentiality of monetary policy in offsetting other forces making for instability is far more limited than is commonly believed. We simply do not know enough to be able to recognize minor disturbances when they occur or to be able to predict either what their effects will be with any precision or what monetary policy is required to offset their effects. We do not know enough to be able to achieve stated objectives by delicate, or even fairly coarse, changes in the mix of monetary and fiscal policy”. Thus, according to Friedman, even Federal Reserve with all the resources at its disposal was at a loss to handle the troubles that occurred and made mistake after mistake greatly reinforcing the destabilizing forces. If, even the Federal Reserve does not have a clue as to the mechanisms that determine economic variables, how will an individual have that knowledge? Moreover, the assumption of rational expectations involves serious contradictions. Let us elaborate. From our above discussion of the assumption of rational expectations it follows that people with rational expectations cannot be fooled except by random events. However, even though these same people constitute the central bank and the government, they are fooled into adopting stabilizing measures whenever recession or inflation occurs. Government and the Central Bank do not stay passive to such crises. They seek to tackle them through a slew of fiscal and monetary measures. When people have rational expectations, why should the people running the government and the central bank behave so irrationally? Their activities cannot be justified by any ulterior motive other than that of stabilizing the economy, since people with rational expectations cannot be fooled. The assumption of rational expectations is surely inconsistent with the stabilization efforts on the part of the policymakers. New classical rational expectation theorists, as we have seen above, explain booms and busts in terms of random shocks. Is this explanation satisfactory? We elaborate on this below. A market economy does not grow steadily over time. It grows through cycles of booms and busts. Periods of recession succeed those of booms and vice versa. Periods of recession during which a country’s GDP falls substantially below its potential level lasts for two years to six years or more subjecting the people without jobs and also those with unutilised expensive productive capacity to tremendous misery and deprivation. One of the major objectives of macroeconomics is to explain these cycles of booms and busts and to suggest ways of stabilizing these movements. An economic theory seeking to explain an economic variable identifies all the major factors that influence the economic variable and constructs a simple model to show how those factors determine the given economic variable. The world is a seamless whole where everything is connected to everything else. Hence there may be myriad factors, other than those that the theory has identified, that have a bearing on the given economic variable. The supposition in this context is that some of these myriad other factors affect the given economic variable

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positively, while the others exert on it negative influences and in the net these positive and adverse effects cancel out each other. The implication is that the whole value of the given economic variable is explained by the factors identified by the theory. If this assumption does not hold, i.e. if the net effect of these myriad other factors on the given variable is non-zero and large, the theory is a failure, as it cannot explain quite a large part of the value of the given variable in terms of the factors it has picked up. In other words, in such a case it is clear that the theory has failed to identify one or more of the factors that exert substantial influence on the given variable. In the new classical rational expectations theory, the net effect of these myriads other factors is captured by the random disturbance term, e. Recession constitutes substantial and long lasting deviation of GDP from its potential value. During recession people remain jobless for two to six years or more. Producers remain saddled with unutilized installed capacity for long driving them to bankruptcy. New classical rational expectations theory explains recession in terms of e. Therefore eÿ may be substantially large. This implies that the theory has failed to identify the factors that cause deviation of GDP from its natural rate and as a result people will regard it as a failure in giving an explanation of recession or cyclical fluctuations of GDP. It gives little consolation to know that the mean of the realized values of eÿ over a period of, say three hundred or three thousand years, will be zero. If a theory attributes an important phenomenon that occurs frequently to unidentified random factors, it fails to explain the phenomenon. New classical rational expectations theory by tracing recessions to random events fails to explain it. If theories of medical science attribute diseases that require medical intervention to unidentifiable random factors, will we take such theories seriously or be content with them? Will it give any consolation to know that the diseases we are suffering from are due to random factors that cannot be known? Will it be of any use to know that in the long run on the average the diseases will not cause any damage, when the long run may be much longer than the lifetime of a man? Obviously, such theories will be rejected by people as trash. We shall make just two other points. First, natural sciences whose progress is far more visible and dramatic than economics’ never make the claim that they have deciphered the mechanisms that govern all the natural factors. They, in fact, say just the opposite. What they know, they say, is infinitely small relative to what they do not know. Had they known all the mechanisms governing all the myriad natural variables, they would have reached their journey’s end. Modern economics, which is just about two hundred years old, makes the claim that it has fully grasped the mechanisms that determine all economic variables. Not only that, it claims that it can accurately (allowing for random deviations, which cancel out on the average over a sufficiently long period of time) predict future paths of all economic variables. It considers it irrational on the part of individual economic agents not to form expectations on the basis of the models that mainstream economics has developed. In sum today’s new classical and new Keynesian theorists claim that economics has reached its journey’s end. However, what is the reality? Economics has failed miserably to predict every single major economic event let alone the minor hiccups. Even when a problem has started, economists have ridiculously failed to gauge its intensity. Economic models are highly simple and weak. They are not meant for making accurate predictions. They are developed to examine what the policy makers can do when an economy gets into troubles and what preventive steps the policy makers can take to minimize the occurrence of crises.

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349

The other point we should make in this context is that the model that yields the NRH, the aggregate supply function in particular, has no satisfactory theoretical foundation. It has been derived from extremely weak assumptions and fables. To say that people who have real stakes will take the model seriously goes against every precept of rationality. Even though Friedman provided a theoretical argument in support of the specific form of the aggregate supply function, Lucas and his associates failed to do so. In their theoretical work, Lucas (1973) and Barro (1976) derive this aggregate supply function using Phelp’s parable of an island economy. They assume that the economy consists of a large number of geographically separate markets or islands indexed by, say, z. The aggregate supply function in each of these islands is assumed to be given by Y s ( z) t

Yn  B ¹ [ p( zt )  Et ( z) pt ]

(12.55)

where Ys(z)t º aggregate supply in the zth island or market in period t, Yn º the natural rate of output in market z. The natural rate of output is the same in every island. a is a constant, which lies between zero and 1, p(zt) º price prevailing in market z and Et(z)pt º economy-wide price of the output as expected in island z. It is assumed that suppliers in each market base their supply decisions, among others, on the economy-wide price of the good, i.e. the price of the good averaged over all islands. However, in any given period, suppliers in an island, who cannot supply to other islands by assumption, cannot observe the prices prevailing in other islands. So they take their decision on the basis of their expected economy-wide price. Lucas and Barro derived the aggregate supply function and the NRH using (12.55). However, neither Lucas nor Barro derives (12.55) from any optimizing exercise on the part of the suppliers. (12.55) is completely ad hoc. Since the specific form of the aggregate supply function, as we have shown above, is crucially important for the derivation of NRH, not only the nature but also the form of the aggregate supply function must have a strong theoretical support. Unfortunately, this condition is not fulfilled.

12.6

THEORY OF REAL BUSINESS CYCLE

Dissatisfied with the failure to devise any substantive theoretical support for the aggregate supply function of the model presented above, Lucas, Prescott and their associates developed the theory of real business cycle (RBC). RBC does away with the NRH altogether. It is based on the classical theory and states that a market economy remains in full employment equilibrium always (i.e. even in the short run), with natural rates of output and employment. However, it extends classical theory to explain business cycles. It achieves this feat by making the production function stochastic. This enables the RBC to explain business cycles in terms of random shocks to the production function, which means random shocks to the country’s ability to convert inputs into outputs. Obviously, the innovation incorporated by the proponents of RBC in the classical model to explain business cycles is very slight. These adverse random shocks to production function may take the form of natural calamities, bad monsoon or socio-political disturbances. Each of these factors disrupts production and distribution. Thus in RBC business cycles do not represent deviation of actual output from its natural rate, but shifts in the natural rate of output itself. We do not consider it optimal to discuss RBC in detail, as it seems highly implausible. Had every recession been accompanied by serious disruption of economic life due

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to adverse natural and socio-political factors, there would have been little mystery about recessions. Keynes, then, would never have thought of writing the ‘General Theory’. The cause of every recession would have then been obvious to everyone. Recession is a puzzle because one cannot trace them to any adverse circumstances, natural or man-made. Had there been such obvious links, economics would not have bothered about explaining business cycles. Cumbrous, complex, inelegant and therefore irksome and boring mathematical deductions cannot hide the obvious motivation for constructing such theories as new classical rational expectations theory or RBC. The lack of talent and imagination is palpable. Obviously absurd and highly contrived assumptions are made to yield the results which the proponents of these theories want. Given the absurdity of the assumptions, the motivation for making them becomes vivid.

12.7 NEW KEYNESIAN THEORY New Keynesian theory (NKT) avowedly seeks to provide microfoundation to the Keynesian theory. It considers the Keynesian theory to be ad hoc as the relations used in the theory do not have any microfoundation. The relations are said to have no microfoundation because they are not derived from any explicit optimizing behaviour of the economic agents. Take, for example, the consumption function. Keynes simply assumes a consumption function instead of deriving it from explicit optimizing behaviour of the consumers. Just like the new classical theory, the new Keynesian theory accepts the NRH. It also treats the theory of rational expectations as the best theory of expectation formation. Thus, it also puts the individuals on the pedestal of the best of economists, policy makers and planners. However, despite individuals behaving like the best of the policy makers, NKT provides some room for the policies to work in the short run, as individuals, despite having rational expectations, do not consider it optimal to change prices. NKT in the short-run attributes fluctuations in output and employment and effectiveness of policies in influencing output and employment to rigidities in nominal and relative (real) prices due to imperfections in market structures. This is the chief distinction between the new Keynesian and new classical theory. In the latter all markets are perfectly competitive and all prices clear markets. We shall discuss some of the new Keynesian models below and show that the NKT fails to provide either an acceptable theoretical framework for macroeconomic analysis or a satisfactory microfoundation to the Keynesian theory.

12.7.1

Nominal Rigidities and Economic Fluctuations

There are two broad strands of thought in the NKT. One set of theories emphasises on rigidities in nominal prices, while the other line of thought focuses on rigidities in real or relative prices. We shall discuss the former first. This body of theories shows that in the face of autonomous shifts in demand profit maximizing producers instead of adjusting the prices of their products to the market clearing levels, find it optimal to adjust their outputs to demand bringing about cyclical fluctuations in GDP. Major features of this set of studies may be summarized as follows. It assumes that markets are imperfect, producers have monopoly power and they set prices taking into account demand and cost conditions of their products. It also postulates that it is costly to change price and refers to the cost of changing prices as menu cost. In the presence

New Classical and New Keynesian Theories

351

of menu cost, it argues, the producers may not consider it optimal to change their prices following autonomous shifts in demand conditions. They may optimally choose to adjust output to demand instead. This is how, invoking menu cost, the new Keynesian theory explains rigidities in nominal prices and fluctuations in GDP in response to autonomous shifts in demand conditions. There are several new Keynesian models that seek to explain short-run cyclical fluctuations in GDP following the line of thought chalked out above. We shall, however, present the model developed by Mankiw (1988), which we think is representative of the body of work referred to above, to exemplify how menu cost helps explain fluctuations in GDP.

The model Mankiw (1988) develops a Walrasian general equilibrium model with imperfect competition to show how menu cost leads to price rigidity and non-neutrality of money. There are two groups of economic agents in the model, households and firms. We focus on the households first.

Households There are a large number of identical households who derive their income in the form of wage and profit from sale of labour and ownership of firms. They hold real balance and derive utility from such holdings. They use all their income and their endowment of real balance for purchasing consumption goods and holding of real balance. Economy produces N number of consumption goods and households derive utility from consumption of all these N consumption goods. Work, however, gives them disutility. The utility function of the households is, thus, given by

U

Ç q1G  R log ÈÊ MP ØÚ  L 1G i 1 i N

1

(12.56)

Households maximize (12.56) subject to the following budget constraint.

Çpq N

i i

M

WL  Q  M

(12.57)

i 1

where qi º amount of the ith consumption good consumed; pi º money price of the ith consumption good, L º amount of labour supply of the households, W º money wage rate; p º nominal profit income of the households, M º demand for money of the households and M º households’ given endowment of money. Households are price takers in all the N consumption goods markets and also in the labour market. So money prices and money wage rates are all given to the individual households. Firms are all joint stock companies so that there is alienation between ownership and management. Hence the aggregate profit earned by the households is also given to the individual households. In the above optimization exercise, therefore, there are N + 2 choice variables of the households, viz. qis, M and L. The Lagrangian function is given by B

Ë Û M qi1G  R log È Ø  L  M Ì Ç pi qi  M  WL  Q  M Ü Ç Ê PÚ 1G i 1 i 1

1

N

M

Í

Ý

(12.58)

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Macroeconomics

First order conditions for maximization are given by (if you find it difficult to derive the FOCs, try the simple case where N = 2).

˜B ˜ qi

qi G  M pi

R

˜B ˜M

M

M

 1  MW

˜B ˜M

Çpq

i i

i

1, 2, 3, ..., N

(12.59)

0

˜B ˜L

N

0

(12.60) (12.61)

0

 M  WL  Q  M

0

(12.62)

i 1

We can solve the N + 3 first-order conditions for the optimum values of qis, M, L and l. Thus, substituting (12.61) into (12.60) to replace l and then solving (12.60) for qi, we have qi

È pi Ø ÉW Ù Ê Ú

È 1Ø É Ù ÊGÚ

À

pi



1

G



W

1

G

qi

À

pi

W qi

G

(12.63)

Equation (12.63) gives the demand function of qi and also the inverse demand function of qi. Again, substituting (12.61) into (12.60) to replace l and then solving for M, we get the money demand function, which is given by M = qW

(12.64)

It is not necessary, for reasons that we shall explain later, to solve for labour supply, L. Equations (12.63) and (12.64) give the demand side of the model, which we derive from the optimizing behaviour of the households. Let us now focus on the supply side.

Firms The model assumes that each of the N consumption goods is produced by a monopolist. There are thus N monopolists in the economy. The ith monopolist produces the ith consumption good using the following production function: qi = L i

i = 1, 2, 3, … N

(12.65)

The ith monopolist’s profit is therefore given by

pi = piqi – WLi

(12.66)

The ith monopolist faces the demand function (12.63). Substituting (12.63) to replace pi in (12.66), we have

Qi

Wqi

1G

 Wqi

(12.67)

The labour market is perfectly competitive so that every monopolist, just like every household, is a price-taker in the labour market. Thus, the ith monopolist chooses qi to maximize pi. The FOC is thus given by (12.68) W(1 – f) qi– f – W = 0

353

New Classical and New Keynesian Theories

Solving (12.68), we get the profit-maximising or optimum value of qi, which is given by

qi

m

È 1 Ø É1  G Ù Ê Ú

È 1Ø É Ù ÊGÚ

(1  G ) (1/ G )

(12.69)

where qim is the profit maximizing and therefore the equilibrium level of output. Substituting (12.69) into (12.63), we get the equilibrium value of pi, which is given by pi = W qi–f = W/(1 – f)

(12.70)

To derive the equilibrium value of W, we have to focus on the money market. Only households hold money in this model and their demand for money is given by (12.64). The supply of money is given by the given endowment of money of the households, M . The money market equilibrium condition is therefore given by

M RW Hence the equilibrium value of W is given by W

M

(12.71)

M

(12.72)

R

Substituting (12.72) into (12.70), we get the equilibrium value of pi, which we denote by pim. It is given by M (12.73) pim (1  G ) 1

R

Dividing (12.73) by (12.72), we get the equilibrium value of È pi Ø É Ù ÊW Ú

È pi Ø É Ù, ÊW Ú

which we denote by

m

. It is given by È pi Ø É Ù ÊW Ú

m

È 1 Ø É1  G Ù Ê Ú

(12.74)

When prices and outputs of the N consumption goods are given by (12.73) and (12.69) respectively, and the value of money wage rate is given by (12.72), all the goods markets and the money market are in equilibrium. At those values of prices, outputs and money wage rate, producers’ profits are at the maximum level, the demand for every good is fully met and households’ demand for money exactly equals their given supply or endowment of money. We shall now show that, when all the goods’ markets and the money market are in equilibrium, so must be the labour market so that the outputs, prices and the money wage rate that equilibrate all the goods’ markets and the money market keep the whole economy in equilibrium. Note that in the households’ budget equation (12.57), qi and M represent demand for qi and demand for M respectively and L on the RHS represents planned supply of labour. Therefore, we rewrite it as follows.

Çpq N

i 1

d i i

 Md

WLs  Q  M

(12.75)

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Macroeconomics

In (12.75), q id, Md and Ls denote demand for the ith good, demand for nominal money balance and supply of labour respectively. In the profit equation (12.64), which is the objective function of the ith monopolist, on the other hand, qi and Li stand respectively for the planned supply of qi and the planned demand for labour of the ith monopolist. Denoting them respectively by qis and Lid, we rewrite the profit equation, (12.64), as pi = piqis – WLid Summing over all is , we have

ÇQ Ç p q

s

Çpq

s

N

N

i

i 1

where Q œ

i 1

Q

Þ

i i

N

i i

 W Ç Ldi N

i 1

 WLd

(12.76)

i 1

Ç Q i and Ld œ iÇ1 Ldi . i 1 N

N

Substituting (12.76) into (12.75) and rearranging terms, we have

pi (qid  qis )  ( M d  M )  W (Ld  Ls ) Ç i 1 N

0

(12.77)

Equation (12.77) gives the Walras Law, which states that the sum of excess demands of all the goods markets, money market and the labour market equals zero. From (12.77) it follows that if all the N goods’ markets and the money market are in equilibrium, so must be the labour market, i.e. the prices and the outputs of the N goods and the money wage rate that equilibrate all the N goods’ markets and the money market also keep the labour market in equilibrium. The equilibrium values of qi and (pi/W) given respectively by (12.69) and (12.74) are shown in Figure 12.15. The equilibrium value of W as given by (12.72) is shown in Figure 12.16. Focus

Figure 12.15 Price and output of the i th monopolist.

New Classical and New Keynesian Theories

Figure 12.16

355

Determination of wage rate.

on Figure 12.15 first. In Figure 12.15, the schedule DD represents the demand function (12.63). It is drawn linear for simplicity. The MC schedule gives the marginal cost of production in terms of labour—see (12.65). Again, for neatness of exposition, we do not show the marginal revenue schedule, even though the equilibrium qi, qim, corresponds to the point of intersection of the marginal revenue and the MC schedule. In Figure 12.16, MD and MS schedules represent money demand function (12.64) and the money supply function respectively. The equilibrium W corresponds to the point of intersection of money demand and money supply schedules. Let us now explain the working of the model with a comparative exercise. Suppose M rises. With all the N goods’ markets in equilibrium, there will emerge initially an excess supply in the money market and, as follows from the Walras Law, a matching amount of excess demand in the labour market. W will therefore rise from its initial equilibrium value labelled W0 in Figure 12.16 to W¢ restoring equilibrium in the money market and thereby in the labour market. The equilibrium values of qi and (pi/W), as follows from (12.69) and (12.74), remain unchanged, as they are independent of the value of M. Hence, if changing pi is not costly, the monopolist would simply raise pi in the same proportion as W and keep qi unchanged. In such a situation, obviously, money is neutral. However, Mankiw assumes that changing price is costly. It involves menu cost. Mankiw assumes further for simplicity that menu cost consists of labour cost only. Thus menu cost in nominal terms, which we denote by Z, is given by Z = zW

(12.78)

Now, the producer will change pi if and only if the menu cost is less than the increase in profit resulting from the change in price. More precisely, the monopolist will compare profits in two situations: the profit he makes if he changes his price and the profit he earns if he does not change his price. If the former is larger than the latter, he will change the price. Otherwise, he will keep the price unchanged. Note that the former is necessarily larger than the latter in the absence of the menu cost. (Explain this point yourself.) However, in the presence of menu cost, the former may be less than the latter. If the monopolist changes his price, his profit in terms of labour, which we denote by pc, will be

Qc

È pi Ø ÉW Ù Ê Ú

m

qim

m

 qi 

z

(using (12.65) and (12.78))

(12.79)

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Macroeconomics

If we multiply both sides of (12.79) by the new equilibrium value of W, which we denote by W¢, we shall get the profit in terms of money. From (12.65) we find that W„

M  dM

(12.80)

R

Let us now compute the profit the monopolist will make if he does not change the price. In this case, he keeps the price unchanged at pim in this situation, which we denote by

pi Ø É Ù ÊW Ú È

„

(1  G )

M — see (12.73). R

È pi Ø ÉW Ù Ê Ú

of the monopolist

pi Ø „ , is given by (using (12.80)) É Ù ÊW Ú È

pim W„

(1  G ) M



M

(1  G ) M M  dM

R

dM

(12.81)

R 1

At ( pi / W ) „ demand for qi, as follows from (12.63), is given by

 È (1  G )M Ø G . É M  dM Ù Ê Ú

When (pi/W)¢

is greater than marginal cost = 1, which we assume to be the case here, monopolist’s profit is maximized if the monopolist produces the qi that is demanded at (pi/W)¢. Thus, monopolist’s profit in terms of labour in this case, which we denote by pnc, is given by 1

Q nc

 È (1  G ) M Ø È (1  G ) M Ø G É M  dM Ù É M  dM Ù Ê ÚÊ Ú

1

–

 È (1  G ) M Ø G É M  dM Ù Ê Ú

(12.82)

If pc > pnc, the monopolist will change the price. Otherwise, he will keep it unchanged. Let us explain the situation with the help of Figure 12.15. In Figure 12.15, when the monopolist changes his price and thereby keeps (pi/W) and qi at (pi/W)m and qim respectively, his profit in terms of labour ignoring the menu cost is given by the sum of the areas B and C, which we denote by B + C. On the other hand, if the monopolist does not change the price, the (pi/W) he charges and the qi he produces are given by (pim/W¢) and qi0 respectively. Accordingly, in this case, the profit in terms of labour is given by the sum of the areas labelled C and D. We denote this area by C + D. Thus, ignoring menu cost, monopolist’s profit, when he does not change his price, goes down by (B – D) in terms of labour. Obviously, if z > (B – D), the monopolist will not change the price. Otherwise, he will. New Keynesian theory claims that menu cost has strong welfare implications. We may use the sum of consumer surplus and producer surplus as an index of social welfare in this case. In the situation where the monopolist produces qim and charges (pi/W)m, social welfare is given by the sum of the areas A, B and C, A + B + C. If the menu cost is sufficiently large, the monopolist decides not to change the price following the increase in money supply. In such a situation, as should be clear from Figure 12.15, the sum of consumer surplus and producer surplus

New Classical and New Keynesian Theories

357

and therefore community’s aggregate welfare goes up from A + B + C by the area (E + D). It is also clear from Figure 12.15 that the sum of consumer surplus and producer surplus and therefore social welfare is at its maximum level when price of qi in terms of labour, (pi/W), equals the marginal cost, which is unity, and the output of qi equals qi*. The social welfare in this case is A + B + C + E + D + F. This is the situation that obtains under competitive conditions, where price equals marginal cost in equilibrium. However, due to monopoly social welfare becomes less. This model shows that sufficiently large menu cost allows the community to recoup a part of the welfare-loss due to monopoly following an increase in money supply. This gain is referred to as aggregate demand externality. Thus, the new Keynesians argue, even if menu costs are small, the price rigidity that it causes may lead to large external benefits for the community as a whole. However, a reduction in money supply under the same conditions brings about a reduction in social welfare. Let us now critically examine the concept of menu cost. Menu cost refers to the cost of changing prices. What kind of cost producers have to incur to change prices? It is said that they have to print new menus or new price catalogues, print the new prices on products and packages, etc. However, a closer scrutiny of the concept of menu cost reveals that it is too insignificant to figure in producers’ pricing decision. First, new prices can be communicated to the distributors, wholesalers and retailers electronically without any cost or at an insignificant cost. Second, menu cost is not something given. If menu cost leads to losses, menus and price catalogues can be designed in such a manner that the cost of making changes in the prices therein becomes insignificant. Producers can also develop practices that reduce menu costs to insignificance. This they will surely do, if menu costs reduce their profit. Third, the additional cost of printing new prices instead of the old ones on the new products and packages is nil. Only changing prices on the unsold products involves cost. If such costs do not warrant price change, new prices need not apply to the already existing unsold stock. That will not make prices of current products rigid. In oligopolies or monopolistically competitive industries, firms compete with one another principally using non-price instruments such as advertising. Advertisements have to be put up regularly to retain market shares. Advertising new prices in such a scenario hardly involves any extra cost. Almost all the major firms today have websites containing detailed information regarding their products. These websites have to be updated regularly as they have to continuously change their product profile to stay afloat in competition. Updating prices in such a scenario hardly involves any additional cost. From the above it follows that menu cost is too insignificant and malleable to affect firms’ pricing decisions in the face of perceptible changes in demand and cost conditions that warrant price change. Actually, the principal reason why firms keep prices unchanged is oligopolistic interdependence as captured in the kinked oligopoly demand curve model. Rigidities in nominal prices also stem from the inability of the firms to perceive even in the case of monopoly the elasticity of the demand function. This incapacitates the firms in identifying the profit-maximizing price or anticipating the impact of changing prices on their profit. This inability forces them to set the price by applying a fixed mark-up, determined by applying rule of thumb, to the average variable cost of production. Since the elasticity of demand is not known, any attempt at changing the price in either direction may saddle the firms including monopolists with large losses. As a result, following autonomous shifts in demand conditions, producers (including monopolists) consider it optimal to adjust their outputs instead

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of their mark-ups. This process of price setting is delineated in Kalecki (1943). From the above it follows that the explanation of rigidities in nominal prices in terms of menu cost is untenable. EXERCISE 12.7 Consider Mankiw’s model on menu cost. Suppose the utility function of the representative qi0.5  0.5 log ( M / P )  L, Ç i 1 10

individual is given by U

0.5

where qi º quantity of the ith

commodity, M º money holding of the indivividual, P º price level and L º amount of labour supplied by the individual. The individual earns wage income and profit income and his endowment of money is ` 1. Every good is produced by a monopolist using the production function qi = Li, where Li º amount of labour used in the production of the ith good. If the representative individual’s endowment of money doubles, how will prices and quantities be affected if the menu cost of every monopolist is 1 unit of labour?

12.7.2 Real Rigidities Having failed to construct a convincing case for nominal rigidities, new Keynesian economics tried to develop models that generate rigidities in real wage rates, which cause output and employment to fall below their respective full employment levels. New Keynesians developed three types of models to explain real wage rigidity, namely implicit contract models, insideroutsider models and efficiency wage models. These models are, however, non-Keynesian as they generate a vertical aggregate supply curve. Obviously, these models cannot explain trade cycles in terms of autonomous shifts in aggregate demand. They have to incorporate random shocks on the supply side to explain short-run economic fluctuations. Some of these models of course make labour demand a function not only of real wage rate but also of the holding of real balance and thereby makes employment fluctuate in response to monetary shocks. However, such specification of the labour demand function is absurd and definitely non-Keynesian, to say the least. Hence we ignore such aberrations. Since these models, for the reason given above, have very little to do with the Keynesian theory, we do not waste time explaining them in detail. Just to exemplify our contention, we shall present here the efficiency wage model developed by Shapiro and Stiglitz (1984). We shall present a simplified version of the model. Even though the model is simpler, it captures satisfactorily the gist of the argument of Shapiro and Stiglitz (1984). The model, though simpler, is more general in the sense that, unlike Shapiro and Stiglitz (1984), it need not focus only on steady state equilibrium situations.

The model We consider for simplicity a one-period economy, where there are two groups of economic agents: firms and workers. Firms cannot perfectly monitor activities of their workers so that workers get scope for shirking work. Workers have no qualms regarding shirking. They shirk work unless they find that they earn larger income out of non-shirking. We shall explain this point below. All workers are identical. Their utility function is given by U=w–e

(12.83)

New Classical and New Keynesian Theories

359

where w º real wage rate and e º effort supplied by the worker. For a worker who decides to shirk, e = 0. For a worker who decides not to shirk work, e e . Thus the utility level derived by a shirker is w, the utility level of a non-shirker is (w  e ) is and the utility level of an unemployed worker is zero. ( w  e ) is positive. If a worker shirks, he can get caught. In the given period under consideration, given the state of monitoring, a shirker gets caught only once. The probability that he is caught is q. Workers know this. If a shirker gets caught, he is fired. If a worker is fired, he may get another job. The probability that a worker will get a job upon being fired depends crucially upon the rate of unemployment denoted by u. We define it as u

LL L

(12.84)

where L œ total supply of labour and L º demand for labour or number of vacancies. The larger the u, the less is the probability that a worker will get a job after being fired. The probability of getting a job after being fired is therefore a decreasing function of u or an increasing function of (1 – u). There are also other factors that influence this probability. For example, even when the rate of unemployment is zero so that number of vacancies equals the number of workers, some workers may not get jobs because of imperfect information or mismatches between skill requirements of jobs and skill endowments of workers or imperfect spatial mobility of labour. However, for simplicity, we ignore those factors here and assume that the probability that a worker gets a job after being fired is (1 – u). We also assume that a worker will get the real wage rate w if he is hired irrespective of whether at the beginning or at some other point of time in the given period. At this stage let us distinguish between the real wage rate paid by a firm and the average wage rate paid by the industry. Let wi denote the real wage rate paid by the ith firm and w denote the wage rate paid by all other firms in the industry. Let us now consider a worker of the ith firm. If he decides to shirk, his expected real wage will be (1 – q)wi + q × (1 – u)w. On the other hand, if he decides not to shirk, his real income will be given by wi  e , where e , which is a constant, denotes the cost of making the effort. One may interpret e as the real compensation needed by a worker to make up for the loss in utility due to the supply of effort. If workers shirk, firms’ output is nil. So it is optimal for every firm to pay a real wage so that there is no incentive on the part of the workers to shirk. We assume that workers are risk neutral. Given these assumptions, the ith firm has to set its real wage rate in such a manner that the following inequality holds wi  e • (1  q) wi  q ¹ (1  u) w

(12.85)

Obviously, the ith firm will pay the minimum of the real wage rates that will do the job. This real wage rate is therefore given by the equation wi

Þ

wi  e

(1  q ) wi  q ¹ (1  u) w  e (1  u) w

(12.86)

It is clear from (12.86) that if u 0, w i  e w . It is quite easy to explain this. When unemployment is zero, shirking is costless. If a worker is fired, the firm firing the worker will fill it up creating a vacancy in another firm, which will then hire this unemployed worker. In this case a firm can induce its workers not to shirk by offering a wage rate, which net of the

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compensation needed for supply of effort is at least equal to the real wage rate being paid by the other firms so that there is no incentive for shirking. Every firm must pay the same real wage rate in equilibrium. We can therefore get the real wage rate that every firm in the industry will pay in equilibrium by substituting w for wi in (12.86) and solving it for w. This yields the following value of the equilibrium w: e Le (12.87) LL LL L Let us now examine the properties of (12.87). Equation (12.87) gives corresponding to every L the minimum w that every firm in the industry should pay to induce the L number of workers not to shirk and supply effort. Equation (12.87) therefore gives the supply price of labour corresponding to every L. When u = 1, i.e. when everyone is unemployed, firms have to pay at least e to induce the hired workers to work. If w is less than e , an employed non-shirker with negative utility or net real income will be worse off than an unemployed worker, whose net real income or utility is zero. So no hired worker will be interested in supplying effort at such a real wage rate. As u falls, it becomes less difficult to get jobs upon being fired. Accordingly, firms have to pay higher real wage rate to induce workers not to shirk. Again, when u = 0 so that there is no unemployment, shirking becomes costless, as fired workers, for reasons we have already explained, get hired immediately. In this case therefore supply price of effort becomes infinitely large. SS curve in Figure 12.17 represents (12.87). In the event there is perfect monitoring of workers’ activities, there is no scope for workers to shirk. Every worker in such a scenario will be willing to supply all their effort at every real wage rate greater than or equal to e . At a real wage rate less than e , a worker’s net real income or utility is negative which is less than the net real income or utility of an unemployed worker. Thus under perfect monitoring the supply of labour is vertical at L for real wage rates greater than or equal to e . The labour supply curve in the case of perfect monitoring is represented by the schedule LL in Figure 12.17. Let us now focus on the behaviour of firms. w

Figure 12.17

e u

Efficiency wage and involuntary unemployment.

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Firms There are M identical firms producing a single good, the output of which is denoted as y, using only one input, labour. The production function of the representative firm is given by y = f(l)

f¢ > 0

and

f² < 0

(12.88)

where l denotes the level of employment in the firm. The profit of the firm is given by

p = y – wl = f (l) – wl

(12.89)

The firm chooses l so that the firm’s profit is maximized. The first-order condition yields f ¢(l) = w

(12.90)

Equation (12.90) gives the demand price of labour of the firm corresponding to every l. It gives corresponding to every l the value of w that makes the given l the profit maximizing level of l, i.e. it gives corresponding to every l the value of w that makes the firm demand the given l. Since all firms are identical and there are M number of firms, l = (L/M), since L denotes the aggregate level of employment. We therefore rewrite (12.90) as f ¢(L/M) = w

(12.91)

Equation (12.91) gives corresponding to every L the value of w that makes every firm want to employ (L/M) amount of labour and therefore all the firms together to employ L amount of labour. We have equilibrium in the model when demand price of labour and supply price of labour are equal, i.e. when the following equation holds Le LL

È

LØ Ù M Ê Ú

f „É

(12.92)

We can solve (12.92) for the equilibrium value of L. Putting this equilibrium value of L in (12.91) or in (12.87), we get the equilibrium value of w. The solution is shown in Figure 12.17, where DD represents the inverse labour demand function (12.91). The equilibrium (L, w), labelled (Le × we), corresponds to the point of intersection of DD and SS. At we all the L number of workers are willing to work, but only Le number of workers find employment. So ( L  Le ) number of workers are involuntarily unemployed. The model presented above is an ‘efficiency wage model’, where the real wage rate gets raised above the market equilibrium real wage rate to generate involuntary unemployment so that shirking becomes costly for the employed workers. In case they shirk and get fired, they will find it difficult to secure another job, if there is unemployment. This creates a disincentive to shirking. It is doubtful whether the problem of monitoring workers’ activities, which lies at the core of the behaviour of the real wage rate in this model, is of much importance at the economy-wide level. Even if we ignore such doubts, the main problem with this model is that, just like the classical model, it generates a vertical aggregate supply curve. Let us explain. Let us start from the equilibrium situation and raise the price level. The real wage rate as a result will fall below its equilibrium level creating excess demand for labour. So money wage rate will go on rising until real wage rate reverts to its equilibrium level. Since the aggregate supply

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curve is vertical, autonomous shifts in demand conditions cannot generate trade cycles. Trade cycles therefore have to be explained in terms of shifts in production conditions or in workers’ attitude towards work that bring about shifts in the labour demand and labour supply curves respectively. (Explain this point yourself.) The explanation of business cycles is therefore completely non-Keynesian. It is in fact closer to the new classical explanation of business cycles. This is the problem with the new Keynesian theories that generate rigidities in the real wage rate.

12.7.3 Rigidities in Interest Rates and Credit Rationing New Keynesian economists also sought to explain why interest rates might be rigid in a market economy. The explanation came from Stiglitz and Weiss (1981). At the core of the explanation is the assumption of asymmetric information, which states that banks do not know the credit worthiness of the borrowers even though they are aware that raising of interest rates drives out of the market, good borrowers, who have sound investible projects and the intention of paying back their loans. So, an increase in interest rate exerts two opposite forces on banks’ income. On the one hand, banks gain as interest income on any given amount of loans supplied by the banks rises. However, there are two negative effects as well. First, the demand for loans falls so that banks have to extend less loans than what they were extending before. Second, as good borrowers move out, the proportion of borrowers defaulting on their loan servicing goes up. Both these factors tend to reduce banks’ income. At low levels of interest rates the positive effect is likely to dominate the negative effects. However, as interest rate rises, both the negative effects are likely to gain in strength so that for sufficiently high interest rates, the negative effects may dominate the positive effect. Therefore, if the market clearing interest rate is sufficiently high, banks may not consider it optimal to allow interest rate to rise to the market clearing level. In such a scenario, the interest rate at which banks’ income attains its maximum level is less than the market clearing level. Accordingly, banks under the conditions specified above fix their interest rates below the market clearing level giving rise to excess demand for bank credit. Banks thus may ration their supply of credit among the prospective borrowers. Stiglitz and Weiss (1981) also show that, shifts in demand for banks’ loans do not produce any impact on banks’ optimum level of interest rate so that such shifts do not produce any impact on the interest rates charged by banks. We now present a simplified version of their paper below.

The model It is assumed that there is a continuum of entrepreneurs. Each entrepreneur has a project. There is uncertainty. Only two states of nature can occur, good and bad. The probability of occurrence of the good state of nature in case of the ith project is pi. Every project yields a positive income in the good state of nature and zero income in the bad state of nature. In the good state of nature the ith project yields qi amount of income. It is assumed that the expected income of every project is a constant, R. Formally, R

pi qi  (1  pi ) ¹ 0

pi qi

i

(12.93)

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Equation (12.93) is of considerable significance. It states that the higher the probability of success of a project, the less is the income it yields. This seeks to capture a feature that is usually observed. Think of the extreme example of buying a lottery ticket or investing in a lottery ticket. The probability of its success is very low, but, if it succeeds, it will yield a very high income per unit of investment. In the event of failure, it will yield nothing. The entire investment will be the loss. On the other hand, consider the case of a farmer cultivating potatoes. The probability of success of this project is much higher than that of lotteries, but in the event of success, the farmer will make much less income per unit of investment than the purchaser of a lottery ticket. (12.93) captures this feature in a simple framework. Every entrepreneur has a given amount of wealth W and the cost of every project is C, which is greater than W. So every entrepreneur has to borrow B = C – W to undertake his investment project. Every entrepreneur can secure this loan from banks. The interest rate on bank loans is denoted by r. Entrepreneurs undertaking investment projects pay back their loans along with interest if their projects succeed. In case of failure, they go bankrupt and cannot pay anything to the banks. So expected net income of the entrepreneur undertaking the ith investment project, denoted by si, is

Ti

pi [ qi  B(1  r )]  (1  pi ) ¹ 0

R  pi B(1  r )

(12.94)

It is assumed that qi > B(1 + r). It is clear from (12.94) that si is a decreasing function of both pi and r. Every entrepreneur has the option of investing his wealth in a safe asset, which yields an income of r with certainty on an investment of W. Expected profit of an entrepreneur from the ith investment project is si – W and his profit from the investment of his wealth in the safe asset is rÿ – W. Entrepreneurs are risk neutral. So entrepreneurs will invest in the ith project iff (R – piB(1 + r)) ³ r

(12.95)

The maximum value of pi that satisfies (12.95) is given by the following equation: (R + piB(1 + r)) = r

(12.96)

Denoting this value of pi by p, we have p

RS B(1  r )

(12.97)

The entrepreneurs who are risk neutral by assumption should be indifferent between the project whose probability of success is p and the safe asset. Still we assume that entrepreneur undertake such investment projects instead of investing in the safe asset. Since the LHS of (12.95), every other thing remaining unchanged, is a decreasing function of pi, entrepreneurs will undertake all the investment projects whose probability of success is less than p and will not undertake the investment projects whose probability of success is greater than p × g(pi) gives the number of entrepreneurs who can undertake the ith project. So number of entrepreneurs who will p

undertake the risky projects is given by

R S B(1  r ) Ô

0

g( pi ) dpi .

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Since every entrepreneur undertaking his risky project takes a loan of B, the aggregate demand for loans (denoted as CD) is given by p

CD

RS B(1r ) Ô

(12.98)

Bg( pi ) dpi

0

where CD denotes demand for loans. Since p is decreasing in r and since all entrepreneurs with projects whose probabilities of success equal or fall short of p demand loans, CD is also decreasing in r. Let us now focus on the banks. The banking sector is perfectly competitive. In equilibrium, therefore, their profit is zero. Accordingly, they seek to maximize their revenue. Let us explain. If banks earn positive profit, new banks enter. These new banks try to attract deposit by offering higher deposit rates. Competition among banks for deposits breaks out. Deposit rates, as a result, rise until banks profit fall to zero. Obviously, how much deposit rate a bank can offer depends upon how much revenue it earns. If a bank is less efficient than others in generating revenue, it will not be able to match the deposit rates offered by others, so it will have to go out of business. Hence, banks seek to maximize their revenue. Banks’ revenue is given by the total amount of interest income and repayment that they secures from their lending. All the entrepreneurs with projects whose probabilities of success equal to or fall short of the cut-off value, p, seek loans from banks. They pay back their loans along with interest charges in the event of success. However, in the case of failure, they do not pay anything. Thus the expected revenue of the banks, denoted as PB, is given by

3B

p Ô

pi B(1  r ) g( pi )dpi

(12.99)

0

Banks choose r in such a manner that (12.99) is maximized. The first-order condition for maximization is given by d3B dr

p

B Ô pi g( pi ) dpi 0

B(1  r ) pg( p)  dp dr

0

(12.100)

Let us now focus on the RHS of (12.100). It shows that an increase in r exerts two opposite p

forces on the expected revenue of the banks. The first term, B Ô pi g( pi ) dpi , gives, everything 0

else remaining the same, the increase in the expected revenue due to the rise in r. This captures the positive force. However, an increase in r also reduces the amount of loans that banks can extend by driving out the best of the borrowers from the market. The second term, which is negative since (dp/dr) is so, captures this negative effect. Note that the shape of PB depends upon the that of g(pi). Stiglitz and Weiss (1981) show that there exists specific forms of g(pi) such that the first term dominates for low values of r and the second term dominates for high values of r so that PB has inverted U shape, when plotted against r. In this case there is a finite and positive r at which PB attains its maximum. Let us denote this r by r*. The situation is shown in the fourth quadrant of Figure 12.18 where r is measured on the horizontal axis and

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Figure 12.18 Credit rationing by banks.

PB is measured in the downward direction on the vertical axis and the schedule PB PB represents (12.99), giving the value of PB corresponding to every r. In the first quadrant, demand for loans, denoted by CD, is measured on the vertical axis. The CD schedule, representing (12.98), gives the amount of demand for loans corresponding to every r. Let us now focus on the supply of loans, which we denote by CS. For simplicity we ignore currency holding by the public and also the excess reserves of banks. Given these assumptions, the supply of broad money, M3, equals total amount of bank deposits and it is given by H/CRR, where H is the stock of high-powered money and CRR denotes the cash reserve ratio stipulated by the central bank. Total supply of bank credit denoted by CS is therefore given by H (12.101) CS (1  CRR) CRR The horizontal CS schedule in Figure 12.18 represents (12.101). The market clearing interest rate corresponding to the point of intersection of the CS and CD schedules is denoted by rc. This market clearing interest rate may be, as shown in Figure 12.18, greater than the revenue maximizing interest rate, r*. In this scenario, obviously, the banks will not consider it optimal to allow the interest rate to rise to the market clearing level. Banks will charge r* at which there is excess demand for credit and the banks will ration their planned supply of credit among the prospective borrowers. Now suppose the Central Bank of the country undertakes expansionary (contractionary) monetary policy by raising H or reducing CRR or both. It will bring about an upward (downward) shift in the CS schedule in Figure 12.18. However, it has, as follows from (12.101), no impact on the PBPB schedule as its shape depends only on the function g(×). Hence the revenue

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maximizing value of r, labelled r* in Figure 12.18, will remain unaffected. Following this change in monetary policy, therefore, banks will keep r unchanged at r* and supply more (less) credit reducing (raising) the extent of excess demand for bank credit at r*. Borrowers will thus get more (less) credit at unchanged interest rates and it will enable them to finance (force them to cut down) some of their planned expenditures which they were unable (able) to undertake before. A change in money supply here affects aggregate demand for goods and services directly and not indirectly through its impact on interest rate. This is the credit view of money. It states that a change in money supply affects aggregate demand by changing the supply of credit and not by changing the interest rate. The view that a change in money supply affects aggregate demand for goods and services through its impact on interest rate is referred to as the money view. The IS-LM model yields the money view. The credit view shows how monetary policy works even when interest rates are rigid. In India, for example, in the pre-reform period interest rates were fixed by the government. The credit view shows how monetary policy can work in such a scenario. The major problem with the Stiglitz-Weiss (1981) model is its assumption of asymmetric information. Market for credit is different from that of oranges or apples. In the case of the latter, the exchange is simultaneous. There is therefore no risk. If you cannot pay, you will not get the apple. In case of credit, the exchange is sequential. The borrower gets the loan today, but he pays back the loan along with interest later. Hence there is risk of default. The lender at the time of extending the loan has to make sure that the borrower has the intention and the ability to pay back the loan. In other words, in the credit market, since the exchange is not simultaneous, demand for loans may also come from bogus borrowers who do not have either the intention or the ability to pay back the loan with interest. The demand for loans of these bogus borrowers is obviously bogus and do not constitute a part of genuine demand for credit. Every lender therefore devises ways of distinguishing genuine borrowers from the bogus ones. That is the most important part of banks’ operations. Banks deny the bogus borrowers loans. This obviously does not mean credit rationing, since demand for loans of such borrowers is not true or genuine demand for loans. Such demand cannot exist in markets for apples or oranges where exchange is simultaneous. There is credit rationing when banks do not consider it optimal to meet genuine demand for loans coming from creditworthy borrowers. Just the fact that banks do not give loans to all the people who ask for loans or do not give some individuals all the loan they ask for does not mean that banks resort to credit rationing, which means intentionally not meeting a part of genuine demand for loans. It may simply reflect banks’ effort at identifying genuine demand for loans from bogus demand for loans. There is no evidence that banks do not meet demand for loans, which they consider genuine, when they have surplus loanable funds. In fact, it is not optimal for banks not to meet genuine demand for loans. Consider a situation where interest rate charged by banks is at such a level that there is an excess of genuine demand for loans over supply. In this case, if interest rate is raised, banks will not be apprehensive of a fall in their revenue or of a rise in default rate, as they are catering only to genuine demand for loans. The increase in interest rate in an excess (genuine) demand situation will only raise their revenue, as the amount of loan they supply either stays unchanged or increases with the rise in interest rates. The increase in the interest rate only reduces excess demand. Banks, to be more precise, give loans only to those, who, they are certain, have the intention to and also are capable of repaying the loans with interest. In case, they are not certain,

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they lend only against collaterals, which cover the risk adequately. Banks’ main business is to screen genuine borrowers from bogus borrowers, i.e. their major effort is directed towards eliminating the kind of information asymmetry assumed in this paper. Banks’ survival depends upon how efficiently they can sort genuine borrowers from bogus borrowers. The paper therefore cannot satisfactorily capture banks’ behaviour. However, interest rates charged by banks may display considerable rigidity, but that must be due to oligopolistic structure of the banking industry and the oligopolistic interdependence captured by the kinked demand curve model of oligopoly. It cannot be due to the kind of information asymmetry assumed in the paper. The sampling of the new Keynesian theory presented above shows that it hardly does any justice to the Keynesian ideas. It is an exercise in retrograde. The theories are poor, weak and unconvincing. It also accepts the assumption of rational expectations, which puts individuals on the pedestal of God. A poor country such as India can ill afford research in this line.

12.8

CONCLUSION

New classical theory accepts the classical theory as the basic macroeconomic theory of a market economy. The problem with the classical theory is that it cannot explain trade cycles, as it concludes that a market economy remains in full employment equilibrium always. New classical theory incorporates minor modification or extensions into the classical theory to make it generate trade cycles. One class of models referred to as the real business cycle theory explains business cycles in terms of exogenous shifts in production conditions. There is obviously nothing new in this result, as it follows straight away from the classical model. Exogenous shifts in production function will definitely lead to fluctuations in GDP in the classical model. Why did this line of thinking not strike Keynes or other economists, who considered the classical theory a failure in explaining trade cycles? The answer is quite simple. Recession then should be due to downward shifts in the production function. Since technological regress is impossible, such shifts must be due to major disruptions in the production process due to adverse natural or socio political factors. These phenomena should be major and perceptible. Had every recession been preceded or accompanied by such phenomena, no one would have bothered to explain them. Moreover, involuntary unemployment of labour is a major feature of recession in a market economy. The classical or the new classical theory cannot explain involuntary unemployment even in times of recession. Another class of models incorporates in the classical model misperception of the price level on the part of some economic agents so that they have to take their decisions on the basis of their expected price level. This class of models assumes that economic agents form their expectations rationally, i.e. they form their expectations on the basis of the model that determines the economy’s price level. Hence these models argue that economic agents accurately predict the price level that prevails in the economy except in the cases where there occurs random shocks to demand or supply side factors. These models show that GDP deviates from its natural rate only in such cases. These theories attribute recessions to unidentifiable random factors and thereby fail to explain recessions. Obviously, a society has little use for theories that explain large-scale unemployment of labour and capital and the stress and miseries that accompany such phenomena to unidentifiable random factors about which no one can do anything.

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New Keynesian theories just like its new classical counterpart accepts the NRH and also the assumption of rational expectations. However, to accommodate the empirical phenomenon of business cycles, it has to, just like its counterpart, concede some deficiency in the functioning of a market economy. It assumes that prices clear markets, but they adjust slowly and therefore fail to clear markets in the short run, even though they do so in the long run. As a result, in the short run burden of adjustment to exogenous shifts in demand conditions falls mainly on ouput and not on price leading to business cycles. The rigidity in the price in the short run is attributed principally to the cost of changing prices, which is referred to as menu cost. However, close scrutiny of the concept of menu cost reveals that it is too insignificant to matter in the pricing decisions of firms. New Keynesian theory also develops models that generate rigidity in the real wage rate above the full employment level leading to involuntary unemployment. These models, however, imply vertical aggregate supply curves so that autonomous shifts in demand cannot generate business cycles. The models are therefore non-Keynesian and they have to explain business cycles in terms of exogenous shifts in production conditions. Such explanations, as we have already explained in the context of the new classical theory, are hardly convincing. New Keynesian theory also develops models that lead to interest rate rigidity. However, such models are also found crucially deficient. From the above it follows that the new classical and the new Keynesian theories constitute an aberration. Their objective is not to explain how a market economy works, but to show that a market economy is highly efficient and contains strong stabilizing mechanisms that keep the economy in the full employment situation except in the very short run. New classical economics at least has a sharp focus. New Keynesian economics in contrast is a hotchpotch and focus-less.

REFERENCES Barro, R. (1976), Rational expectations and the role of monetary policy, Journal of Monetary Economics, 2 January, 1–32. Friedman, M. (1968), The role of monetary policy, American Economic Review, 58, March, 1–17. Kalecki, M. (1943), Studies in Economic Dymanics, George Allen and Unwin, London. Lucas, R. (1973), Some international evidence on output–inflation tradeoffs, American Economic Review, 63, June, 326–334. Mankiw, G. (1985), Small menu costs and large business cycles: a macroeconomic model of monopoly, Quarterly Journal of Economics, 100, 2 (May). Pesaran, M.H. (1984), The new classical macroeconomics: a critical exposition, in Ploeg van der, F., Ed., Mathematical Methods in Economics, John Wiley & Sons. Solow, R. (1969), Growth Theory, Oxford University Press, New York. Shapiro, C. and Stiglitz, J. (1984), Equilibrium unemployment as a discipline device, American Economic Review, 74 (June), 433–444. Stiglitz, J. and Weiss, A. (1981). Credit rationing in markets with imperfect information, American Economic Review, 71, 3 (June), 393–410.

13

Modern Theories of Growth A Critique

13.1 INTRODUCTION The objective of the modern theory of growth is to explain the growth in the trend values of aggregate output and employment. Its focus is therefore on the long run. It is based on the natural rate hypothesis (NRH). The NRH states that in the short run a market economy behaves in accordance with the Keynesian theory, while the classical theory best describes its behaviour in the long run. The NRH in its turn is based on the concept of natural rate of unemployment. It is defined as the rate of unemployment that obtains when demand for and supply of labour are equal. But, why should there be unemployment in such a situation? The exponents of the NRH have given two major reasons, namely imperfect information and imperfect spatial and occupational mobility of labour. Even if there are vacancies and an equal number of suitable unemployed people, firms may not have the information regarding the availability of suitable candidates and unemployed people may also lack information regarding the availability of suitable vacancies and both the parties may have to spend some time searching before the vacancies get filled up. By the time one set of vacancies gets filled up, another set of vacancies is created and a new group of people enter the labour market. This is how unemployment may persist, even when demand for and supply of labour are equal. Similarly, concentrations of unemployment and vacancies may be in different geographical areas and occupations and hence unemployment may persist despite matching number of vacancies because of imperfect mobility of labour. It is assumed that because of shifts in aggregate demand for final goods and services, the rate of unemployment is above the natural rate in times of recession and below it in times of boom so that the trend value of the rate of unemployment equals the natural rate in every year. In other words, in the long run, the economy is always in the situation of full employment. The growth in the trend values of output is therefore due to growth in the supplies of labour and capital and also due to technological progress that brings about shifts in 369

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the production function. Accordingly, in the long run we are in the world of the classical theory, where output is determined by the supply side factors. The NRH invokes the Keynesian theory only to explain the deviation of the actual rate of unemployment from its trend value in every year (or in every short period, which is a year at the maximum). The NRH thus neatly compartmentalizes the study of the behaviour of aggregate output and employment into two separate fields: one analyses the trend values of output and unemployment and the other focuses on deviations of actual values of aggregate output and employment from their respective trend values in different short periods. The former constitutes the long-run macroeconomics, while the latter is the subject of short-run macroeconomics. The importance of NRH can therefore hardly be overestimated in macroeconomics today. Accordingly, it is imperative to subject it to close scrutiny. We have already pointed out in the previous chapter that the NRH has little theoretical basis. It is at the best an ad hoc assumption. The concept of natural rate of unemployment is also not very clear and does not seem to be of any importance in the context of a matured market economy. We shall here briefly focus on this issue. The proponents of NRH point out that no one has ever observed an economy without unemployment. However, at the same time they find it hard to believe that a market economy never achieves full employment. They refuse to subscribe to the view that demand deficiency and involuntary unemployment may be, as held by Keynes and also by the Keynesians in the heydays of Keynesianism, the natural state of affairs in a market economy. Instead, they assume that there exists unemployment even in situations of full employment and invokes imperfections in information dissemination and mobility of labour to explain that. They point out that an economy is always in a state of flux. Not only does the aggregate demand fluctuate, so also does the composition of aggregate demand. The shifts in the composition of aggregate demand engender switch in demand from one kind of labour to another and also from goods and services produced in one region to those produced in another region. Following the innovations of computers, for example, demand switched to computers from typewriters and thereby to computer operators from typists. This kind of shifts in demand is referred to as sectoral shifts. Since sectoral shifts occur all the time in market economies, it is argued, unemployment is inevitable in such economies because of imperfections in information dissemination and imperfect mobility of labour across occupations and regions, even when aggregate demand for and aggregate supply of labour are equal. The kind of unemployment that is given rise to by the sectoral shifts on account of the imperfections noted above is called frictional unemployment. The above argument, though seems plausible superficially, wilts when subjected to close scrutiny. Let us explain. First, focus on the case of imperfect information alone and ignore imperfect mobility of labour, i.e. assume for the present that information is imperfect, but labour is perfectly mobile. Start from a situation of full employment. Suppose there takes place a change in the composition of demand in favour of one industry at the expense of another. The favoured sector will recruit and expand, while the other sector will downsize. It is argued that this will lead to unemployment as the contracting sector will release labour, but the expanding sector will take time to recruit because of lack of information regarding the availability of suitable unemployed candidates. The unemployed workers will also take some time to collect information regarding the availability of suitable vacancies. This argument does not seem acceptable. The reasons are the following. First, in this age of information revolution, there are a large number of ways of advertising vacancies. There are numerous newspapers, TV channels,

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internet and so on. Information can be made available and recruitments can be done within a very short period of time. Second, firms also take time to sack, if they think that the change is temporary, as it is costly to train new recruits, to make them adapt to the new environment, to learn about their skills, sincerity, honesty, etc. This phenomenon is referred to as labour hoarding and it is quite common. Firms downsize only when they think that the shift is a longterm one. Finally, if sectoral shifts are regular and important, as the proponents of NRH emphasize, the workers are always under the threat of losing jobs, while firms are also under the threat of losing profit because of the delay involved in filling up vacancies. Under these circumstances it is quite natural that institutions and practices will emerge to take care of the problem. Employment agencies will emerge to place the workers apprehending job cuts in firms expecting a favourable turn in demand. Firms of repute are likely to emerge specializing in supplying suitable candidates to firms immediately on demand. These firms will act as an intermediary between workers under the threat of losing jobs and workers about to enter the labour market on the one hand and the firms seeking to expand and hire on the other. Hence unemployment given rise to by imperfections in the information dissemination system does not stand up to close scrutiny. It should be particularly unacceptable to those who believe in the efficacy of the market mechanism. Ironically, it is those very people who harp on the imperfections in information dissemination for giving rise to frictional unemployment. Let us now consider the case of imperfect mobility of labour. Start from a situation of full employment and consider a shift in demand in favour of doctors at the expense of engineers, giving rise to excess demand for doctors and just the opposite for engineers. If wages and prices are perfectly flexible, they will adjust and clear markets for both types of labour. There will be no unemployment in this case. However, if wages and prices are rigid, sectors employing doctors will not expand because of shortages of doctors, but those employing engineers will contract. In this case, the impact of the demand shift is similar to that of a contraction in aggregate demand. Engineers become involuntarily unemployed—as they are willing to work at the going wage rate for the engineers and an increase in aggregate demand will reduce their unemployment. Two points emerge from the above example. First, sectoral shifts create unemployment if and only if wages and prices are rigid. The unemployment is therefore involuntary. Second, if sectoral shifts are accompanied by price rigidity and give rise to unemployment due to imperfect mobility of labour, they will in no time snowball into full-fledged recessions. The contracting firms will cut output, but the firms planning expansion will fail to do so because of paucity of suitable labour. Aggregate income will therefore fall reducing aggregate demand and thereby inducing further cut in aggregate output. The contracting firms will lose and therefore will be in financial difficulty. Default rate will rise putting the lending institutions in trouble. They will ration credit more severely. It will reduce demand again. These contractions will mutually reinforce and cumulate and push the economy in a recession. From the above it follows that, if unemployment is due to sectoral shifts, there is rigidity in the price system. Moreover, if sectoral shifts combine with price rigidity and imperfect mobility of labour, they generate strong recessionary forces. If one admits that sectoral shifts, price rigidities and imperfect mobility of labour are common features of market economies, as the proponents of the NRH do, one also concedes that a market economy is normally recession prone and demand deficiency and involuntary unemployment are rules rather than exceptions. In other words, the implication of the assumptions of the proponents of the NRH is that demand deficiency

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and involuntary unemployment are chronic and systemic in decentralized market economies. Sectoral shifts that generate unemployment are hardly as innocuous as the proponents of the NRH make us believe. They have strong destabilizing and contractionary impact. Thus, in a market economy today, it is sensible to regard the observed unemployment as being involuntary— a product of wage rigidity and inadequacy of aggregate demand. The latter is due to various factors including sectoral shifts. Even though the mismatch between the structure of labour demand and that of labour supply has been attributed to sectoral shifts in the above discussion, it can occur even without any kind of sectoral shifts. It is a general feature of market economies. Let us explain. Consumption decisions and decisions to invest in physical and human capital in such economies are taken by individual economic agents independently of one another in an uncoordinated manner. Individual decision makers cannot have any idea as to what the total demand would be for any particular good or for any particular type of labour or what the total supply would be of any particular type of labour. The input–output relationships across different sectors of production and different types of labour change continuously with innovations of new technology, products, etc. Individuals do not and cannot have information regarding these relationship or their changes. Accordingly, the structure of labour demand that is yielded by the composition of aggregate demand and the structure of labour supply that arise out of individuals’ investments in different kinds of human capital can match only accidentally. The phenomenon of sectoral shifts makes the scenario more unpredictable. Moreover, prices and wages are also normally rigid because of different kinds of market imperfections. Hence, involuntary unemployment and demand deficiency are likely to be chronic and systemic in unplanned market economies. Let us generalize the above argument. Mismatches in demands and supplies of the kind discussed above are by no means confined to labour markets alone. They apply to physical capital also with equal force. Capital too is imperfectly mobile across different industries. A steel plant can only produce steel; it cannot produce power or any other product. A mismatch between the structure of demand for capital services yielded by the composition of aggregate demand and the structure of the supply of capital services is also quite likely to occur in market economies. Thus, even though aggregate demand for capital services equals their aggregate supply, there may be excess demand for one kind of capital service (such as the ones producing power or transport) and excess supply of some other kind (such as the ones producing consumer durables). If prices are rigid, as is normally the case, because of oligopolistic interdependence in case of private goods and administered prices in case of public goods, these mismatches will not get corrected through movements in prices in the short run. Let us illustrate with an example. Suppose in a given period, there occurs in an economy excess demand for roads, water supply, etc., and an excess supply of consumer durables. Prices of the former are non-existent, as they are public goods. Hence they cannot rise to correct the situation. Prices of the latter may not fall because of oligopolistic interdependence. Hence the situation will give rise to substantial excess capacity in the consumer durables industry saddling the investors with heavy losses. We can show the problem in a different way also. Since different sectors of production are interdependent through input–output relationships, investments made in different lines of production in any given period have to synchronize to ensure full utilization of capacity for the economy as a whole. In the example given above, the capacity output of the road and water supply sector is too low to enable the rest of the economy to fully utilize its productive capacity.

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In this kind of a situation, serious economic problems will arise leading to recession. In the sectors having excess supply of capital, a substantial part of expensive capacities created will remain unutilized and the investors will incur heavy losses. They are likely to default on their loan obligations creating financial difficulties for the banks and other lending institutions. These institutions’ ability to lend will get restricted. They will also be more cautious in their lending. This will reduce credit supply and consequently aggregate demand, which will further aggravate the situation pushing the economy into recession. The kind of problem specified above is and should be systemic in market economies since consumption decisions and decisions to invest in physical and human capital are made by individual consumers and investors in an uncoordinated manner and prices are rigid for reasons already discussed. This problem is referred to as that of coordination failure. It is called disproportionality crisis by Marx. This is a, if not the, major factor that makes a market economy recession prone. Alternatively, it makes demand deficiency a chronic problem in a market economy. In times of high rate of growth or boom, when capacities are created at a high rate in different areas of production in an uncoordinated manner, the problem of coordination failure makes newly created expensive capacities idle in different lines of production due to scarcities of certain specific kinds of labour or shortages of some crucial inputs badly hurting investors’ morale, even though there may be sizeable excess capacity and unemployment on the aggregate. This has, as we have already pointed out, adverse financial implications, which push the financial institutions on the back foot aggravating the damage to business sentiments. The problem of the real sector gets magnified through its impact on the financial sector. This process is referred to as that of financial accelerator—see Bernanke et al. (1998). These mutually reinforcing forces push the economy into recession much before the state of full employment is reached. Again, in an economy in recession, with the increase in the pool of unemployed workers, availability of all kinds of workers becomes plentiful; supplies of social goods improve due to governments’ efforts at stabilizing the economy and with the easing up of fiscal constraints on public expenditure. With idle capacities everywhere, supplies of all kinds of goods become more abundant too. These improvements in supply side factors again begin to boost business morale leading to a resurgence in economic activities. The point of this whole discourse is that price rigidities and mismatches between the structures of aggregate demand and those of capital and labour due to coordination failure are an integral feature of a market economy. They are systemic and generate chronic demand deficiency and involuntary unemployment. They are the main reason why booms turn into recession much before the state of full employment is reached. Even the current recession in the US ravaging the developed world has its roots in massive over-investments in the real estate far in excess of genuine demand for housing. The reason, again, lay in large scale coordination failure. The increasing profitability of investment in the housing sector led to tremendous overinvestment in housing precipitating the crash. It thus seems more sensible to regard the observed unemployment in a market economy as being involuntary. Apart from the argument spelt out above, there are other factors that tend to make aggregate demand deficient. People have to save to fend for old age, infirmity, etc. Hence consumption demand usually falls far short of aggregate output. Investment is highly risky and people are generally risk averse. Government expenditure is subject to severe budget constraints, given governments’ obsession with revenue and fiscal deficits. For these reasons also demand deficiency may be the norm rather than an exception. Even casual empiricism shows that

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nominal prices and wages are fairly rigid and there is no dearth of supplies of goods and services at their given prices. If demand deficiency and involuntary unemployment are chronic, it means that in times of recession the rate of involuntary unemployment is large and it is small in times of boom. Besides the factors noted above, there is another reason why a market economy may fail to achieve full employment. Usually, there is an asymmetry in the price adjustment processes. Prices and wages are often found to be inflexible downward, but they are not so in the upward direction in the event of shortages. The reason is not far to seek. First consider the prices of produced goods and services. Markets of these goods are oligopolistic. When there is excess capacity in the firms, no firm risks cutting its price unilaterally, as it will lead to a price war saddling all the firms with losses. When all firms in an industry engage in competitive price cuts, it has ruinous implications for them all. But in times of shortages, firms may unilaterally raise their prices, as there is no risk of losing customers to the rivals, since every producer is capacity constrained. In case of labour, as Keynes pointed out, money wages do not fall in the face of unemployment on account of workers’ resistance. Worker unions resist such cuts. Firms may also consider it imprudent to cut wages unilaterally to earn the infamy of being a bad employer. If a firm gets singled out as a bad employer, it will not be able to retain or get to recruit the best of the workers and thereby will lose out in competition. Unemployment and recession go hand in hand. In times of unemployment, there is recession and firms have insufficient demand for their products. A unilateral cut in wages in such a situation and the consequent adverse response of the workers may be enormously costly to the firms. Any kind of supply failure in such a situation may lead to a sizeable loss in market share and this loss may far outweigh the gain due to the wage cut. There are also minimum wage legislations setting floors to money wages. In the event of labour shortages, however, firms can offer higher money wages without the adverse consequence noted above. This explains the asymmetry in the price adjustment mechanism. This asymmetry coupled with the problem of coordination failure may check output expansion in times of boom much before full employment is attained. Let us explain. Capital structure and labour structure, as we have already explained, are far from balanced in market economies, given the lack of coordination among the individual decision makers and that of information. Hence, as aggregate demand rises relative to productive capacity, shortages of various kinds of goods and labour begin to crop up putting upward pressure on prices. This is the standard trade-off between inflation and unemployment that the traditional Phillips curve captures. Since the government and the central bank do not want the rate of inflation to rise beyond some tolerable levels, they may adopt contractionary programmes much before the full employment level of output is reached. This may also be one of the reasons why a market economy never attains full employment. In this case, even though prices move in the upward direction, it cannot do so fully to adjust the pattern of demand to that of supply owing to government intervention. Once we accept that demand deficiency is chronic, a position which seems to be much more sensible and logical than the NRH, the sharp division between the short-run and long-run analyses in macroeconomics dissolves altogether. The focus shifts to the year-on-year growth rates, which have to be explained using the short-run models only. The above observations throw the area of growth wide open. It need not necessarily be the exclusive preserve of long run macroeconomics that focuses solely on the supply side factors. It may be better to study growth by focusing on the year-on-year growth using the Keynesian

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models. The short-run Keynesian model determines Y or Yt. Given Yt–1, it determines a growth rate as well. We have already discussed Keynesian theory in detail in earlier chapters. So, here we shall focus mainly on the theories based on the NRH. In fact, we shall present below some of the major models of the modern growth theory, which are all based on the NRH, and assess the results they yield. The modern growth theory is based on the pioneering work of Solow (1956). The model he developed is referred to as the Solow model or the theory of neoclassical growth. It attributes differences in the long-run growth rates of per capita output across countries to variations in the rates of technological progress. However, Solow did not try to explain crosscountry differences in the rates of technological progress, but treated them as given. In his view—see Solow (2000)—both growth and technological progress are highly complex phenomena and are subjects of separate fields of study in their own right. Any attempt at explaining both of them within the framework of a single model, according to Solow, imposes severe restrictions on both the quests and makes both of them poorer. Hence, while developing his growth theory, he took the rate of technological progress of a country as exogenously given. The neoclassical growth theory held sway until the mid-eighties. Then came the pioneering works of Romer (1986) and Lucas (1988), which started what we call today the endogenous growth theory. Contrary to the view held by Solow, the endogenous growth theory seeks to endogenize or explain the rate of technological progress. It attempts at identifying the key factors that drive technological progress. Some of these are human capital formation, R&D, learning by doing, etc. We shall discuss both the neoclassical theory of growth and the endogenous growth theory below. The neoclassical growth theory was developed by Solow in response to the seminal works of Harrod (1939) and Domar (1946). In fact, it is these two studies that aroused tremendous interest in growth theory and started an avalanche of research in the area. Neoclassical growth theory was one major output of this massive research effort. Before discussing the neoclassical growth theory therefore we shall present the models of Harrod and Domar. We shall discuss here the model of Harrod, which is usually referred to as the Harrod–Domar model. Domar’s model is slightly different from Harrod’s, but both of them arrived at more or less the same result independently.

13.2 HARROD–DOMAR MODEL Harrod and Domar dynamized Keynesian theory to show that a market economy is inherently unstable. It has a natural tendency to generate either spiraling inflation or cumulative recession. The result is so startling that it took the intellectuals by storm giving rise to a frenzy of research to soften the result. Efforts were also made to extend Harrod–Domar model (HDM) to generate trade cycles and thereby to explain them. HDM considers a closed economy without government. It assumes a proportional saving function as given by St = sYt

(13.1)

where St º aggregate saving in period t, s º constant average and marginal propensity to save and Yt º GDP in period t.

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It assumes the following investment function: It = v×(Yt – Yt–1)

(13.2)

where It º aggregate investment, v º constant. Equation (13.2) states that investment in period t is a proportional function of the increase in output from period t – 1 to period t. The implication is that producers have to add to the capital stock, i.e. they have to invest, to raise output and for every unit increase in output in any given period from that in the previous period the producers in the given period have to make a constant v amount of investment. Obviously, there is equilibrium in the goods market in period t iff sYt = v×(Yt – Yt–1)

(13.3)

i.e. iff (Yt  Yt 1 ) Yt

s v

(13.4)

Equation (13.4) implies that there is equilibrium in the goods market in every period iff the growth rate of GDP,

(Yt  Yt 1 ) , assumes a unique value, s/v. Let us elaborate a little. Suppose Yt

the growth rate of GDP in period t equals (s/v), i.e. suppose (13.4) holds. Then in period t, saving and investment are equal, i.e. (13.3) is satisfied. Thus, if in any given period producers expand their production at the rate (s/v), goods market will be in equilibrium in that period. Thus the rate of growth, (s/v) is sufficient for equilibrium in the goods market. Again, suppose the goods market is in equilibrium in period t, i.e. suppose (13.3) holds in period t. Then, as follows from (13.3), the rate of growth of GDP is (s/v). This rate of growth is therefore also necessary for goods market equilibrium. Harrod calls this rate the warranted rate of growth. Let us now examine the situation where the growth rate of GDP differs from the warranted rate. Suppose (Yt  Yt 1 ) s ! Yt v This means that sYt = St < It = v×(Yt – Yt–1). Hence there is an excess demand in the goods market in period t. This yields a devastating result. It implies that, if producers plan to expand output at a rate higher than the warranted rate, there will emerge excess demand or shortages giving the producers the signal that their planned rate of expansion is too low to meet the demand for goods and services. Hence they will plan a higher rate of expansion giving rise to excess demand and shortages again. Thus, if the growth rate planned by the producers exceeds the warranted rate, the producers will be induced to go on raising it over time. On the other hand, if the producers’ planned rate of growth falls short of the warranted rate, there will emerge excess supply inducing the producers to think that their planned rate of expansion is too high. Accordingly, they will reduce their planned rate of expansion perpetuating the problem of over production. Hence the planned rate of growth will go on falling over time. Thus, the HDM shows that the warranted rate of growth, the rate of growth that keeps the economy in equilibrium, is a knife-edge, i.e. it is unstable. We shall henceforth refer to this problem of instability of the warranted rate of growth as the first problem of HDM.

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Harrod points to another problem. He assumes that there is a maximum sustainable growth rate of GDP, given the growth rate of population and labour force, which he regards as being exogenously given. He calls this the natural rate of growth and denotes it by n. Obviously, the warranted rate of growth and the natural rate of growth are unlikely to be equal except by accident. When the two are not equal, a market economy is in another problem. Suppose n > (s/v). If the actual growth rate equals (s/v), unemployment will emerge and grow over time. If the actual growth rate exceeds (s/v), it will go on increasing until it hits n. It cannot increase any further. However, as we have explained above, there will be excess demand in every period in this situation. As a result, there will be inflationary spiral in the economy. If the actual growth rate is below (s/v), then, as we have noted above, the rate of growth will go on falling leading to cumulative growth in unemployment. (Explain the problems that will crop up if n < (s/v).) Let us now make an evaluation of the HDM. Obviously, a market economy is not as unstable as is pointed out by the HDM. Growth rates in a market economy fluctuate a great deal, but they do so within limits. Consider, for example, the figures in Table 13.1, which shows that India was in recession during 2000–01 to 2002–03. However, this phase was followed by a period of high growth from 2003–04 to 2007–08. The growth rate slumped a little again in 2008–09. Growth rates usually follow a cyclical pattern as evinced by Table 13.1. Periods of high growth rates are followed by those of low ones and vice versa. Thus the growth rate, as predicted by HDM, neither goes on rising steadily over time nor does it keep on falling monotonically, even though the average or the trend growth rate may show a tendency to rise, as is the case in India. These fluctuations in year-on-year growth rates are best explained using the short-run models. Table 13.1 Year-on-year growth rates of India’s GDP and its components at constant Prices: 2000–01 to 2008–09 2000–01 2001–02 2002–03 2003–04 2004–05 2005–06 2006–07 2007–08 2008–09 GDP Agriculture1 Industry Services (I)2 (I – MC)3 C4 G5 Exports ELEM6 Imports Remittances 1

4.0 –0.2 6.4 5.7 –3.5 –3.8 3.2 0.9 18.0 23.9 8..2 5.7

5.2 0.8 2.4 6.9 –2.9 –4.0 6.2 2.3 1.5 1.1 1.5 22.3

3.8 1.8 6.8 7.5 17.0 15.1 2.7 –0.4 17.8 17.2 17.7 3.8

8.4 10.0 6.0 8.8 19.9 19.5 5.8 2.6 10.8 10.4 12.6 20.6

8.3 0.0 8.5 9.9 19.5 19.1 5.2 2.6 32.3 33.4 35.1 -13.3

Agriculture includes forestry and fishing. I stands for gross investment. 3 (I – MC) stands for gross investment net of import of capital goods. 4 C denotes private final consumption expenditure. 5 G denotes public final consumption expenditure. 6 ELEM stands for exports net of export related imports. 2

9.2 5.9 8.0 11.0 19.4 16.8 8.7 5.4 20.2 22.9 27.9 12.9

9.7 3.8 10.6 11.2 10.9 9.3 7.1 6.2 21.8 25.6 24.4 10.0

9.2 5.1 7.5 11.1 16.9 19.0 6.5 7.0 4.6 5.1 8.2 24.1

7.1 2.6 4.2 9.2 9.7 6.8 16.8 21.5

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The short-run Keynesian model determines Y or Yt. Given Yt–1, it determines a growth rate as well. However, in the Keynesian model, infinitely large number of growth rates are consistent with equilibrium. If Yt equals its full capacity, full employment or the potential level, the growth rate in period t is at its maximum. The growth rate may be less than that. It may even be zero or negative. If the growth rate is much less than its potential level, the economy is in recession. If it is close to its maximum value, the economy is in boom. The HDM is not much different from the short-run Keynesian model. The former is just a derivative of the latter, yet HDM finds that one and only one growth rate is consistent with equilibrium. Moreover, the equilibrium in the short-run Keynesian model is stable, given its assumptions, but it is not so in the HDM. We shall show below that these startling results of the HDM are due to the specific forms of the saving and investment functions assumed in the HDM. Let us elaborate. We can solve (13.3) for the equilibrium value of Yt. It is given by

Yt

vYt 1 vs

(13.5)

From (13.5) it follows that for a meaningful equilibrium to exist v has to be greater than s. We do not get this restriction in HDM because it solves (13.3) not for Yt but for the equilibrium growth rate, which is not inconsistent with negative values of Yt and Yt–1, i.e. theoretically GDP can grow at the warranted rate even when values of Yt and Yt–1 are negative. From (13.5), it also follows that the equilibrium value of (Yt/Yt–1) or the equilibrium growth rate, which is nothing but (Yt/Yt–1) – 1, is a function only of s and v. The solution of (13.3) is shown in Figure 13.1 under the assumption that s > v. Otherwise, the equilibrium output will be negative, which will make the HDM meaningless. Figure 13.1 shows that, if Yt 1

Yt01, the equilibrium value of

Yt equals Yt0 that corresponds to the point of intersection of the saving schedule, SS and the investment schedule, I I.

Figure 13.1 Instability in HDM.

Modern Theories of Growth: A Critique

The warranted growth rate is obviously

Yt0  Yt01

379

s . From Figure 13.1 it is clear why the v

0

Yt equilibrium growth rate in the HDM is unstable. If the producers plan a lower growth rate in

period t, the output in period t will be less than its equilibrium value, Yt0 . Since the investment schedule in Figure 13.1 cuts the saving schedule from below, at any Yt less than the equilibrium level of Yt, Yt0 , there will be excess supply. Hence the producers will go on lowering the output and thereby the growth rate towards zero. Again, if the producers plan a growth rate higher than the warranted growth rate in period t, they will produce more than the equilibrium level of Yt, Yt0 , bringing about, as follows from Figure 13.1, excess demand for goods and services. Hence producers will go on expanding output and thereby the growth rate until the maximum or the potential growth rate is reached. To see why the results of the HDM, namely the uniqueness of the equilibrium growth rate and its instability, are due to the specific forms of the saving and investment functions, it is best to use the Keynesian saving function which is supported by data. If we do that, the saving function and the equilibrium condition are to be rewritten as

St and

 S  sYt ;

 S  sYt

S !0

(13.6)

v ¹ (Yt  Yt 1 )

(13.7)

Solving (13.7) for Yt, we get

Yt

S  vYt 1 sv

(13.8)

The equilibrium Yt yielded by (13.8) is positive if S > vYt–1 and s > v. Yt > 0 also when S < vYt–1 and s < v. We shall, however, focus on the former case. Figure 13.2 shows the solution of (13.7) in the former case. Figure 13.2 shows that, if Yt 1 Yt01, the equilibrium value of

Figure 13.2

Stability in the HDM.

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Yt equals Yt0 that corresponds to the point of intersection of the saving schedule, SS and the investment schedule, II. From (13.8) and also from Figure 13.2, it is clear that the lower the Yt–1, the higher is Yt, i.e. the equilibrium growth rate is non-unique and it is a decreasing function of Yt–1. It is also evident from Figure 13.2 that the equilibrium growth rate is stable.

If, given Yt 1

Yt01, the producers plan a growth rate less than the equilibrium one, Yt will be

less than its equilibrium value, Yt0 . However, as is clear from Figure 13.2, in this case, contrary to the HDM, there will be excess demand inducing the producers to produce more. This expansion will continue until the equilibrium growth rate is achieved. Thus the instability result of the HDM goes too. Investment in any given period may not depend just on the expansion in output envisaged in the current period. Quite a large part of investment may be made with the future, even distant future in mind. Thus the major part of investment in any given period may be driven by investors’ expectations regarding future or their animal spirits. Thus the investment function is likely to have a large autonomous component. If we incorporate an autonomous component, I , in the investment function, (13.2), the equilibrium value of Yt will be given by I  S  vYt 1 (13.9) sv and our result derived above will be strengthened. From the above it follows that if we modify either the saving or the investment function or both even slightly, all the major results of the HDM go away, i.e. the warranted rate of growth ceases to be unique and unstable. However, (13.9) has another feature. It solves Yt as a function of Yt–1 and thereby tells a story of evolution of Y over time—a story that the short-run Keynesian theory does not contain. In Figure 13.3, YY represents (13.9). It plots the value of Yt as given by (13.9) corresponding to every different value of Yt–1. From Figure 13.3 we find that if the absolute value of the slope of YY, v/(s – v), is less than unity, Y will approach cyclically a stationary value, labelled Y* in Figure 13.3, over time and hence the growth rate of Y will eventually fall to zero. If, as shown in Figure 13.3, the initial value of Y is Y0, its value will be Y1 in the next period and Y2 in the period after the next and so on. The implication of the above discussion is that, if investment or consumption in any given period depends on the past or future values of income or other variables, growth rates of different periods become linked with one another and one has to develop a dynamic model to capture the behaviour of the growth rate of income over time. However, the possibility of this kind of a scenario seems remote. Since, as we have argued, demand deficiency is likely to be chronic, it is not necessary to make investment to raise output from one period to the next. Investment is usually made with a much longer run scenario in view. Investment is therefore principally governed by the animal spirits of the investors. Borrowing cost or interest rate of the given period may also play a role in the determination of investment. Inventory investment usually depends on the current income and interest rate. Aggregate consumption depends on current income in the main. Thus, unless there are compelling evidences to suggest otherwise, it is best to use the short-run Keynesian model to explain the year-on-year growth rates. No separate theory seems to be needed to explain the long-run growth, which is nothing but the average of the short-run growth rates and as such is likely to reflect chronic demand deficiency. This is corroborated by the persistence of unemployment over time. Yt

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Figure 13.3

381

Evolution of Y over time.

It should be noted in this context that in India both demand and supply constraints operate at the same time and this makes the study of growth much more complicated. Let us elaborate. Even casual empiricism shows that in India prices of privately provided nonagricultural goods are highly rigid and there is no dearth of these goods at these rigid prices. Hence outputs of these goods are demand driven. However, there are many publicly provided goods in India, which are supplied either free of charge or at non-remunerative administered prices, and there are marked shortages of these goods. These goods include power, potable water, roads, water from major irrigation projects, etc. Outputs of these goods are capacity constrained. Output of the agricultural sector is also given in the short run, since agriculture is a nature process, production requires a pre-specified period of time and there is no scope for adjusting output during the time that elapses between one sowing season to the next. To explain growth in India’s GDP in a given year, one has to therefore undertake a disaggregated study. Growth in the privately provided non-agricultural goods has to be explained in terms of growth in their demand, while the growth in the publicly provided goods and agricultural output will be determined by the growth in their productive capacity due to investments in earlier periods. Note that productive capacity in agriculture depends crucially on public investment in major irrigation in dry land areas, flood control facilities in areas prone to flooding, inventions of better seeds, farming practices, etc. The last two in India also depends crucially upon public investment in agricultural R&D. Thus Keynesian economics does not apply fully to Indian macroeconomy. When GDP is demand driven, its growth can be explained in terms of growth in the autonomous components of aggregate demand, namely investment, government consumption and export. From the data in Table 13.1 one can compute the growth rates of these components of aggregate demand. But the sum of these growth rates, as one can easily check, cannot explain fully the growth performance of GDP in India during the period under consideration—see in this context Rakshit (2009). We shall now critically assess the major theories based on the NRH. In fact, we shall discuss the pioneering work of Solow (1956) and the endogenous growth theory that it gave rise to and evaluate the results they yield. The model Solow (1956) developed is referred to as the Solow model or the neoclassical theory of growth.

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EXERCISE 13.1 (a) Suppose in an economy investment function is given by It = 4(Yt – Yt–1) and people save one-fifth of their income. If the goods market is in equilibrium in every period, at what rate is the GDP of the economy growing? If the economy grows at the rate derived above in every period, will the goods market be in equilibrium in every period? What conclusion do you draw from your answers to the two questions given above? Suppose in this economy the producers are increasing their production at the rate of 6 per cent. Will they be satisfied with their expansion rate? If not, then how will they revise their expansion rate? Will this revision solve the problem faced by the producers? Explain. Suppose the natural rate of growth of the economy is 8 per cent and in the initial period the growth rate of the economy was 6 per cent. Will this economy eventually be subject to severe inflationary pressure? Discuss. (b) Suppose the saving and investment functions in an economy are given by St = 100 + 0.25Yt and It = 4(Yt – Yt–1). How much output will be produced in equilibrium in period T, if YT–1 = 100. What is the equilibrium growth rate? Is this equilibrium growth rate stable? Explain. How does aggregate output evolve over time? Illustrate graphically.

13.3

NEOCLASSICAL THEORY OF GROWTH

The neoclassical theory of growth or the Solow model addresses the issue of the determination of the growth rate of per capita GDP in a market economy in the long run. It is based on the NRH. Accordingly, it builds on the classical model and assumes, ignoring the natural rate of unemployment for simplicity, that in every period there is full employment of the existing quantities of capital and labour in production and the economy produces the full employment level of output. Aggregate output in every period is therefore given by Yt = F(Kt, Lt)

"t

(13.10)

where F(×) º the production function, Kt º stock of capital existing in period t and Lt º amount of labour in efficiency units existing in period t. We shall explain the concept of labour in efficiency units shortly. Henceforth we shall refer to labour in efficiency units simply as labour. The following assumptions are made regarding the production function: F(0, L) = 0, F(K, 0) = 0; FK > 0, FL > 0, FKK < 0, FLL < 0

and

Ë lim FK (K , L ) lim FL (K , L ) ‡;Û L 0 Ì K 0 Ü Ì lim FK (K , L ) lim FL (K , L ) 0 Ü Í K ‡ Ý L ‡

The first two conditions state that both the inputs are essential for production. The next two conditions state that marginal productivities of both labour and capital are positive. Fifth and sixth conditions imply diminishing marginal productivity of each of the two inputs and the last set of conditions within the third brackets, referred to as the inada conditions, state that marginal productivity of capital (labour) approaches zero as amount of capital (labour) approaches infinity

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and it approaches infinity as amount of capital (labour) approaches zero. The production function also displays constant returns to scale. Hence we can write (13.10) in per capita terms as follows: ÈK

FÉ Ê

f„

FK ! 0, f ”

L

Ø

, 1Ù Ú

1 Y L

À

LFKK  0, lim f „ k

0

y

f (k )

‡ and lim f „ 0 k

‡

(13.11)

Y K and k œ . L L Note that the signs of f ¢, f ² and the limits of f ¢ follow from the assumptions regarding the production function as given by (13.10). Let us now explain the concept of labour in efficiency units. Let L denote labour in natural units. Solow assumes that technological progress is labour augmenting, i.e. it enables a given amount of natural labour to contribute more to production. To illustrate with an example, suppose ten hours of work put in by workers using a given technology and capital stock, can produce a given amount of output. However, with a better technology, the same number of hours of work supplied by the workers can produce more using the same amount of capital as before. This means that use of better technology enables, for example, ten hours of natural labour to produce as much as, say, fifteen units of natural labour using the inferior technology. Thus, in the above example, under the new technology, ten hours of natural labour becomes fifteen units of labour in efficiency units. In Solow’s model, labour in efficiency units is defined as

where y œ

L = A L

(13.12)

where A is an index of technology. An increase in A, corresponding to every given L, raises the amount of labour in efficiency units. Technological progress here increases the efficiency of natural labour so that any given amount of natural labour can produce more. If the amount of natural labour available in period t is Lt, the amount of labour in efficiency units available in period t is Lt = At Lt

(13.13)

where At is the labour augmenting factor of the technology being used in period t. Since in this model Yt depends only on Kt and Lt, growth in output occurs through growth in capital and labour in efficiency units. Regarding natural labour it is assumed that it grows 1 dLt 1 at an exogenous rate, n, i.e. it is assumed that œ  L t œ Lˆ t n. Similarly, it also assumes  L dt L t

t

that the technological progress occurs at an exogenously given rate, m. The rate of technological progress is given by the rate of growth of At. This means that

1 dAt 1 œ A t œ Aˆ t At dt At

m . If we

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multiply either m or n by 100, we express the growth rate in question in percentage terms. Thus the Solow model does not seek to explain either the growth rate of the natural labour force or the rate of technological progress. The above two assumptions imply that the supply of labour in efficiency units grows at the exogenously given rate, m + n. The point may be established in the following manner. Taking log on both sides of (13.13) and then differentiating with respect to time, t, we get 1 dLt Lt dt

È Éœ Ê

1  Lt Lt

Ø Lˆ t Ù

œ

Ú

Aˆ t



ˆ Lt

(13.14)

mn

Capital grows through investment. How is investment determined? We shall now focus on that. It is assumed that the economy is in equilibrium with the full employment level of output in every period. It is assumed further that whatever is saved in the full employment situation is invested. Thus Solow ignores the first problem of HDM. The model assumes a simple proportional saving function. It is given by S = sY

(13.15)

Since whatever is saved is invested by assumption, investment in every period is given by It = sYt

(13.16)

It denotes gross investment. It is also assumed that in every period a fixed fraction of the existing capital stock depreciates. Hence increase in capital stock in period t,

È dKt Ø œ É Ê dt Ù Ú

K t , is given by

It  E Kt

(13.17)

sYt  E K t

(13.18)

K t Substituting (13.16) into (13.17), we get

K t

Dividing both sides of (13.18) by Kt, we have

K t ˆ œ K t Kt

s

Yt E Kt

s

yt E kt

(13.19)

Therefore the rate of growth of capital stock, using (13.11), is given by Kˆ t

s

f ( kt ) E kt

(13.20)

From (13.20) it follows that the rate of growth of aggregate capital stock is determined by kt, given s, d and the parameters of the production function. It may therefore be instructive to know how kt grows over time. Now, log kt = log Kt – log Lt

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Differentiating the above equation with respect to time (t), we have È k Ø kˆt É œ t Ù Ê kt Ú

Kˆ t



Lˆ t

s

f (kt ) kt

 E  (m 

n)

(' Lˆt

m  n, see (13.14))

(13.21)

As Solow model examines how GDP or per capita GDP in a market economy grows over time, it is a dynamic model. A static model does not consider time explicitly and focuses just on one period and on equilibrium. A dynamic model, however, focuses on a special type of equilibrium situation called steady state. A steady state is defined as an equilibrium situation where every endogenous variable grows at a constant rate. Note that in the Solow model, the economy is in equilibrium with the full employment level of output in every period. This means that all the endogenous variables, Yt, Kt, St and It and their per capita counterparts only assume equilibrium values in Solow model. So, to identify the steady state, we have to only consider the situation where they grow at constant rates over time. We now show that there is steady state in Solow model if and only if k is constant over time. Start with the growth rate of aggregate capital stock as given by (13.20). Note that, if k is constant, so is Kˆ and y—see (13.20) and (13.11). Constancy of y implies that rates of growth of Y and L are equal, i.e. both the variables have the same growth rate, m + n. If Y grows at the constant rate, m + n, so must S and I—see (13.15) and (13.16). Thus, if k is constant, the economy in Solow model is in steady state, i.e. it is in equilibrium in every period and every endogenous variable grows at a constant rate. Note that the growth rates of k and y are zero, when k is constant. Thus constancy of k is sufficient for steady state. We shall now show that constancy of k is also necessary for steady state. Note first that f ¢ is a strictly decreasing function of k by assumption—see (13.11). Hence, at every k average productivity of capital, [f (k)/k], is greater Ë k Ì 0 Í

Ô

Û

f „( v)dv Ü

Ý . This is clearly k illustrated in Figure 13.4 where marginal productivity of capital at any given point on the production function, f (k), is given by its slope at that point, while the corresponding average productivity of capital is given by the slope of the straight line joining the given point to the origin. Given this result, we can show that Kˆ , as follows from (13.20), is strictly decreasing

than the marginal productivity of capital, f ¢(k), since [ f ( k ) / k ]

t

in k. Let us prove this below. Differentiating [sf(k)/k] with respect to k, we have Ës Î Ì Ï f „(k )  Ík Ð

f ( k ) ÞÛ ˆ ßÜ < 0 for all 0 < k < ¥. This proves the point. Hence, if K t is constant, so k àÝ is k. This implies that constancy of k is also necessary for steady state. Thus we have steady state if and only if k is constant, i.e. if and only if kˆ

sf ( k )  (E  n  m ) k

0

(13.22)

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Figure 13.4 Relationship between marginal and average productivities of capital.

Obviously, if any k assumes the value that satisfies (13.22), it will remain constant over time and the economy will be in steady state. We can therefore solve (13.22) for the steady state value of k. Given the assumptions regarding the production function, (13.22) yields a unique, positive and finite steady state value of k. Let us prove. From assumptions regarding the production function we find that at k sf (k ) k 0 k lim

lim sf „( k )

k

0

0,

sf ( k ) k

0 . Therefore by L’Hospital’s rule, 0

‡ (from inada conditions). Again, at k = ¥,

sf ( k ) k

‡ . Therefore by ‡

sf ( k ) sf ( k ) L’Hospital’s rule, lim is also continuous lim sf „(k ) 0 (from inada conditions). k ‡ k k ‡ k in k and, as we have already pointed out, is monotonically decreasing in k. From all the above

observations it follows that

sf (k ) falls monotonically and continuously from ¥ to 0 as k rises k

from 0 to ¥. Hence there must exist a positive and finite k for which (d + m + n). Since

sf ( k ) will be equal to k

sf (k ) is strictly decreasing in k, there cannot exist any other value of k for k

sf ( k ) equals (d + m + n). Therefore there must exist a unique, positive and finite steady k state value of k that will satisfy Eq. (13.22). The solution is shown in Figure 13.5 where the steady state k, labelled k*, corresponds to the point of intersection of the horizontal line corresponding to (d + m + n) and the [sf(k)/k] line in the upper panel. In the lower panel, we plot the production function, f(k). The steady state value of y, labelled y*, corresponds to k* on this production function.

which

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Figure 13.5 Existence, uniqueness and stability of steady state.

13.3.1 Transitional Dynamics Transitional dynamics refers to the process of adjustment of the endogenous variables in nonsteady state situations. The Solow model has an interesting transitional dynamics. It states that an economy’s k and therefore y, whatever be their initial values, always gravitate towards their respective steady state values denoted by k* and y* respectively. Let us explain. Since

sf ( k ) is k

sf (k ) > () k*,

strictly decreasing in k,

sf ( k ) – (d + m + n) > ( m + n at k0. Hence, capital begins to grow at a faster rate than labour in efficiency units, i.e. kˆt —see (13.21) and (13.22)—becomes positive. Accordingly, k begins to rise from k0 and it continues to rise until the rate of growth of capital, [(sf(k)/k) – d ], falls to the level of m + n. This happens at the new steady state k, k1. With the rise in k, per capita output, y, also rises to its new steady state value, y1. This is clear from Figure 13.6.

Mathematical derivation of the result We can derive the effect of an increase in s on steady state values of k and y mathematically also using the steady state condition, (13.22). Putting the steady state value of k denoted by k* into (13.22), we get the following identity:

sf (k * ) k

*

œ (E  m  n) À sf (k * ) œ (E  m  n)k *

(13.26)

Taking total differential of both the sides of the above identity, we get sf ¢(k*)dk* + f(k*)ds = (d + m + n)dk*

(13.27)

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Macroeconomics

Let us explain the above equation. In both the initial and the new steady states, the LHS and the RHS of (13.26) are equal. Hence the change in the LHS of (13.26) from the initial steady state to the new steady state should be equal to the change in the RHS of (13.26) from the initial to the new steady state. Of all the determinants of the LHS, the values of only k* and s change from the initial steady state to the new steady state. The value of s changes by ds by hypothesis, while the value of k* changes since it is an endogenous variable. k* changes by dk*, which is an unknown quantity. The LHS of (13.27) gives the change in the value of the LHS of (13.26) due to ds and dk* amounts of changes in s and k* respectively. Hence the LHS of (13.27) gives the change in the value of the LHS of (13.26) from the initial steady state to the new one. Again, the only determinant of the RHS of (13.26) that changes from the initial steady state to the new steady state is k*, as it is an endogenous variable, by dk*, which is unknown. Hence the RHS of (13.27) gives the change in the value of the RHS of (13.26) from the initial steady state to the new steady state. Hence the two sides of (13.27) are equal. Since both f ¢(k*) and f(k*) are evaluated at the initial value of k*, they are constant and known. Note that, we know both f(×), as it is exogenously given, and the initial value of k*. Accordingly, (13.27) contains only one unknown, dk*. We can therefore solve (13.27) for dk*. dk *

f ( k * )ds (E  m  n)  sf „(k * )

!0

(13.28)

Let us now explain the sign of (13.28). We know that the steady state is stable. At the steady state value of k we know from (13.22) that (sf(k) – (d + m + n)k) is zero. Since the steady state k is stable, (sf(k) – (d + m + n)k) falls (i.e. becomes negative) with a rise in k from its steady state value and rises (i.e. turns positive) with a fall in k from its steady state value. This is because, when (sf(k) – (d + m + n)k) is negative (positive), the rate of growth of capital stock falls short of (exceeds) the rate of growth of labour in efficiency units and decreases (increases). Therefore (sf(k) – (d + m + n)k) varies inversely with k in the neighbourhood of the steady state k in Solow model, i.e. [¶(sf(k) – (d + m + n)k)/¶k] = sf ¢(k) – (d + m + n) < 0 in the neighbourhood of steady state in Solow model. Hence the denominator of (13.28) is positive. Let us now explain (13.28) verbally. Following the given increase in s, the LHS of (13.26) exceeds the RHS by ëf(k*)dsû at the initial steady state k. At the initial steady state k therefore the rate of growth of capital exceeds the rate of growth of labour in efficiency units and as a result k starts rising. The economy achieves a new steady state when the LHS of (13.26) becomes equal to its RHS again, i.e. when [(sf(k) – (d + m + n)k)] falls to zero again, through the rise in k. Now, (sf(k) – (d + m + n)k) falls in absolute value by ((d + m + n) – sf ¢(k*)) per unit increase in k from k*. Therefore [(sf(k) – (d + m + n)k)] will fall in absolute value by ëf(k*)dsû to zero, when k rises from k* by {ëf(k*)dsû/((d + m + n) – sf ¢(k*))}. EXERCISE 13.2 (a) Examine the effect of an increase in (i) n and (ii) d on steady state values of k, y and growth rates of the endogenous variables in Solow model. (b) Suppose the production function is given by Y = KaL1–a. Examine the impact of an increase in the share of capital in Solow model. Suppose the rate of technological progress is nil so that At = 1 "t and therefore Lt = Lt "t. Develop the Solow model for

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this special case. Examine the effect of an increase in the (i) the saving ratio and (ii) the rate of growth of population in this model. In the light of your answers do you expect the countries with low saving ratio and high rate of growth of population to be richer in the long run? (c) Incorporate government in the Solow model under the assumption that the government spends a fixed fraction, a, of its tax revenue and the tax function is proportional. Is it possible for the government to make the country richer in the long run? Explain. (d) Derive the impact of an increase in the rate of technological progress, m, on steady state values of per capita capital stock and per capita output. Also derive its impact on the growth rates of aggregate and per capita capital stock, aggregate and per capita output, real rental rate and real wage rate of natural labour.

13.3.4 Evaluation of the Central Results of the Solow Model Let us now examine whether or how one can apply these results of the Solow model to explain the long-run growth performance of a country. In this context, two alternative assumptions are possible. One may assume, for example, that in the long run an economy is always in steady state. If this assumption is made, the per capita growth rate of GDP in the long run must be equal to the rate of technological progress. This implies that the rate of growth of the trend values of GDP should exceed the trend rate of growth of the labour force by the rate of technological progress. Surprisingly, none of the major empirical studies carried out so far make this assumption. Obviously, Solow model cannot explain long-run growth performance if the above assumption is made. In fact, data given in Table 13.2 do not give any prima facie support to the result of the Solow model. It shows that countries with a high per capita growth may have a low total factor productivity (TFP) growth, which is a measure of the rate of technological progress, and vice versa. Thus the UK with a per capita growth of 1.75 per cent had a TFP growth rate of 0.8 per cent, while the US with a higher per capita growth of 2.01 per cent recorded a lower TFP growth rate of 0.76 per cent. The result becomes all the more startling when we find that South Korea and Taiwan with negative per capita growth rates of –4.7 per cent and –4.4 per cent had TFP growth rates of 1.7 per cent and 2.6 per cent respectively. Hong Kong, whose per capita growth rate of 1.9 per cent was close to that of the UK registered a substantially higher TFP growth rate of 2.3 per cent. Thus the data do not seem to support the result of the Solow model, if we assume that the economies in the long run are more or less in steady state all the time, i.e. the trend values of the endogenous variables of the Solow model reflect more or less their steady state values always. Alternatively, one may assume that the economies even in the long run are usually out of steady state. When an economy is not in steady state, its growth rate, as we have mentioned above, is determined by the parameters of the Solow model. Let us explain. Suppose the production function of the economy is Cobb–Douglas. It is given by Y = KaL1–a. This means that in the long run, GDP of the economy is given by Yt KtB L1t B . Taking log on both sides and then differentiating both sides with respect to time, we get

Yˆt

B Kˆ t  (1  B )Lˆt

(13.29)

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Table 13.2 Per Capita Growth Rate and Technological Progress Country

Growth rate GDP

Contribution capital

Contribution labour

TFP growth rate

Per capita growth rate

OECD countries 1960–1995 Canada a = 0.42

0.0369

0.0186

0.0123

0.0057

0.0077

UK a = 0.37

0.0221

0.0124

0.0017

0.0080

0.0175

US a = 0.39

0.0318

0.0117

0.0127

0.0076

0.0201

Japan a = 0.43

0.0566

0.0178

0.0125

0.0265

0.0276

East Asian countries 1966–1990 Hong Kong a = 0.37

0.073

0.030

0.020

0.023

0.0190

Singapore a = 0.49

0.087

0.056

0.029

0.002

0.0279

South Korea a = 0.30

0.103

0.041

0.045

0.017

–0.0470

Taiwan 0.26

0.094

0.032

0.036

0.026

–0.0444

a=

Estimates of OECD countries are taken from Jorgenson and Yip (2001). Estimates of East Asian countries are taken from Young (1995) (QJE, 110, August, 641–680). The last column is the authors’ own calculations.

Substituting the values of Kˆ t and Lˆ t as given by (13.20) and (13.14) respectively into the above equation, we get Yˆt

B (sktB  E )  (1  B )(m  n)

(13.30)

From (13.29) and (13.30) it follows that the rate of growth of GDP is a weighted average of the rates of growth of labour in efficiency units and capital. Moreover, in out of steady state situations, where Kˆ › Lˆ , the rate of growth of GDP is, given a, an increasing function of s, t

t

m and n and a decreasing function of d. Even though all the empirical studies in the mainstream growth theory assume the economies to be out of steady state, none of them has tried to verify this result. This is surprising in view of the fact that the Solow model dominated growth literature for nearly three decades. We have dwelt on this issue later in the concluding section. From the above it follows that the rate of technological progress is an important determinant of the rate of growth of GDP in Solow model in both steady state and out of steady state situations. Hence we shall discuss below how the rate of technological progress is measured in the mainstream growth theory.

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The rate of technological progress is measured on the basis of a number of assumptions, which are extremely hard to accept. The mainstream macroeconomists assume that there exists an aggregate production function that displays constant returns to scale and factors of production are paid in accordance with their marginal productivities. For simplicity, suppose that the aggregate production function is Cobb–Douglas and it is given by Y AK B L1B . Note that the power of each factor gives the share of its income in GDP, when the price of each factor equals its marginal productivity. Taking logarithm on both sides of the Cobb–Douglas production function specified above and differentiating them with respect to time, we get

Yˆ

Aˆ  B Kˆ  (1  B )Lˆ

(13.31)

From (13.31) it follows that the part of the growth in GDP that is due to growth in capital and labour is given by B Kˆ  (1  B ) Lˆ . The remaining part of the growth in GDP, Yˆ  [B Kˆ  (1  B )Lˆ ], is due to growth in A, Aˆ . Aˆ , which is referred to as Solow residual or total factor productivity growth, is usually regarded as a measure of technological progress. The above discussion suggests a method of measuring Aˆ . Suppose one wants to measure the rate of technological progress in an economy in a given decade. One can do so by estimating the average growth rates of GDP, capital and labour and the average shares of capital and labour during the decade and then by computing {Yˆ  ÍB Kˆ  (1  B ) Lˆ Ý} for the given decade. This method of estimating the rate of technological progress is far from satisfactory for reasons that we shall explain shortly. (Barro and Sala-I-Martin (2004) refers to the above measure of technological progress as the primal measure. They have discussed a dual measure also. But the latter is based on the same set of assumptions as the former.) Let us now explain why the above method of measuring the rate of technological progress is flawed. It is so because it assumes that the markets are perfectly competitive and factors are paid in accordance with their marginal productivities. The concept of marginal productivity cannot exist even in one’s imagination. Obviously, almost all the markets in modern developed economies today are oligopolistic. In countries like India also, this is true except for the markets of agricultural goods, which are competitive. Thus, most of the producers earn supernormal profit. This means that return on capital far exceeds its marginal productivity. It is in fact not necessary to resort to marginal productivity theory of factor pricing to develop a measure of technological progress. The theory is patently false. Mark-up pricing rule in oligopolistic industries is regarded as the norm by many writers, see, for example, Kalecki (1954). Under this rule, price is set by applying a fixed mark-up to the average variable cost of production. For the economy as a whole, the average variable cost consists only of labour cost (assuming a closed economy for simplicity). If the requirement of labour per unit of output is l, the average price of goods and services under the mark-up pricing rule is given by P = mlW

m>1 (13.32) where P º the average price of goods and services, m º the fixed average mark-up and W º the average money wage rate. In (13.32), m is historically and exogenously given. It is to be estimated from the data on costs and prices. Given the difficulty of estimating demand functions and the complexities thrown on it by oligopolistic market structures and the price rigidity that

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the oligopolistic interdependence entails, the application of a historically given mark-up to the average variable cost to set up the price seems to be eminently sensible and therefore rational. From (13.32) it follows that the share of labour in GDP =

and

WlY PY

share of profit or capital in GDP =

WlY N lWY PY  WlY PY

1

(13.33)

N 1

1

N

(13.34)

Equations (13.33) and (13.34) determine factor shares in terms of the average mark-up, m. It also suggests a measure of technological progress. Since labour is much more variable than capital, labour requirement per unit of output may be regarded as a technology-determined variable. So the rate of decline in l, i.e. the rate of increase in the average productivity of labour, may be taken to be an index of the rate of technological progress. This is quite a satisfactory measure of technological progress in an economy with an insignificant agricultural sector. This is because in the non-agricultural sector diminishing return to labour is not much pronounced and this makes the labour requirement per unit of output more or less constant corresponding to any given technology. Since there are usually restrictions on hiring and firing of labour and also on account of phenomena such as labour hoarding, sectoral shifts, etc., it may be sensible to use the trend values of l for measuring the rate of technological progress. Finally, it is extremely difficult to accept the Solow model as a theory of long-run growth. In this model, per capita output or the rate of growth of per capita output is an endogenous variable. However, it is hard to imagine the parameters of the Solow model such as s, d, n, etc., as being independent of per capita output especially in the long run. An increase in per capita output raises individuals’ capacity to save and thereby tends to step up s. It also tends to lower n. It also tends to make more resources available to the government per capita, which in turn improves per capita supplies of public goods such as drainage, protection from natural calamities, public administration, defence, etc. leading to a fall in d. Obviously, in this kind of a scenario, the Solow model ceases to hold. It has been claimed that in the long run the saving function is proportional. However, Indian data do not support this. As we find from Table 13.3, saving ratio has increased steadily over time along with per capita income. Thus the Solow model breaks down altogether at least in the context of the Indian economy. Table 13.3

s1 y2 1 2

Saving ratio and per capita income in India (1950–51 to 2006–07)

1950s

1960s

1970s

1980s

1990s

1991–92 to 1996–97

1997–98 to 2002–03

2003–04 to 2006–07

9.7 6737

12.3 7888

17.2 8880

19.0 10691

23.0 14761

22.7 14012

24.1 17812

32.7 22776

s represents gross domestic savings as percentage of GDP. y represents per capita GNP at factor cost at constant 1993–94 prices. It is measured in Rupees (crore).

Source:

CSO

Modern Theories of Growth: A Critique

Table 13.4

Average annual growth rate (%) of gross domestic product Average annual growth rate (%) of GDP

Country Low-income countries Middle-income countries High-income countries China Vietnam Ireland India United States United Kingdom Japan France Source:

395

PPP per capita GNP ($)

Rank

1990–2000

2000–2004

2004

2004

4.7 3.8 2.7 10.6 7.0 7.5 6.0 3.5 2.7 1.3 2.0

5.5 4.7 2.0 9.4 7.2 5.1 6.2 2.5 2.3 0.9 1.5

2258 6644 31009 5890 2700 32930 3120 39820 31430 29810 29460

108 149 8 144 3 14 18 20

World Development Indicators 2006, The World Bank.

EXERCISE 13.3 (a) Suppose in the long run the economies are more or less in their steady states. How will you explain (i) long-run growth rates of a country and (ii) cross-country differences in the long-run growth rates? Explain. (b) Suppose the economies are usually out of steady state even in the long run. How will you explain (i) long-run growth rates of a country and (ii) cross-country differences in the long-run growth rates in such a scenario? Explain.

Important issues in Solow model There are certain features of Solow model, which have received considerable attention in the growth literature. We shall discuss them here.

13.3.5 Golden Rule of Capital Accumulation The ultimate objective of economic activities is consumption. The question that naturally arises in the context of the Solow model is whether there exists a steady state at which consumption per efficiency unit of labour is maximized. Let us elaborate. Note that in Solow model, as follows from (13.22), there exists a unique steady state corresponding to every given s, given the values of d, n, m and the production function. In fact, steady state can occur at every given k, provided s assumes the appropriate value. To derive the value of s for which the steady state will occur at a given k, say, k0, we have to substitute k0 for k in (13.22) and solve it for s. Obviously, the value of consumption per efficiency unit of labour, denoted by c, is likely to vary from one steady state to another. Hence it may be useful to identify the steady state at

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which c is maximum. Note that, if c in any given period, say period t, is maximum, so is consumption per unit of natural labour. We refer to consumption per unit of natural labour as per capita consumption and denote it by c . Maximization of ct implies maximization of ct, since ct = Atct and At is the same for every value of ct. Hence it is worthwhile to identify the steady state at which c attains its maximum value. Denoting steady state values of k, y and c by k*, y* and c* respectively, we have c* = (1 – s)f (k*)

(13.35)

From (13.22) it follows that in steady state sf (k*) = (d + m + n)k*

(13.36)

Substituting (13.30) into (13.29), we have c* = f (k*) – (d + m + n)k*

(13.37)

Equation (13.37) yields the steady state value of per capita consumption as a function of k* alone, given d, m, n and the production function. We can therefore identify the k* that maximizes c* by carrying out the following maximization exercise:

max c* k*

f ( k * )  (E  m  n)k *

The first-order and the second-order conditions for profit maximization are given by

and

f ¢(k*) = d + m + n

(13.38)

f ²(k*) < 0

(13.39)

Given the assumptions regarding the nature of the production function, the second-order condition, (13.39), is always satisfied. The value of k* that satisfies (13.38) therefore maximizes c*. It is called the golden rule k*. We shall denote it by kg*. Corresponding to the golden rule k*, as follows from (13.38), the marginal productivity of capital equals (d + m + n). Let us explain why. Note that per capita saving in steady state equals (d + m + n)k* so that the steady state value of per capita consumption is given by (13.37). If the steady state value of k, k*, goes up, then due to per unit increase in k* steady state value of per capita output goes up by f ¢(k*) and that of per capita saving rises by (d + m + n) so that steady state value of per capita consumption, c*, increases by f ¢(k*) – (d + m + n). So, if at the initial value of k*, f ¢(k*) > ( (d + m + n). f ¢, as we know, is continuous and strictly decreasing in k*. Moreover, f ¢ falls continuously from ¥ to 0 as k* rises from 0 to ¥. Since f ¢ assumes all values from 0 to ¥, as k* rises from 0 to ¥, there will obviously exist a finite and positive k* corresponding to which f ¢(k*) = (d + m + n). This k* is kg*. Since f ¢ is strictly decreasing in k, at every k* > k g*, f ¢(k*) < (d + m + n) and vice versa. Therefore, if k* is raised (lowered) from any value less (greater) than kg*, c* will rise (fall) by [f ¢(k*) – (d + m + n)] ((d

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+ m + n) – f ¢(k*)) per unit rise (fall) in k*. The magnitude of this rise (fall) declines with the increase (decrease) in k* and becomes zero when k* = kg*. The relationship between c* and k* is shown in Figures 13.7 and 13.8. In Figure 13.7, the value of c* corresponding to any k* is given by the vertical distance between the f(k*) and (n + m + d)k* schedules corresponding to the given k*. Thus at k 0* , the value of c* is given by the length of the line ab in Figure 13.7. Similarly, at k1*, the value of c* = 0. It is also clear that the golden rule k* corresponds to that point on the schedule f(k) at which its slope equals (n + m + d). This is point d in Figure 13.7. The value of c* corresponding to this point is given by the distance de. The value of k* corresponding to this point is kg*. The maximum value of c* is denoted by c *g. At k* = 0, both f(k*) and (n + m + d)k* are zero and so is c*. It is clear from Figure 13.7 that as k* rises from zero, so does c*. Both rise together until k* equals k g*. When k* rises beyond k g*, c* begins to fall and eventually becomes zero, when k* equals kg*. The value of c* corresponding to every different value of k* as derived from Figure 13.7 is plotted in Figure 13.8.

Figure 13.7 Derivation of the golden rule k.

Figure 13.8

Relationship between c* and k*.

EXERCISE 13.4 (a) Consider the production function Y = K0.2L0.8. Derive the values of the golden rule k and s, when d = 0 and n = .01. Explain your result. What is the value of c*, when k* = 0.5. At what value of will the steady state occur at k* = 2? (b) If you know the average values of the rental rate, n, m and d of an economy over a decade, can you say anything regarding whether the economy was in the golden rule steady state or not in the given decade? Explain. (c) Suppose marginal productivity of capital is a function not only of k but also of a parameter a and an increase in a raises the value of marginal productivity of capital. Examine the effect of a given increase in a on the golden rule k and the golden rule s.

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Derive the result mathematically. Explain the result. Finally, derive the result graphically also.

13.3.6 Dynamic Efficiency in a Market Economy In the previous section we have seen that in the Solow model there exists an s, referred to as the golden rule s, such that in the steady state that it yields, the per capita consumption is at the maximum possible level. Note that s is the fraction of GDP that is used for capital formation, i.e. for augmenting future productive capacity and future production, and people derive utility from consumption, but not from capital accumulation. Hence, when s equals the golden rule s, allocation of resources between consumption and capital accumulation must be in some sense optimum or efficient. This is why the golden rule s is also referred to as the golden rule of capital accumulation. When do we call an allocation of GDP between current consumption and investment efficient or optimum? This takes us to the issue of dynamic efficiency of a market economy. Dynamic efficiency refers to the efficiency in the allocation of GDP between current consumption and capital accumulation. A market economy is said to be dynamically efficient if by changing the saving ratio, s, it is not possible to raise per capita consumption above its initial level at every point of time subsequent to the point of time at which the saving ratio is changed. Below we have shown that, if an economy oversaves, i.e. if the saving rate of an economy exceeds its golden rule level, it is dynamically inefficient. However, if the saving ratio equals or falls short of the golden rule s, it is dynamically efficient. Let us prove this point. Note that the steady state per capita capital stock, as follows from (13.22), is a function of the saving ratio, s, given d, n, m and the production function. Suppose in an economy the saving rate is s0 > sg, where sg is the golden rule saving rate or saving ratio. Suppose the steady state values of k and c corresponding to the saving ratio, s0, are k0* and c0* respectively. Accordingly, c*0 (1  s0 ) f (k0* ). As shown in Figure 13.9, the economy is in steady state with k * k0*, when the saving ratio is s0. Now suppose the saving ratio falls from s0 to s*g at the point of time t0 and remains there thereafter. Then at once, with y and k remaining unchanged at their initial steady state values, c will rise from c*0 (1  s0 ) f ( k0* ) to c1 (1  sg ) f (k0* ). The situation is shown in Figure 13.10 where per capita consumption and time are measured on the vertical and horizontal axes respectively and c at t0 rises from c0* to c1. However, k will not stay put at k0*. With the fall in s, as shown in Figure 13.9, the rate of growth of aggregate capital stock will decline from Í{s0 f (k0* ) / k0*}  EÝ

m  n to [{sg f ( k0* ) / k0*}  E ]  m  n . Hence k will start falling

from k0* and along with it y = f(k) and c

c1

(1  s*g ) f (k ) will also be falling from f ( k0* ) and

(1  sg ) f (k0* ) respectively. In fact c will fall monotonically from c1 to c*g

(1  sg ) f ( k g* ) ! c*0

as k falls from k0* to its new steady state value, k g*, which is the steady state value of k corresponding to the golden rule saving ratio, sg. The situation is shown in Figures 13.9 and 13.10. Therefore at every point of time following the reduction in s, per capita consumption in

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Figure 13.9 Dynamic efficiency in the Solow model, when s > sg.

Figure 13.10 Behaviour of consumption when s > sg.

the economy is higher than its initial steady state value, c0*. Therefore an economy that oversaves is dynamically inefficient. Let us now focus on the situation where s < sg. Suppose the saving ratio is s1 < sg. The steady state k that corresponds to s1, as shown in Figure 13.11, is k1*. Obviously, the steady state y is f( k1*) = y1 and the steady state per capita consumption is (1  s1 ) f ( k1* ). Consumption is plotted against time (denoted by t) in Figure 13.12, which

c1*

shows that per capita consumption of the economy equals c1* at every t < t1. Now, suppose the saving ratio rises at t = t1 to sg. Then at once, with y and k remaining unchanged at their initial steady state values, c will fall from c1*

(1  s1 ) f (k1* ) to c0

(1  sg ) f (k1* ) at t = t1, see

Figure 13.12. However, k* will not stay put at k1*. With the rise ins, as shown in Figure 13.11, the rate of growth of aggregate capital stock will go up from Í{s1 f ( k1* ) / k1*}  EÝ *

Í{sg

m  n to

f (k1* ) / k1*}  EÝ ! m  n . Hence k will start rising from k1* and along with it y = f (k) and

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c = (1 – sg)f(k) will also be increasing from f ( k1*) and c0 = (1 – sg)f ( k1*) respectively. In fact, c will increase monotonically from c0  c1*, with the rise in k. It will eventually move above c1* and in course of time equal to c*g

(1  sg* ) f (k * (s*g )) ! c1* as k rises from k1* to its new steady

state value, kg* . The situation is shown in Figures 13.11 and 13.12. Thus, in this case, per capita consumption does not remain above its initial value at every point of time following the rise in s. It falls and remains below its initial steady state value for some period of time, which in reality may be fairly long. Thus this policy makes the individuals who live during this period of lower consumption worse off in the interest of the future generations who will be born in the periods of higher consumption. This policy clearly cannot make future generations better off without making the present generations worse off. Hence an economy that undersaves is dynamically efficient—see the definition of dynamic efficiency at the beginning of this section. Similarly, show yourself that an economy where s = sg is necessarily dynamically efficient.

Figure 13.11

Dynamic efficiency in the Solow model, when s < sg.

Figure 13.12 Behaviour of consumption when s < sg.

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From the above it follows that, when an economy undersaves, the policymaker does not have a clear choice. Whether she will go in for a policy of raising s or not depends upon how much weight she attaches to the welfare of the present generation relative to that of the future generations. If she attaches equal weights to the welfare of all generations, she will go in for the policy, as it will raise the welfare of an infinite number of future generations at the expense of a finite number of present generations. Under the assumption that a market economy has a stable constant-returns-to-scale production function in the long run, attempts have been made to check whether a given economy is dynamically efficient or not. This has been done in the following manner. It is assumed that the given economy is in steady state so that the average growth rate of its GDP in a given long period, say a decade, gives its steady state growth rate, which equals (d + n + m), during the given period. From the data on the average share of capital and the average ratio of GDP to aggregate capital stock during the given period, one can estimate the period’s average marginal productivity of capital. Let us explain. The share of capital, when capital’s price equals its (˜Y /˜K )K . Obviously, if we multiply it by Y/K, we get the Y marginal productivity of capital, ¶Y/¶Y. This average marginal productivity of capital is taken to be the steady state value of the marginal productivity of capital. If it is found to be equal to or greater (less) than the average rate of growth of GDP, it means that the steady state capital stock per efficiency unit of labour during the given period is equal to or less (greater) than the golden rule capital stock per efficiency unit of labour—see Figure 13.7. This implies that the average saving ratio of the economy during the given period is equal to or less (greater) than the golden rule saving ratio, and hence the economy is dynamically efficient (inefficient). This kind of exercise may not make much sense for quite a number of reasons. First, the assumption of a stable constant-returns-to-scale production function for the economy as a whole in the long run seems implausible. Second, the price of capital in reality far exceeds its marginal productivity, given the dominance of oligopolistic market structures in modern economies. Third, the assumption that the economy is in steady state is incongruous with the assumption of almost all the empirical studies on the Solow model. Finally, even the trend values of parameters such as the saving ratio, rate of depreciation, etc. vary from one year to the next. So the steady state changes continuously. Decadal average of the capital–output ratio is unlikely to give the steady state value of the ratio during the decade, as the decade has different steady states in different years. To get around this particular problem, what we can do is that we can assume that the economy is always more or less at the steady state in the long run all the time. Given this assumption, we can calculate the ratio of the trend value of capital to the trend value of output for each year and interpret it as the steady state value of the ratio in that year. Then using the trend value of the share of capital for the given year, we can calculate the steady state value of the marginal productivity of capital of the given year and then figure out whether it is greater or less than the sum of the trend values of m, n and d of the given year. However, all the other objections noted above will apply to this method also. The most damaging problem is that marginal productivity of any factor is inconceivable. A teacher cannot teach without using services of other factors. This is true of every factor. Marginal productivity of any factor is as impossibility.

marginal productivity, is given by

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EXERCISE 13.5 (a) Suppose the production function of an economy is given by Y = K0.5L0.5, s = 0.5, d = 0 and m + n = 0.1. Examine whether the economy is dynamically efficient or not. (b) Incorporate government in the economy presented in the above problem. Suppose the government taxes the GDP at the rate, a and spends b fraction of the tax revenue on consumption. What policies can the government adopt to maximize steady state value of per capita private consumption? Explain.

13.3.7 Unconditional and Conditional Convergence Let us ignore technological progress. This amounts to assuming A to be equal to unity for all t—see (13.12). This implies that L and L are equal. Hence y and k stand no longer for output and capital per efficiency unit of labour but for output and capital per natural unit of labour, i.e. they represent per capita output and per capita capital stock respectively. In the absence of technological progress, Solow model gives the impression that the poorer an economy, i.e. the less the per capita output of an economy, the higher is its growth rate. Let us derive this result using a Cobb–Douglas production function as follows: Y

K B L1B

(13.40)

Taking log on both sides and then differentiating with respect to t, we get

Yˆ

B Kˆ  (1  B )Lˆ

(13.41)

Thus we find from (13.41) that the growth rate of aggregate output is the weighted average of the rate of growth of capital and the rate of growth of natural labour. Now, Kˆ

sY E K

(13.42)

Dividing both sides of (13.40) by L, we have y = ka

(13.43)

Note that here, as we have mentioned above, y º Y/ L and k º K/ L. Using (13.43), we can write (13.42) as

 B sLk E K

Kˆ

sk B E k

s

k

1B

E

(13.44)

From (13.44) it follows that Kˆ is a strictly decreasing function of k and its value falls monotonically from ¥ to –d, as k rises from 0 to ¥. Substituting (13.44) into (13.41), we get Yˆ

B ËÌ

s

1B Ík

Û  E Ü  (1  B ) n Ý

(' Lˆ

n)

(13.45)

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Therefore yˆ

Yˆ



Lˆ

B ËÌ

Ík

s 1B

Û EÜ Bn Ý

B ËÌ

Ík

s 1B

E 

Û

nÜ

(13.46)

Ý

Equation (13.46) yields the following. Note that there is steady state in the economy iff s kˆ  E  n 0 . Hence, for yˆ to be positive, k and therefore y have to be less than their 1B k respective steady state values. Since yˆ is found to be positive on the average for all the countries, k and y are assumed to be less than their respective steady state values for every country. We also find that the lower the value of k and therefore that of y relative to their respective steady state values the higher is the growth rate, yˆ . This gives the impression that the poorer an economy, the higher is the growth rate of its per capita output. Hence poor countries will eventually catch up with the richer ones. This is the notion of absolute convergence. However, Solow model does not support this notion. It yields this result only for those countries that have the same values of s, d, n and the same production function. This notion of convergence is referred to as that of conditional convergence. As we shall discuss later, quite a large part of the empirical literature on modern growth theory has focused on the issue of convergence and they have found evidences in support of conditional convergence. It is, however, as we have pointed out already, extremely difficult to accept the Solow model as a theory of long-run growth. Hence the emphasis on the issue of convergence seems unwarranted. EXERCISE 13.6 (a) Explain why poorer of the countries having different values of d, n, f and s may not grow at faster rates than richer countries. Illustrate graphically. (b) Countries like India are referred to as labour surplus countries, where labour is abundant relative to capital. In this scenario, suppose the production function is fixed coefficient and output is determined by the available quantity of capital only. Recast Solow model under these assumptions. Will you get absolute or conditional convergence in this framework? Explain. (c) Solow model assumes diminishing return to inputs, but not diminishing return to scale. Since the stock of natural resources is fixed, diminishing return to scale in capital and labour seems to be as natural as diminishing return to input. If both these diminishing returns hold in Solow model, the growth rate of per capita output will eventually fall to zero in the long run. Do you agree? Actually, with the rise in per capita income, qualities of both capital and labour improve in the long run offsetting the tendencies to diminishing returns to both scale and input. Recast Solow model in this scenario.

13.4 ENDOGENOUS GROWTH THEORY The mainstream growth theory since the mid-eighties tried to extend the Solow model by endogenizing the rate of technological progress. In other words, they tried to formulate theories that explain the Aˆ of the Solow model presented above. Pioneering attempts in this regard were

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made by Lucas (1988) and Romer (1986, 1990). The growth theory that they developed is referred to as the endogenous theory of growth. It is a vast literature, which is still growing at a fast rate. To give a flavour of this theory, we shall discuss the studies of Lucas and Romer.

13.4.1

Human Capital Formation and Growth

In Solow model technological progress is labour augmenting, i.e. it raises efficiency of labour. Efficiency of labour increases for many reasons. One of the most important of them is obviously acquisition of skill or education. Efficiency or productivity of a skilled or educated labour is much more than that of an unskilled or uneducated one. Doctors, engineers, managers and similar other highly skilled workers earn much more than ordinary clerks. The latter in their turn are much better off than the unskilled agricultural and other similar workers. Lucas (1988) seeks to capture the link between individuals’ decision to invest in education and per capita growth. The connection between the two consists of an increase in the efficiency of labour due to acquisition of education or skill. Investment in education or acquisition of skill is referred to as investment in human capital formation. We shall present here a simplified version of the model developed by Lucas (1988), which we think brings out the intuition behind Lucas’ work more clearly. It also yields all the results of the original work. This version is cast in an overlapping generations framework, where there are a large number of identical households and a large number of identical firms. In every period, each household has two members—a parent and a child. Number of households and the size of every generation in every period are assumed to be the same and fixed. There is thus no population growth. Every individual lives for two periods. In the first period, she is a child. In the second period, she is a parent. Parents are decision makers in households. For simplicity the model abstracts from physical capital or investment in physical capital. Production is carried out with human capital only. Human capital is nothing but labour in efficiency units. In every period, the parent in a household has a given amount of human capital, which she supplies fully in the labour market. The child by assumption inherits her parent’s human capital. In every period, the child in every household can work and thereby contribute to the income of the household or the child can study. In fact, in this model, the child can devote a part of her time to work and the rest to acquisition of skill or education. The parent decides how her child should allocate her given endowment of time or human capital between work and human capital formation. This is the only choice problem of the parent. Here the parent does not save any part of her household’s income. The entire income is spent on consumption. There is a one-period lag between investment in human capital and acquisition of human capital. The time or human capital a child invests in human capital in a given period enables her to acquire additional human capital in the next period. Thus the only cost of acquiring skill consists of the loss in households’ income due to the time devoted by the child to skill acquisition. All other costs of acquiring skill are ignored here for simplicity. Parents derive utility from their households’ consumption in the current period and also from the amount of human capital their children will acquire in the next period. Utility function of the parents in period t is given by Ut = a log Ct + b log ht+1

(13.47)

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where Ut º utility derived by the parents in period t, Ct º households’ consumption in period t, ht+1 º human capital acquired by the children in period t + 1 due to their investment in human capital formation in period t, and, finally, a and b are the parameters of the utility function. Parents’ endowment of human capital in period t is denoted by ht. Children in period t inherit this amount of human capital by assumption. They devote a fraction bt of their inherited human capital to acquisition of more human capital. The rest of their human capital, (1 – bt)ht, they devote to production. The parents in period t decide on the value of bt. It is assumed for simplicity that only human capital is needed to acquire more human capital. No other resources are required for human capital formation. The production function of human capital is given by ht+1 = ht + mbtht

m>0

(13.48)

Equation (13.48) states that if btht amount of human capital is devoted to human capital formation by the children, their human capital will increase in the next period by mbtht. Firms produce a single consumption good using only human capital. Their production function is given by Y=H

(13.49)

where H denotes the amount of human capital used in production. There are thus two markets in this model, a market for the produced consumption good and a market for human capital. It is assumed that both the markets are perfectly competitive. From (13.49) it follows that the marginal productivity of human capital is unity. Hence demand price of labour in terms of the good produced is unity. The demand function for human capital is shown in Figure 13.13. In Figure 13.13, real wage or wage in terms of the good produced, denoted by W, is measured on the vertical axis and demand for and supply of

Figure 13.13 Determination of the wage rate in the Lucas model.

human capital are measured on the horizontal axis. The demand for human capital function is horizontal at W = 1. Thus whatever be the supply of human capital, the equilibrium real wage rate of human capital is unity unless of course the supply curve of labour is also horizontal, which is, as we shall shortly show, not the case here.

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In period t, parents supply ht amount of human capital and the children supply (1 – bt)ht amount of human capital. Thus in period t, households supply [ht + (1 – bt)ht] amount of human capital. By selling this much human capital they earn Wt[ht + (1 – bt)ht] amount of income in terms of the good produced, since Wt º the real wage rate in period t. Households consume the whole of this income in period t. Therefore Ct = Wt[ht + (1 – bt)ht]

(13.50)

Equation (13.48) gives the amount of human capital the children of period t will acquire in period t + 1, when their parents allow them to devote bt fraction of their human capital for acquisition of more human capital. Substituting (13.48) and (13.50) into the parents’ utility function (13.47), we get Ut = a log Wt[ht + (1 – bt)ht] + b log(1 + mbt)ht

(13.51)

Since both the markets are perfectly competitive, Wt is given to the parents. ht is also given. Thus the only variable in (13.51) that the parents can choose is bt and the parents choose this so that their utility is maximized. The first-order condition for maximization is given by ˜U t

˜Ct

a b ( Wt ht )  N ht Wt [ ht  (1  Ct )ht ] (1  NCt )ht

0 Þ

a

b

[2  Ct ]

(1  NCt )

One can easily check that the second order condition for maximization,

˜ 2Ut

˜Ct2

N

(13.52)

 0, is satisfied.

We can therefore solve (13.52) for the optimum value of bt. It is given by

Ct

2b N  a N (b  a )

(13.53)

The solution of (13.52) is shown in Figure 13.14, where bt is measured on the horizontal axis, a

b

N are measured on the vertical axis. The former gives the marginal (1  NCt ) [2  Ct ] cost of raising bt and the latter gives the marginal benefit of raising bt. Let us explain. From (13.50) it follows that, following a unit increase in bt, the children supply ht amount of less labour. Hence children’s wage income and therefore households’ income and consumption go down by Wtht. This reduces households’ utility. From the utility function, (13.51), it follows that

while

and

a unit reduction in Ct lowers utility by

a . Hence Wtht amount of decline in Wt ht (2  Ct )

consumption reduces households’ utility by

a ¹ Wt ht Wt ht (2  Ct )

a (2  Ct )

. This is therefore the

marginal cost of raising bt as this is the amount of utility households’ lose following a unit increase in bt. A unit increase in bt also exerts a positive impact on households’ utility by raising

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the amount of human capital the children of period t will acquire in the next period. This amount is given by mht—see (13.48). If children’s future human capital rises by 1 unit, households’ utility, as follows from (13.51), increases by

b (1  NCt )ht

. Hence the amount of increase in

households’ utility from mht, the amount of increase in the children’s future human capital is b (1  NCt )ht

¹

N ht

bN

1  NCt

. Since a unit increase in bt raises households’ utility by

bN

1  NCt

by

raising children’s future human capital, it is referred to as the marginal gain of raising bt. At the optimum bt labelled b* in Figure 13.14, marginal gain and marginal cost of raising bt are equal. Consider a bt, say b0 < b*. At b0, as is clear from Figure 13.14, marginal gain of raising bt is greater than the marginal cost by AB. This implies the following. If b is raised from b0 by unity, the gain in households’ utility due to the increase in the future human capital of the children is given by Bb0, while the loss in households’ utility due to the fall in households’ consumption is Ab0 < Bb0. Hence the net gain in households’ utility is Ab0 – Bb0 = AB. Thus it is optimal for the households to raise b from b0. Similarly, if bt > b*, it is optimal to lower bt. Hence at the optimum bt, marginal cost and marginal gain are equal.

Figure 13.14 Determination of bt .

We find from (13.53) that the optimum value of bt is independent of Wt. It is a function only of the parameters of the utility and the human capital formation functions. The optimum value of bt is therefore the same in every period. We denote this optimum bt by b*. The supply of labour in period t is accordingly given by ht

 (1 

C * )ht Ct

ht

È  É1  Ê

2b N  a Ø h . This N (b  a) ÙÚ t

labour supply is represented by the vertical labour supply line in Figure 13.13. Labour supply line is vertical in every period. Hence, as should be clear from Figure 13.13, the equilibrium real wage rate is unity in every period. Accordingly, the whole of the value of aggregate output

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accrues as wage income to the households. In period t, the equilibrium output, as follows from (13.49), is given by

Yt

ht

È  É1  Ê

2b N  a Ø h N (b  a) ÚÙ t

(13.54)

Since b* is the same in every period, the equilibrium value of aggregate output in period t + 1, as follows from (13.54), is given by Yt 1

ht 1

È  É1  Ê

2 bN  a Ø h N (b  a) ÙÚ t 1

From (13.54) and (13.55), it follows that the rate of growth of aggregate output,

(13.55) Yt 1  Yt , is Yt

given by Yt 1  Yt Yt

ht 1  ht ht

(13.56)

The human capital formation function, (13.48) and (13.56) yield that Yt 1  Yt Yt

ht 1  ht ht

NC *

2 N a  a  Nb N ( b  a)

(13.57)

Therefore in this model aggregate output and human capital from the parent to the child grow at the same constant rate over time. Since population growth is zero here, per capita output also grows at the same constant rate as the aggregate output. The economy is therefore in steady state. From (13.57) we find that the per capita growth rate depends upon the parameters of the utility and the human capital formation functions. Equation (13.57) also yields that the per capita growth rate is an increasing function of b*. We can therefore easily show how the parameters of the utility and the human capital formation functions affect per capita growth rate using Figure 13.14. If parents derive more utility from current consumption, i.e. if a becomes larger, the MC schedule in Figure 13.14 shifts upward, while the MG schedule remains unaffected. Hence b* will fall reducing per capita growth rate. Again, if parents give more importance to their children’s human capital formation, i.e. if b rises or if the productivity of human capital in human capital formation rises, the MG schedule in Figure 13.14 shifts upward, but the MC schedule remains unaffected raising b*. Thus the model attributes higher per capita growth rate of a country to higher values of b and m and lower value of a. In other words, the model does not treat the rate of growth of efficiency of labour, given by Aˆ in Solow model, as exogenously given. It shows that Aˆ is an increasing function of b and m and a decreasing function of a. This is how the model endogenizes per capita growth rate or the rate of growth of efficiency of labour. EXERCISE 13.7 In India, is children’s education a matter of choice for every parent? Recast the Lucas model in the case where children’s education is not a matter of choice for f fraction of the parents.

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How is the steady state growth rate likely to vary with an increase in f? Given this result, will you expect a poorer country to grow at a faster rate?

Evaluation of the Lucas model There are two features in the model presented above that distinguish it from the Solow model. First, unlike the Solow model, it does not take the rate of growth of the efficiency of labour, Aˆ , as given. It makes it an increasing function of b, the fraction of the children’s endowment of time devoted to acquisition of education—see the human capital formation function (13.48). Second, it goes farther and does not take b as given. Instead it derives the value of b from the optimizing behaviour of the households. It thus provides a micro-foundation to b. Let us focus on the second distinguishing feature of the Lucas model. It identifies b as the single most important determinant of the per capita growth rate and then proceeds to derive its value from the optimizing behaviour of the households. As a result, it gets the optimum value of b as a function of the parameters of the utility function. This extension seems unwarranted. Parameters of the utility functions cannot be observed. Hence the theory that attributes per capita growth rates to the parameters of the utility functions cannot be empirically verified. Such a theory is obviously useless. In a growth theory therefore it is much better to take b as exogenously given. Empirically verifiable measures of b can be readily constructed. Hence a theory that explains per capita growth rate in terms of b is empirically verifiable and therefore useful. There is another problem of determining b in the framework of a growth theory. Determination of each of the two variables, viz. growth rate and b, is highly complex and attempts at explaining both of them within a single model severely restricts the scopes of both the quests and thereby make both of them poorer. Each of these two issues is a separate field of study in its own right. To illustrate, focus on the probable determinants of b. The theory of determination of b that we get in the Lucas model is extremely simple. It abstracts from most of the complex factors that are involved in the determination of b. We elaborate on this point below. Factors pertaining to the decision to acquire skill or education are likely to vary from person to person and also from country to country. In a poor country like India, the decision may not be a choice problem for many individuals. For them how much education they can give their children is severely constrained by their income. People who live below poverty line starve regularly and suffer from malnutrition. Obviously, they cannot afford to give their children any education. The problem of getting something to eat everyday takes up all their energy and resources. They can hardly think beyond that. Thus, even when tastes and preferences are identical, the poor people cannot afford to give their children as much education as the rich. When incomes of different people are different, the aggregate budget constraint is of little use. In such a case income distribution is crucial in determining the economy-wide b. Besides income, other objective conditions of the households may be different. Even in the same income class, sources of income may vary. Families with labour income as the principal component of their income are likely to give more education to their children than those who derive their income mainly from non-labour sources. Again, within the same income class, children with greater abilities and more favourable inclinations to learn are likely to receive more education. Children of more educated parents get better guidance and instructions and hence are likely to

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receive more education. Infrastructure, education system, quality of educators and that of the educational institutes vary from country to country and also from one locality to another within any given country. Obviously, children living in better-endowed localities are likely to receive more education. In countries needing highly skilled workers on a large scale in production, education is more rewarding and this is likely to give greater inducement to people to get educated. Investment in human capital is risky. It has long gestation lags. There are uncertainties of various sorts at different stages of the process. Cost of education is independent of households’ income. Hence the cost of education as a proportion of income falls as we move from the low income households to the high income households. Thus the risk of investing in human capital is much less for the rich. Moreover, the risk to all households involved in the investment in human capital is less in well managed stable economies with low rates of unemployment. Thus the list of factors affecting skill acquisition is almost endless and is a separate area of research in its own right. It may therefore be imprudent to give micro foundation to b in a growth model. The two issues should be kept separate to do justice to both. Finally, nothing remains unchanged for ever let alone tastes and preferences and production functions. Thus infinite horizon models or lifetime horizon models attributing long-run growth to parameters of utility functions and production functions make little sense. From the above discussion it follows that for the purpose of developing growth models it seems sensible to take b as given and to leave its determination to a separate area of research. In what follows we shall do precisely this. We shall recast the model of Lucas within the framework of the Solow model treating b as well as the saving ratio, s, as given. Determination of s is as complex as that of b and derivation of its value from the optimizing behaviour of the economic agents is accordingly as inadvisable as that in the case of b within the framework of a growth model. One major problem with the Solow model, as we have pointed out earlier, is that its parameters are likely to be a function of per capita income. One may argue that the Lucas model is free from that problem. However, tastes and preferences are likely to change substantially, particularly in the long run, with the rise in per capita income and all the other changes that accompany it, such as better education, better health, greater association with the richer people, greater awareness of the general surroundings, etc. Production functions of poor and rich countries are also likely to be substantially different. Thus both the Lucas model and Solow model have the problem mentioned above. The only difference is that changes in tastes and preferences cannot be easily documented, while changes in the saving ratio are perceptible. There is therefore no great harm in recasting the Lucas model in the framework of the Solow model. We shall henceforth refer to this extended Solow model as the Solow–Lucas model. To recast the Lucas model in the framework of the Solow model, we have to incorporate the human capital formation function of the former in the latter. Doing this, we extend the Solow model as follows. We consider an economy where the size of the population and that of the labour force are given. The production function is assumed to be Cobb–Douglas. It is given by

Y

K B H 1pB

(13.58)

where Y º output, K º stock of physical capital used in production, Hp º stock of human capital used in production. There is also a human capital formation function, which is taken from

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Lucas (1988). Individuals devote their existing human capital to acquire more human capital. The human capital acquisition function is given by

H

N Hh

(13.59)

where m is a constant and Hh º amount of human capital devoted to acquisition of human capital. The stock of human capital available in period t is denoted by Ht. It is assumed that the individuals devote a fixed fraction, b, of it to human capital acquisition and the rest to production so that (13.60) Hht = bHt where Hht º Hh in period t Hpt = (1 – b)Ht

and

(13.61)

where Hpt º Hp in period t. It is also assumed that

and

St = sYt

(13.62)

I t = St

(13.63)

Using (13.62), (13.63) and (13.58) and assuming depreciation of physical and human capital to be zero, we get

where kt œ

sH 1ptB K tB

sYt Kt

Kˆ t

sktB kt

Kt

s

kt1B

(13.64)

Kt . H pt

Substituting (13.60) into (13.59) and then solving for Hˆ t , we get

Hˆ

NC

(13.65)

From (13.60), (13.61) and (13.65) we also find that Hˆ

Hˆ p

Hˆ h

NC

(13.66)

It follows from (13.58), (13.64) and (13.66) that the economy is in steady state if and only if kˆt

Kˆ t  Hˆ pt

s kt1B

 NC

0

(13.67)

We can solve (13.67) for the steady state value of kt. The solution of (13.67) is shown in Figure 13.15. It is clear that a unique steady state exists and it is stable. The steady state growth rate of per capita output is given by mb. Obviously, it is an increasing function of m and b. This model therefore yields all the verifiable results of Lucas (1988). In our view it is best to leave the determination of m and b to separate areas of research.

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Figure 13.15

Steady state and stability in the Solow–Lucas model.

EXERCISE 13.8 Consider the modified Lucas model. How will you expect the steady state growth rate to change in this model following an improvement in the quality of the education system? Explain.

13.4.2 Investment in R&D and Growth Romer (1988) develops a detailed model to identify the determinants of investments in R&D. In his model, the amount of labour available is fixed. The economy is divided into two sectors— one sector produces final goods and the other sector engages in R&D. The latter produces designs and intermediate inputs based on these designs. The number of designs available in period t is denoted by At. The rate of growth of the number of designs, Aˆ , determines the steady t

state growth rate of per capita GDP in the model. The production function of designs used in the model is (13.68) A H AL A Aˆ H L A

À

where g is a constant and LA denotes the amount of labour allocated to the R&D sector. The purpose of the model is therefore to identify the factors that determine the allocation of the fixed amount of labour between production of final goods and R&D. It shows that the amount of labour allocated to R&D in steady state depends upon the parameters of the utility function, the productivity of labour in the R&D sector represented by g in (13.68), the given amount of labour available in the economy and the parameters of the production function determining the productivity of the innovated inputs. The higher the productivity of the innovated inputs, the greater the productivity of labour in R&D and the larger the stock of labour available, the greater is the amount of labour allocated to R&D and hence the higher is the per capita growth rate. This model can be criticized on two counts. First, the detailed micro-theoretic model developed here to determine the allocation of the given stock of labour between the two sectors is too simple minded to merit serious consideration. Second, all the verifiable results yielded

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by the model can be derived just by incorporating (13.68) into the Solow model and treating the allocation of the given stock of labour between the two sectors as being exogenously given. Let us first focus on the first of the two objections. Investment in R&D is lumpy and risky. The degree of risk involved in investments in R&D depends crucially upon the level of competition. The richer firms can bid away the best brains by offering higher pay. Hence only a few giants in every industry undertake R&D activities. Countries like India cannot even keep their own best brains to themselves. They lose them to the richer countries. In today’s globalized world, foreign capital and foreign goods have more or less free entry. Under these circumstances domestic firms in countries like India can hardly afford to undertake R&D activities. Success of R&D depends significantly on the availability of quality manpower, which again depend upon the whole host of factors discussed in the context of the Lucas (1988) model. In addition, it depends upon the degree of development of a country. In the absence of restrictions on immigration and emigration of quality workers, poorer countries are likely to lose most of their best brains to richer countries. The next question relates to the scope of utilization in R&D of whatever quality manpower remains available in poorer countries. Since investments in R&D are lumpy and risky, firms have to attain a minimum size before it can even afford to undertake R&D. Size of firms grows with the development of a country. The more developed a country, the larger is the size of its firms and the greater is their financial might. Even though firms of a country can afford to undertake R&D, whether they will consider it profitable to do so depends upon the financial might of their foreign rivals. In the face of much mightier foreign rivals and in the absence of any kind of insulation from foreign competition, the domestic firms may consider it imprudent to undertake R&D. Even within the geographical boundary of a poor country like India, compensations to workers in foreign multinationals are many times larger than those in domestic companies. Even in the richest of the nations, the R&D sector is oligopolistic and dominated by just a handful of giant firms. These factors are completely missing in Romer (1990). Its description of the R&D sector, which is assumed to be perfectly competitive, is superficial at the best. Even casual consideration of facts suggests that the bulk of the R&D activities goes on in the richest of the countries, which, however, do not grow at the fastest rate. On the other hand, countries like India are recently growing at much faster rates, with little investments in R&D. Let us now consider the second issue. Incorporating in the Solow model the production function of the R&D sector, (13.68), treating the supply of labour to be fixed at L , assuming a fixed fraction, s, of L to be allocated to R&D, and finally taking a Cobb–Douglas production function, we can represent the Solow model as follows: Yt

K tB ( At (1  T ) L )1B

(13.69)

St = sYt

(13.70)

I t = St

(13.71)

Equations (13.68)–(13.71) give the basic equations of the extended Solow model. We shall henceforth refer to it as the Solow–Romer model. From (13.70) and (13.71) it follows that K t = It = sYt (assuming depreciation to be zero for simplicity)

(13.72)

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Therefore Kˆ t

sYt Kt

(13.73)

Dividing both sides of (13.69) by At(1 – s) L , we get yt

where yt

Yt and kt At (1  T ) L

ktB

(13.74)

Kt . At (1  T ) L

Dividing both the numerator and the denominator of the expression on the RHS of (13.73) by At(1 – s) L , and then manipulating terms, we have Kˆ t

s

(13.75)

kt1B

For reasons we have explained earlier, we have steady state in this model iff kˆt

Kˆ t  Aˆ t

0 (since (1 – s) and L are fixed)

(13.76)

Substituting (13.68) and (13.75) into (13.76), we have kˆt

s kt1B

 HT L

0

(13.77)

We can solve (13.77) for the steady state value of kt. The solution is shown in Figure 13.16. It is clear from (13.77) and also from Figure 13.16 that (13.77) yields a unique and stable steady state value of kt.

Figure 13.16

Steady state and its stability in the Solow–-Romer model.

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From Eqs. (13.74)–(13.77), it follows that in steady state

Kˆ t

Yˆt

HT L

(13.78)

Thus (13.78) shows that the per capita growth rate is an increasing function of the productivity of labour in R&D, g, the allocation of the given stock of labour to R&D as indexed by s and the given stock of labour available. Thus the model yields all the major verifiable results of Romer (1990).

Evaluation of the endogenous growth theory The endogenous growth theory that took off phenomenally from the pioneering studies of Lucas and Romer presented above broadened the set of determinants of the per capita growth rate of a country. They traced the per capita growth rate not only to the educational attainment of the people and the share of resources devoted to R&D but also to a whole host of other factors such as the rule of law, democracy, openness of the economy, etc. The general problem with the endogenous growth theory is that all the different determinants of per capita growth rate that this literature identifies are increasing functions of per capita income. Accordingly, they assume the highest levels in the most developed of the countries and the lowest levels in the least developed ones. The endogenous growth theory thus predicts that the per capita growth rate should be the highest in the most developed countries and the lowest in the least developed ones. Facts, however, are completely contradictory to this prediction. Table 13.4 shows that the average annual growth rates of GDP during 1990–2000 and 2000–2004 were the highest in the low income countries, the second highest in the middle income countries and the lowest in the high income countries. It also shows that China ranked 108 on the basis of per capita income in 2004 recorded the highest growth during the given periods followed by Vietnam ranked 149. The third highest growth rate was recorded by Ireland ranked 8, but the fourth highest growth rate was recorded by India ranked 144. The richest countries such as the US, the UK, Japan and France ranked 3, 14, 18 and 20 respectively recorded quite modest growth rates. The endogenous growth theory therefore prima facie does not stand up to even casual empirical scrutiny. In what follows we shall dwell on the empirical studies that have been made on the endogenous growth theory.

13.5 EMPIRICAL RESULTS AND CONCLUDING REMARKS Empirical studies on the mainstream growth theory, which includes the Solow model and the endogenous growth theory, focus on three issues in the main, namely growth accounting, explanation of cross-country differences in the long-run rates of growth and convergence. Growth accounting assumes that there are three sources of growth, viz., rate of growth of capital, rate of growth of labour and technological progress. It seeks to decompose the growth rate of GDP into the contributions of these three sources (see, for example, Barro and Sala-I-Martin (2004)). We have already explained the problems with this kind of exercise. The other studies are cross-section studies and they seek to explain cross-country differences in growth rates. To that end they regress long-run per capita growth rates of different countries on a whole host of

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factors in addition to per capita output as explanatory variables such as educational attainment, infant mortality rate, life expectancy, rule of law, degree of democracy, etc. Note that per capita income must be an important determinant of all these factors in the long run. The higher the per capita output, the greater is the ability of the people to spend on education, health and less is likely to be the incidence of crime. Again, the higher the per capita output, the greater is the taxable capacity of the people and therefore the larger is the amount of resources at the command of the government leading to greater provision of public goods such as public administration, healthcare, education, potable water, sanitation, etc. per capita. For both the reasons, the richer a country the greater is likely to be the values of the explanatory variables mentioned above. Accordingly, per capita growth rate should be the highest in the richest of the nations. Unfortunately, as we have already pointed out (see Table 13.4 in this context), there is prima facie no evidence to that effect. These studies also claim that they have found evidences for conditional convergence even though not for absolute convergence (see Barro and Sala-I-Martin (2004) in this context). In other words, they have found that if all other variables are held constant, an increase in per capita income tends to lower the per capita growth rate and vice versa. The meaning of this result is the following. If, for example, in India, per capita income changes alone in the long run and all other explanatory variables remain unchanged, the long-run growth rate in India will tend to fall. The mainstream growth theorists regard this result as an evidence of conditional convergence. This means that every country tends to move towards its respective steady state. As we have already pointed out, this kind of exercise hardly makes any sense. The notions of conditional convergence follow from the Solow model. Since the saving rate, the rate of growth of population and the rate of depreciation are all functions of the per capita income in the long run, the model breaks down altogether. In fact, tastes and preferences too change drastically in the long run. They change with changes in individuals’ surroundings and environment that accompany growth in income. Under these conditions, the endogenous growth models also cease to hold and the steady states that they derive become meaningless. This is the basic problem of developing a long-run theory of growth. To quote Keynes, “in the long run we are all dead”. If we look at the aggregative groupwise raw data, we find that, as we pointed out earlier, the long-run growth rate varies inversely with the degree of development (see Table 13.4). This is in sharp contrast with the predictions of the endogenous growth theory. If we focus on more disaggregated countrywise data (see Table 13.4), we find that many of the richest of the nations persistently grow faster than many of the poorest nations, while some poor nations grow at a much faster rate than many of the richest nations. Actually, countries with high per capita income have many advantages, which the others do not have. Governments have larger resources per capita, which enables them to supply better and more public goods per capita. This implies better infrastructure, better administration, greater protection of life and assets and better quality of human capital leading to higher productivity of capital. People can also spend more on education and health contributing to the quality of human capital. The rich nations can also afford to engage in R&D on a larger scale, given the superior financial might of their firms and their greater access to quality manpower. All these factors create a solid base for the high rates of growth from the supply side. In other words, all the explanatory variables identified by the mainstream growth theory for explaining per capita growth rate assume the highest values in

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the richest of the nations. Accordingly, if the mainstream growth theory is true, per capita growth rate should be the highest in the richest of the nations. Despite this, they in fact grow at the lowest rate. Obviously, this contradiction is due to the focus of the endogenous growth theory on the supply side factors alone. In reality, even in the long run, demand side factors remain crucially important. Hence, the following may be a much more sensible explanation of the cross-country differences in the growth performances. Poorer countries have much greater urgency to grow fast to remove poverty, to catch up with the rich to cope with the international competition and even for self defence. This induces many of the governments in developing countries to play active roles in promoting growth. Moreover, in poor countries most of the people have a little protection against the elements of nature, diseases, etc. They hardly have enough to eat. To stay in power even in totalitarian regimes on a sustained basis, support of these people is crucial. Competition among politicians for power therefore brings the development issues in the forefront for garnering support. Hence government plays an important role in promoting development in these countries. Governments’ policies range from direct public investment in different sectors to subsidization of saving and investment. This contributes to sustaining a high rate of growth in demand for goods and services. In the developed countries, since per capita income is much higher, the urgency of growth is much less. Moreover, most of these countries are against large and influential governments. They recommend minimization of government intervention in economic matters. For these reasons governments in these countries do little to directly stimulate growth. Growth in consumption is likely to slacken with development. The constraint that income puts on consumption eases with the increase in per capita income. But factors such as the physical capacity to consume, the time available for consumption, etc. also act as constraints and they gain in importance with the rise in per capita income and fall in the rate of growth of population. The rate of growth of consumption in developed countries accordingly depends crucially upon the rate of arrival of new and superior quality consumption goods in the market. In richer countries therefore growth in consumption demand and, therefore, that in investment are largely innovation driven. The growth rates are accordingly low. New investment does not add to capacity much. It leads to better products and makes a part of the existing productive capacity obsolete. For these reasons growth rates in rich countries may be low. The mainstream growth theory’s predictions go wrong as they focus only on the supply side factors and ignore the demand side factors completely.

REFERENCES Barro, R.J. and Sala-I-Martin, X. (2004), Economic Growth, Prentice Hall, New Delhi. Bernanke, B., Gartler M., and Gilchrist, M. (1998), The financial accelerator in a quantitative business cycle framework, NBER Working Paper 6455. Domar, E.D. (1946), Capital expansion, rate of growth and employment, Econometrica, 14, April. Harrod, R.F. (1939), An essay in dynamic theory, Economic Journal, 49, June. Jorgenson, D.W. and Yip, E. (2001), Whatever happened to productivity growth? In E.R. Dean, M.J. Harper and C. Hulten, Eds., New Development in Productivity Analysis, Chicago University Press.

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Kalecki, M. (1954), Theory of Economic Dynamics: An Essay on Cyclical and Long-run Changes in Capitalist Economy, Allen & Unwin. Lucas, R.E. Jr. (1988), On the mechanics of economic development, Journal of Monetary Economics, 22, July. Rakshit, M. (2009), India amidst the Global Financial Crisis, Economic and Political Weekly, Vol. 44, No. 13, March 28–April 03. Romer, P.M. (1986), Increasing returns and long-run growth, Journal of Political Economy, 94, October. ______(1990), Endogenous Technological Change, Journal of Political Economy, 98, October, Part II. Solow, R.M. (1956), A contribution to the theory of economic growth, Quarterly Journal of Economics, 70, February. Young, A. (1995), The tyranny of numbers: confronting the statistical realities of the East Asian growth experience, Quarterly Journal of Economics, 110, August.

Index

Adjustment mechanisms, 178 Adjustment rules, 80, 94, 112, 178 Aggregate national saving, 36 Agriculture and allied activities, 50 Ando, 270 Annual effective rate, 124 Annual percentage rate (APR), 125 Annualized interest rate, 124 Asymmetric information, 362 Autonomous component of AD, 82 Autonomous expenditure multiplier, 85

Balanced budget multiplier (BBM), 102 Bernanke, 373 Bonds, 120, 123 Business saving, 35 Business transfers, 34 Buyers’ credit, 45

Call money market, 120 Capital, 7 Capital consumption allowance, 29 Capital stock, 14, 28 Capitalist bloc, 4 Cash reserve ratio (CRR), 130 Casual labour, 56 Certificates of deposits, 123, 125 Classical dichotomy, 218

Classical zone, 194 Classical zone of the LM, 193 Close-ended funds, 136 Comparative static exercises, 82 Compounding, 127 Compounding periods, 127 Coupon, 120 Current account deficit, 38 Current account surplus, 37

Deflationary gap, 87, 88, 104, 109 Demand liabilities, 133 Demand side factors, 74 Disproportionality crisis, 373 Dividend, 13 Double counting, 9

ECB, 44 Economic agents, 7 Effective annual interest rate (EAR), 128 Equities, 13 Expected daily forward rate, 147

Face value, 120 Factors of production, 7 Financial accelerator, 373 Financial institutions, 120 419

420

Index

Financial markets, 120 capital, 120 money, 120 primary, 120 secondary, 120 Financial sector, 120 Fiscal policy, 107 Fiscal policy stance, 113 Fiscal powers, 113 Fisher, 270 Fisher’s model of intertemporal choice, 270 Fixed capital, 287 Flow variable, 291 Flows, 291 Foreign investment, 44 Foreign transfers, 33 Friedman, 270 Full employment level of employment, 216 Full employment level of GDP, 216 Full employment real wage rate, 216

GDP deflator, 63 Globalisation, 4 Government administration and defence, 17, 18 Government consumption, 20 Government saving, 35 Gross Domestic Product (GDP), 8 Gross domestic saving, 38 Gross profit of a firm, 11 Gross value added (GVA), 10 Growth effect, 388

High-powered money, 140 Households, 7

Imperfect information, 328 Income method of estimating GDP, 12 Income velocity of circulation of money, 195 Induced component of AD, 82 Industry, 50 Inflationary gap, 88, 104, 105, 109, 110 Inputs of production, 7 Interest, 8 Interlinkage between the real sector and the financial sector, 163 Intermediate inputs, 9 Internal rate of return, 288 Inventory, 14 Involuntary unemployment, 5

Keynesian consumption function, 268, 270 Keynesian cross, 75 Keynesian theory, 309, 350 Keynesian zone, 193 Knife-edge, 376

Labour, 7 Labour force participation rates, 54 Labour force, 54 LAF, 160, 161 Lags in export, 45 Land, 7 Laspeyere’s price index, 61, 63 Leads and lags in export, 45 Level effect, 388 Liberalisation, 4 Life cycle theory of consumption, 267 Liquid, 137 Liquidity, 137 Liquidity adjustment facility, 155 Liquidity preference theory, 150, 151, 291 Liquidity trap, 192, 193 Long-run equilibrium, 325

Marginal efficiency of capital, 288 Market economy, 75 Market segmentation theory, 151 Market yield to maturity, 127 Menu cost, 350 Mixed recall period (MRP), 58 Modigliani, 270 Monetary aggregate, 138 Monetary authority (central bank), 171 Monetary base, 140 Monetary policy, 151, 160 Monetary stabilization scheme (MSS), 155, 158, 161 MPCE, 58 Multiplier, 86

National income (NI), 32 National sample survey organization (NSSO), 58 Natural rate, 326 Natural rate of interest, 207 NAV, 136 Net domestic product (NDP), 10 Net domestic saving, 38 Net foreign transfers, 38 Net value added (NVA), 10 Neutrality of money, 220

Contents New classical, 328 New classical theories, 309, 318, 338 New Keynesian theory (NKT), 309, 350 Nominal GDP, 48

Open ended funds, 136 Open market operation (OMO), 155, 158, 160, 161 Organization of petroleum exporting countries (OPEC), 310 Organized sector, 52 Overnight or one-day loans, 155

Paasche’s price index, 61 Paradox of thrift, 95 Permanent income hypothesis of consumption, 267 Personal disposable income, 35 Personal income (PI), 33, 35 Phillips curve, 313, 318 expectation augmented, 319, 323 Policy irrelevance proposition, 344 Poverty line, 57 Poverty ratio, 58 Precautionary, 292 Precautionary demand for money, 296 Preferred habitat theory, 151, 152 Present value, 124, 126 Privatisation, 4 Profit, 8 Proprietorship firms, 35 Public consumption, 20 Public sector enterprises, 17, 18 Purchasing power parity (PPP) measure, 66

Quantity theory of money, 219, 220

Random disturbance term, 340 Rational expectations, 341 new classical model, 341 theorists, 342 Real balance, 171, 172 Real balance effect, 223 Real business cycle (RBC), 349 Real business cycle theory, 367 Real GDP, 49 Recall period (URP), 58 Regular wage, 56 Relative income hypothesis of consumption, 268

421

Rent, 7 Repo market, 120 Required reserve (RR), 130 Responsibilities, 113 Retained earning, 13 Rupee debt service, 45

Salaried, 56 Saving, 35 Say’s law, 206, 207 Self-employed, 56 Services, 50 Short term to India, 45 Simple Keynesian model, 75 Social or public goods, 17 Speculative, 292 Stability of equilibrium, 80 Stabilization, 107, 115 Stagflation, 310 Stocks, 13, 291 Stock of fixed capital, 14 Stock of fixed capital and inventory, 14 Supplier credit, 45 Supply side factors 74

T-bills, 120, 123, 124 Term structure of interest rates, 146 Time liabilities, 133 Trade cycle, 287, 290 Transaction demand for money, 293, 296 Transaction motive for holding money, 292 Transfer incomes, 33 Treasury bills (T-bills), 120, 123

Unbiased expectations theory, 151 Undistributed profit, 13 Unemployment rate, 54 Unorganized sector, 52 Usual principal and subsidiary status (UPSS) employment, 53

Volatility, 287

Wages, 7 Warranted rate of growth, 376 Wholesale price index, 3 Workforce, 2, 54

MACROECONOMICS Macroeconomics, which along with microeconomics forms one of the two most general fields of economics, deals with the entire economy—national, regional and global economy. As macroeconomics encompasses the performance, structure, behaviour, and decision making of the whole economy, it impinges on the lives of all the people in a country and the world in general. This comprehensive and well-organized text strives to dwell on the multidimensional aspects of macroeconomics in such a fashion that the concepts are explained with great precision and clarity. The authors, Dr. Ambar Ghosh and Dr. Chandana Ghosh, with their expertise and their wealth of experience in teaching the subject, try to strike a balance in treatment of the subject. That is to say, the text is neither too heavily mathematical nor entirely bereft of mathematics—indeed, it gives the right mix of mathematics and theory. The book discusses in detail Keynesian economics, which focuses on aggregate demand to explain levels of unemployment and the business cycle, as well as New Keynesian economics which is based on rational expectations and efficient markets. Under these two broad categories, the book covers such topics as national income accounting, aggregate demand and determination of GDP, and the IS-LM model. Besides, the text analyzes the Classical Theory dealing with aggregate supply, money market; the complete Keynesian model; and the consumption and investment functions. The book clearly explains and rejects new Classical and new Keynesian theories. The book concludes with a critique and rejection of modern theories of growth and the implications of growth for the economy.

Chandana Ghosh Ambar Ghosh

KEY FEATURES ◆ Explains the concepts in an easy-to-understand language. ◆ Includes numerous exercises within the text as well as at the end of each chapter. ◆ Illustrates the concepts with the help of examples, figures and tables. This book is intended mainly as a text for undergraduate and postgraduate students of Economics for their course in Macroeconomics. Besides, all those who wish to delve deeper into the complex yet fascinating subject of Macroeconomics should find reading the book useful and rewarding. THE AUTHORS CHANDANA GHOSH, PhD, is Assistant Professor at the Economic Research Unit, Indian Statistical Institute, Kolkata. She has 22 years of teaching and research experience. She has co-authored the book Economics of the Public Sector, published by PHI Learning. Her areas of interest are Theory of Growth and Inequality, New Keynesian Economics, and Macro Problems of Indian Economy. AMBAR GHOSH, PhD, is Professor of Economics, Jadavpur University, Kolkata. Earlier, he was Professor of Economics at Presidency College, Kolkata. Besides, he has taught at many other institutions such as University of Calcutta, Indian Institute of Management Calcutta, as guest faculty. He is the co-author of the book Economics of the Public Sector.

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