MICRO-ECONOMICS

OPTIMAL DECISION-MAKING

BY PRIVATE FIRMS AND PUBLIC AUTHORITIES

MICRO-ECONOMICS

Optimal Decision-Making

by Private Firms and Public Authorities

by

CLAUDE ABRAHAM AND ANDRE THOMAS

SPRINGER-SCIENCE+BUSINESS MEDIA, B.V.

MICROECONOMIE

DECISIONS OPTIMALES DANS L'ENTREPRISE ET DANS LA NATION

Second edition in 1970 by Dunod, Paris

Translated from the French by D. V. Jones

Library of Congress Catalog Card Number 79-188001

ISBN 978-94-017-2269-8 ISBN 978-94-017-2267-4 (eBook) DOI 10.1007/978-94-017-2267-4

All Rights Reserved Copyright © 1973 by Springer Science+Business Media Dordrecht

Originally published by D. Reidel Publishing Company, Dordrecht, Holland in 1973 Softcover reprint of the hardcover 1st edition 1973

No part of this book may be reproduced in any form, by print, photoprint, microfilm, or any other means, without written permission from the publisher

Sur quoi la fondera-t-il, l'economie du monde qu'il veut gouverner? Sera-ce sur le caprice de chaque particulier? Quelle con­fusion! Sera-ce sur la justice? Ill' ignore.

B. PAScAL, Pensees

PREFACE

The origin of this work is to be found in the cyclostyled course on 'The optimal allocation of resources in the firm and in the Nation' taught by Mr Boiteux at the Centre d'Etudes des Programmes Economiques (C.E.P.E.), Paris from 1957 to 1960. Of course, several successive later rewritings and a great many additions have profoundly altered the initial version: starting from a remarkably clear and concise exposition of eco­nomic theory, we have ended with a book that is several hundred pages long. It is not at all certain that Mr Boiteux would recognise this intellec­tual sponsorship. Nor is it certain that the gain in information justifies such an increase in size. However that may be, the initial plan has survived. Without Mr Boiteux this book would never have been undertaken: it is a pleasant duty for us respectfully to acknowledge our debt to him here.

Microeconomic analysis, that is to say that analysis which results from the study of the behaviour and activities of individual decision-units, was for a long time the main concern of the neo-classicists. Quite recently the introduction of macroeconomic theory, dealing with aggregate quan­tities, seemed to relegate it to second place. But this is not where it belongs: we tend to agree with Mr Raymond Barre that there are "two different scales of analysis that complement rather than contrast with one another". Microeconomic theory, which was ignored for a time, is the sole basis for the real calculations carried out by public authorities and by private firms. It gives us valuable insights into the role of prices. It allows us to rediscover by summation the National Income Accounting identities. Above all, it constitutes an irreplaceable language. But, to be effective, it must function in a global landscape, that is to say in a macroeconomic environment.

The majority of microeconomic arguments make use of a very simple idea which has been the very making of operational research: every economic agent is subject to a variety of constraints and has an objective which can be expressed mathematically by a certain function that we shall call a satisfaction function, which he tries to maximise or minimise.

VIII MICRO-ECONOMICS

From this follow the successes and the failures of microeconomics: the successes, because the adopted mathematical formulation has shown itself to be capable of useful and universall application; the failures, because the goals of men cannot easily be encompassed in a few equa­tions .... Microeconomics has therefore two faces: to parody a famous phrase, one could say that sometimes it portrays men as they are and often it portrays economic units as they ought to be.

The conception and the writing of this work were inspired by the following principles:

(i) As regards its basis, we have tried to bring out two streams of thought: -the first concerns to general exposition of economic theory or, more

precisely, microeconomic theory; - the second is arranged around an analysis of the unit of production,

whether public or private. 'The optimal allocation of resources' teaches us to formulate consistent calculations of profitability. At the same time it puts us on guard against the difficulties which may arise, as well as against the inadequacy of certain assumptions.

The analyses of optimal allocation may be undertaken on the basis of different systems of ethics. Sufficient intellectual rigour nevertheless allows us to draw out a common fund of results: "Thanks to economic analysis, it is becoming easier to synthesise complementary points of view, and easier to lay bare the genuine basic contradictions that are sometimes hidden beneath tendentious arguments. " 2 The systematic use of economic models whose assumptions are assiduously listed avoids confusion be­tween the deductions and conclusions of axiomatic analysis on the one hand, and concrete reality on the other.

We have limited ourselves to the framework of accounting economics and have not tried to describe financial institutions. This serious gap will no doubt be filled one day, for the techniques of actuarial decision-making now constitute a very elaborate body of doctrine.

(ii) The form of a book assumes great importance when the book has a primarily pedagogic aim.

(a) The use of mathematics and, more precisely, mathematical models was essential. As a rule, the level of a university introductory year in science is adequate for an understanding of the main results. Those which require a deeper knowledge can be left aside without penalty; in any case engineers and economics graduates with a science background will be

PREFACE IX

able to read this textbook without difficulty. Moreover, we have preferred logical rigour to mathematical rigour. In our view, excessively technical proofs should not take precedence over the process of deduction and the economic interpretation of the models.

(b) Economic theory leads directly to industrial applications. There already exist some excellent books dealing with this subject. Therefore, although we have not disdained examples, this work remains essentially didactic.

(c) The large number of variables makes it impossible to use a univocal system of notation. We have however endeavoured to adopt or adapt the most usual notations.

In its present form, this book has been or is being used as a course-book at the Centre d'Etudes des Programmes Economiques (C.E.P.E.), at l'Ecole Nationale du Genie Rurale, des Eaux et Forets (E.N.G.R.E.F.), at l'Ecole Nationale des Pants et Chaussees (E.N.P.C.). As a result its production has led to a continuous dialogue with the students whose criticisms and suggestions have been of great value.

The book's plan was referred to above: it consists of two parts of roughly equal inportance:

-The first five chapters are devoted to a genera/look at economic theory, which numerous authors have considerably enriched in recent years. Among French writers we can name in particular Messrs Allais, Debrue and Lesourne. After production and consumption, after Pareto's 'obstacles' and 'tastes', it is possible to describe an economic equilibrium, to construct a 'social mechanism', following the Lausanne School tradition. Several recent lines of research relating to imperfect competition, axiomatic theory and the stability of equilibrium allow us, we believe, to underline the model's extreme generality and its limitations.

Chapter IV attempts to summarise the main theories of the economic optimum. Now equilibrium describes a way in which economy can func­tion. It is not an ideal in itself. After the work of A. C. Pigou, the concept of welfare became established in economics: "Ethics", writes J. Hobson, "are never an intrusion into economics; the same facts are both economic and ethical."

A suitable generalisation of Pareto's formulation and a clear explana­tion of the social welfare function provide a common language for a good many hypotheses.

X MICRO-ECONOMICS

Within the framework of this book it was unfortunately impossible to review the various economic systems and to compare them with the concepts of the theory. The calculation of marginal costs and planning 'a la fran~aise', the German-style 'social market economy', and the recent efforts of certain Soviet economists would provide the reader intent on concrete applications with a good many fascinating subjects for reflection. Chapter V introduces time into the analysis and leads to the important definition of the discount rate. Several observations must be made on this topic:

(a) the discount rate summarises the arbitrage of an economic unit between the present and the future; it is therefore not the same as the various rates of interest, which are exogenous institutional data;

(b) the discount rate is a product of marginal analysis. Its use is not necessarily legitimate in the study of large investments;

(c) the discount rate is independent of the type of economy (capitalist or socialist). For example, with the aim of selecting profitable operations under the National Plan, Kantorovich has proposed a coefficient, which he calls 'normal efficiency', that gives rise to identical calculations.

- The next six chapters are centred on some fundamental problems of the theory of production. After two chapters devoted to marginal costs and investment choice, we tackle, very briefly, a subject which is full of promise but also very controversial: that of public investment. To tell the truth, the method of approach to these problems has hardly changed since the last century: Jules Dupuit's consumer's surplus remains the pivot of our formulations. But every day administrators and engineers working for public authorities have to take highly important decisions on the basic of certain calculations. These have therefore become operational, so it was important for us to emphasise their difficulties and their full implications.

The replacement of plant and machines and their amortisation form the subject of two chapters. There are two very traditional subjects. But the recent studies of Messrs Desrousseaux, Lhermitte and their teams have brought about a real revolution in this area of thought. Their results allow us to give a rigorous definition of amortisation within the frame­work of perfect forecasting, thereby underlining the highly subjective nature of the value of a production good. Now amortisation is revealed as the stumbling-block of the theory of firms' production cost, and, more

PREFACE XI

generally, of the theory of capital: "The depreciation of capital is at the very heart of the thought process which leads an individual to acquire a capital good. "3

Chapter XI describes the relationships between economic theory and

normal accounting concepts. It is based on two main ideas. On the one hand economists usually argue in terms of real monetary flows, while accountants, by means of amortisation and various special funds and accounts, introduce fictitious monetary flows. On the other hand micro­economics is based on marginal analysis, while current practice is often content with the traditional language of standard cost and profit margins. A comparison between theory and business practice seemed to us un­avoidable if perhaps premature.

- The last chapter takes up a thankless but necessary task: the intro­duction of an uncertain world, the substitution for the attractive but unrealistic analysis of perfect forecasting of the more complex and true to life schema of the 'calculated adventure' of which Mr Pierre Masse is so fond. In the search for decision criteria, the economist humbly re­discovers- if he had for a moment been able to forget it- that a man's action is a projection into the future. He thus returns to the everlasting problem of philosophy.

Before ending this introduction, we should like to thank all those who have contributed to the creation of this book: Mr Edmond Malinvaud who, by entrusting one of the authors with the teaching of microeconom­ics at the C.E.P.E. showed in him a confidence of which this book is the fruit and the evidence of his gratitude. Messrs Prou, Boiteux, Lhermitte, Lesourne and Deheim whose encouragement, advice and comments made possible the writing and then the improvement of this work. Mr Jacques Fayette who agreed to read the chapters on economic theory and let us have his criticisms and suggestions. Mr Jacques Thedie was initially to have collaborated in writing this book: he will recognise in places ideas which are dear to him but that he has never had the oppor­tunity to publish. We hope that all will find here the expression of our sincere gratitude.

May 1969 CLAUDE ABRAHAM

ANDRE THOMAS

XII MICRO-ECONOMICS

NOTES

1 To such an extent that it has proved possible to apply this formulation to the State, that is, to the macroeconomic entity par excellence. 2 Jacques Lesourne, Le calcul economique, p. 244. 3 Alain Cotta, La depreciation du capital et le sujet economique, p. 327.

TABLE OF CONTENTS

PREFACE Vll

CHAPTER I I PRODUCTION 1

1. General Principles 1 1.1. Definition 1 1.2. The Theory of Production and Measures of Value 2 1.3. The Characteristics of Production 3 1.4. Outline Description of a Production Unit 4

2. Factors of Production and Production Functions 6 2.1. Production: Factors and Techniques of Production 6 2.2. The Principle of Non-Wastage and the Production

Function 8 2.3. Properties of Production Functions 9

2.3.1. Geometric Representation and Properties 9 2.3.2. The Law of Non-Diminishing Returns 11 2.3.3. The Law of Diminishing Marginal Returns 13

2.4. Examples of Production Functions 17 2.4.1. Theoretical Examples 17 2.4.2. The Combination of Techniques 19

2.5. Generalisation: the Multi-Product Firm 25 2.6. Production Functions and the Real World 27

3. Choice of Factors and Production Cost 28 3.1. The Minimum Cost Principle 28 3.2. Cost of Production, Marginal Cost and Average Cost 33 3.3. Business Practice and the Achievement of Minimum

Cost 38 4. Choice of a Level of Production 40

4.1. The Criterion of Profit Maximisation 40 4.2. Economic Interpretation. Perfect Competition and

Monopoly 45 4.3. Generalisation: the Multi-Product Firm 47

XIV MICRO-ECONOMICS

CHAPTER II I CONSUMPTION 53

1. Indifference Surfaces and the Theory of Choice 53 1.1. Axioms of the Theory of Choice. Indifference

Surfaces 54 1.2. Analytical Properties of Indifference Surfaces.

Satiety Curves 57 2. The Criterion of Maximum Utility 59

2.1. The Principle of Choice of the Optimal Consumption ~~ ~

2.2. Generalisations 62 2.2.1. Introduction of La hour 62 2.2.2. Introduction of Time Constraints 63

3. Demand Functions 3.1. The Definition and Mathematical Properties of

Demand Functions 66 3.2. Elasticities 68 3.3. Aggregate Demand 73

4. Critique of the Concept of 'Homo Oeconomicus' 74

CHAPTER III I ECONOMIC EQUILIBRIUM 80

1. The Classical Theory of Competitive Economic Equilibrium 80 1.1. Basic Assumptions 80 1.2. The Equilibrium Equations 82

2. The Classical Theory and the Price Mechanism 87 2.1. The Assumptions of a Perfect Market 88 2.2. The Law of Supply and Demand 89 2.3. Some Applications of the Law of Supply and

Demand 103 2.4. Monopoly and Oligopoly 108

3. Generalisations of the Theory of Equilibrium 113 3.1. Stability of Equilibrium 114 3.2. Axiomatic Theory of Equilibrium 118

4. Importance and Limitations of the Theory of Competitive Equilibrium 130

TABLE OF CONTENTS XV

CHAPTER IV I THE SOCIAL ECONOMIC OPTIMUM 138

Part 1- The Pareto Optimum 138 1. The Optimal Organisation of Production 139 2. The Distribution Optimum 144 3. The Pareto Optimum 148 4. The Theory of Social Welfare and the Role of Prices 152 5. Generalisations of the Pareto Model 156 6. The Limitations of the Theory of the Economic Optimum 164

Part 2- The Social Welfare Function 167 7. The Development of Collective Decisions on the Basis of

Individual Choices 168 7.1. The Compensation Principle 168 7.2. Procedures for Social Decision-Making 171

8. Social Welfare Function and Comparison of Economic States 173 8.1. Social Welfare and State Satisfaction 173 8.2. Comparison of States of the Economy 175

9. Elements of a Formalisation of State Action 184

CHAPTER VI DISCOUNTING 192

I. General Principles 192 2. Discounting and the Theory of Consumer Choice 196

2.1. Satisfaction and Income 196 2.2. Theory of Discounting 198 2.3. Choice of an Optimal Income Stream 202 2.4. The Discount Rate and the Distribution Optimum 208

3. Discounting and the Theory of the Firm 209 3.1. The Firm Owned by an Individual 210

3.1.1. The Case Where There Exists No Investment Project. The Definition of Profit and the Law of Present Values 210

3.1.2. The Case Where Investment Projects Exist 211 3.2. Joint-Stock Company 216

3.2.1. The Case Where There Exists No Investment Project. Perfect Market for Equities 216

XVI MICRO-ECONOMICS

3.2.2. The Case Where There Exist Investment Projects 218

3.2.3. The Case of an Imperfect Market 219 3.3. Time and Production Functions 222 3.4. Generalisation of the Equations of the Economic

Optimum 227 4. Discounting and Social Welfare 228

CHAPTER VI I MARGINAL COSTS 234

1. The Importance of Marginal Costs 234 2. The Classical Theory of Short and Long Term Marginal

Costs 236 2.1. The Model of the Firm with Strictly Limited Output

and the Paradox of Partial Cost 236 2.2. Long Term Marginal Cost 237 2.3. Sale at Marginal Cost 246

3. Linear Programming and Marginal Costs 248 3.1. The Fundamental Problem of Linear Programming 248 3.2. The Dual Problem 251 3.3. The Fundamental Theorem of Duality and Its

Interpretation 253 4. The Problem of the Peak. Study of Periodical Demand 256 5. Random Demand 265 6. Marginal Costs and Discounting 269

6.1. Discounted Marginal Costs 269 6.2. Development Costs and Contraction Costs 274

7. Marginal Costs and Social Costs 275 8. Some Aspects of Marginal Cost Pricing 279

CHAPTER VII I THE CHOICE OF INVESTMENTS 290

1. General Principles 290 1.1. Definition and Examples 291 1.2. Classification oflnvestments 291 1.3. Parameters of an Investment 292 1.4. Average or Internal Rate of Return, Marginal Rate

of Return 293

TABLE OF CONTENTS XVII

1.5. Criteria of Investment Choice 297 1.6. The Structure of Projects 298

2. Choice of Projects in a Stationary Economy with no Financial Constraints 299

3. Choice of Projects in a Stationary Economy with a Financial Constraint 311

4. Choice of Projects in a Dynamic Economy with no Financial Constraint 318

5. Choice of Projects in a Dynamic Economy with a Financial Constraint 322

CHAPTER VIII/ PUBLIC INVESTMENT AND STATE CHOICE 328

1. Social Welfare and National Surplus 329 1.1. Summary of the Main Results 329 1.2. Surpluses and the Behaviour of Firms. Geometric

Interpretation of the Surpluses 334 1.3. Example of a Calculation of a Surplus: Road

Investments 338 1.4. Fictitious Costs and Real Costs 341

2. The National Surplus 341 2.1. Social Goods 341 2.2. State Surpluses 342 2.3. The Value of Human Life 343

3. The Choice of Public Investments 349 3.1. Choice of the Discount Rate 349 3.2. Public Investment and Macroeconomic Policy 355 3.3. The Choice of Large Investments 356

CHAPTER IX I THE REPLACEMENT OF EQUIPMENT 361

I. General Principles 361 1.1. Factors in Replacement 361 1.2. The Fundamental Concepts of Replacement 364

2. Theoretical Setting of the Problem 367 2.1. The Problem of the Optimal Chain. The Three

Period Equation 367

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2.2. The Problem of Replacement 377 3. Theory of the Adverse Minimum 382

3.1. Assumptions and Calculations 382 3.2. Formulae for the Generalised Adverse Minimum 389

4. Optimal Strategy and Industrial Economics 393

CHAPTER X I AMORTISATION 398

1. The Concept of Amortisation 398 1.1. Industrial Amortisation 398 1.2. Financial Amortisation. Basic Formulae 399 1.3. Economic Amortisation 400 1.4. Economic Amortisation and Financial Amortisation 412

2. Study of Depreciation Rules 414 2.1. Notation and General Formulae 414 2.2. Common Depreciation Rules 416

3. Amortisation of a Fleet of Homogeneous Machines 419 3.1. Assumptions and General Formulae 419 3.2. Particular Cases 423

4. Fiscal Amortisation and Investment 425 Annex: The Repayment of a Loan in a Period of Monetary Instability 430

CHAPTER XI I ACCOUNTING COSTS AND ECONOMIC THEORY 435

1. Structure of the Balance Sheet and General Accountancy 436 1.1. Outline of the Accounting Mechanism 436 1.2. Structure of the Balance Sheet. Economic Profit and

Accounting Profit 439 1.3. Problems of Financial Structure 446

1.3.1. Generalisation of the Preceding Outline 446 1.3.2. Study of Financial Structure. Net Circulating

Capital and Ratios 449 1.4. Financing an Investment Plan 452

2. Calculation of Total Unit Costs and Analytical Accounting 453 2.1. Comparison of Methodologies 453 2.2. Analysis of the Accounting Model 455

3. Industrial Criteria 463

TABLE OF CONTENTS XIX

CHAPTER XII f CRITERIA OF CHOICE IN THE FACE OF AN

UNCERTAIN FUTURE 470

1. Decisions in the Face of a Risky Future 471 1.1. The Criterion of Expected Value 472 1.2. Attempts at a Solution 475

1.2.1. Axiomatic Approach of the American School 475 1.2.2. Risk of Ruin and Safety Indicator 478

1.3. Economy Subject to Risk 479 2. Decisions in the Face of an Uncertain Future 482

2.1. Completely Uncertain Future 482 2.2. Subjective Probabilities 488 2.3. Search for a Provisional Solution 490 2.4. The Economics of Uncertainty 499

3. The Concept of Plan or Strategy 501