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ARROW AND THE FOUNDATIONS OF THE THEORY OF ECONOMIC POLICY Also by George R. Feiwel

*ARROW AND THE ASCENT OF MODERN ECONOMIC THEORY (companion volume) *ISSUES IN CONTEMPORARY AND WELFARE (editor) *ISSUES IN CONTEMPORARY MACROECONOMICS AND DISTRIBUTION (editor) SAMUELSON AND NEOCLASSICAL (editor) THE INTELLECTUAL CAPITAL OF MICHAL KALECKI GROWTH AND REFORMS IN CENTRALLY PLANNED ECONOMIES THE SOVIET QUEST FOR ECONOMIC EFFICIENCY INDUSTRIALIZATION AND PLANNING UNDER POLISH SOCIALISM (2 volumes) NEW ECONOMIC PATTERNS IN CZECHOSLOVAKIA THE ECONOMICS OF A SOCIALIST ENTERPRISE In preparation * AND MODERN ECONOMIC THEORY (editor) *IMPERFECT REVISITED: JOAN ROBINSON AND BEYOND (editor) *Also published by Kenneth J. Arrow Arrow and the Foundations of the Theory of Economic Policy

Edited by George R. Feiwel Alumni Distinguished Professor and Professor of Economics, University of Tennessee

M MACMILLAN PRESS © George R. Feiwel 1987 Softcover reprint of the hardcover 1st edition 1987

All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission.

No paragraph of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright Act 1956 (as amended).

Any person who does any unauthorised act in relation to this publication may be liable to criminal prosecution and civil claims for damages.

First published 1987

Published by THE MACMILLAN PRESS LTD Houndmills, Basingstoke, Hampshire RG2l 2XS and London Companies and representatives throughout the world

British Library Cataloguing in Publication Data Arrow and the foundations of the theory of economic policy l. Arrow, Kenneth J. 2. Economics I. Feiwel, George R. 330.1 HBll9.A75 ISBN 978-1-349-07359-7 ISBN 978-1-349-07357-3 (eBook) DOI 10.1007/978-1-349-07357-3 Two-volume set ISBN 978-0-333-42410-0 'The Theory of Economics does not furnish a body of settled conclusions immediately applicable to policy. It is a method rather than a doctrine, a technique of thinking, which helps its possessor to draw correct conclusions.'

'Practical in has always rested on its role in putting debates on economic policy on a deeper foundation. Arrow's formulation of the problem makes that deeper foundation explicit, and his approach is of central importance to economic policymaking.'

'If I am not for myself, then who is for me? And if I am not for others then who am I? And if not now, when?' RABBI HILLEL Contents

Notes on the Contributors xvii Preface xxxiii 1A The Many Dimensions of Kenneth J. Arrow 1 George R. Feiwel 1 Formative Years 2 1.1 Background and Early Outlook 2 1.2 City College and Columbia 9 1.3 Cowles and Rand 15 2 An Impressionistic Portrait of the Man and Scholar 23 3 Values and Opportunities 41 4 Design of Organization 51 4.1 What is an Organization? 52 4.2 , Transaction Costs, Property Rights, and Profit 55 4.3 and Non-market Organizations 67 4.4 Government and Economic Policy 70 5 Freedom, Equality, and 79 6 Distributive and Efficiency 89 1B Social Choice: the Science of the Impossible? 116 Peter J. Hammond 1 Introduction 116 2 Background 117 3 The Borda Rule and Irrelevant Alternatives 119 4 Independence of Irrelevant Alternatives 122 5 Is Dictatorship the Only General Possibility? 123 6 Interpersonal Comparisons and Independence of Irrelevant 125 7 Which Alternatives are Relevant? 127 8 Conclusion 128

PART 1: SOCIAL CHOICE, UTILITARIANISM, AND BEYOND 2 Ordinal Utilitarianism 135 Allan F. Gibbard 1 The Problem 137 2 Dividing a Cake 139

Vll Vlll Contents

3 The Egalitarian Planet 141 4 The Bases of Moral Concern 143 5 Epistemological Worries 145 6 Quantities, Norms, and Economics 147 7 Paretian Income Distribution 149 3 Sparks from Arrow's Anvil 154 Paul A. Samuelson 1 Lerner-Vickrey-Samuelson (L-V-S) 'Extended Sympathy' 155 2 No Necessity for Additive Utilities 157 3 Taking the Sympathy Out of 'Extended Sympathy' 157 4 Lerner's Way 159 5 A Better Way? 160 6 Harsanyi's Additive Ethics 161 7 The Bentham-Harsanyi Straitjacket 163 8 Rawls's Gratuitism 166 9 Foley-Varian Fairness 168 10 Relevance of So-called Irrelevants? 169 11 Finale 171 4 On Reconciling Arrow's Theory of Social Choice With Harsanyi's Fundamental Utilitarianism 179 Peter J. Hammond 1 Introduction and Outline 179 2 Motivation for Consequentialism 183 3 Consequentialism and Ordinal Choice 184 4 Consequentialism and Expected 188 5 Social Choice of Interpersonal Consequences 189 6 Individual Norms and Ethical Liberalism 190 7 An 'Idealized' Vickrey-Harsanyi Utilitarianism 193 8 The Fundamental Individual Norm and Harsanyi's Utilitarianism in Idealized Form 195 9 Independence of Irrelevant Althernatives and Dictatorship 198 10 Independence of Ethically Irrelevant Consequences 200 11 Domain Restrictions Implied by Ethical Liberalism and the Fundamental Individual Norm 203 12 Ethical Dictatorship of the Fundamental Individual Norm 205 13 Consumer Sovereignty, Attitudes to Risk, and the Distribution of Income 208 Contents IX

14 Risk-Taking Behaviour and the Basic Theorems of Classical Welfare Economics 210 15 Conclusion 214

5 Arrow's Independence Condition and the Bergson-Samuelson Tradition 223 Murray Kemp and Yew-Kwang Ng 1 The Three Components of Condition IIA: Individualism, Ordinalism, and Independence 224 2 The Bergson-Samuelson Tradition Implies All Three Components 228 3 Samuelson's and Mayston's Counter Arguments 230 Appendix: Arrow, Samuelson, and Ordinalism 235 I Background 236 2 Ordinalism in Name 236 3 Ordinalism in Substance 238

6 Maximizing Freedom of Decision: an Axiomatic Analysis 243 1 Axioms on Freedom 244 1.1 Basic Concepts 244 1.2Axioms 244 2 Models of the Axioms 245 2.1 Benthamite Maximizer 247 2.2 Cardinality Maximizer 248 2.3 Qua-Maximizer 248 3 Aggregation of Freedom Preferences 249 4 Approximate Measurement of Freedom 251

7 Arrow and the Problem of Social Choice 255 and Koichi Suga 1 Introduction 255 2 Pareto Libertarian Paradox: hie rhodus, hie salta 256 3 Golden Rule: First Interpretation 258 4 Golden Rule: Second Interpretation 259 5 A Formal Model of Social Decision Making 262 6 Conclusion 268

8 Utilitarianism and Modern Economics 273 Gunnar M yrdal X Contents

PART II: WELFARE AND DISTRIBUTION

9 The Optimum Order Revisited 281 1 Scope and Nature of the Subject 281 1.1 Why Revisit the Subject? 281 1.2 The Concept of Social Order and the Variables Entering its Analysis 282 1.3 Institutions, their Operation Equations, and the Optimal Order 283 1.4 Scientific Chosen 284 1.5 Notation Used in Illustrative Models 286 1.6 Organization of the Argument 287 2 Relevance of the Concept of an Optimal Social Order 288 2.1 Co-existence of Many Differing Social Orders 288 2.2 Opinions on Optimal Social Order 289 2.3 An Optional Social Order as a Long-term Goal 290 2.4 Changes in Data and Preferences 290 2.5 Changes in Different Cultures 291 2.6 Conclusion 292 3 Variables, Relations, and Simplifying Assumptions 292 3.1 and Services, Private or Collective; Role in Welfare Functions 292 3.2 Actors, Production Factors; Workers and Occupations; Learning 293 3.3 Production Processes; Hierarchies; Counterproduction; Production Functions 295 3.4 Welfare: its Measurement, Determinants, and Aggregation 297 3.5 The 298 3.6 Externalities and the Costs of Institutions 299 3. 7 Role of Ownership 300 4 Aspects of the Optimal Order 301 4.1 The Role of Markets; Two-part Pricing as a General Device 301 4.2 Labour of Different Qualities and Occupations 303 4.3 Private and Collective Goods 308 4.4 Income Redistribution; Equity 312 4.5 The International Division of Labour 314 4.6 Optimum Level of Decision Making 316 Contents xi

4. 7 Dynamics of the Optimum Order; Exhaustibility of Resources 317 5 Relevant Differences Between Optimal and Existing Orders 319 5.1 Introduction; Discrimination 3I9 5.2 320 5.3 Deviations in Redistribution 321 5.4 Non-optimal Collective Sector 322 5.5 International Division of Labour 323 5.6 Decision Structure 323

10 Information, Welfare, and Product Diversity 328 Steven C. Salop and Joseph E. Stiglitz 1 Introduction 328 2 The Model 330 3 Effects of Reducing the Cost of Information 334 4 Effect of Imperfect Information on the of Diversity 336 5 Conclusion 339

11 On the Fair Allocation of Indivisible Goods 341 Eric S. Maskin 1 Introduction 341 2 The Model 342 3 Fair Allocations 345

12 Income Distribution and Differences in Needs 350 Anthony B. Atkinson and Franfois Bourguignon I Introduction 350 2 Dominance for All Groups 352 3 The Interrelation Between Income and Needs 356 4 Second-degree Dominance for Incomes 359 5 Second-degree Dominance for Needs 364 6 Conclusion 366 Appendix: Necessity of Dominance Conditions 367

13 When is a Fixed Income Distribution Optimal? 371 John S. Chipman I Introduction 371 2 Formulation and Solution of the Problem 373 3 Conclusion 378 Xll Contents

14 Peak Pricing, Congestion, and Fairness 382 William J. Baumol and Dietrich Fischer 1 Fairness and Peak Pricing 383 1.1 On the Criteria of Equity 383 1.2 The Possibility of Pareto Improvement in the Classical Peak-Pricing Model 385 1.3 Sufficient Conditions for Peak Pricing not to be a Pareto Improvement 385 1.4 Cases where Peak Pricing can be a Pareto Improvement 388 1.5 Pareto Improvement under Scale Diseconomies 389 1.6 The Case where a Zero Off-peak Price Loses 392 1. 7 A Ramsey Congestion Model 398 1.8 Differences in Taste Relative to Congestion 402 1.9 Pricing Reversals and Pricing Benefits to Peak Users in the Classical Peak-pricing Model 404 2 Conclusion: Potential Unfairness of Peak Pricing 406 15 The Tension Theory of Welfare 410 Jan Tinbergen

PART III: GROWTH, CHOICE, AND UTILIZATION OF RESOURCES 16 No Growth, No Fluctuations 421 Hukukane Nikaido 1 An Overview 421 2 The Model 425 3 The Evolution of the Economy 430 4 What Happens When () is not Higher than n 440 5 Conclusion 442 17 The Life-cycle Hypothesis as a Tool of Theory and Policy 447 Mordecai Kurz 1 The Life-cycle Hypothesis 447 2 Formal Modelling with Linear Expenditure Functions 451 2.1 General Conceptual Development 451 2.2 Constructing Tests of the Life-cycle Hypothesis 456 2.3 The Sample, Data Limitations, Non-linear Age Profiles and Final Specifications 457 Contents xiii

3 Estimation of Model (17.12) With Three Age Groups 461 3.1 Estimation and Test of the Life-cycle Hypothesis: Single-head Families 461 3.2 The Effects of Social Security and Private Pensions: Single-head Families 466 3.3 Estimation and Test of the Life-cycle Hypothesis: Two-head Families 468 3.4 The Effects of Social Security and Private Pensions: Two-head Families 473 4 Estimation of the Plan Updating Model (17 .12') With a Correction for Heteroskedasticity 476 5 The Issue of Planned Early Retirement 476 6 Wealth Profile Evidence 478 7 Is the Strict Life-cycle Hypothesis Viable? 485 Appendix: Construction of Social Security Wealth 486 18 The Credit Mechanism and its Implications 491 1 The Basis of the Credit Mechanism 492 1.1 Credit Today and its Historical Origins 492 1.2 Cash Safekeeping and Payment on Behalf of Depositors 493 1.3 The First Step in the Creation of the Credit Mechanism: the Loan of Funds not Owned by the Bank 494 1.4 The Second Step in the Creation of the Credit Mechanism: the Loan of Money the Bank does not Hold (loans make deposits) 495 1.5 The Development of the Banking System towards Fractional Coverage of Call Liabilities (Fractional-reserve Banking) 496 1.6 The Present Structure and Operation of the Credit Mechanism 497 2 The Essence of Banking 498 2.1 Representation of a Bank's Balance Sheet 498 2.2 The Essence of Banking Today 500 2.3 The Amount of Reserves 501 3 The Creation of Money Through the Credit Mechanism 502 3.1 What is Money? 502 3.2 Demand Deposits 502 XlV Contents

3.3 Time Deposits 503 3.4 The Creation of Money Through the Credit Mechanism 504 3.5 Maturity Differences and the Creation of Money 505 3.6 The Overall Creation of 'Money' by the Credit Mechanism 506 3. 7 Other Assets 508 3.8 The '' 508 3.9 The Creation of Euro-dollars ex nihilo by the European Banks 510 4 The Money Supply, Economic Activity, and Growth 510 4.1 The Money Supply and Global Expenditure 510 4.2 Growth and 513 4.3 Regulation of the Money Supply 517 5 The Creation of Money, the Creation of Purchasing Power, and the Distribution oflncome 518 5.1 The Creation of Purchasing Power through the Credit Mechanism 518 5.2 The 'Miracles' of Credit 520 5.3 True and the Creation of Purchasing Power ex nihilo 521 5.4 Inflation through the Credit Mechanism and Public Opinion 522 6 Foundations of Sound Money in an Efficient Economy 523 6.1 The '1 00 per cent Money' Plan of the Chicago School and its Gaps 523 6.2 The Main Defects of the Present System of Credit 524 6.3 Bases of a Reform 525 6.4 Advantages of the Proposed System 526 Postscript for 1984 527 Appendix: the Present Value of Future Interest Returns 529

PART IV: THE LIMITS OF ORGANIZATION AND ALTERNATIVE APPROACHES 19 The Limits of Organization Revisited 565 John K. Whitaker 1 The Limits of Organization 566 Contents XV

2 Reflections on Arrow's Themes 574 3 Conclusion 580 20 and the New 584 Oliver E. Williamson 1 What is the New Institutional Economics (NIE)? 585 1.1 NIE: Key features 586 1.2 Alternative Traditions 586 2 Arrow's Impact 588 2.1 Institutions Matter 588 2.2 Rational Spirit 590 2.3 Information Processing and Incentive and Control Differences 591 2.4 Transaction Costs 591 2.5 Behavioural Assumptions 592 3 Some Loose Ends 593 3.1 Trust 594 3.2 Institutional Detail 594 3.3 Government 595 4 Conclusion 596 21 On Some Economic Aspects of a Fragile Input: Trust 600 Harvey Leibenstein 1 Introduction 600 2 Self-interest and Trust 601 3 Substitutes for Trust 603 4 Limited Trust, the Employment Relation, and Effort Conventions 606 22 An Eclectic View from Cambridge: an Interview 613 R. C. 0. Matthews

PART V: IMAGES OF ARROW 23 Arrow on Arrow: an Interview 637 Kenneth J. Arrow 24 Arrow-the Breadth, Depth, and Conscience of the Scholar: an Interview 658 Robert J. Aumann 25 'Partners in Crime': an Interview 663 XVI Contents

26 The Young Scholar: an Interview 666 Theodore W. Anderson 27 Axiomatic Soul Searching 672 Howard Raiffa 28 A Younger Colleague's View from Harvard: an Interview 678 Jerry R. Green 29 Arrow's Contributions to 680 Victor R. Fuchs 30 The Impact of Arrow's Contribution to Economic Analysis 683 Michael D. lntriligator Appendix: K. J. Arrow-Works Most Frequently Cited in 1966-83 687 31 Ken Arrow - Success Without Pressure: an Interview 692 Seymour Martin Lipset 32 The University Citizen: an Interview 701 Donald Kennedy 33 Making Music at Stanford: an Interview 705 Gerald J. Lieberman 34 There is Music in Economics 713 George R. Feiwel

PART VI: ARROW'S REFLECTIONS ON THE ESSAYS 35 Reflections on the Essays 727 Kenneth J. Arrow Appendix A: Biographical Sketch of Kenneth J. Arrow 735 Appendix B: The Bibliography of Kenneth J. Arrow 739

Index 752 Notes on the Contributors

Maurice Allais is Professor of Economics, Ecole Nationale Superieure des Mines de Paris and Director of the Centre d'Analyse Economique (Centre National de Ia Recherche Scientifique). For many years he has also been Professor of Economic Theory, Universite de Paris and was also Professor of Economics, Institut de Hautes Etudes Interna­ tionales de Geneve. A recipient of many distinguished awards, he is a of the , a Member of the International Statistical Institute, and an Honorary Member of the American Economic Association. He is also Officier de Ia Legion d'Honneur. He has made important contributions to g.e.t. utility theory, capital and interest theory, and risk, monetary dynamics, time series, and has also written on French economic policy, pure and applied theory of international trade, and various industries. He has contri­ buted significantly outside economics and operations research, namely to the theory of gravity. He is a prolific writer whose many books include A Ia Recherche d'une Discipline Economique; L'Jmpot sur le Capital et Ia Reforme Monhaire; La Theorie Generale des Surplus; and Expected Utility Hypothesis and the Allais Paradox: Contemporary Discussions on Rational Decisions under Uncertainty with Allais' Rejoinder (editor with 0. Hagen).

Theodore W. Anderson, formerly Professor of Mathematical Statis­ tics, , is Professor of Statistics and Economics, . He was Visiting Professor of Mathematics, University of Moscow; Visiting Professor of Statistics, Universite de Paris, Sherman Fairchild Distinguished Scholar, California Institute of Technology; Wesley C. Mitchell Visiting Professor of Economics, Columbia University; and Visiting Research Professor of Economics, New York University. A former editor of the Annals of Mathematical Statistics and long-time member of the editorial board of Psychome­ trika, he has served as President of the Institute of Mathematical Statistics and Member of the Executive Committee, Conference Board of the Mathematical Sciences. He is a Fellow of the American Association for the Advancement of Science, American Statistical Association, the Econometric Society, Royal Statistical Society, a Fellow and Member of the Council of the Institute of Mathematical Statistics, and a Member of the International Statistical Institute. He

xvii xviii Notes on the Contributors is a Fellow of the American Academy of Arts and Sciences and a Member of the National Academy of Sciences. He has made signifi­ cant contributions to mathematical statistics and has published over I 00 articles. His books include An Introduction to Multivariate Statistical Analysis; The Statistical Analysis of Time Series; A Biblio­ graphy of Multivariate Statistical Analysis (with J. Das Gupta and G. P. H. Styan); and An Introduction to the Statistical Analysis of Data (with S. L. Sclove).

Kenneth J. Arrow, our protagonist, is Joan Kenney Professor of Economics and Professor of Operations Research, Stanford Univer­ sity. He was formerly James Bryant Conant University Professor of Economics, . He has been President of the Econo­ metric Society, the American Economic Association, the Institute of Management Sciences, the Western Economic Association, the Inter­ national Society for Inventory Research, and is currently President of the International Economic Association. He has received the medal of the American Economic Association and the Nobel Memorial Prize in Economic Science. A recipient of numerous honorary degrees, most recently from the University of Cambridge, he is a Fellow and past Vice-President of the American Academy of Arts and Sciences, a Member of the National Academy of Sciences, and a Corresponding Member of the British Academy. His many contributions include Social Choice and Individual Values; Essays in the Theory of Risk Bearing; The Limits of Organization; General Competitive Analysis (with F. H. Hahn), and six volumes of Collected Papers of Kenneth J. Arrow. He has also contributed to Issues in Contemporary and Welfare and Issues in Contempor­ ary M acroeconimcs and Distribution.

Anthony B. Atkinson is Professor of Economics and Chairman of the International Center for Economics and Related Disciplines, London School of Economics and Political Science. He was formerly Pro­ fessor of Economics, University of Essex; Professor of and Head of Department, University College, London; and Visiting Professor, MIT. A Fellow of the Econometric Society and a Member of its Council and Executive Committee, he is a Governor of the National Institute of Economic and Social Research, a Fellow of the British Academy, and editor of the Journal of . He has written extensively on public economics, distributive justice, income distribution, and macroeconomic policy. He is the author of Notes on the Contributors xix

more than ten books, including Poverty in Britain and the Reform of Social Security; Economics of Inequality; Social Justice and Public Policy; and Lectures on Public Economics (with J. E. Stiglitz).

Robert J. Aumann is Professor of Mathematics, Hebrew University of Jerusalem. He was a Fellow of the Institute for Advanced Studies, Hebrew University of Jerusalem and Visiting Professor, and Department of Statistics, Yale University; Center for Operations Research and , Universite Catholique de Louvain; Department of Economics, Stanford University; Mathema­ tical Sciences Research Institute (Berkeley); and Ford Visiting Re­ search Professor of Economics, University of California (Berkeley). He is a Fellow of the Econometric Society, a Foreign Honorary Member of the American Academy of Arts and Sciences and was awarded the Harvey Prize in Science and Technology. He is a leading and prolific contributor to the theory of games, the author of Values of Non-Atomic Games (with L. S. Shapley) and a contributor to Issues in Contemporary Microeconomics and Welfare.

William J. Baumol is Joseph Douglas Green Professor of Economics, Princeton University and Professor of Economics, New York Univer­ sity. He is a Guggenheim and Ford Faculty Fellow, an Honorary Fellow of the London School of Economics and Political Science, a Fellow of the American Academy of Arts and Sciences and of the Econometric Society, and a Distinguished Fellow of the American Economic Association. Past President of the American Economic Association, Eastern Economic Association, and the Association of Environmental and Resource , and recipient of several honorary degrees, he is currently the President of the Atlantic Economic Society and a Founding Member of the World Resources Institute. He has contributed extensively to a wide range of topics, including microeconomic theory, theory, and . He is the author of fourteen books, including Welfare Economics and the Theory of the State; Business Behavior, Value and Growth; Economic Theory and Operations Analysis; Per- forming Arts: the Economic Dilemma (with G. Bowen); The Theory of Environmental Policy (with W. E. Oates); Contestable Markets and the Theory of Industry Structure (with J. C. Panzar and R. D. Willig); and the successful textbook Economics: Principles and Policy (with A. Blinder). He is also a contributor to Issues in Contemporary Microeco­ nomics and Welfare. XX Notes on the Contributors

Fran~ois Bourguignon is Professor of Economics and Chairman for Comparative and Quantitative Economics, Ecole des Hautes Etudes en Sciences Sociales, Paris and Associate Research Fellow of the Ecole Normale Superieure. He is a recipient of the Merritt Brown Prize for the best thesis, University of Western Ontario and the Bronze Medal for Academic Achievement, Centre National de la Recherche Scientifique. A former Assistant Professor, University of Toronto, he was Visiting Professor, Concordia University and Birk­ beck College, University of London. He has published a number of articles primarily on income distribution in various countries, , and development economics. His monographs include Statistical Analysis of Income Distribution in Chile (in Spanish); International Migration and Economic Choice (with G. Gallais­ Hamanno; and The 19th Century French Economy: A Macro-Econo­ metric Analysis (with M. Levy-Leboyer).

John S. Chipman, formerly at the Cowles Commission and Harvard University, is Regents' Professor of Economics, University of Minne­ sota and Stiindiger Gastprofessor, University of Konstanz. He was Visiting Professor at the following universities: Harvard, Duke Vanderbilt, Chicago, and Rochester and the Stockholm School of Economics; a Fellow of the Center for Advanced Study in the Behavioral Sciences; Associate Editor of and the Cana­ dian Journal of Statistics; and co-editor of the Journal of . A Fellow of the Econometric Society, the American Statistical Association, and the American Academy of Arts and Sciences, he has received the James Murray Luck Award of the National Academy of Sciences. He has contributed significantly to welfare economics, international trade theory, and statistics and is a keen student of the history of economic thought. In addition to numerous articles, he has written The Theory of Inter-Sectoral Money Flows and Income Formation.

George R. Feiwel is Alumni Distinguished Service Professor and Professor of Economics, University of Tennessee. He has been on several occasions Visiting Professor, Harvard University and Univer­ sity of California (Berkeley), Visiting Professor, University of Stock­ holm, and on several occasions has been Senior Faculty Visitor, University of Cambridge. A Guggenheim Fellow, he is the author of more than ten books, including The Economics of a Socialist Enter­ prise; The Soviet Quest for Economic Efficiency; Industrialization Notes on the Contributors xxi

Policy and Planning under Polish Socialism, 2 vols; The Intellectual Capital of Michal Kalecki; and Growth and Reforms in Centrally Planned Economies. He is also a contributor to, and editor of, Samuelson and ; Issues in Contemporary Mic­ roeconomics and Welfare, and Issues in Contemporary Macroecono­ mics and Distribution.

Dietrich Fischer is Assistant Professor of Economics, New York University. A former Visiting Researcher at the Institute for Ad­ vanced Studies (Berlin), Economic Affairs Officer of the UN Confer­ ence on Trade and Development, and Visiting Professor, National Politechnic Institute (Mexico City), he is Coordinator of the Explora­ tory Project on the Conditions of Peace and Research Fellow, Geneva International Peace Research Institute. He has written many research papers in , industry structure, public eco­ nomics, distributive justice, and war and peace. He is also the author of Preventing War in the Nuclear Age.

Victor R. Fuchs is Professor of Economics, Stanford University and Research Associate, National Bureau of Economic Research. A former Vice-President of the National Bureau of Economic Research and Fellow of the Center for Advanced Study in the Behavioral Sciences, he taught at Columbia University, New York University, City University of New York, Graduate Center, and the Mount Sinai School of Medicine. He is a Fellow of the American Academy of Arts and Sciences and a Member of the Institute of Medicine, National Academy of Sciences. A leading authority on health economics, he has also written many papers on productivity, labour economics, and industry structure and location. He is the author of more than ten books, including Changes in the Location of Manufacturing in the United States Since 1929; The ; Who Shall Live?; and How we Live.

Allan F. Gibbard, formerly at the Universities of Chicago and Pittsburgh and Visiting Professor at Stanford University, is Professor of Philosophy at the University of Michigan. Before embarking on graduate study at Harvard (where he played an important role in the interdisciplinary seminar Arrow and Rawls then conducted), he was for two years with the US Peace Corps in Ghana. A Fellow of the Econometric Society, he was in 1975-6 a Fellow of the Center for Advanced Studies in the Behavioral Sciences and in 1985-6 a Visiting XXII Notes on the Contributors

Fellow at All Souls College, Oxford. He has made significant contri­ butions to ethics and the foundations of modal logic and his work has had a major impact on the development of and the theory of incentives. He is currently working on a book on the concept of rationality.

Jerry R. Green is Professor and Chairman, Department of Eco­ nomics, Harvard University and Research Associate, National Bu­ reau of Economic Research. A former Fellow of the Center for Advanced Study in the Behavioral Sciences and Overseas Fellow, Churchill College, Cambridge, he is a Fellow of the Econometric Society and the recipient of the J. K. Galbraith prize for teaching in Economics (Harvard) and the Distinguished Alumni Award from the University of Rochester. He was Visiting Professor of Economics, Universite Catholique de Louvain and the Hebrew University of Jerusalem, Maitre de Recherche, Ecole Polytechnique, Centre Natio­ nal de Recherche Scientifique, and Directeur d'Etudes, Ecole des Hautes Etudes en Sciences Sociales. He was associate editor of Econo­ metrica and Quarterly Journal of Economics and is the editor of Economic Letters. He has written more than seventy papers on g.e.t. and applications, public economics, uncertainty, information, and incentives. He is also the author of Incentives in Public Decision Making (with J. J. Laffont) and the editor of Some Aspects of the Foundations of General Equilibrium Theory: The Posthumous Papers of Peter J. Kalman and General Equilibrium, Growth and Trade: Essays in Honor of Lionel McKenzie (with J. Scheinkman).

Peter J. Hammond, Formerly Professor of Economics, University of Essex, is Professor of Economics, Stanford University. A Fellow of the Econometric Society, he was a Fellow of the Institute of Advanced Studies, the Hebrew University of Jerusalem and Joseph A. Sebum­ peter Visiting Professor, University of Graz. A major contributor to welfare economics and social choice theory, he has written over fifty papers ranging over the fields of optimal growth and exhaustible resources, rational individual choice, distributional objectives in welfare economics, uncertainty, information, incentives, g.e.t., in­ complete markets, and extensive games. He is the author of four lectures on Schumpeterian themes in the modern welfare economics of production published in Lectures on Schumpeterian Economics (editor C. Seidl) and a contributor to Issues in Contemporary Microe- Notes on the Contributors xxiii conomics and Welfare. He is currently at work on a book Welfare Economic Theory.

Leonid Hurwicz is Regents' Professor of Economics, University of Minnesota. He is a Distinguished Fellow of the American Economic Association, a Fellow of the American Academy of Arts and Sciences, a Member of the National Academy of Sciences, a Member of the Academy of Independent Scholars, and past President of the Econo­ metric Society. He has been a Fellow of the Center for Advanced Study in the Behavioral Sciences and Visiting Professor, the Cowles Commssion (), Stanford University, Harvard University (where he was also Frank W. Tausig Visiting Research Professor), University of California (Berkeley), Tokyo University, and from 1984 to 1985 he was Sherman Fairchild Distinguished Scholar, California Institute of Technology. In 1980 he was awarded an Honorary Doctor of Science Degree from Northwestern Univer­ sity. He has made notable contributions to g.e.t., design of mechan­ isms for resource allocation, and general economic theory and statis­ tics. Among his numerous publications is Studies in Resource Allocation Processes (with K. J. Arrow). He has also contributed to Issues in Contemporary Microeconomics and Welfare.

Michael D. Intriligator is Professor of Economics and of Political Science and Director of the Center for International and Strategic Affairs and of the Interdisciplinary Colloquium on Mathematics in the Behavioral Sciences, University of California (Los Angeles). A former Woodrow Wilson Fellow, Ford Faculty Research Fellow, and four-time recipient of the Warren C. Scoville Distinguished Teaching Award, he is a Fellow of the Econometric Society and a Member of the International Institute for Strategic Studies and of the Council on Foreign Relations. He is an associate editor of the Journal of Optimization Theory and Applications; Inter­ national Journal of Applied Analysis; Journal of Business and Eco­ nomic Statistics; Journal of Interdisciplanary Modelling and Simula­ tion, and Conflict Management and Peace Science. He has written many papers in mathematical economics, econometrics, health eco­ nomics, and strategy and arms control. He has edited more than ten books, including the Handbook of Mathematical Economics, vols 1-3 (with K. J. Arrow) and is the author of Mathematical Optimization and Economic Theory; Econometric Models, Techniques, and Appli- xxiv Notes on the Contributors cations; A Forecasting and Policy Simulation Model of the Health Care Sector (with D. E. Yett, L. Drabek, and L. J. Kimball); and Problems in Mathematical Economics (with G. Egerer, L. J. Helms, and D. A. Starett).

Murray Kemp is Research Professor of Economics, University of New South Wales. He has been Visiting Professor at the Universities of Paris, Mannheim, Essex, and Minnesota, and at Columbia University and MIT. He has contributed significantly to the theory of internatio­ nal trade, resource economics and welfare economics. His many publications include The Pure Theory of International Trade and ; Three Topics in the Theory of International Trade: Distri­ bution, Welfare, and Uncertainty; Variational Methods in Economics (with G. Hadley); and Essays in the Economics of Exhaustible Re­ sources (ed. with N. V. Long). He is also a contributor to Issues in Contemporary Microeconomics and Welfare.

Donald Kennedy is President of Stanford University. Formerly Benja­ min Crocker Professor of Human Biology, Vice-President and Pro­ vost, Stanford University; Senior Consultant, Office of Science and Technology Policy, Executive Office of the President; and Commis­ sioner of Food and Drug Administration; he is a Fellow of the American Association for the Advancement of Science, the American Academy of Arts and Sciences, and the American Philosophical Society, and a Member of the National Academy of Sciences. A recipient of several honorary degrees, he participates in a number of national committees and boards of trustees,_ among which are the board of Overseers, Harvard College; Board of Trustees, the Confer­ ence Board; Board of Directors, Institute for World Environment and Resource Studies and the Council on Financing Higher Education; and he is the Chairman, Division of Biology, Assembly of Life Sciences, National Academy of Sciences and National Research Council. He is the author of more than sixty papers on the compara­ tive physiology of sense organs, especially visual systems and of The Biology of Organisms (with W. M. Telfer).

Mordecai Kurz is Professor of Economics and Director of Economics, Institute for Mathematical Studies in the Social Sciences (IMSSS), Stanford University. A Ford Faculty Fellow, Guggenheim Fellow, and Fellow of the Institute for Advanced Studies, the Hebrew University of Jerusalem, he is a Fellow of the Econometric Society Notes on the Contributors XXV and an associate editor of the Journal of Economic Theory. Among the many important consulting posts he has held was that of Special Economic Advisor, the President's Commission on Pension Policy. He is the author of more than sixty papers in areas ranging over growth and capital theory, g.e.t., public economics, income distribu­ tion, , and labour supply and social policy, and of Components of of National Output; and Public Investment, the Rate of Return, and Optimal (with K. J. Arrow). He is also a contributor to Issues in Contemporary Microeco­ nomics and Welfare.

Harvey Leibenstein is Andelot Professor of Economics and Popula­ tion, Harvard University. Formerly Professor of Economics, Univer­ sity of California (Berkeley), he was a Guggenheim Fellow and a Member of the Institute of Advanced Studies, Princeton University. He is the author of many articles on the microeconomics of human fertility, the X-efficiency theory (the non-allocative aspects of inef­ ficiency), the application of the prisoner's dilemma paradigm to normal economic behaviour, and the economics of conventions and institutions. Among his books are Economic Backwardness and Eco­ nomic Growth; Beyond Economic Man; and Inflation, Income Distribu­ tion and X-Efficiency.

Gerald J. Lieberman is Vice-Provost and Dean of Graduate Studies and Research and Professor of Statistics and Operations Research, Stanford University. A 1972 recipient of the Shewhart Medal of the American Society for Quality Control, he is a Fellow of the American Association for the Advancement of Science, the American Statistical Association (of which he was also Vice-President), the Institute of Mathematical Statistics, and the American Society for Quality Con­ trol (of which he was also National Director), a past president of the Institute of Management Sciences, and a Member of the International Statistical Institute. The author of nearly fifty papers in statistics and operations research, his books include Handbook of Industrial Statis­ tics (with A. H. Bowker); Engineering Statistics (with A. H. Bowker); and Introduction to Operations Research (with F. S. Hillier).

Seymour Martin Lipset is Caroline S. G. Munro Professor of Polit­ ical Science and Sociology, Stanford University and Senior Fellow, Hoover Institution. Formerly George D. Markham Professor of Government and Sociology, Harvard University and Professor of xxvi Notes on the Contributors

Sociology and Director of the Institute of International Studies, University of California (Berkeley), he has held a number of visiting appointments, inter alia, at the Chinese Academy of Social Sciences, University of Warsaw, Free University of Berlin, and he was Henry Ford Visiting Research Professor of Political Science and Sociology, Yale University. A recipient of honorary degrees from Villanova University and the Hebrew University of Jerusalem, he is a Fellow of the American Academy of Arts and Sciences and the American Philosophical Society and a Member of the National Academy of Sciences, National Academy of Education, the Finnish Academy of Science, and the Spanish Institute of Politics. Past President of the Sociological Research Association, American Political Science Asso­ ciation, and International Society of Political Psychology, he is President of the World Association for Public Opinion Research and co-editor of Public Opinion. He is the author of a great number of scientific and popular articles in sociology and political science and the author and editor of about forty books, including Agrarian Socialism; Social Mobility in Industrial Society; Political Man: The Social Basis of Politics; Rebellion in the University; Education and Politics at Harvard (with D. Riesman); The Confidence Gap: Business, Labor, and Government in the Public Mind (with W. Schneider); and Consensus and Conflict: Essays in Political Sociology.

Eric S. Maskin, formerly at MIT, is Professor of Economics, Harvard University. A Research Fellow at Jesus College and Overseas Fellow, Churchill College, Cambridge, he is also a Guggenheim and Sloan Fellow. He is a Fellow of the Econometric Society and an associate editor of Social Choice and Welfare and a former American editor of the Review of Economic Studies. A by training, intro­ duced- and, indeed, inspired- by Arrow to go into economics, Mas­ kin has written nearly forty papers in the last six years ranging over the fields of g.e.t., game theory, social choice, welfare economics, incentives, and information.

R. C. 0. (Robin) Matthews is Master of Clare College, Cambridge and Professor of Political Economy, University of Cambridge. Formerly Drummond Professor of Political Economy, Oxford University and Chairman of the Social Science Research Council, he is currently President of the Royal Economic Society, Chairman of the Panel of Academic Consultants, Bank of England, and a Member of the Economic Policy Committee, Social Democratic Party. He is also a Notes on the Contributors xxvii

Fellow of the British Academy. His many publications in , growth theory, and theory include A Study in Trade Cycle Theory; The Business Cycle; and British Economic Growth 1856-1973 (with C. H. Feinstein and J. C. Odling-Smee). More recently his have shifted towards greater stress on the interdisciplinary approach.

Gunnar Myrdal, political and social critic par excellence, Professor Emeritus, University of Stockholm, was awarded the Nobel Memorial Prize in Economic Science in 1974- the first Swede to be so honoured. A former Senator in the Swedish Parliament, Chairman of the Postwar Planning Commission, and Minister of Commerce, , he was pxecutive Secretary of the UN Economic Commis­ sion for Europe and Director of the Institute of International Eco­ nomic Studies, University of Stockholm. A recipient of more than thirty honorary degrees, at the beginning of his career he significantly contributed to (macro )economic theory and later has extended his interests to such fields as sociology, social and economic institutions, economic development, methodology, and critique of . A prolific writer, he is the author of more than fifteen books, including such classics as An American Dilemma: The Negro Problem and Modern Democracy; Asian Drama: An Inquiry into the Poverty of Nations, 3 vols; Beyond the Welfare State; Challenge to Affluence; and Against the Stream.

Yew-Kwang Ng is Professor of Economics, Monash University (Austra­ lia). He was a Visiting Nuffield Foundation Fellow, Nuffield College, Oxford; a Visiting Simon Senior Research Fellow, Manchester University; and a Visiting Professor, Virginia Polytechnic Institute. He is editor of Mathematical Social Sciences and of Social Choice and Welfare. He has written a number of papers in the areas of welfare economics, microeconomics, and microeconomic foundations of mac­ roeconomics and is also the author of Welfare Economics: Introduc­ tion and Development of Basic Concepts and Mesoeconomics: A Micro­ Macroeconomic Analysis. He has also contributed to Issues in Con­ temporary Microeconomics and Welfare and Issues in Contemporary Macroeconomics and Distribution.

Hukukane Nikaido, formerly at the Tokyo College of Science, Osaka University, and Hitotsubashi University, is Professor, Institute of Socio-, University of Tsukuba (). A Fellow XXVlll Notes on the Contributors

of the Econometric Society and several times Member of its Council and past President of the Japanese Association of Economics and Econometrics, he was Visiting Research Associate, Applied Mathematics and Statistics Laboratory (working in Arrow's project), Stanford University; Visiting Professor and Ford Foundation Faculty Research Fellow, University of Minnesota; Ford Foundation Rotat­ ing Visiting Professor, University of California (Berkeley); and Visit­ ing Professor, University of Southern California. He has made significant contributions to g.e.t. and has written a number of papers on game theory, growth theory, income distribution, and macroeco­ nomics. His books include Convex Structures and Economic Theory; Introduction to Sets and Mappings in Modern Economics; and Mono­ polistic Competition and .

Howard Raiffa is Frank P. Ramsey Professor of Managerial Eco­ nomics, a joint chair of the Graduate School of Business Administra­ tion and the Kennedy School of Government, Harvard University. A Fellow of the Center for Advanced Study in the Behavioral Sciences, a Ford Visiting Research Professor, Stanford University; and a Visiting Professor, , he has served as the Director of the Institute of Basic Mathematics for Application to Business and the first Director of the International Institute for Applied Systems Analysis, Laxenberg (Austria). He is a Fellow of the Institute of Mathematical Statistics, American Statistical Association, Econo­ metric Society, American Institute for Decision Sciences, Association for Public Policy Analysis and Management, and of the American Academy of Arts and Sciences. He is the recipient of the Medal of Arts and Letters of Austria, a Special Citation from the Soviet Academy of Sciences, and the 1984 Distinguished Contribution Award from the Society of Risk Analysis. He is a major contributor to statistical and risk and uncertainty. He has written more than ten books, including Games and Decisions (with R. D. Luce); The Art and Science of Negotiation; and The Logic and Psychology of Decision Making (with D. Bell and A. Tversky).

Steven C. Salop is Professor of Economics, Georgetown University Law Center. He was formerly associated with the Federal Trade Commission where he held several major posts at the Bureau of Economics. He is currently associate editor of the Journal ofIndustrial Economics and the International Journal of Industrial Organization. A Visiting Professor at MIT, he is the author of a number of papers in Notes on the Contributors xxix various areas, including information and antitrust, imperfect infor­ mation and product differentiation, advertising regulation and infor­ mation dissemination, strategic antitrust analysis, airline compe­ tition, exclusionary practices, and joint ventures.

Paul A. Samuelson, a master economist par excellence, is the first American Nobel Laureate in economic science, Institute Professor at MIT (and an 'institution' in his own right), and our protagonist in Samuelson and Neoclassical Economics. He has been President of the Econometric Society, the American Economic Association, and the International Economic Association. A recipient of the , the Albert Einstein Commemorative award, and more than twenty-five honorary degrees (including from the University of Chicago and Harvard University- his alma maters), he is a Corres­ ponding Fellow of the British Academy, a Fellow of the American Academy of Arts and Sciences, and a Member of the National Academy. An active consultant to many government agencies, Eco­ nomic Advisor to President Kennedy, and in 1964 Chairman of the President's Task Force for Maintaining American Prosperity, he was for nearly twenty years bi-weekly columnist for Newsweek magazine. His rich output of papers is now available in four volumes of The Collected Scientific Papers of Paul A. Samuelson. He is also the author of Foundations of Economic Analysis, Linear Programming and Eco­ nomic Analysis (with R. Dorfman and R. M. Solow), and of the most influential modern economics textbook, Economirs, now in its twelfth 'incarnation'.

Joseph E. Stiglitz is Professor of Economics, Princeton University. Formerly Drummond Professor of Political Economy, Oxford University and Professor of Economics, Stanford University and Yale University, he was Oskar Morgenstern Distinguished Fellow and Visiting Professor, Institute for Advanced Studies and Mathematics, Princeton; Visiting Fellow, St. Catherine's College, Oxford; Visiting Professor, University of Canterbury (New Zealand), and Tapp Re­ search Fellow, Gonville and Caius College, Cambridge. A Guggen­ heim and Fullbright Fellow, he is a Fellow of the Econometric Society and of the American Academy of Arts and Sciences and recipient of the John Bates Clark medal of the American Economic Association. A former associate editor of the Journal of Economic Theory and and American editor of the Review of Economic Studies, he is associate editor of and XXX Notes on the Contributors

Managerial and Decision Economics and co-editor of the Journal of Public Economics. He is the author of nearly two hundred papers in a very broad range of fields covering the economics of information, uncertainty (basic concepts, market equilibrium, risk and agriculture, portfolio analysis, and theory of corporate finance), theory of taxa­ tion, public economics, distribution of income and wealth, growth and capital theory, natural resources, development and trade, macro­ economics, and the theory of imperfect competition. He is also the co­ author of The Theory of Commodity Price Stabilization (with D. Newberry); Lectures in Public Economics (with A. B. Atkinson); and co­ editor of New Developments in the Theory of Market Structure (with E. Mathewson). He is currently finishing a textbook on public finance.

Koichi Suga, Lecturer in Economics, Asia University (Tokyo) is among the newest crop of social choice theorists. A graduate student of Kotaro Suzumura at Hitotsubashi University, he has also worked with Suzumura on a paper on Gibbardian libertarian claims revisited.

Patrick Suppes is Lucie Stern Professor of Philosophy and Director of the IMSSS, Stanford University. A holder of honorary degrees from the Universite Rene Descartes and the University ofNijmegen, he is a Fellow of the American Association for the Advancement of Science, American Psychological Association, and American Academy of Arts and Sciences; a Member of the National Academy of Education, International Institute of Philosophy, Society of Experimental Psy­ chologists, and the National Academy of Sciences; a Foreign Member of the Finnish Academy of Science and Letters; an Associate Foreign Member of the Societe Fran~aise de Psychologic; and a Titulary Member of the Academic Internationale de Philosophie des Sciences. He is past President of the Pacific Division, American Philosophical Association, American Educational Research Association; National Academy of Education; and International Union of History and Philosophy of Science. A prolific contributor in a wide range of fields from mechanics through mathematics, game theory, logic, probability theory to learning theory, philosophy and methodology of science, semantics, and education, he has written more than 250 scientific papers, a number of popular articles, several elementary mathematics textbooks. and edited nearly twenty books. He is also the author of fifteen books, including Introduction to Logic; Decision Making: An Notes on the Contributors xxxi

Experimental Approach; Axiomatic Set Theory; and Probabilistic Metaphysics.

Kotaro Suzumura, formerly at the Kyoto Institute of Economic Research, Kyoto University, is Professor of Economics, Hitotsubashi University. He was British Council Visiting Scholar, Faculty of Economics and Politics, University of Cambridge; Lecturer, London School of Economics and Political Science; and Visiting Professor, Stanford University. He is the editor of Economic Studies Quarterly (the journal of the Japanese Association of Economics and Econo­ metrics) and of Social Choice and Welfare. He has published a number of papers in welfare economics, social choice theory, theory of economic planning, industrial organization theory, and law, institutions and economic systems. Aside from books in Japanese, he is the author of Rational Choice, Collective Decisions and Social Welfare.

Jan Tinbergen, the first recipient (together with ) of the Nobel Memorial Prize in Economic Science (1969), is Professor Emeritus, Erasmus University- the former Netherlands School of Economics where he was Professor of Development Planning until 1973. He was also Claveringa Professor oflnternational Cooperation at Leiden University from 1973 to 1975. He was formerly Director, Central Planning Bureau, Netherlands Government and adviser to various governments and the United Nations on development prob­ lems. A recipient of some twenty honorary degrees and many other awards and prizes, he contributed vastly in the areas of econometric business-cycle research, economic policy and welfare economics, development planning, and income distribution. His many books include Statistical Testing of Business Cycle Theories 2 vols; Centrali­ zation and Decentralization in Economic Policy; Economic Policy: Principles and Design; Development Planning; Income Distribution: Analysis and Policies; and Mathematical Models of Economic Growth (with H. C. Bos). He is also a contributor to Issues in Contemporary Macroeconomics and Distribution.

John K. Whitaker is Professor of Economics, University of Virginia. Formerly Professor of Economics, University of Bristol, a Visiting Bateman Lecturer, University of Western Australia, and Honorary Research Fellow, Birkbeck College, University of London, he has served as President of the History of Economics Society and as xxxn assistant editor of the Review of Economic Studies. A foremost auth­ ority on Alfred Marshall, he has also written on business cycles and growth theory, capital theory, and . He is the author of The Early Economic Writings of Alfred Marshall, 1867-1890, 2 vols, and is currently editing two volumes of the correspondence of Alfred Marshall.

Oliver E. Williamson, formerly Charles and William L. Day Professor of Economics and Social Science and Director of the Center for the Study of Organizational Innovation, University of Pennsylvania, is Gordon B. Tweedy Professor of the Economics of Law and Organiza­ tion, Yale University. A Guggenheim Fellow and Fellow of the Center for Advanced Study in the Behavioral Sciences, he was also Peterkin Lecturer, Rice University; Visiting Professor, University of Warwick; Distinguished Visiting Professor, University of Kyoto; and Distinguished Visiting Scholar, Texas A & M University. He is a Fellow of the Econometric Society and of the American Academy of Arts and Sciences and co-editor of the Journal of Law, Economics, and Organizations. He is the author of numerous articles on managerial behaviour, industry structure, internal firm organization, transaction costs, antitrust, , imperfect competition, and welfare economics. A contributor to an alternative theory of the firm, he is the author, inter alia, of The Economics of Discretionary Behavior: Managerial Objectives in the Theory of the Firm; Corporate Control and Business Behavior: An Inquiry into the Effects of Organi­ zation Form on Enterprise Behavior; Markets and Hierarchies: Analy­ sis and Antitrust Implications. Preface

These two volumes are about the ascent, vicissitudes, and lacunae in the science and art of modern economics, and about Kenneth Arrow, his architectonic contributions to and impact on the theoretical and and moral and political philosophy of our age. They are about 'music in economics', about one of its truly creative composers, inspiring conductors, virtuoso instrumentalists and con­ structive critics. They are about Kenneth Arrow and some other makers of modern economic theory, both when they are right and when they are wrong, about their finished and unfinished symphonies; and about their glorious harmonies, strident dissonances, and false notes. (It is self-evident that it is easier to criticize than to create. Maugham reminds us that when one looks at a Mondrian painting one is tempted to comment how easy it seems; one could do it oneself, all one needs is a tube of red paint, a tube of black, and a ruler; he then challenges, 'try'!) These volumes are about the new era of accretion of economic knowledge and about the axiomatization of economic theory in many fields. They are in large measure about the flowering of general equilibrium theory (g.e.t.), its rich accomplishments, unresolved cen­ tral issues, and major 'scandals'; and about the quest, perils, feats, and failures in overcoming them. They are about the recent strides forward and they offer a glimpse of the future. 'Prediction is always difficult, especially of the future', to borrow a statement attributed by Arrow to John von Neumann. When many years from now scholars come to reckon and reassess Arrow's contributions and influence, they may approach the subject from a different perspective and shift their focus of emphasis. Nonetheless the picture that emerges from these pages firmly places Arrow among the giant master economists of all time. He contributed to changing the course of modern economics (and to some extent of political and moral philosophy) by a number of distinct intellectual innovations. However, the sum total of his impact far exceeds his specific contribu­ tions, extending as it does to the mode of analysis, way of thinking, formulation of problems, and to continually opening up new direc­ tions of research. Arrow shares in the extension, transformation, reformulation, refining, and generalization of received theory. But more importantly he is largely instrumental in influencing, reorient-

xxxiii XXXIV Preface ing, reshaping, and conceptually enriching the economics of our age. Not only is the economics of the second half of the twentieth century to a large measure associated with Arrow's name (either directly or indirectly, through a chain of derived work), but he is the fountain­ head of the new discipline of social choice.

INTRODUCTION TO THE TWO VOLUMES Within the (un)usual constraints under which any such study labours, we have tried to provide a comprehensive composite analysis of Arrow's approach and contributions to, and his impact on, modern economics seen from various vantage points, angles and perspectives and communicated in various forms. But no matter how hard one tries, how blessed one is with high quality collaborators, and how advantageous the division oflabour, an effort of such ambitious scope is perforce incomplete and imperfect. The scope of Arrow's work is so wide and his influence so far­ reaching, that even without presuming to cover the vast territory in all its multifaceted richness it soon became evident in planning this project that we would have to resort to two volumes in order to convey the dimensions of the Arrovian phenomenon. Various chapters in these volumes attempt to provide the essence of Arrow's contributions and his approach and way of thinking. Others are mirrors of the prodigious impact he has on the moving boundaries of economics and other social sciences. Still others offer alternative approaches to issues that form an integral part of Arrow's concerns. An important feature of these two volumes is the historical record and insights provided in the interview chapters- the commentaries and reflections of our protagonist and basically three groups of individuals: the makers of modern g.e.t., the younger generation of leading g.e. theorists and outstanding economists from other fields, and Arrow's colleagues who contribute to a composite picture of the man and scholar. A note ofwarning and 'bounded' apology: one of the drawbacks of the interview format is that the scope, direction, and emphasis of the coverage in part reflect the interests of the interviewer. One of the advantages of this format is its informality. It affords a privileged insight into the make-up of the interviewee, one that is rarely available in his written word, particularly if he is a strong 'devotee of the axiomatic method'. It affords a glimpse (and in some cases much more) of how his mind works. Remarkably it removes or reduces Preface XXXV many inhibitions or conventions that bind scholars in more formal discourse. Since there is much more to a s_9holar than the production of 'robust results', it is hoped that these interview chapters will provide the reader with insights into economic philosophy and into the sociology of the making of economics and will provide the young scholar with some inspiration. A special effort has been made to preserve the informality of the interviews. We have refrained from editing (subject to the required minor corrections) to preserve the flavour, style, and spontaneity of the dialogues. Still the reader is alas short-changed, for we cannot convey here the 'irreproducibles', such as the enthusiasm and dedi­ cation to the subject, the tone of voice, the intense concentration, the mode of reaction, the warmth, smile- and sometimes the disquietude of our interviewees. The reader will appreciate that in a study of an economist whose vision of the world is the general dependence of everything on everything else, the division of the material into two volumes is not without its perils. In a very essential sense there is a profound congruence in Arrow's work in g.e.t., statistical decision theory, and the theory of social choice. All three may be thought of as key component parts of system design. Grosso modo the developments in g.e.t. and beyond constitute the vast territory of Arrow and the Ascent of Modern Economic Theory- an inseparable basis for Arrow and the Foundations of the Theory of Economic Policy which takes us into the realms of social choice theory, welfare and distribution, resource utilization, and organization. It also takes us on an exploration of the man and scholar, his values, motivations, and perceptions- all so inextricably intertwined with policy prescriptions and instruments.

Arrow and the Ascent of Modern Economic Theory

The introductory chapter (1) to this volume sets the stage by placing Arrow's contributions in the prism of the potentials and limits of economic analysis. We attempt to guide the reader through and to analyze the vast territory of Arrow's contributions from his first significant accomplishment in the social sciences (thus, not counting his 'On the Use of Winds in Flight Planning')- the pathbreaking creation of social choice theory- through the making of modern g.e.t., to his contributions in applied g.e.t. More specifically the prologue to this chapter provides a brief characterization of Arrow's scholarly achievements and his impact on the development of eco- XXXVI Preface

nomics since the early 1950s. We then proceed to review 'new' welfare economics, and Arrow's extension of the fundamental theorems of welfare economics, and we draw the relationship between the social welfare function and social choice theory. In the next section we examine why it is only with the standard Arrow-Debreu model that g.e.t. came of age, and we examine the Arrow-Hurwicz contributions to stability of general models. The discussion then proceeds to the interrelationship between existence and effi­ ciency and some of the more recent extensions of g.e.t. The ensuing two sections concentrate on Arrow's fundamental contributions to uncertainty and information. The first highlights his contribution to the theory of individual choice under uncertainty, measures of , and his ingenious construction of contingent securities as a theoretical device for risk sharing. The second focuses on his percep­ tion of the role of information as a key to many unresolved problems in economics, on information as a commodity, on uneven distribution of information (derived from his study of the economics of medical care), on the economics of discrimination, and on Arrow's contribu­ tion to the centralization-decentralization debate. We then take the reader through Arrow's various contributions to production, capital, and demand theories, more specifically focusing on issues such as the optimal accumulation of capital and inventories, the process of learning, and innovations. Aside from information and uncertainty, an important common theme of these somewhat diffuse contributions is the recursiveness of optimization, captured in general mathematical form as dynamic programming or control theory. After a brief summing up that involves some methodological discourse, we digress to an Appendix that attempts to place Arrow and modern economics within the context of the dynamics of economic thought, discusses some criteria of evaluation of progress in economics, contrasts the W alrasian and Marshallian approaches, and provides some glimpses of Arrow as a historian of economic thought. Part I is an important historical record: an oral history by the makers of modern g.e.t. A word about its cast. In the preface to the second volume (on g.e.) of his collected papers, Arrow calls attention to Debreu, Hurwicz, and McKenzie as the 'major contributors' to modern g.e.t. The reader will have no difficulty in detecting the major 'flaw' in Arrow's listing-namely, the omission of his own name from this distinguished group of scholars who have been invited to share with us their recollections of and reflections on the creative genesis of their ideas and their perspectives on the development of the science Preface xxxvii and art of economics. We are grateful to the participants and share with Professor McKenzie his regrets at being unable to take part. Although the specific questions were tailored to fit the interests and expertise of particular interviewees, the basic line pursued here was aimed at eliciting the master economists' perceptions of how develop­ ments in modern economic theory have enriched our understanding of economic processes, the real meaning of progress in analytical techniques, the policy implications, some of the challenges to the mainstream and their specific contribution, and the direction in which economics is going. Whatever else needs to be said about the contents of this oral history, what emerges clearly is that the developments were not merely exercises in technical virtuosity (pyrotechnics), but provided fundamentally new economic insights; that the motivation, accomplishments, and concerns of the 'makers' were widely at vari­ ance with some common misperceptions; and that modern economic theorists are not smug- they are vigilantly aware of the remaining gaps, and in a world of exaggerated claims, they continually point to the limits of analysis and try to extend the boundaries of the potentials. In Chapter 2 Arrow answers a very broad spectrum of questions ranging from the creative genesis of his major contributions, through observations on developments in g.e.t. and on the evolution of economics in general, to the topics on which he is now concentrating, revealing in the process fascinating glimpses of his personality- a topic that in stricto sensu we pursue with Arrow in Chapter 23 of the companion volume. At the outset Arrow recalls how he came across the ideas of social choice and existence, how the joint paper with Debreu evolved, and characteristically he provides arguments on both sides of the question of centrality of the existence theorem. He discusses his contributions with Hurwicz on stability and then pro­ ceeds to more general and more specific questions of g.e.t., ranging from the advantages of g.e. thinking, through disequilibrium eco­ nomics; dynamics and historical time; and relationship with game theory, the need to extend g.e.t. to new contexts, in particular to im­ , incomplete markets, and asymmetric informa­ tion. Arrow also recalls the creative genesis of his contributions to uncertainty, production, and growth, and some of his applied work (particularly the economics of medical care). In fact he does not view theory as feeding on itself, but rather as generated by applied problems. He speaks of his growing caution and modesty with regard to the possibilities of synthesizing g.e.t., statistical methods, and xxviii Preface

social choice criteria into a form of economic planning. He offers us an insight into his own ordering of his contributions and some of his disappointments. He then proceeds to some general questions, includ­ ing the essence of the difference between economics and the natural sciences, realism of assumptions, a classification of the most import­ ant contributions in the last fifty years, partial equilibrium thinking, new classical macroeconomics, , and the large and small questions in economics. Arrow deplores modern economists' lack of interest in the important question of income distribution and in studying comparative economic systems. He believes that the most important economic contribution of the nineteenth century was the vision of the general economic interdependence and that our twen­ tieth-century vision has been altered significantly by the concept of of information- an idea whose consequences are not yet fully understood. Essentially imperfect competition and imperfect infor­ mation- which are closely related- are grounds for rather serious departures from neoclassical economics. His current interests center on communication and information gathering in private and collec­ tive spheres which he intuitively believes have deep implications for macroeconomics. Gerard Debreu's work has been an inspiration and model of ascetic elegance and rigorous thinking for the younger generation of theor­ ists. As the irrepressible noted in a review of Theory of Value: An Axiomatic Approach, Debreu deals only with definitive results; he does not speculate or share with the reader the wider implications of his work nor does he reveal his thought processes. We are fortunate, indeed, that in Chapter 3, Debreu allows us fascinating glimpses into hitherto hidden realms. It is an of this study and 'bounded' pleasure to show that Frank is 'strong' on analysis, but 'short' on prediction. Chapter 3 opens with ~ebreu's discussion of the centrality of the existence theorem and its essential meaning, not as a statement about the real world, but about the validity of the g.e. model; of the progressive weakening of the assumptions needed to prove existence; and of the intereaction between g.e.t., applied problems, and policy. He recalls the creative genesis of his work on the proof of existence and how, after their initial independent, essentially similar, discover­ ies, he and Arrow joined forces in what has come to be known as the canonical Arrow-Debreu model. Debreu muses on the advantages and disadvantages of being in a minority position such as that of mathematical economics in the early 1950s. He speaks of the exten­ sions of the g.e. model and of the progress in the last thirty-five years Preface xxxix which has been far beyond his expectations. He stresses that he tends to see theorizing in economics as being essentially mathematical in nature, but this does not mean that higher mathematics is essential to do good economic theory. In fact, there is a lurking danger of doing bad economic theory by using tools that are more sophisticated than needed. Debreu also reminds us that economists must always remain aware of the limits of what they can achieve. He does not believe that a general theory that will encompass the whole of economics will ever be available. He emphasizes that the most important things in economics are not specific topics or theorems but methods; that is, he believes that fifty years from now economic theory will have changed considerably, but the use of mathematical models, rigour, generality, and simplicity are here to stay. Debreu is currently interested in two broad avenues of research: I. further progress on the idea that one must make assumptions about the distribution of the characteristics of economic agents in order to explain the properties of , and 2. complexity theory which, he believes, may influence the economic theory of information. In the postwar period Leonid Hurwicz is identified as a leading system designer in the great tradition of Aristotle, More, J. S. Mill, and Lange. He is not only an erudite, technically sophisticated, and proverbially precise scholar whose first-hand insights illuminate the topics of Chapter 4, but he is also a warm and humorous raconteur who adds the human touch to otherwise perhaps dry subjects. The major theme of Chapter 4 is the stability of equilibrium, a crucial subject on which Arrow and Hurwicz so fruitfully collabor­ ated in many papers that later constituted a substantial part of their Studies in Resource Allocation Processes. Hurwicz recalls that their joint work brought them into contact with two strands of thought: 1. the work on stability primarily by Samuelson and Hicks, and 2. system design by Lange and Lerner. He reflects on their formulation of the notion of global stability rather thim the stability of a particular equilibrium point, on the comple­ mentarity of the work of Gale and Scarf on instability, and on the relationship of stability theory to business cycle theory. He also offers some fascinating insights into the creative genesis and development of the significant work on decentralized systems and incentives that he has done subsequently. He points out that the concept of g.e.t. that he uses in system design may or may not refer to a perfectly competitive xl Preface mechanism, and in his sense there is no conflict between game theory and g.e.t. Hurwicz both defends neoclassical theory from its critics and speaks of the need to go beyond. Part II focuses on the Arrovian vision and impact on the mathema­ tical method in economics and on applications of g.e.t. It opens with Chapter 5 where Bliss discusses the Schumpeterian concept of vision and distinguishes two aspects- namely, vision of facts and vision of meaning. After pointing to the difficulties of employing these concepts in analyzing the work of a living scholar, Bliss applies them to Arrow's work. He argues that Arrow views the economic problem as essentially a question of democratic economic planning. However, in its application this view is circumscribed by Arrow's understanding of the inescapable difficulties that stand in the way offormulating a clear and valid objective (the social welfare function) for economic plan­ ning, and by his strong conviction that real-life markets are very imperfect transmitters of information when compared with those that the planning problem requires. In Chapter 6, 'Mr Game Theory', , discusses economics and the mathematical method. He speaks of the methodo­ logical differences between game theory and g.e.t., of the influence of game theory on Arrow and on modern economics in general, and of mathematical economics and game theory as art forms. he also touches on rationality, co-operation, and the selfish motive and vividly illustrates the dualism within Arrow in this connection. Aumann compares economics to other sciences where falsifiability should not be used as a touchstone. Finally, he discusses some new developments in mathematics that may prove useful in eco­ nomics. Mas-Colell offers in Chapter 7 a perspective on development of g.e.t. from the vantage point of a leading mathematical economist one generation removed from Arrow-Debreu. Among the many issues he raises are the extensions of g.e.t. into new areas, the dramatic change in techniques of analysis- namely, the renaissance of differentiability and its implications for recent and future developments. Here emerges a fascinating and perplexing picture of the dynamics and dialectics of the development of economic science and the sociology ofknowledge. Mas-Colell also offers telling glimpses of the possible future path of development and the extent to which avant-garde mathematics shapes or conditions the development of economic theory. Another leading second-generation mathematical economist, Son­ nenschein, speaks of the 'Arrow era'. In Chapter 8 he stresses Arrow's conceptual contributions, but also reflects on the appeal of the Preface xli Arrow-Debreu methods to scholars of a rigorous or formal bent of mind and on the appropriateness of these methods to the investi­ gations to which they have been applied. He singles out the Arrow­ Hurwicz view that an allocation mechanism is very much an object of choice. He points to the diversity and pervasiveness of Arrow's influence on modern economics, from Lucasian business cycle theory to medical economics. Sonnenschein also reflects on the creative genesis of his initial argument, suggesting that aggregate demand functions are not restricted by the conditions that the individual demand function arise from utility maximization. The characteriza­ tion theorems have in some ways blown away myths and changed theorizing. He also speaks on more general questions- namely, the importance of the existence theorem, the subsequent extensions of g.e.t., and the stronger rationality and computability attributed to economic agents in game theory. And finally he addresses himself to much broader issues, such as the differences between economics and the natural sciences, the realism of assumptions, criticism of mathe­ matical economics, and large v. small questions. Arrow's contemporary and colleague at the Cowles Commission, the distinguished master builder of macroeconometric models, Law­ rence R. Klein (a phenomenon in his own right) vividly recalls in Chapter 9 the intensive work at Cowles in the late 1940s on macroeco­ nometric model building and the insistence that everything done in that connection be firmly based on economic theory. Macro­ economics at Cowles was an integrated branch, closely tied into the whole programme. Marschak insisted that a bridge be built between micro and macroeconomics. The star-studded team soon fell apart as the early model did not perform satisfactorily. However, the later stages in the development of the macroeconometric models that Klein describes for us were fundamentally set on the basis of that early experience. He points to the usefulness of the existence proof for macroeconometric model building, to the great accomplishments of Arrow and Debreu in clarifying the meaning of the price system, and to the applicability of the Arrow-Hurwicz contributions on stability to problems that preoccupied builders. Klein contrasts his approach to the aggregation problem (from micro to macro), derived from his experience at Cowles, with Samuelson who says that one should take the macroeconomy as it is and not to try to derive it as an analogue of optimizing. Klein emphasizes the strong imprint left on him by the Walrasian 'Cowles-way' of thinking about the economy in terms of an interrelated system. Part III, on the theory of resource allocation, provides in the first xlii Preface chapter a historical introspection from the pen of a participant in the development of modern g.e.t. and in the ensuing chapters some attempts at solving pressing open questions. It opens with Negishi's discussion of the non-existence of equilibrium (Chapter 10). He notes Arrow's remarkable contribution to the proof of existence of an equilibrium for a competitive economy. The necessity of proving existence becomes clearer in the face of the case where no equilibrium exists, even though indifference curves, production functions, and the like are fairly well behaved. Negishi points to W. T. Thornton's On Labour ( 1869) as containing the first examples of the non-existence of equilibrium. He considers these examples quite remarkable in the sense that they spring from the discontinuity of demand curves, since other unsuccessful attempts to show non-existence of equilibrium failed because of their assumption of continuity. However, these examples, as well as that of Wald, are unsuccessful attempts at showing the non-existence of equilibrium, if we consider not the Walrasian tatonnement with recontract, but the non-tatonnement without recontract. From such a non-tatonnement point of view, a truly important example of the non-existence of equilibrium is the one provided by Arrow; that is the case where a Pareto optimal allocation cannot be viewed as a competitive equilibrium. Building on the canonical Arrow-Debreu model, in chapter 11 Wilson takes a first step in the construction of a for a simple model of a bid-ask market. The main result he establishes is that a generalization of the constructed by Peter Cramton for bilateral bargaining satisfies at least the necessary conditions for an equilibrium of the multilateral trading model. Such an equilibrium could be interpreted as an endogenous process of matching buyers and sellers, in which their impatience for trade derives from pressure from other traders who are competing for the opportunity to transact; in turn, as in the work of and in related work on auctions, their relative impatience determines the terms of trade. A key feature is that delay in offering or accepting a serious bid or ask is a trader's main signal about his private information. The proposed equilibrium provides predictions about the proportions of gains from trade that would be realized and about the series of prices that would be observed. The g.e. analysis of imperfect competition is an area in which Arrow's contributions have been central. It is also an area whose development he considers crucial. However, despite the subject's fundamental importance, it has recently received little attention. In Preface xliii

Chapter 12 Roberts focuses on the example of an economy in which firms set prices for all the goods in which they are interested (except the numeraire) recognizing how consumers' optimizing resource­ supply and product-demand decisions are influenced by these choices and by the that will occur if their choices do not balance. He obtains an explicit solution for the imperfectly competitive general Nash equilibrium. This equilibrium exhibits properties that are quite different from what one would intuitively expect on the basis of partial equilibrium analysis. Roberts suggests interesting extensions in the future. In the following chapter (13) Pratt and Zeckhauser pick a theme illuminated both by Arrow's social choice theory and his contribu­ tions to the proof of existence and to major issues of welfare economics. It is a theme also related to market performance in the presence of such market imperfections as externalities and asymmet­ ric information. In broad terms Prati and Zeckhauser are concerned with problems involving externalities, uncertainty, private infor­ mation, and differing objectives among players, making team theory inapplicable, dictatorship and other 'pinning' mechanisms inadequa­ tely informed, and laissez-faire also inefficient. Efficiency may still be achievable if appropriate financial incentives can be created to induce agents to take actions that are optimal for the group. The incentives they consider are transfer payments that may take the form of penalties, subsidies, compensation, taxes, and the like. Their central question is: under what circumstances can a group, using incentive­ based decentralization, achieve as high an expected value as a team? They observe that in a surprisingly general class of circumstances, a group of self-interested agents, observing private information and sending signals that may not be verifiable, relying solely on incentive payments to guide their actions, can do as well as a fully co-operating team with identical communication possibilities. The payments, which can be required to balance across agents, are designed to provide each agent with a monetary incentive equal to the expected externality conveyed to the group by his actions, including the signals he sends. For such incentives to be implementable, it is sufficient that each element of each agent's information either become public, be signalled by him, or be independent of the information of others; and his non-public information cannot affect another agent's value. The result obtained by Pratt and Zeckhauser applies to multistage situa­ tions. They illustrate the mechanism with a pollution-control ex­ ample. xliv Preface

Discrimination entails the efficiency and equity of an entire eco­ nomic system. In Chapter 14 Wan studies job discrimination caused by asymmetric information. His findings complement the Arrow­ Phelps theory of statistical discrimination. His approach can be traced to the concept of that Arrow propagated in economics. According to the statistical discrimination theory, unin­ formed firms judge the worker's human capital by race or sex, and those who suffer such bias will accumulate less human capital, thus completing the vicious circle. It is a model with an evil system, but without any evil people. In contrast, Wan assumes that workers enjoy private information regarding their effort in a random production model. Effort makes more of a difference in some jobs than in others. Profit-seeking firms offer incentive-compatible contracts including 'no-shirking' bribes. The size of the latter may differ from job to job. Firms may thus allot better jobs to their favourite workers. Only legal sanctions can assure equal treatment for equally qualified workers. The starting point of Chapter 15 is Arrow's persistent concern with establishing the consistency of models that imply full utilization of resources with those that permit underutilization (e.g., Keynesian models). Reder claims that underutilization of resources does not always imply involuntary of labour. He argues that the degree of resource utilization varies with transaction costs and indicates the extent of failure to realize potential gains in productive efficiency through further specialization in order to avoid transaction costs. Under interesting though restrictive assumptions, Reder shows that transaction costs can be raised or lowered by exogenous varia­ tions in the level of effective demand. Hence exogenous increases in effective demand increase the degree of resource utilization. Chapter 15 is concerned with models in which all but one market clear in each period with zero transaction (defined as equal to search) costs. The 'other' market also clears, but requires use of search time to do so. If the other market is the labour market, there will be search unemploy­ ment in equilibrium with the level of employment varying with the level of effective demand. But if the other market is the market for goods, there will be no unemployment although output and the degree of resource utilization will nevertheless vary with level of effective demand. In principle, underutilization of resources thus reflects deficiency of aggregate demand but does not imply failure of the labour market to clear. In the real world, of course, unemployment is intimately related to the level of effective demand, but Reder con­ siders Keynes's attempt to identify less than full resource utilization Preface xlv with the pecularities of the labour market as misguided for it created an unnecessary theoretical problem. In the final chapter (16) of Part III Dasgupta and David take an information-theoretic approach to the economics of science, extend­ ing Arrow's pioneering analysis of the allocation of resources for industrial research and invention. They address the question: is there a valid economic distinction between scientific and technological research, and if there is, what implications may this have for public policy? A brief review points to deficiencies in several of the criteria proposed for distinguishing 'scientific' from 'technological' research, such as the degree of generality, abstractness, or practicality of the knowledge sought, or the source of the financial support. They suggest that a primary differentiation arises between science and technology conceived as social constructions, and is manifested in the greater urgency shown by the 'scientific' community towards the disclosure of newly acquired information. Scientists, qua scientists, may be thought to be devoted to the growth of the stock of knowledge as a public consumption good, whereas the technological community is concerned with the flow of rents that private parties derive from discoveries and inventions. From this perspective, Dasgupta and David reconsider the role of priority as a basis for allocating rewards among scientists, its compatibility with the norm of disclosure, and the ambiguous status of patent systems. Certain ineluctable conflicts between the goals of the two research communities point to the persisting economic need for public subsidies to sustain the scientific attitude. Decision making under uncertainty is the large theme of Part IV. In the opening chapter (17) Harsanyi deals with the Arrovian question of attitudes towards risk. He asks: in what sense do people's von Neumann-Morgenstern (vNM) utility functions express their atti­ tudes towards gambling? He distinguishes intrinsic attitudes towards gambling, as determined by taste or distaste for the process of gambling itself, from instrumental attitudes towards gambling- that is, willingness or unwillingness to gamble for the sake of the prizes­ as determined by the relative importance assigned to these prizes and to the stakes at risk. Harsanyi argues that axioms of the vNM utility theory completely restrict the vNM utility functions to representing instrumental attitudes towards risk taking and prevent them from representing intrinsic attitudes towards gambling. It has often been claimed that vNM utility functions are morally irrelevant and, therefore, have no place in welfare economics and in ethics, a theme xlvi Preface also discussed by Hammond in Chapter 4 of the companion volume. This would be true only if these utility functions measured intrinsic attitudes towards gambling. But, in fact, they measure instrumental attitudes towards gambling and, therefore, measure the relative importance assigned to various , information that is of obvious moral significance. Accordingly, Harsanyi argues, vNM utility functions have a perfectly legitimate role in welfare economics and in ethics. In Chapter 18 Brock proposes a new theory of price forecasting. He discusses the normative implications of Bayesian decision theory for 'rational' price forecasting and then the normative theory of price forecasting. This theory is based on Arrow's characteristization of general equilibrium under uncertainty via contingent commodities and contingent prices. Central to the theory is the concept of a forecasting model in 'stochastic structural form'- a probabilistic generalization of structural form microeconomic models. The model determines endogenously a probability distribution on price. The prices are called Arrow-Bayes prices. Brock then contrasts the Arrow-Bayes model with familiar econometric forecasting models, in particular Bayesian structural models that he criticizes for their linearity as well as the epistemology of their underlying information sets, in particular their inability to capture the true variance ('riski­ ness') of prices in a forecasting context. Brock studies the estimation of Arrow-Bayes forecasting models by means of an 'expert-system' of the kind postulated in the new field of artificial intelligence. In conclusion, he discusses some insights gained from implementing the Arrow-Bayes models which have been helpful in explaining the observed volatility of the prices of copper and of the US dollar. The following chapter (19) generalises some of the insights by Arrow and Green and is part of a large literature on the economics of uncertainty that owes much to Arrow's work in the field. In particu­ lar, Bray and Kreps study models in which agents are unable to form as usually understood, because they are ignor­ ant of certain parameter values. The authors make the very demand­ ing assumption that, this ignorance apart, agents fully understand the workings of the model, including the usually non-stationary dynamics induced by learning and forecast feedback, and learn about the model in an optimal fashion, using a correctly specified likelihood function which amounts to assuming a more general rational expectations equilibrium than usual. They show that this assumption and the Preface xlvii

Martingale Convergence Theorem imply that beliefs converge with probability 1 and will not converge to an incorrect conclusion. In a market model, where the underlying structure of the economy is stationary, trades are continuous in beliefs and the rational expec­ tations equilibrium is unique, this result implies convergence to rational expectations equilibrium in the usual sense. Continuing along the theme of Arrow's contributions to decision making under uncertainty which have provided a foundation that is now standard in monetary and , Friedman and Roley provide three conclusions related to the three sections of Chapter 20: first, asset demands with the familiar properties of wealth homogeneity and linearity in expected returns follow as close approxi­ mations from expected utility maximizing behaviour under the as­ sumptions of constant relative risk aversion and joint normally distributed asset returns. Second, although such asset demands exhi­ bit a symmetric coefficient matrix with respect to the relevant vector of expected asset returns, symmetry is not a general property and the available empirical evidence warrants rejecting it for both institutio­ nal and individual investors in the US. Finally, in a manner analogous to the finite maximum exhibited by quadratic utility, a broad class of mean-variance utility functions also exhibitis a form of wealth satisfaction that necessarily restricts its range of applicability. In Chapter 21 Kuenne draws upon Arrow's seminal work in the theory of risk bearing to analyze the oligopolistic firm's bidding decision in a government tender. He abandons the comfortable assumptions of competitive bidding and probes into the interfirm expectations using subjective probability, one of Arrow's early advo­ cacies. He uses a Weibull distribution to approximate the shapes of firms' density functions for winning, and investigates the existence of an bidding rent or surplus in firms' bids. He examines the expected behaviour of bid prices and oligopoly rents when shifts in firms' expectations of winning occur and government furnished information is provided. He also obtains expressions for the expected value of information to the firm when privately acquired. It is fitting to conclude this part with a chapter (22) where Townsend argues that the Arrow-Debreu model, extended to include Arrow's celebrated construct of contingent securities, is rich in empirical implications both directly on its own and indirectly by having stimulated contributions that seek to explain otherwise ano­ malous observations. xlviii Preface

The foregoing is much enhanced by Arrow's reflections on those chapters that do not specifically assess his work, presented in Part V as a conclusion to this volume.

Arrow and the Foundations of the Theory of Economic Policy

The introduction to this volume consists effectively of two chapters: the first (lA) focuses on Arrow's development as an individual and scholar, his values and overriding social and economic concerns and the second (lB) examines his unique creation of the theory of social choice. It is hoped that Chapter lA complements and sheds further light on Arrow's more technical contributions explored in Arrow and the Ascent of Modern Economic Theory, at least for those readers who believe that biography matters. More specifically, Chapter lA traces Arrow's family background and early socio-political outlook. It takes us through his undergraduate and graduate education and the forma­ tive influences of the environment at the Cowles Commission and Rand Corporation. An attempt is then made at brushing in bold strokes the vivid characteristics of the man and scholar, followed by an exposition of his view of the human interaction as tension between personal and social values and their confrontation with limited opportunities. We then proceed to examine Arrow's perception of design and redesign of organization as a supplement to, or improve­ ment of, the existing system. The two final sections of this chapter deal with the Arrovian concept of freedom, equality and democracy and his abiding interest in and concern for distributive justice. It is only appropriate to follow an exposition of Arrow's writings on the concept and desirability of distributive justice by a chapter on the means that can be used to achieve this end. And it is only fitting that Chapter lB is written by Peter Hammond as an assessment of Arrow's work in social choice and of some recent developments. Hammond perceives Arrow's question to be: is there some acceptable middle ground between the Condorcet paradoxes and the ethical repugnance of an extreme dictatorship? He asks: What Arrow social welfare functions satisfy the Pareto condition and independance of irrelevant alternatives and are also non-dictatorial? Arrow's disquiet­ ing answer is: None. Numerous escape routes from Arrow's theorem have been devised and Hammond stresses relaxation of Arrow's independence condition to one that he calls the independence of irrelevant utilities, appropriate for Sen's powerful notion of the social Preface xlix welfare functional. But this route is not entirely satisfactory, either. It leads to fundamental questions regarding the very nature of the 'alternatives' to be considered in the independence of irrelevant alternatives condition- questions quite new to social choice theory. In Hammond's words: 'Arrow has led us to an enormous mountain and helped us to great heights. Every time we think we are reaching the summit, however, yet higher and higher peaks appear in sight over the ridge immediately before us'. It is our good fortune to have such a knowledgeable guide as Hammond on such a remarkable adventure. Part I deals with social choice and utilitarianism and with attempts at breaking through the confines of the Impossibility Theorem. In the opening chapter (2), Gibbard provides a fundamental discussion of utility used in social choice theory. This chapter is related to Arrow's critique of utilitarianism which, according to Gibbard, has brought to moral theory the full force of the ordinalist revolution in economics. Gibbard interprets Arrow as holding out hopes for an ordinal utilitarianism, without settling firmly in favour of a particular ver­ sion. As Arrow shows, under some specific conditions, even the minimal content of the Pareto principle yields strong results. It is this minimal content of ordinal utilitarianism that Gibbard explores in this chapter. He argues that preference orderings are no substitute for happiness in moral theory; happiness has a moral significance that preference orderings lack if they are understood in a sense that satisfies the austere canons of operationalism. However, if preference orderings are understood epistemologically more liberally, quantita­ tive notions of an individual's good should be admissible by the same standards. Gibbard then contends that there is no good reason to constrict utilitarian theory with ordinalistic restrictions. Chapter 3, by 'one of the greatest economic theorists of all time' (to use Arrow's words), , was sparked by Arrow's 1985 Tanner Lectures at Harvard. Samuelson points out that deduced ethical rules of any plausibility are usually explicit or implicit sym­ metry arguments, for example, the Vickrey-Samuelson-Lerner defense of egalitarianism when each of a group of egoists joins in a unanimous vote for equality under the supposition that all are subject to asymmetric probability distribution for high or low incomes- a demonstration that can be freed of the 'expected-utility dogma'. Further, he shows that (1) by contrast, the 1955 Harsanyi proof (that an interpersonal social welfare function must be Bentham-like, strongly separable and additive) rests squarely on the 'expected-utility dogma'; (2) Rawls's or 'difference' principle is gratuitous in Preface

the sense of being able to command a unanimous vote against itself by normal people with less than infinite risk aversion; and (3) Varian's definitions of fair allocation are capable of deviating from optimal feasible configurations and involve implicit symmetry commitments. Samuelson stresses that where asymmetries obtain in the real world (as between sexes or species), notions of sympathy (where one may have to envisage being either a man or a woman or a cockroach and a human) are invoked as the straw out of which the bricks of definite ethical mandates are to be deduced by contrived symmetry syllogisms. He uses an example of rock bottom simplicity, involving a handful of states of the world and a few atomic egoists, to exposit a rich and restrictive calculus of revealed ethical preference. This provides him, inter alia, a reason to doubt the attractiveness of the familiar axiom of Independence of Irrelevant Alternatives. In Chapter 4 Hammond takes up the challenge of Arrow's social choice paradox, suggesting that it may not be insoluble. His approach involves using cardinalization of both individual and social welfare measures based on behaviour in risk taking situations. He argues that this approach can be justified by analyzing sequential decisions in decision trees. The major part of this chapter proceeds through several logical steps to derive a form of utilitarianism closely akin to Vickrey and, more especially, Harsanyi, while the latter part considers how the contradictory postulates of Arrow's Impossibility Theorem can be modified to accommodate this form of utilitarianism. Ham­ mond concludes that Arrow's social choice theory can be reconciled with an 'ideal' version ofHarsanyi's 'fundamental' utilitarianism, but at three very significant costs: 1. the independence of irrelevant alternatives must be weakened to, say, independence of ethically irrelevant mixed consequences; 2. the fundamental individual norm must be dictated in the event of unresolvable differences of opinion over what it should be; and 3. consumer sovereignty must be abandoned if attitudes to risk and tastes for gambling are not to be the arbiters oftrade-offs between total income and equality. In the next chapter (5) Kemp and Ng interpret Arrow's contro­ versial independence-of-irrelevant-alternatives condition as equiva­ lent to three subconditions: individualism, independence, and ordina­ lism. Individualism requires that social ordering depend only on individual preferences. Independence requires that the social ordering of any subset of alternatives depend only on information pertaining to these alternatives. This is compelling due to the mutually exclusive Preface li nature of social alternatives. Ordinalism rules out information on the intensities of preferences. They also interpret the Bergson-Samuelson tradition of writing social welfare as a function of individual ordinal utilities as implying all three subconditions. Since the other conditions of Arrow's Impossibility Theorem (weak Pareto principle, freedom of individual orderings, and non-dictatorship) are also accepted by the Bergson-Samuelson tradition, the latter, according to Kemp and Ng, is subject to Arrow's theorem, and the Little-Samuelson rejection of Arrow's theorem as irrelevant to welfare economics becomes itself irrelevant with the impossibility propositions of Kemp, Ng, and Parks within the framework of a fixed set of individual preferences. Kemp and Ng consider the admission of interpersonal comparable cardinal utilities (rejecting ordinalism) as the only reasonable way to have a consistent social welfare function, and show that the recent attempts by Samuelson and Mayston to defend ordinalism are unsuccessful. There is a manifest relationship between the ideas presented by Suppes in Chapter 6 and Arrow's fundamental work on social choice. More specifically, Suppes sets himself the task of presenting an explicit axiomatic theory of freedom maximization. The judgements of freedom required in the theory are concerned with comparisons of different sets of decisions. One set is preferred in the sense of freedom to another if it seems to offer greater freedom of choice. Suppes argues that it is a mistake to always look for a utility function either of individuals or societies. In many situations we want to retain freedom of choice in a direct sense. The theory he develops here is for the individual, but he also provides extensions to methods of aggregation. Because the axioms lead to strong measurement of freedom prefer­ ences- namely, a ratio scale- multiplicative aggregation rules related to the Nash social welfare function can be used. This is followed by Chapter 7 where Suzumura and Suga show how the abstract social choice theory may be construed as a useful and practical framework for examining the role played by moral princi­ ples in resolving social conflicts. They shed further light on the philosophical and distributive implications of the paradox of social choice. For brevity's sake they confine their attention to a Pareto libertarian paradox a Ia Sen and Gibbard, and concentrate on the role played in this context by the so-called 'Golden Rule' of the Gospel: 'Do unto others as ye would that others do unto you'. They formulate two alternative interpretations of this rule in the social choice framework each of which is successful in resolving the two-person example of the paradox in question. These alternative interpretations are, however, divergent: the first version fails to provide generally a lii Preface

resolution for this class of paradoxes, whereas the second, when generalized, leads to a general possibility theorem. The point of this exercise lies not in the (in)appropriateness of the Suzumura-Suga interpretations of the Golden Rule, but in the claim that the general workability of a moral principle in resolving social conflicts may be formally established by constructing choice with unlimited applicabi­ lity. This part concludes with Chapter 8 where Myrdal- the grand old critic of mainstream economics- perceives welfare theory, with its foundations in utilitarian moral philosophy and steeped in hedonistic associational psychology, as developed by the first generation neoc­ lassical economists at a time when both these foundations ceased to be fully accepted by professional philosophers and psychologists. He dates the apparent isolation of economics from other social sciences from about that time, and challenges modern economists for forget­ ting that welfare theory is founded on obsolete moral philosophy and psychology, for remaining insular, out of touch with developments in other social sciences, and for not conducting realistic psychological and sociological research about economic behaviour. Myrdal also argues for recognizing the value frame of research in order to clear the scientific investigations as much as possible from distorting biases, and for the development of a psychology and sociology of social sciences and scientists. It is a distinct privilege to open Part II on welfare and distribution with Chapter 9 where Tinbergen revisits the optimum order in an attempt to clear up the ideological rhetoric that surrounds the far from pure forms of capitalism and socialism in the world today. An important feature of his approach is that for him the set of institutions is the fundamental unknown of the optimal social order and that more than one solution can exist- an approach that is so characteris­ tic of Arrow's work as well. While the search for an optimal mix of centralization and decentralization and growth rates continues, here Tin bergen sets himself the task of providing a theoretical frame as a basis for quantitative empirical research. He is concerned with the variables to be used for analysing the operation of national and the much less developed supranational institutions (such as production units, schools, health care centres, markets, and public agencies) and the roles they play in optimizing the population's welfare. The variables determining human welfare imply the quantities of (material and non-material) goods and services consumed. Tinbergen dis­ tinguishes between private and collective goods, and discusses pro­ ductive effort and abilities on which human welfare depends. He Preface liii derives the optimal social order from the maximization of the social welfare function under a number of restrictions (e.g., production functions and budget constraints). Tinbergen favours measurability of social welfare along Pigovian lines and advocates a specific way of performing the measurement. In Chapter 10 Salop and Stiglitz pick up two central themes of Arrow's work: information and welfare. The analysis of welfare economics in the presence of imperfect information is a subtle and difficult matter. It is clear that the standard proofs do not apply directly; it is also clear that economies with imperfect information will in general not perform as well as economies with . The authors construct a simple model that allows them to address the question of whether an improvement in information improves wel­ fare. They specifically take into account not only the direct effect of the better information, but the indirect effect; since information affects demand curves, market structure will change with a change in information. They show that though increased information may lower welfare, as a result of increased market power, 'normally' an increase in informative improves welfare for two reasons: the direct effect, plus the indirect effect from effective competition. Moreover, if obtaining information is costly, increased product diversity may lower welfare. Chapter 11 deals with g.e. in the context of indivisible goods, hence where several standard g.e. hypotheses are not satisfied. Maskin shows, however, that the classic Arrow-Debreu techniques can be suitably modified to overcome this difficulty. More specifically, he is concerned with the existence of fair allocations with indivisible goods- that is, an allocation of goods across consumers is fair if no consumer prefers another's consumption bundle to his own and if it is Pareto efficient. When preferences and goods are well-behaved, one can establish the existence of a fair allocation in a pure exchange economy by simply observing that a competitive allocation is fair when agents have the same initial endowments. Naturally the same method of proof can be tried when goods are indivisible. To give agents equal endowments, it may be necessary to assign them fractio­ nal shares of some goods, which in itself causes no conceptual difficulty but which, unfortunately, may not generate a competitive equilibrium. Indeed, a fair allocation itself may not exist unless a certain amount of a perfectly divisible good is also available. In Theorems 2 and 3 Maskin shows that, given enough of the divisible good, an equal-endowment competitive equilibrium (possibly includ­ ing a system of taxes and subsidies) exists, and so hence does a fair liv Preface allocation. The proof relies on the standard Arrow-Debreu technique of choosing prices that maximize the value of aggregate excess demand and finding a fixed point of the cross product of this correspondence and excess demand. In Chapter 12 Atkinson and Bourguignon pursue the subject of distributive justice- a subject that has been at the heart of many of Arrow's contributions, and one in which he maintains a constant interest. The treatment of differences in needs in assessing economic equity arouses very different reactions: some people regard such differences as grounds for rejecting any analysis of income inequality; others simply apply equivalence scales to reduce the analysis to a single variable (income per equivalent adult). Neither is fully satisfac­ tory, and in this chapter the authors seek to follow an intermediate path. They derive criteria that can be used to make comparisons of distributions of income where there are differences in needs. They explore how these criteria, and the extent of the ranking that they permit, depend on social judgements about needs. The resulting procedure is easily implemented and is analogous to the construction of Lorenz curves. Also on the subject of income distribution, Chapter 13 focuses on the social welfare function. Chipman assumes individual preferences to be homothetic, and represented by continuous, concave, and strictly quasi-concave utility functions that are positively homo­ geneous of degree 1. He also assumes the social welfare function to be an increasing, concave, and continuously differentiable function of the individual utilities. Then a necessary and sufficient condition that the optimal proportionate distribution of income among individuals be fixed, independently of prices, aggregate income, and individual preferences (subject to the above restrictions), is that the social welfare function be an increasing, continuously differentiable func­ tion of a weighted geometric mean of the individual utilities, with exponents equal to the distributive shares. Fairness is the theme of Chapter 14, which is so much in the spirit of Arrow's long-standing concern with issues relating to social justice and with those relating to pure economic efficiency. Baumol and Fischerexamine the fairness properties of Pareto- optimal differentia­ tion between peak and off-peak period prices. They show that in the classical model of this issue in which higher peak pricing is adopted merely to induce demand to shift towards off-peak periods, thereby on resources needed to construct capacity, the is likely to be incrementally unfair in the sense that while off-peak users are likely to benefit, peak users must be harmed in a wide variety of Preface lv circumstances. However, they also point to and explore several systematic exceptions. They then turn to the more interesting case in which high-peak-period use creates disutility for the users, and show that here efficiency may well require higher prices in periods of lower use, and that this can yield benefits to all affected parties. In Chapter 15 Tinbergen deals with empirical specification of inidivual welfare functions- a task that is related to Arrow's path­ breaking theoretical work on social choice. Aware of the 'multivar­ iate' structure of welfare, Tinbergen concentrates, however, on the economic treatment and considers two groups of welfare determi­ nants: those related to consumption and those related to productive effort. While he does not dwell on the details of consumption, he is concerned with the characteristics of productive effort (ability and schooling). There is much to Keynes's argument that economic theory does not provide a body of settled conclusions immediately applicable to policy; rather it is a mode of reasoning that helps the possessor to draw the correct conclusions. Part III encompasses contributions to themes that have pervaded Arrow's economic thought and writings, but that have not been at the heart of his theoretical innovations. They include his concern for unemployment, cyclical fluctuations, resource utilization, and specific policy recommendations. In the opening chapter (16) Nikaido models and works out the dynamics of growth cycles of a capitalist economy. He does so on the basis of two views: I. is the recognition that actual unemployment is to a considerable extent involuntary, so that monetary magnitudes retain some of their traditional importance for the analysis of short-term eco­ nomic fluctuations- a view that Arrow also holds-contrasted with the view that only real magnitudes matter, a view that is defendable only if the labour market (and all other markets) are assumed to clear at all times. 2. is the negation of the modern dichotomy of treating separately fluctuations as short-term phenomena and growth as evolution of supply capacity in the long run, free of fluctuations. Actual growth occurs through fluctuations, while growth gives rise to fluctuations. Growth and fluctuations are so interrelated that they are mutually causes and effect. In Nikaido's model output is determined by effective demand originating in intended investment within the supply capacity, depending on the existing capital and labour. The intended investment is governed by the capital-labour ratio and the excess of the profit rate over the equilibrating the money lvi Preface market. The saving thus determined results in actual investment, from which ensues capital accumulation. The supplies oflabour and money grow steadily at given constant rates. These are modelled to a dynamic process in which growth and fluctuations are interrelated, and their entanglement generates the evolution of the system. The process generates an undamped cyclical growth. Chapter 17 contributes to the discussion of the scientific viability of the life-cycle hypothesis, contrasts it with the intergenerational equili­ brium theory of family behaviour, and offers a clarification of the theoretical foundations of the social security controversy. Kurz reports on the results of a statistical test in which both the life-cycle theory and the effects of social security and private pensions on family savings were evaluated. The analysis is based on a new and most comprehensive data file compiled from a random sample of families in the USA taken in September 1979 by the President's commission on Social Security. This chapter discusses two broad tests of the strict life-cycle hypothesis: the prediction that a rise in social security wealth depresses private savings, and the predited 'hump' savings and implied age-asset profile. Kurz concludes that Feldstein's original analysis of the effect of social security on personal savings has not been borne out by subsequent research. Also studies of the age­ wealth profile yield results that contradict the life-cycle hypothesis due to its rieglect of the questions ofintergenerational transfers and of the mystique of accummulation of wealth and power flowing there­ from. Kurz believes that neither the life-cycle nor the intergeneratio­ nal hypotheses can provide a uniform view of behaviour of the entire population. The diversity of behaviour has to be recognized in formulating an appropriate theory of savings. In Chapter 18 Allais attempts to clarify the concept of the money supply and to analyze the process by which the credit mechanism creates money and purchasing power, considering time as well as demand deposits and the link between the creation of money, growth, and income distribution. He provides an analysis of the banking system taking account of the maturity breakdown of assets and liabilities. He then shows that, like the notion of desired cash balances, the cash balances held (i.e., the money supply) is a psycholo­ gical notion whose usually considered magnitudes are approximate indicators only. This analysis is based on the notion of rates of substitutability. He relates the creation of purchasing power by the credit mechanism to the proposition that the purchasing power created is represented by the discounted present value of the interest corresponding to the created. Allais also analyses the Preface lvii conditions implied by a reform that would remove the major flaws of the existing credit system. The main text of this chapter is illustrated in special notes by some comments on the world economy and the US economy in 1984, in relation to the potential instability of the whole national and international banking system. Part IV provides alternative outlooks and commentaries on sub­ jects that are very closely interwoven with Arrow's concept of the organization. More specifically, the central arguments of Arrow's Limits of Organization are set out in Chapter 19. Whitaker considers these and related aspects of Arrow's work in the context of intellec­ tual developments in economics of the past twenty years. He suggests that Arrow's view of organizations as evolutionary and adaptive, due to constraints on the receipt and processing of information, offers an alternative paradigm that unfortunately has not been followed up by economists. In Chapter 20 Williamson emphasizes how influential Arrow's contributions to the study of complex economic organizations have been on the development of the new institutional economics. He shows that Arrow's interests in the institutional attributes of market and non-market modes of organization are of long standing, endur­ ing, and reflect an awareness of the limits of such mainstream approaches as the conception of the firm as a production function, the extension of g.e.t. to deal with uncertainty, and the applied price theory orientation. More specifically, he traces Arrow's stance that institutions matter to his 1963 paper on medical care and his 1959 paper (with W. M. Capron) on the operation of shortages in the market for scientists and engineers. He stresses Arrow's impact through his contributions to information and and his writings on externalties, market failures, and transaction costs. Williamson points to Arrow's acceptance of bounded rationa­ lity and opportunism (or moral hazard) in his treatment of economic organization. Obviously one of the loose ends in the study of complex economic organization is the highly complicated task of design of a control system for government. It is in the area of desirability of government intervention where markets fail that Williamson takes issue with Arrow. And another loose end that Williamson mentions is Arrow's observation about the importance of trust in economic organization. Precisely that topic is picked up by Leibenstein in Chapter 21. He focuses on the economic consequences of the absence of trust, particularly in employment relations. He uses a version of the prisoner's dilemma to show that self-interest based on mutual lviii Preface

distrust can lead two parties to choose a combination of actions that makes both worse off than a set of alternative combinations. Costs arising from distrust include loss of exchanges forgone (hiring of people), post-exchange difficulties due to misplaced trust (refunds, seeking payment for damages, litigation), and costs of substitutes for trust (insurance, monitoring, sanctions, rewards, litigation). He points to mutual limited trust and intrafirm conventions as a partial solution to the lack of complete trust. For a firm with some market power and a group of employees with some effort discretion there is a tendency for both to move towards minimum wages and minimum effort, a prisoner's dilemma problem. But limited trust based on social conventions may impose a preferable solution that may still be suboptimal. Peer-group sanctions may establish an effort convention that reduces free riding. Wage and working condition conventions may help account for wage stickiness and disturbances due to inflation. Robin Matthews wears many hats: he has contributed to and is involved in many subjects, earthy and theoretical. A man of many talents, his special background affords us yet anothe! perspective. Eclectic in the best Marshallian and Keynesian tradition and 'branded' for life as a student and colleague both of Hicks and Robertson and of Kahn, Kaldor, and Joan Robinson, and as a sometime 'partner in crime' of Hahn, Robin delivers his many insights in an impeccable Queen's English whose intonations and music we cannot, alas, reproduce. In Chapter 21 he shares with us his reflections on the functions of economic theory and the relationship between our awareness of what are central theoretical issues and the exigencies of specific historical periods. He speaks of the advantages of interdiscip­ linary research and of the dangers of economic imperialism. Switch­ ing to the more pragmatic, Matthews reflects on the conservative upsurge in economic policy, with particular reference to the UK, on the vicissitudes of the welfare state, and on the pros and cons of egalitarian income distribution. he comments on the limits of neoclas­ sical growth theory, on Schumpeter's perceptions of the economic process, on business cycle theory, and on new classical macro­ economics. An attempt at a composite picture of Arrow is made in Part V. The complex man and scholar is seen through his own eyes and those of his various colleagues. In Chapter 23 Arrow shares with us some recollections of his early years: his early interest in statistics, Hotell­ ing's indelible impression on him and the congruence of their ideas, his attraction to economics, and his impressions ofWald, Burns, J. M. Preface lix

Clark, and Albert Hart. He speaks of his disquietude about his apparent inability to find a challenging Ph.D. thesis topic. He recalls his initial contact with the Cowles Commission group, in particular how impressed he was by Marschak's personality and approach, the atmosphere of verbal violence fostered at Cowles by Marschak, and his own resistance to the research programme in econometric model building and readier acceptance of the switch to activity analysis. He recalls the excitement of the formative years at Rand, the big splash of game theory, and the importance for g.e.t. of the mathematical techniques discussed at Rand. He speaks of his research colleagues at Cowles most of whom have contributed vastly to modern economics and achieved due renown. Arrow recalls his early years at Stanford and his stint at Harvard. He confides his propensity to get involved in 'worthy' causes and his need to feel useful. He discusses his perception of altruism and trust in our society and concludes with a fascinating analysis of the conservative trend and the inevitable cyclicity of political moods. This is followed by a succession of impression. In the first chapter (24) Aumann muses about the extraordinary depth and breadth of Arrow; about his true modesty, his friendliness and his involvement in the world around him. In Chapter 25 Hurwicz paints a vivid and generous portrait of Arrow, the collaborator and reflects on the missionary-type service Arrow performs in the applied work he does. In the next vignette (Chapter 26) Anderson provides us with some fascinating insights into the reception of Arrow's thesis on social choice at Columbia and on the relationship between Arrow's work and the development of statistics in the last thirty years or so. Raiffa reflects in Chapter 27 on the profound impact that Arrow's work has had on his own pursuits. In the following snapshot (Chapter 28) Green offers a general appreciation of Arrow's accomplishments and points to the beneficial impact of his work in applied economics which as a result has become far more open to the theoretical approach. And another silhoutte is provided by Fuchs (Chapter 29), who naturally stresses Arrow's unique contribution to the economics of medical care. In the next chapter (30) Intriligator attempts a general assess­ ment of Arrow's impact on the development of economics by means of a tabulation of his works most frequently cited in 196Cr83, though admittedly that measure is not without its drawbacks. In Chapter 31 Lipset presents an intriguing and insightful portrait of the man and scholar, his motivations and underlying tensions. The following two chapters (32, 33) illuminate Arrow's lifelong attachment to Stanford University and his extraordinary services as a university citizen- an lx Preface important facet of his life. In Chapter 34 we attempt a summary on a rather whimsical note. Again, a fitting conclusion to this volume is Part VI where Arrow reflects on those chapters that do not deal directly with his work or personality.

ACKNOWLEDGEMENTS The advantages of division of labour is a commonplace in economics, generally traced to , but actually of much more ancient vintage, going back at least as far as Plato. Never have I been so fully aware of how it enhances output and improves its quality as in the process of design, gestation, and fruition of this study. Mere words cannot convey how grateful I am to my 'partners in crime', not only for their contributions in a tangible sense, but for their moral support; the atmosphere of enthusiasm, creativity, and professionalism that was created; and the psychic income derived from working with them. So many of the contributors went beyond the product with which their name is identified in the table of contents; they offered constant encouragement, good advice, and comments on some papers (includ­ ing the introductions) that singling them out as I must is indeed an ingrate task. Mel Reder's involvement with this project is very special. When I invited him to contribute I knew him only by repute and of his role in the 'formative' stages of the Stanford economics department. He knew even less about me. Unaware that I had refrained from informing Arrow of this study, Mel consulted him andfortunately let the cat out of the bag. When, with great delicacy, Mel told me what transpired, I was emboldened to approach Kenneth and ask for his co-operation. In this way Mel has contributed greatly to the overall quality and design of the project (not to speak of his counsel and support throughout the process of gestation). Peter Hammond is a truly extraordinary supporter among the many who have sustained this project. He was involved in many aspects throughout the process of design, gestation and fruition and brought to it his special dedication, dispassionate advice, and good nature. Moreover the project gained a true friend in Mrudula Ham­ mond. I am indebted to Gerard Debreu not only for his co-operation in helping us to understand better the mathematical economics of our age that he in such a large measure shaped, but for his impeccable courtesy and friendliness that make working with him a pleasure. Very special thanks are also due to Lawrie Klein for sitting down to an interview late at night after a very long day at an exhausting Preface lxi meeting and for his longstanding encouragement and good advice. Leo Hurwicz is a fount of knowledge and wisdom on which I drew once again. I am indebted to him for the intensive sessions at the California Institute of Technology of which these interviews are only a partial reflection. I also owe much gratitude for special encourage­ ment, wise counsel, intensive discussions andjor extensive comments on the introductions to , Bob Aumann, Will Baumol, Woody Brock, John Chipman, Paul David, , Murray Kemp, Donald Kennedy, David Kreps, Bob Kuenne, Andreu Mas­ Colell, , Robin Matthews, , Kwang Ng, Hugo Sonnenschein, Kotaro Suzumura, Jan Tinbergen, and Richard Zeckhauser. At various stages of this project the discussions I had with M. Abramovitz, R. Dorfman, J. T. Dunlop, E. Glustoff, B. G. Hickman, H. S. Houthakker, D. Jorgenson, L. J. Lau, J. Margolis, F. Modigliani, J. R. Moore, M. Morishima, J. Rawls, N. Rosenberg, T. Scitovsky, E. Sheshinski, H. A. Simon, A. M. Spence, L. Summers and M. Weitzman were very helpful and their good advice and encouragement are deeply appreciated. I hope it will not be taken amiss if I thank collectively the many participants of the IMSSS summer economics seminars at Stanford for fruitful discussions over a number of years. Such anonymity, however, cannot apply to the dynamic M. Kurz or to the perennial enfant-terrible-in-residence, F. H. Hahn. It is with much gratitude that I acknowledge the very beneficial and stimulating interchanges with G. Dantzig, S. Karlin, G. Kramer, and D. Landes who have provided fascinating insights into the many dimensions of Kenneth Arrow. I am also deeply grateful to for her willingness to answer many questions about her brother's formative years. I am a bankrupt when it comes to acknow­ ledging earlier discussions and influences. But in this case I would be seriously remiss not to mention my indebtedness to two extraordinary and very different economists who alas are no longer with us- Jasha Marschak and Joan Robinson. Parts of this study were written in Kenneth Galbraith's hospitable homes in Cambridge and Newfane. While unfortunately my style was not improved by transference, I greatly profited from his vision of the world, wisdom, insights, and extraordinary kindness. I appreciate the many services rendered by a number of individuals in various institutions and the discussions with students in several seminars. Alas I have to thank them collectively. In view of the special burden I imposed on the reference library of the University of lxii Preface

Tennessee, I am pleased to single out its Head, Robert Bassett. Kenneth Arrow's office and particularly his dedicated secretary Rosemary Ciernick were very helpful, as was Lillian Zabahon, during my many visits to Stanford. I am also grateful to John Pratt for exceptional assistance (transcending the contributor's intellectual input) at the very last moments of completion of this study. I also wish to thank Michael Aronson of and Alvin Klevonick, the Director of the Cowles Foundation for Research in Economics for their co-operation. I appreciate Keith Povey's editorial help and am grateful to Tim Farmiloe of Macmillan for his keen interest and sound advice. It is customary to absolve all those acknowledged from all remain­ ing flaws; I do this with relish. One person, however, shares responsi­ bility for much that is right and wrong with this study: it is my wife Ida who actively participated at every stage. Since she performs unremunerated labour, I offer her the following concluding words of 's 1867 inaugural address at St Andrews University:

I do not attempt to instigate you by the prospect of direct rewards, either earthly or heavenly; the less we think about being rewarded in either way, the better for us. But there is one reward which will not fail you, and which may be called disinterested, because it is not a consequence, but is inherent in the very fact of deserving it; the deeper and more varied interest you will feel in life: which will give it tenfold its value, and a value which will last to the end. All merely personal objects grow less valuable as we advance in life: this not only endures but increases.

It is in this spirit that these two volumes were written: what an extraordinary intellectual and spiritual experience it has been; how remarkable the process of learning by doing; and how rewarding to share it with such a highly motivated, intellectually powerful, stimu­ lating, and appreciative group of scholars. It goes without saying that our greatest debt of gratitude is to Kenneth Arrow for providing the intellectual capital of this study. But we are beholden to him for much, much more: I am at a loss for words to express how grateful we are to you, Kenneth, for generously granting us a privileged insight into one of the great minds in economics of all time, sharing your thoughts and feelings, revealing Preface lxiii clues to your motivations, and above all for the way you have done this: for your great warmth and elegance and for your high standards of personal and professional behaviour. With great affection and friendship, these two volumes are dedicated to you Kenneth.

GEORGE R. FEIWEL