EQUILmRIUM AND DYNAMICS David Gale, 1991 Equilibrium and Dynamics
Essays in Honour of David Gale
Edited by Mukul Majumdar H. T. Warshow and Robert Irving Warshow Professor ofEconomics Cornell University
Palgrave Macmillan ISBN 978-1-349-11698-0 ISBN 978-1-349-11696-6 (eBook) DOI 10.1007/978-1-349-11696-6 © Mukul Majumdar 1992 Softcover reprint of the hardcover 1st edition 1992 All rights reserved. For information, write: Scholarly and Reference Division, St. Martin's Press, Inc., 175 Fifth Avenue, New York, N.Y. 10010
First published in the United States of America in 1992
ISBN 978-0-312-06810-3
Library of Congress Cataloging-in-Publication Data Equilibrium and dynamics: essays in honour of David Gale I edited by Mukul Majumdar. p. em. Includes bibliographical references (p. ). ISBN 978-0-312-06810-3 1. Equilibrium (Economics) 2. Statics and dynamics (Social sciences) I. Gale, David. II. Majumdar, Mukul, 1944- . HB145.E675 1992 339.5-dc20 91-25354 CIP Contents
Preface vii Notes on the Contributors ix
1 Equilibrium in a Matching Market with General Preferences Ahmet Alkan 1
2 General Equilibrium with Infinitely Many Goods: The Case of Separable Utilities Aloisio Araujo and Paulo Klinger Monteiro 17
3 Regular Demand with Several, General Budget Constraints Yves Balasko and David Cass 29
4 Arbitrage Opportunities in Financial Markets are not Inconsistent with Competitive Equilibrium Lawrence M. Benveniste and Juan Ketterer 45
5 Fiscal and Monetary Policy in a General Equilibrium Model Truman Bewley 55
6 Equilibrium in Preemption Games with Complete Information Kenneth Hendricks and Charles Wilson 123
7 Allocation of Aggregate and Individual Risks through Financial Markets Michael J. P. Magill and Wayne J. Shafer 148
8 Survival under Production Uncertainty Mukul Majumdar and Roy Radner 179
9 Equilibrium Theory with Possibly Satiated Preferences Andreu Mas-Colell 201
10 On the Existence of a Stationary Optimal Stock for a Multi-sector Economy with a Nonconvex Technology Tapan Mitra 214
v vi Contents
11 A Note on Optimal Development in a Multi-sector Nonconvex Economy Mukul Majumdar and Bezalel Peleg 241
12 A Genuine Keynesian Growth Cycle Hukukane Nikaido 247
13 On Perfectly Coalition-proof Nash Equilibria Bezalel Peleg 259
14 Efficiency of Marginal Cost Pricing Equilibria Martine Quinzii 269
15 A Long-open Question on Utility and Conserved-energy Functions Paul A. Samuelson 287
16 How (and When) to Communicate with Enemies Joel Sobel 307
17 The Multiple Partners Game Marilda Sotomayor 322
18 Gale Tales William A. Brock 355
Selected Publications of David Gale 358 Preface
We present this collection of essays to David Gale who - as a teacher, colleague or friend - has shared his thoughts and intellectual creativities with us throughout his distinguished academic career. His research has displayed astonishing depth and breadth. By combining precision and rigour with an elegant, relaxed style of exposition, he has set standards for generations of researchers in economic theory all over the world. He has written papers on, among others, such diverse themes as compact sets of function rings; game theory; convex sets and linear inequalities; linear programming and Kuhn-Tucker Theorems; classical mechanics; flows in networks; abstract algebra; revealed preference theory; Walrasian equilib• rium theory; global univalence of mapping; intertemporal eqUilibrium with overlapping generations; money and interest; optimal development in a multi-sector economy; technological change; transfer problems and trade theory; the optimal strategy for serving in tennis; commutative topological groups; periodic functions; algorithms; economics of fair division; mar• riage and matching problems; auction theory; manifolds, ... The collection of studies in this volume reflects the small subset of David Gale's work that has had profound influence in areas of economics that overlap with our own interests and competence. One can readily identify some of the key papers that have stood the test of time and will endure as classics. His 1955 'The Law of Supply and Demand' and his 1963 'A Note on Global Instability of Competitive Equilibrium' are duly acknowledged in equilibrium theory for their depth and exposition. Two landmarks in intertemporal economics, 'On Optimal Development in a Multi-Sector Economy' (1967) and the subsequent 'Pure Exchange Equilibrium of Dynamic Economic Models' (1973), reflect a continuation of his interest in economic dynamics that goes back to his earlier masterly elucidation of von Neumann-Koopmans activity analysis models. Indeed, his book The Theory of Linear Economic Models (1960) was immediately acknowledged as a classic, and has had a lasting impact. The paper with Nikaido, 'The Jacobian Matrix and Global Univalence of Mappings' (1965), stimulated by Samuelson's famous theorems on factor price equalisation, has played a key role not only in international trade, but also in identifying the unique• ness of the Walrasian equilibrium. But, as we proceed, we recognise that any such list reflects our own bias: game theorists remember Gale as a pioneer; his work on assignment and matching problems has broken new ground and spawned a significant literature; and one can go on and on. David Gale was born on 13 December 1921. His undergraduate edu• cation was at Swarthmore College. He took his Ph.D. in mathematics in 1949 at Princeton University and participated in basic mathematical vii viii Preface research on garnes, linear programming, and convex analysis in what was probably one of the USA's most productive outpourings of mathematical research. Notables of this period included von Neumann, Gale, Kuhn, and Tucker. David spent fifteen years at Brown University before moving to Berke• ley. He holds an appointment in three departments there, and still remains as keen and imposing as he was to us some twenty-five years ago! We are grateful to all the contributors for their patience. We would also like to thank Professors B. Dutta, M. Ali Khan, E. Dierker, R. Vohra, N. Yannelis, D. Easley, H. Wan, T. Ichiishi and A. Roth for their advice and comments on various studies in this volume. Research assistance from Santanu Roy and Manjira Roychoudhury is gratefully acknowledged. Mrs Alicia Merrick and Mrs Ann Stiles steered the project to its com• pletion. We are most appreciative of the support from the Department of Economics at Cornell, and from Messrs T. M. Farmiloe, S. Gerrard and K. Povey at the publisher.
MUKUL MAJUMDAR WILLIAM A. BROCK Notes on the Contributors
Ahmet Alkan is on the faculty of the Department of Management in the School of Economics and Administrative Science at Bogazici University, Bebek, Istanbul. He received his Ph.D. from the University of California (Berkeley) where his dissertation was supervised by David Gale. His primary areas of research include dynamic efficiency and the theory of matching equilibrium.
Aloisio Araujo is a professor at the Instituto de Matematica pure e Apli• cada, Rio de Janeiro. He received his Ph.D. degree from the University of California (Berkeley), where he met David Gale. A fellow of the Econ• ometric Society, he is well known for his research in probability theory, the theory of general equilibrium (involving models with infinitely many commodities) and turnpike theory in dynamic models.
Yves Balasko is Professor of Economics at the University of Geneva and of Mathematics at the University of Paris I (Pantheon-Sorbonne). A fellow of the Econometric Society, he has made definitive contributions to gen• eral equilibrium theory (with special emphasis on the differential point of view) and to the literature on dynamic models with overlapping gener• ations. He is the author of the well-known monograph Foundations of the Theory of General Equilibrium.
Lawrence M. Benveniste is on the faculty of Boston College. He received his Ph.D. degree from the University of California (Berkeley), where his dissertation was supervised by David Gale. He is the author of several influential papers related to intertemporal efficiency, money in models with overlapping generations and dynamic programming.
Truman Bewley is Alfred Cowles Professor of Economics at Yale University. He received his Ph.D.s in economics and mathematics from the University of California (Berkeley). A fellow of the Econometric Society and a fellow of the Guggenheim Foundation, he is duly acknowledged as one of the outstanding mathematical economists of his generation. His deep and definitive papers have enriched both static and dynamic equilib• rium theory.
William A. Brock is Vilas Research Professor of Economics at the Univer• sity of Wisconsin (Madison). He received his Ph.D. from the University of California (Berkeley), where his dissertation was supervised by David Gale. A fellow of the Econometric Society and of the Guggenheim
ix x Notes on the Contributors
Foundation, he has been one of the dominant figures in dynamic econ• omics. Over the last twenty years, his contributions have spanned a variety of topics and his current research focuses on chaotic dynamic systems in economics.
David Cass is Miller Professor of Economics and Director, Center for Analytic Research in Economics and Social Sciences, at the University of Pennsylvania. A fellow of the Econometric Society and of the Guggenheim Foundation, he is a co-editor of Economic Theory. His papers on efficient and optimal growth have left indelible impressions on capital theory. His research focuses on introducing financial market imperiections into the Walrasian equilibrium framework.
Kenneth Hendricks is on the faculty of the Department of Economics at the University of British Columbia. He has published research papers in the areas of game theory, economics of information and energy economics. He is engaged in a long-term project studying the auctions for offshore oils and gas leases.
Juan Ketterer is on the faculty of Graduate School of Industrial Adminis• tration at Carnegie-Mellon University. His current focus of research is on models of asset-pricing and financial markets.
Michael J. P. Magill is Professor of Economics at the University of Southern California. He is a leading contributor to the literature on intertemporal equilibrium theory, stability of dynamic models and on the existence of equilibrium with incomplete markets.
Mukul Majumdar is Warshow Professor of Economics at Cornell Univer• sity. He received his Ph.D. from the University of California (Berkeley), where he met David Gale. A fellow of the Econometric Society and of the Guggenheim Foundation, he is a co-editor of Economic Theory. His primary area of research has been the theory of intertemporal allocation of resources.
Andreu Mas-Colell is Louis Berkman Professor of Economics at Harvard University. A fellow of the Econometric Society, the Guggenheim Foun• dation and of the Sloan Foundation, he is duly acknowledged as one of the outstanding mathematical economists of his generation. His collaboration with David Gale led to a significant contribution to the literature on the existence of a Walrasian equilibrium. He is the author of the monograph The Theory of General Economic Equilibrium: A Differentiable Approach.
Tapan Mitra is a Professor of Economics at Cornell University. A fellow of Notes on the Contributors xi the Sloan Foundation, he is one of the leading figures in research on intertemporal economics and the economics of renewable and exhaustible resources. His insights into the structure of models with recursive decisions have led to a large number of decisive results that have enhanced the scope of capital theory.
Paulo Klinger Monteiro is on the faculty of the Universidade Federal do Rio de Janeiro. His collaborative research with Aloisio Araujo has led to a number of important papers on economic equilibrium with an infinite dimensional commodity space, and its implications for finance.
Hukukane Nikaido is Professor of Economics at Tokyo International University. A fellow of the Econometric Society and a former President of the Japan Association of Economics and Econometrics, he is one of the pioneers of modern mathematical economics. His masterly articles have played a major role in the development of competitive equilibrium analysis. His collaboration with David Gale led to a landmark in the analysis of global univalence of mappings. He also made a notable contri• bution to the turnpike theory of capital accumulation. He is the author of Convex Structures and Economic Theory, a valuable monograph for re• searchers in mathematical economics.
Bezalel Peleg is Professor in the Institute of Mathematics at the Hebrew University of Jerusalem. A fellow of the Econometric Society, he is one of the outstanding mathematical economists in the world. His numerous contributions have illuminated game theory, static equilibrium theory, intertemporal economics and voting theory.
Martine Quinzii is on the faculty of Economics at the University of Southern California. She is noted for her research on the problems of resource allocation with indivisibilities and increasing returns. She is engaged in studying asymmetric information, imperfect competition, financial markets and monetary theory.
Roy Radner is a Distinguished Member of Technical Staff at A T & T Bell Laboratories and a Research Professor at New York University. A past President of the Econometric Society, a distinguished Fellow of the Ameri• can Economic Association and a member of the National Academy of Sciences of the USA, he is regarded as one of the most original economic theorists in the world. His path-breaking work on organisation theory, and on the economics of uncertainty, information and missing markets has significantly influenced the development of research in these areas. Econ• omic theory is often viewed as a box of tools, and it has been noticeably enriched by many of Radner's innovative ideas and techniques. xii Notes on the Contributors
Paul A. Samuelson is Institute Professor, Massachusetts Institute of Tech• nology. As one of the greatest economic theorists of all time, he stands out, even among the winners of the Nobel Memorial Prize in economics. His research on factor price equalisation, on optimal growth and his model with overlapping generations led to important papers by David Gale.
Joel Sobel is Professor of Economics at the University of California (San Diego). He received his Ph.D. from the University of California (Berke• ley), where his thesis was supervised by David Gale. A fellow of the Econometric Society, he is well known for his innovative papers on optimal distribution, bargaining and signalling games.
Marilda Sotomayor is on the faculty of the Department of Mathematics at Pontificia Universidade Catolica do Rio de Janeiro. She is the co-author (with Alvin Roth) of the monograph 'Two-sided Matching: A Study in Game Theoretic Modelling and Analysis' .
Wayne J. Shafer is Professor of Economics at the University of Illinois (Urbana-Champaign). A co-editor of the Journal of Mathematical Econ• omics, he is noted for his decisive contributions to several topics in Walrasian equilibrium theory.
Charles Wllson is Professor of Economics and Co-director of the C. V. Starr Center for Applied Economics at New York University. A fellow of the Econometric Society and of the Sloan Foundation, he is well known for his innovative research on information economics, the theory of games, money and general equilibrium. His research focuses on experimental economics.