Allocation under Uncertainty: Equilibrium and Optimality: Proceedings from a Workshop sponsored by the International Economic Association PDF
Preview Allocation under Uncertainty: Equilibrium and Optimality: Proceedings from a Workshop sponsored by the International Economic Association
INTERNATIONAL ECONOMIC ASSOCIATION CONFERENCE VOLUMES, Numbers 1-50 NUMBER 41 Allocation under Uncertainty: Equilibrium and Optimality Allocation under Uncertainty: Equilibrium and Optimality Proceedings from a Workshop sponsored by the International Economic Association EDITED BY JACQUES H. DREZE with the assistance of F. Delbaen. L. Gevers R. Guesnerie and D. Sondermann © International Economic Association 1974 Softcover reprint of the hardcover 1st edition 1974 978-0-333-15061-0 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 1974 This 50-volume set reprinted 1986 jointly by THE MACMILLAN PRESS LTD Houndmills, Basingstoke, Hampshire RG21 2XS and London Companies and representatives throughout the world and YUSHODO CO. LTD 29 Saneicho, Shinjuku-ku Tokyo 160 Japan. Tel: 03(357)1411 Published in the United States and Canada by STOCKTON PRESS 15 East 26th Street, New York, N.Y. 10010 50-volume set ISBN 978-0-333-40626-7 ISBN 978-1-349-01991-5 ISBN 978-1-349-01989-2 (eBook) DOI 10.1007/978-1-349-01989-2 Transferred to digital printing 1999 02n90 Contents Acknowledgements vii List of Participants ix Preface and Introduction xi PART ONE: INDIVIDUAL DECISIONS 1 Axiomatic Theories of Choice, Cardinal Utility and Subjective Probability: a review Jacques H. Dreze 3 2 Two-Period Models of Consumption Decisions Under 24 Uncertainty: a survey Agnar Sandmo 3 Optimum Accumulation Under Uncertainty: the Case 36 of Stationary Returns to Investment James A. Mirrlees PART TWO: GENERAL EQUILIBRIUM 4 Allocation Under Uncertainty: a survey Roger Guesnerie and Thierry de Montbrial 53 5 Optimality of Equilibrium of Plans, Prices and Price 71 Expectations Roger Guesnerie and Jean-Yves Jaffray PART THREE: INDIVIDUAL RISKS IN LARGE MARKETS 6 Optimum Allocation of Risk in a Market With Many 89 Traders Yaffa Caspi 7 Stochastic Preferences and General Equilibrium 98 Theory Freddy Delbaen 8 The Allocation of Individual Risks in Large Markets 110 Edmond Malinvaud PART FOUR: OPTIMUM INVESTMENT WITH ASSET MARKETS 9 Investment Under Private Ownership: Optimality, 129 Equilibrium and Stability Jacques H. Dreze 10 Competitive Equilibrium of the Stock Exchange and 167 Pareto Efficiency Louis Gevers 11 Discount Rates for Public Investment Under 192 Uncertainty Agnar Sandmo vi Contents PART FIVE: SHORT-RUN EQUILIBRIUM WITH MONEY 12 On the Short-Run Equilibrium in a Monetary 213 Economy Jean-Michel Grandmont 13 Temporary Competitive Equilibrium Under Uncertainty 229 Dieter Sondermann 14 Continuity of the Expected Utility Freddy Delbaen 254 Acknowledgements This volume contains one section of the studies which were prepared for the Workshop in Economic Theory organised by the International Economic Association in Bergen in 1971. The Asso ciation owes its gratitude to the Ford Foundation at whose sug gestion the Workshop was undertaken and who were almost entirely responsible for its financing. In addition the Association is indebted to the Director of the Course, Professor James A. Mirrlees, and to his co-Directors, Professor Jacques Dreze, the Editor of this volume, and Professor Edmond Malinvaud. Thanks are also due to the Norwegian School of Economics and Business Administration, Bergen, which made available accommodation and library facilities, and in particular to Dr Agnar Sandmo who was in charge of the local secretariat and organisation. List of Participants J. A. Mirrlees, Oxford, England, Director J. H. Dreze, coRE, Louvain, Belgium, Co-director (first two weeks) E. Malinvaud, INSEB, Paris, France, Co-director (last two weeks) A. Sandmo, Norwegian School of Economics and Business Administration, Bergen, Norway, Local Organiser M. G. Allingham, University of Essex, England C. Berthomieu, University of Nice, France Mrs. Y. Caspi, Hebrew University, Jerusalem, Israel P. Champsaur, INSEE, Paris, France A. Chekhutov, Association of Soviet Economic Scientific Institutions, Moscow, U.S.S.R. F. Delbaen, University of Brussels, Belgium L. Eekhoudt, University of Mons, Belgium J. Flemming, Nuffield College, Oxford, England L. Gevers, coRE, Louvain, Belgium J.-M. Grandmont, CEPREMAP, Paris, France R. Guesnerie, CEPREMAP, Paris, France P. J. Hammond, Nuffield College, Oxford, England M. Jones-Lee, University of York, England S. Littlechild, Graduate Centre for Management Studies, Birmingham, England M. Marchand, University of Mons, Belgium T. de Montbrial, Ecole Polytechnique and Commissariat du Plan, Paris, France P. van Rompuy, University of Leuven, Belgium P. Ruys, University of Tilburg, Netherlands U. Schlieper, University of Saarland, Germany C. Seidl, University of Vienna, Austria C.-H. Sivan, University of Stockholm, Sweden D. Sondermann, University of Saarland, Germany D. Soskice, University College, Oxford, England L. Tomasini, Einaudi Institute, Turin, Italy Preface and Introduction Jacques H. Dreze CENTER FOil OPERATIONS RESEARCH AND ECONOMETRICS, LOUVAIN The workshop organised by the International Economic Association and held in Bergen, 18 July-14 August 1971, differed in several respects from the well-known Symposia regularly sponsored by the Association. These Symposia have typically brought together, for a week, a group of senior economists interested in a specific topic. The topic is chosen first, the participants are then selected (by invitation) from among leading authorities on that topic. The proceedings con sist mostly of original research papers and give a comprehensive picture of the state of research in a given area. The Bergen workshop was organised in a different spirit. The purpose was to promote the professional development of young economists engaged in teaching or research at European universities. Although initially approached to organise an advanced summer course in economic theory, the directors of the workshop-James A. Mirrlees, Edmond Malinvaud and myself - preferred to entrust all teaching to the participants themselves. The announcement of the workshop indicated that participants would be expected to prepare, circulate and present both a research paper and a survey paper. The survey papers were meant to serve as a form of systematic teaching and also to provide a common, broad background against which the more specific research contributions could be evaluated. The announcement further stated that the work would be concentrated in two or three areas of economic theory, to be selected on the basis of interests expressed by participants, and invited young European economists to apply for participation. When the twenty-five participants were selected, from a group of some seventy qualified applicants, it turned out that 'uncertainty' provided a central theme around which the workshop could most conveniently be organised. It was also decided to devote the first week (out of four) of the workshop to the general theory of resource allocation under uncertainty. The ten papers prepared for that first week (four survey papers and six research papers) form the basic material in the present volume. Although no systematic publication of proceedings had been planned, it was felt that these papers con stituted a sufficiently articulate presentation of the current state of xii Preface and Introduction theorising to justify collecting them in a volume. It was also felt that the educational purpose of the workshop would be enhanced if these papers were carefully revised (or even rewritten, in some cases) in the light of the discussions at the workshop. Four papers not presented during the first week of the workshop were added to the volume, namely Chapters 3, 8, 9 and 14. The chapter by Mirrlees on Optimum Accumulation (Savings) is a re vised version of the first part of a paper which he presented during the third week of the workshop. It forms a natural complement to Sandmo's paper in Part 1, and was included for that reason. Chapters 8 and 9 reproduce papers, by Malinvaud and myself respectively, that were not presented, but were circulated and dis cussed informally at the workshop. They were included so as to render Parts 2 and 3 more complete and self-contained. Chapter 14 consists of a technical note, written during the work shop, which generalises some results in Chapter 13. The final responsibility for organising the first week of the work shop, and for editing this volume, was mine. But I received sub stantial assistance in both tasks from Freddy Delbaen, Louis Gevers, Roger Guesnerie and Dieter Sondermann. During the spring of 1971, all four of them were in residence at the Center for Operations Research and Econometrics in Louvain, and we worked as a team in selecting topics, discussing the contents of survey papers and editing research papers. This close cooperation was continued during and after the workshop; all the papers in this volume have been read by at least one of them, and many have been substantially improved as a consequence. Most of the credit for the success of the first week of the workshop, and for whatever merits the present volume may possess, belongs to these four talented and congenial young econ omists. The papers were read by Mrs. Alan Kirman, who patiently amended our style and grammar; she deserves much gratitude from the readers, as well as from the authors, of this volume. The manuscript was prepared for the printer by Mrs. Jacques Vincent, who had already typed and retyped several papers and who handled competently the administrative tasks connected with editing this volume. Mrs. Jean Verkaeren and Mrs. Vincent proof-read the whole volume and collated the references. I wish to thank them for their valuable assistance. Thanks are due to the Center for Operations Research and Econo metrics, which covered secretarial costs, and to the Fonds de Ia Recherche Fondamentale Collective, Brussels, for general support of research in this area, and specific support of the work of Gevers and Sondermann (under contracts No. 611 and No. 968).
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