Table Of ContentINTERNATIONAL 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
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First published 1974
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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).
