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The Economics of Uncertainty and Information
Laffont, Jean-Jacques.
MIT Press
9780262121361
9780585134413
English
Microeconomics, Uncertainty.
1989
HB173.L2352513 1989eb
338.5
Microeconomics, Uncertainty.
cover
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Page iii
The Economics of Uncertainty and Information
Jean-Jacques Laffont
1
2
translated by
John P. Bonin and Hélène Bonin
The MIT Press
Cambridge, Massachusetts
London, England
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Page iv
Sixth printing. 1999
© 1989 The Massachusetts Institute of Technology
Published in France under the title
Cours de théorie microeconomique. II. à conomie de l'incertain et de l'information by
Economica, Paris, 1986
© 1986 Jean-Jacques Laffont
All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical
means (including photocopying, recording, or information storage and retrieval) without permission in
writing from the publisher.
This book was set in Times Roman by Asco Trade Typesetting Ltd., Hong Kong, and printed and bound in
the United States of America.
Library of Congress Cataloging-in-Publication Data
Laffont, Jean-Jacques, 1947[Cours de théorie microéconomique. Economie do l'incertain et de l'information.
English]
The economics of uncertainty and information/Jean-Jacques Laffont; translated by
John P. Bonin and Hélène Bonin.
p. cm.
Translation of: Cours de théorie microéconomique. Vol. 2. Economie de l'incertain
et de l'information.
Includes index.
ISBN 0-262-12136-0
1. Microeconomics. 2. Uncertainty. I. Title.
HB173.L2352513 1989
338.5dc19
88-132.50
CIP
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Page v
Contents
Preface
ix
Mathematical Notation and Definitions
xi
Introduction
1
1 Individual Behavior under Uncertainty
6
1.1 The Expected Utility Hypothesis
6
1.2 The Theory of von Neumann and Morgenstern
9
1.3 Nonprobabilistic Consequences
14
Suggested Readings
18
References
18
2 Measuring Risk Aversion and Risk
19
2.1 Measures of Risk Aversion
19
2.2 Measures of Risk
24
2.3* The Maximin Criterion
30
2.4* Proof of Pratt's Theorem
31
2.5* Stochastic Dominance
32
2.6* Generalization of the Expected Utility Hypothesis
33
2.7* Risk Aversion with Many Goods
35
Suggested Readings
38
References
38
3 Certainty Equivalence
3.1 Certainty Equivalence
40
40
3
4
3.2 First-Order Certainty Equivalence
44
3.3 A More General Notion of First-Order Equivalence
50
3.4* The Irreversibility Effect
52
3.5* The Arrow-Lind Theorem
53
Suggested Readings
54
References
54
4 Information Structures
55
4.1 Prior Information
55
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Page vi
4.2 Information Structure without Noise
56
4.3 Information Structure with Noise
62
4.4 The Demand for Information
66
4.5* Proof of Blackwell's Theorem
68
Suggested Readings
68
References
69
5 The Theory of Contingent Markets
4
70
5.1 A New Interpretation of the Edgeworth Box
70
5.2 Generalization
75
5.3 Different Information Structures
77
5
5.4 The Value of Information
79
Suggested Readings
81
References
81
6 Equilibria with Perfect Foresight in Incomplete Markets
82
6.1 Back to the Arrow-Debreu Equilibrium
82
6.2 The Equilibrium with Perfect Foresight
84
6.3 The Normative Analysis of Equilibria with Perfect Foresight
88
6.4 Existence of Equilibrium
94
6.5 On the Incompleteness of Markets
96
6.6* Law and Economics
99
6.7* Sunspot Equilibria
99
Suggested Readings
101
References
101
7 The Stock Market
103
7.1 Competitive Equilibrium in the Stock Market
103
7.2 Several Special Cases
109
7.3 The Modigliani-Miller Theorem
115
7.4 Concluding Remarks
116
7.5* The Capital Asset Pricing Model
117
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6
Page vii
Suggested Readings
119
References
119
8 The Theory of Insurance
8.1 Contingent Markets and Insurance
121
8.2 Moral Hazard
125
8.3 Adverse Selection
128
8.4 Concluding Remarks
133
Suggested Readings
134
References
134
9 The Transmission of Information by Prices
135
9.1 The Green-Lucas Equilibrium
135
9.2 The Problem of the Existence of Equilibrium in Systems of Incomplete
Markets
143
9.3 Welfare
Analysis of
Green-Lucas
Equilibria
146
Suggested Readings
151
References
151
10 Adverse Selection and Exchange
6
121
153
10.1 The Characterization of Incentive Compatible Contracts
153
10.2 The Selection of a Contract
159
10.3 Competition among Agents
164
10.4 Repeated Contracts
169
10.5 Examples
174
7
Suggested Readings
178
References
179
11 Moral Hazard and Exchange
180
11.1 The First-Order Condition Approach
151
11.2 Validity and Limitations of the First-Order Condition Approach
187
11.3 Competition among Agents
190
11.4 Repeated Principal-Agent Relations
193
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Page viii
11.5 Concluding Remarks
195
Suggested Readings
196
References
197
Worked Problems
199
Exercises without Solutions
277
Index
285
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7
8
Page ix
Preface
This book is the second of a
series of volumes intended to be
used in a year-long course in
economic theory designed for
advanced undergraduate or
graduate students. Each volume
can be read independently from
the others. In the introduction to
the present book, I will review
the background that I assume of
the reader.
Avoiding whenever possible
complicated mathematics, I have
sought to make available to the
student a treatise in
microeconomic theory that takes
into account the latest
developments. The chapters end
with optional (starred) sections
that may be skipped in an initial
reading and with lists of references
and recommended readings that
will allow the student to delve
more deeply into the topics that
have been discussed. These
readings will fill in some of the
gaps in my presentation and
encourage the student to do further
research. The volume ends with a
series of exercises, which are
preceded by a series of worked
problems. These problems and
exercises will help the student
evaluate his or her understanding
of the course.
For this volume I have relied on the works of many authors. I am particularly indebted to my teachers, E.
Malinvaud and K. Arrow. I have also benefited greatly from discussions with C. Henry, J. Green, R.
Guesnerie, R. Kihlstrom, and E. Maskin and from the works of G. Debreu, R. Radner, O. Hart, B.
Holmström, S. Grossman, M. Rothschild, and J. Stiglitz. I thank M. Boyer, J. Crémer, G. Dionne, M.
Magill, P. Picard, M. Quinzii, and J. Tirole for their comments on some of the chapters.
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Page xi
Mathematical Notation and Definitions
Notation
∃ there exist(s)
∀ for any
belongs to
is a subset of
if and only if
Let
and
. Then
denotes the scalar (dot) product.
Definitions
1. A binary
relation Ri
defined on Xi
is
A preordering is a transitive and reflexive binary relation.
2. A set
is convex
.
A function f(.) defined on RL is quasi-concave
is convex.
3. A preference relation Ri is convex
.
A function f(.) defined on RL is concave
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9
10
Page 1
Introduction
Before beginning this book, the reader should be familiar with probability theory and should have a complete
understanding of the two fundamental theorems of welfare economics derived from the "basic
microeconomic model." These theorems are developed, for example, in the first five chapters of Edmond
Malinvaud's Lectures in Microeconomic Theory. In this introduction, I review briefly their significance after
presenting the notation of the basic model that will be used throughout. I conclude with an outline of the book
devoted to the economics of uncertainty and information.
I.1 Notation
The economy consists of L economic goods indexed by l = 1, ..., L, I consumers indexed by l = 1,...,I, and J
firms indexed by j = 1,...,J. The indices corresponding to economic agents will always be superscripts, and
those corresponding to goods will be subscripts.
Let Xi be the consumption set for consumer i; this set is often taken to be the positive orthant .1 The
quantity consumed of good l by consumer i is represented by , and
characterizes the
consumption bundle of consumer i. Consumer i's preferences are represented either by a complete
preordering (that is, by a complete, reflexive, transitive binary relation)2 denoted by Rl or by a utility function
denoted by Ui(.). Then Ri1Rix2 means: consumer i either prefers the bundle of goods xi1 to the bundle of goods
xi2 or is indifferent between them. Substituting Pi for Ri indicates strict preference. The preordering Ri is
represented by a utility function Ul(.) if and only if
Consumer i's initial endowment
is denoted by
. Let
be the production
vector for producer j. We usually
follow the convention that
outputs (products) have a
positive sign and inputs (factors)
a negative sign. Essentially, this
convention permits us to write
the profit of firm j as the inner
(dot) product
1.
2.
See the mathematical definitions, p. ix.
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