Markets, information,
and uncertainty
Essays in economic theory in honor of
Kenneth 1 Arrow
Markets, information, and uncertainty is a collection of essays by leading
theorists offering powerful new insights on the role of uncertainty and
information in today's market. This book features Kenneth Arrow on
information and the organization of industry, Roy Radner on new tech­
nologies, Graciela Chichilnisky and Frank Hahn on human-induced
uncertainty, Geoffrey Heal and Walter Heller on the creation of new
markets, and Edmund Phelps on unemployment, among topics investi­
gated by other eminent practitioners. It is an authoritative collection
offering imaginative and fresh approaches to economic theory.
Graciela Chichilnisky holds the UNESCO Chair of Mathematics and
Economics at Columbia University and is Director of Columbia's
Program on Information and Resources. In 1995 she was awarded the
Lief Johansen award from the University of Oslo and was the 1994--5
Salimbeni Professor at the University of Siena. Professor Chichilnisky is
recognized as one of the world's leading applied and theoretical scien­
tists, having originated the concept of "basic needs," which is widely used
in economic development and was explicitly adopted by 150 nations in
the UN Agenda 21 at the 1992 Earth Summit. She has served as advisor
to organizations including the Organization of Economics Cooperation
and Development, the United Nations, and the Organization of
Petroleum Exporting Countries (OPEC), in the areas of international
economics and environmental policy. Professor Chichilnisky is a member
of the board of directors of the Natural Resources Defense Council and
is the author of eight books and some 160 scientific articles.
Kenneth J. Arrow
Markets, information, and
uncertainty
Essays in economic theory in honor of
Kenneth J. Arrow
Edited by
GRACIELA CHICHILNISKY
Columbia University
. . .�.:. CAMBRIDGE
;:;
..
UNIVERSITY PRESS
CAMBRIDGE UNIVERSITY PRESS
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, Sao Paulo, Delhi
Cambridge University Press
The Edinburgh Building, Cambridge CB2 8RU, UK
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
Information on this title: www.cambridge.org/9780521553551
© Graciela Chichilnisky 1999
This publication is in copyright. Subject to statutory exception
and to the provisions ofrelevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 1999
This digitally printed version 2008
A
catalogue record for this publication is available from the British Library
Library of Congress Cataloguing in Publication data
Markets, information, and uncertainty: essays in economic theory in
honor of Kenneth J. Arrow I edited by Graciela Chichilnisky.
p.
cm.
Includes index.
ISBN 0-521-55355-5
1. Economics.
2. Arrow, Kenneth Joseph, 1921-.
Joseph, 1921-.
II. Chichilnisky, Graciela.
HB71.M29
1999
330 - dc21
ISBN 978-0-521-55355-1 hardback
ISBN 978-0-521-08288-4 paperback
I. Arrow, Kenneth
97-25548
CIP
Contents
Preface
List of contributors
Page vii
ix
Section I. Information and markets
Introduction
Graciela Chichilnisky
3
1.
Information and the organization of industry
Kenneth J. Arrow
19
2.
Equilibrium in an economy with information goods
Vladimir I. Danilov, Gleb A. Koshevoy, and
Alexandr I. Sotskov
26
Section II. Uncertainty and finance
3. The formulation of uncertainty: Prices and states
Jacques H. Dreze
45
4. A remark on incomplete market equilibrium
Frank Hahn
67
5.
Existence and optimality of a general equilibrium with
endogenous uncertainty
Graciela Chichilnisky
72
6.
Market equilibrium with endogenous price
uncertainty and options
Peter H. Huang and Ho-Mou Wu
97
7.
Catastrophe futures: Financial markets for unknown risks
Graciela Chichilnisky and Geoffrey Heal
v
120
v1
Contents
Section III. Market externalities and justice
8. Moral hazard and independent income in a modern
intertemporal-equilibrium model of involuntary
unemployment and mandatory retirement
Edmund S. Phelps
On the optimal schedule for introducing a new technology,
when there is learning by doing
P B. Linhart and Roy Radner
10. Price and market share dynamics in network industries
Geoffrey Heal
1 1 . Exchange in a network of trading posts
Ross M. Starr and Maxwell B. Stinchcombe
12. Equilibrium market formation causes missing markets
Walter P Heller
13. Toward a general theory of social overhead capital
Hirofumi Uzawa
14. On population externalities and the social rate of discount
David A. Starrett
15. Trade and Welfare
Tito Cordelia, Enrico Minelli, and Heracles Polemarchakis
16. History as a widespread externality in some Arrow-Debreu
market games
Peter 1 Hammond
17. Redistribution by a representative democracy and
distributive justice under uncertainty
Peter Coughlin
9.
143
165
191
216
235
253
305
322
328
362
Author index
377
Subject index
380
Preface
This book emerged from the celebration of Kenneth Arrow's 70th
birthday at a workshop entitled "Columbia Celebrates Arrow's
Contributions" in October 1991. This took place at Columbia University,
where he studied between 1941 and 1950, and obtained his PhD degree
under the supervision of Harold Hotelling and Albert Hart. The papers
presented at that workshop to a most enthusiastic audience were special.
It was a heartwarming event. It was later suggested that those papers,
and those of other authors closely related to Ken Arrow, be compiled
in a volume in his honor to memorialize this happy occasion.
Uncharacteristically for such a volume, the book starts with a paper by
Arrow himself, which he presented at the Columbia workshop. His piece
on information and uncertainty reflects upon the future of industrial
societies in a most original and thoughtprovoking manner. Each subse­
quent author reflects on an aspect of the uncertainty-information axis,
which, as argued below, is a representation of a tug-of-war between the
individual, whose life is short and whose capacities to predict are limited,
and society, which exists in a more atemporal world.
Many thanks are owed to the authors who kindly helped with the
process of producing this book, and to close associates and colleagues at
Columbia who provided invaluable support: Drs. Yun Lin and Yuqing
Zhao, Geoffrey Heal, Bruce Greenwald, Ned Phelps, David Krantz and
Duncan Foley; also to colleagues at Stanford University where some
of the work was completed: Paul Milgrom, David Starrett, and Paul
Ehrlich, and to my daughter Natasha Chichilnisky-Heal, and Kim Stack
and Grace Fernandez of the Program on Information and Resources
(PIR) at Columbia. Thanks also to Scott Parris and Louise Calabro of
Cambridge University Press who provided continued support, and
Shirley Kessel who kindly compiled the indexes. The UNESCO Chair
at Columbia University offered research facilities to PIR for producing
this book, supported warmly by UNESCO Director General Federico
Mayor and by Drs. Jorge Werthein and Pierre Lasserre of UNESCO, by
Jonathan Cole, Provost of Columbia University, and by Vice Provosts
Michael Crow and Peter Eisenberger. Many thanks are owed to them
all. Research support from the U.S. National Science Foundation and the
vii
viii
Preface
Sloan Foundation to Columbia University were very valuable in com­
pleting this book.
In the process of putting this book together I learned a great deal from
the authors. I found all the chapters interesting and at times challenging.
Some are pathbreaking. It is my pleasure to offer this book in honor of
the man who inspired them.
Graciela Chichilnisky, New York, July 1998
Contributors
Kenneth J. Arrow
Joan Kenney Professor of
Economics, Emeritus
and Professor of Operations
Research
Department of Economics
Stanford University
Stanford, CA 94305-6072
USA
Graciela Chichilnisky
UNESCO Professor in
Mathematics and Economics
Director, Program on Information
and Resources
Columbia University
405 Low Memorial Library
New York, NY 10027
USA
Tito Cordelia
Professor, CORE
Universite Catolique de Louvain
34 Voie du Roman Pays
B-1348 Louvain la Neuve
Belgium
Peter Coughlin
Professor, Department of
Economics
University of Maryland
College Park, MD 20742
USA
IX
Vladimir I. Danilov
Professor, Central Institute of
Economics and Mathematics
Russian Academy of Sciences
Krasikova 32 Moscow 1 17418
Russia
Jacques Dreze
Professor, CORE
Universite Catolique de Louvain
34 Voie du Roman Pays
B-1348 Louvain la Neuve,
Belgium
Frank Hahn
Professor, Faculty of Political
Economy
University of Siena
53100 Siena
Italy
Peter Hammond
Professor, Department of
Economics
Stanford University
Stanford, CA 94305
USA
Geoffrey Heal
Garrett Professor of Public Policy
and Corporate Responsibility
Columbia University
Graduate School of Business
New York, NY 10027
USA
x
Contributors
Walter P. Heller
Professor, Department of
Economics
University of California at San
Diego
9500 Gilman Drive
La Jolla, CA 92093-0508
USA
Peter H. Huang
Professor of Law
University of Pennsylvania
Law School
3400 Chesnut Street
Philadelphia, PA 19104
USA
USA Gleb Koshevoy
Professor, Central Institute of
Economics and Mathematics
Russian Academy of Sciences
Krasikova 32 Moscow 117418
Russia
P.
B. Linhart
Information Sciences Center
AT&T Lab-Research
Florham Park, NJ 07932
USA
Enrico Minelli
Professor, CORE
Universite Catolique de Louvain
34 Voie du Roman Pays
B-1348 Louvain la Neuve
Belgium
Edmund S. Phelps
Professor, Department of
Economics
Columbia University
1004 International Affairs
Building
Mail Code 3308
New York, NY 10027
USA
Heracles Polemarchakis
Professor, CORE
Universite Catolique de Louvain
34 Voie du Roman Pays
B-1348 Louvain la Neuve
Belgium
Roy Radner
Professor, Stern School of
Business
New York University
44 W. 4th Street
New York, NY 10012
USA
Alexandr I. Sotskov
Professor, Central Institute of
Economics and Mathematics
Russian Academy of Sciences
Krasikova 32 Moscow 1 17418
Russia
Ross M. Starr
Professor, Department of
Economics
University of California at San
Diego
9500 Gilman Drive, Dept. 0508
La Jolla, CA 92093-0508
USA
David A. Starrett
Professor, Department of
Economics Building #235
Stanford University
Stanford, CA 94305
USA
Maxwell B. Stinchcombe
Professor, Department of
Economics
University of Texas, Austin
Austin, TX 78712
USA
Contributors
Hirofumi Uzawa
Professor, Research Center on
Global Warming, RICF
The Japan Development Bank
1-9-1 Otemachi, Chiyoda-ku
Tokyo 100
Japan
xi
Ho Mou Wu
Professor, Department of
Economics
College of Law
National Taiwan University
Taiwan ROC
SEC TI ON I
Information and markets
Introduction
Graciela Chichilnisky
The mystery of brilliant productivity will always be the posing of new
questions, the anticipation of new theorems that make accessible valu­
able results and connections. Without the creation of new viewpoints,
without the statement of new aims, mathematics would soon exhaust
itself in the rigor of logical proofs and begin to stagnate as its substance
vanishes. Thus, mathematics has been most advanced by those who dis­
tinguished themselves by intuition rather than by rigorous proofs. 1
Few people fit this description. Kenneth J. Arrow is one of them. Who
is Kenneth Arrow?
Although very well known, Arrow remains somewhat of a mystery. His
brilliant productivity over a period of about fifteen years - from 1950 to
the mid-1960s - spanned the most interesting fields in economics, bringing
the power of mathematics and statistics to bear on novel approaches to
economic analysis and important issues of economic policy. He left an
important mark on the fields of market economics, social choice and
welfare economics, the economics of uncertainty, information, and math­
ematical programming. After that period the fountain of innovative ideas
shifted ground. The shift took him away from pathbreaking innovation
and into somewhat more conventional thinking,2 and increased his pro­
fessional ascendancy. Since the late 1960s Arrow's role as an editor and
intellectual organizer has been consolidated in several books and edited
volumes offering the last word on contemporary history of economic
thought. The shift was somewhat surprising. Why this change in gears?
The change has been attributed to his professional generosity - his pro­
clivity for never saying no to a request - and for concentrating mostly on
1
Herman Wey! reproduces this quote from Felix Klein's lectures on the history of
Mathematics, in his
Unterrichtsblatter ftir Mathematik und Naturwissenschaften 38, 177-8
(1932).
2
Without, however, changing the level of mathematical formalization of his work.
3
4
G. Chichilnisky
the work of others. There is, however, an alternative interpretation.
Innovation, some say, is costly and can lead to professional unease. This is
particularly true in economics, a field where dissidence and cynical values
abound. Arrow's originality and creativity had a cost. Is it possible that
Arrow decided to follow the smoother road - a safer road which leads to
professional acceptance, preeminence, and influence?
Arrow's multifaceted personality may explain the mystery. He always
appears to reflect back what the observer projects upon him. A man
at home in the most staid and conservative academic institutions, Arrow
has nevertheless won over many of those who have sought to change the
academic rules. Kenneth Arrow was always an insider in the clothes of
an outsider. His economics appealed to those who prefer raw and free
markets, as well as to those who prefer restrained markets, or even justice
and planning. Ned Phelps's chapter in this book touches on this facet of
his personality. Arrow's work appealed to those who prefer realism to
elegance, and also to those who prefer elegance over realism. On a per­
sonal level this made him a very popular figure to very different audi­
ences. His disarmingly candid and charming demeanor has a cautious
streak. Arrow's beautiful blue eyes reflect wonder, and shine with intel­
ligence and humanity while incisively measuring up the personality and
weakness of the opponents. Arrow does not win an argument. He seeks
to win the other side over. Often he succeeds.
The source of this somewhat unusual personality may be found in his
life experience growing up in New York City. The Depression left on
Arrow an indelible mark. His father was a victim of the largest and most
severe wave of unemployment recorded in this country, and this may
have created deep insecurities which meshed with remarkable intellec­
tual clarity and strength. This combination could have originated an
unusual and appealing personality.
Born in 1921 in New York City to Harry and Lillian Arrow, young
Kenneth was raised in the city and did his undergraduate studies at that
remarkable educational institution: City College of New York. After
graduating in 1940, he went in 1941 to Columbia University where he
studied under its great original thinker, Harold Hotelling. Columbia was
at this stage the top U.S. institution in economics. Yet little enthusiasm
existed at Columbia for what is now known as neoclassical price theory,
the field on which Arrow's contributions are based. All attempts to intro­
duce formal or rigorous thinking at Columbia have met with hostility
during the years, even at present. In this context Arrow's Ph.D. disserta­
tion, filed in 1950 under Albert Hart, was hardly recognized as a contri­
bution to economics. Instead it started a new era in the field now called
social choice theory.
Introduction
5
Arrow says that he was led to study social welfare functions at Rand
and through this he discovered results on elections at the same time
as Duncan Black. He went on to formalize an axiomatic theory in his
dissertation-monograph, "Social Choice and Individual Values," which
appeared in 1951. His contribution was in a way small, but in another,
decisive. His generalization of famous voting paradoxes in an accessible
yet formal manner attracted widespread attention from unexpected
quarters. His result, called an "impossibility theorem," was mysterious
and teased the imagination of the reader. Here is Kenneth Arrow
proposing something so simple that surely it can be solved. Yet he shows
it cannot. His elementary techniques teased the reader even more.
Everyone could read his results, without even knowing calculus, every­
one could try his or her hand at the problem. The mystery propelled
many to write and rewrite Arrow's results in different forms and varia­
tions, leading to what some critics called a combinatorial patchwork. But
the sheer volume of the field prevailed and became known as social
choice theory.
Several factors delayed Kenneth Arrow's completion of his graduate
studies. A major one was World War II. Arrow served with the Weather
Division of the Army Air Force where he wrote his first scientific paper,
"On the use of winds in flight planning." In 1946 Arrow returned to
Columbia for doctoral studies with Harold Hotelling; in 1947 he joined
the Cowles Foundation at the University of Chicago where Jacob
Marschak, Leo Hurwicz, and Tjallings Koopmans were on the faculty.
Arrow considered becoming an actuary but Koopmans advised him
against it.
In 1947 Kenneth Arrow married Selma Schweitzer, then a graduate
student at the University of Chicago. In 1950 he completed his Ph.D. dis­
sertation at Columbia, published in 1951 under the title Social Choice
and Individual Values. Immediately thereafter he published An Exten­
sion of the Basic Theorems of Classical Welfare Economics, developed
for the Berkeley Symposium on Mathematical Statistics and Probability,
proving formally that a competitive equilibrium is Pareto efficient.
Kenneth Arrow joined Stanford University in 1949, as an assistant
professor of economics and statistics.
In the early 1950s he collaborated with Gerard Debreu in the for­
malization of Walrasian general equilibrium theory and the proof of the
existence of a competitive equilibrium. Both were working on the same
problem, each facing different difficulties, when Tjallings Koopmans
brought them together. Their work is a triumph of simplicity and gener­
ality, and is based on a simple but crucial insight: that a market equilib­
rium is no more than a balance between supply and demand. They never
6
G. Chichilnisky
explain how the market behaves outside of equilibrium, or how it adjusts
toward an equilibrium. This has puzzled many scientists from other dis­
ciplines, where an equilibrium is the rest point of a dynamical system.
The work of Arrow and Debreu defines an equilibrium without defining
a dynamical system. Prior to their work, a market equilibrium was for­
malized as the "rest point" of price or quantity adjustments processes
representing trade. Their approach is different. It is obviously weak in
explaining the dynamics of the system - how markets come to equilib­
rium - but as often happens its weakness is also its strength. It cuts short
the unending arguments about how trading occurs outside of equilibrium
which had plagued the mathematical foundations of the theory of
markets. That supply must match demand was, however, never debated;
therefore their work cut the Gordian knot. They solved the problem
by bypassing it. Concentrating only on the uncontroversial market
clearing conditions, supply matck demand, they followed Nash and
Von Neumann and proved the existence of a market clearing
equilibrium by fixed point methods. This led to their paper, "Existence
of an Equilibrium for a Competitive Economy," and to the successful
adoption of what is now called the Arrow-Debreu model as an abstract
standard with respect to which market behavior is measured. With
Leo Hurwicz, Arrow collaborated during the mid-1950s on issues con­
nected with mathematical programming, decentralization, and the sta­
bility of competitive equilibrium.
In 1962 Arrow served on the research staff of the Council of
Economic Advisers; he was a visiting fellow at Churchill College,
Cambridge, in 1967, where he collaborated with Frank Hahn, leading to
the production of his book General Competitive Analysis. He also col­
laborated on studies on continuous time optimal control with Mordecai
Kurz, resulting in his book Public Investment, the Rate of Return and
Optimal Fiscal Policy. Arrow taught at Harvard University from 1968 to
1979, a period during which his productivity slowed down. He received
the Nobel Prize in Economic Sciences in 1972, at the age of 51. In 1974
he set an agenda for the future in his presidential address to the
American Economic Association and in his Fels Lectures, The Limits to
Organization, published about the same time. It was in this year that I
met him. Invited by Kenneth Arrow to Harvard University as a research
associate, I dedicated myself to research and then turned to teaching as
a lecturer, until 1978. This period did not appear to be specially produc­
tive at the time, but during those four years I completed my second Ph.D.
dissertation, this one in economics, and produced new research on what
would become recurrent themes of my work, introducing and develop­
ing the concept of basic needs, creating a model of North-South trade,