Markets, information and uncertainty essays in economic theory in honor of kenneth j arrow

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
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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,


Introduction

7

introducing Hilbert spaces in infinite economies, developing an alterna­
tive topological theory of social choice, and laying the foundations of
limited arbitrage as a unifying conceptive resource allocation. The latter
two results establish that two seemingly unrelated strands in Arrow's
work, his impossibility theorem of social choice and his theorem on the
existence of a competative equilibrium, are so closely related as to be
one and the same. Based on this, I introduced3 a new concept of social
diversity, defined in terms of endowments and preferences of the traders
of an Arrow-Debreu economy. A limitation on social diversity (limited
arbitrage) is both necessary and sufficient for a resolution of the social
choice problem and for the existence of competitive equilibrium. This

relation between social choice and markets was not known to Arrow
himself. I did not realize this as I began to develop the topological
approach to social choice which is at the foundation of this work. The
question came to me as a surprise: Could one find such a close connec­
tion between two parts of Arrow's work market equilibrium and social
not apparent to their author? The mystery remains today.
Did Kenneth Arrow have an influence on my work? Yes. But in a
rather unusual way. He never suggested a problem, and seemed extraor­
dinarily interested in topics of which he knew little and on which he had
never worked - an unusual trait. His attitude, at the time and even now,
was that of an enthusiastic Ph.D. student rather than that of a professor. I
do not know how he elicited from me the intellectual production he did.
Except that he faithfully and patiently had lunch with me once a week at
the Harvard Faculty Club which had then opened its doors to women for
the first time; he endured all my bouts of enthusiasm, shared my despair
about the referees and editors who rejected my work, and corrected and
offered criticisms of my writing. He even proofread my early papers. This
behavior, I now know, was somewhat extraordinary. I have been trying to
imitate Arrow with my own students, on the grounds that one thanks
one's intellectual parents by giving more of the same to others, and it
has proven difficult. Those years at Harvard researching with Kenneth
Arrow's support were happy and fruitful. Can one ask for more?
I left Harvard for Columbia University just at the time that Arrow
returned to Stanford University, where he became Joan Kenney
Professor of Economics and Professor of Operations Research in 1978.
He retired in 1991.
Despite his urban origins, or perhaps because of them, Arrow always
sought suburban life. He lives on the Stanford campus with his wife. They
adopted two sons, David and Andrew. Both followed artistic careers,
3

G. Chichilnisky, "Arbitrage, gains from trade, and social diversity: A unified perspective
on resource allocation," American Economic Review 84, No. 2, May 1994, 427-34.


8

G. Chichilnisky

which Arrow considers more risky than the academic road. Since his
retirement in 1991 Arrow has embarked on an ambitious traveling
schedule, becoming part of many policy oriented institutions and com­
mittees, including the Intergovernmental Panel on Climate Change
(IPCC) and the Blue Ribbon Committee created to evaluate the
damages done by the Exxon Valdez oil spill in Prince Andrew Sound.
Both dealt with environmental issues, the former on a global scale.
This book follows another, Essays in Honor of Kenneth Arrow,
volumes I, II, and III, edited by W. Heller, R. Starr, and D. Starrett (1986),
in that it contains the contributions of friends and students of Kenneth
Arrow who write in his honor on topics on which he inspired them.
The present book has a somewhat different origin and purpose,
however. It emerged from the celebration of Arrow's seventieth birth­
day at a workshop entitled "Columbia Celebrates Arrow's Contri­
butions" which took place at Columbia University in October 1991. The
papers presented at that workshop to a most enthusiastic audience were
special. It was a heartwarming event. It was then suggested that the
papers, and those of other authors who could not attend, be compiled in
a volume in Arrow's honor to memorialize the happy occasion.
Since I have been puzzled by Arrow's recent reluctance to offer path­
breaking ideas, I insisted on a piece from him. His chapter, Information

and the Organization of Industry, is based on a lecture, Lectio Magistralis
of the Laurea Honoris Causa, which he gave when he received an hon­
orary degree from the Universita Catolica of Milano, on April 12, 1994. It
is published with the permission of the Universita Catolica.Arrow's paper
makes tantalizing assertions which are not proved or developed fully. The
paper could lead to seminal developments, but Arrow said he would have
preferred it to contain a formalization of its concepts. His view of formal­
ization is that it helps develop a subject. In this he is correct. Formalization
lays the foundations on which others can build solid edifices. In any case
the future holds the key: His piece belongs to the future.
Arrow's paper is about the economics of information and the organi­
zation of industry, a subject which has interested him for many years.
Arrow reminds us that information is a rather unusual commodity in that
the same piece of information can be used over and over again, by the
same or different producers. Once created, information is not scarce in
the economic sense, so it is difficult to make information into property.
Furthermore, the use of information leads to the most extreme form of
economies of scale, the existence of fixed costs. Information therefore
challenges the basic concepts on which markets are constructed. Two
social innovations, patents and licenses, are designed to create artificial
scarcities where none exist naturally. These scarcities are needed to


Introduction

9

create incentives for undertaking the production of information in the
first place. This is because information can be very costly to produce.
Arrow's paper walks us through the far reaching implications of the

peculiar properties of knowledge for the structure of markets and the
stability of the firm. It explains his perception of the shift in today's
industrial societies. Information is becoming one of the most valuable
"commodities" in the industrial world. Though costly, once produced it
should be distributed as widely as possible for efficiency, because it can
be shared without diminishment. The informational content in software,
an extremely important sector of today's economy, is used to exemplify
the issues. Arrow develops this theme, explaining how an information
theory of value could be developed, and the impact this could have on
the theory of the firm and property rights. His piece is somewhat futur­
istic: It maps out the main problems the "knowledge intensive" economy
is likely to meet as it proliferates.
Kenneth Arrow's chapter and the one that follows, by Vladimir
Danilov, Gleb Koshevoy, and Alexandr Sotskov, emphasize the need for
a new algebra to understand the economics of information. As already
pointed out, information is an unusual good in that it can be used time
and again without exhausting itself. The chapter by Danilov, Koshevoy,
and Sotskov moves matters forward by defining an algebra that formal­
izes this characteristic and studies the existence of prices that clear
markets with information goods such as software. The three authors .
define an algebraic structure, a semilattice, to deal with the unusual fea­
tures of information. In their economy every consumer is a producer.
They prove the existence of a market equilibrium and show that it
belongs to the core, namely, it is an allocation of information goods from
which no coalition of traders would wish to deviate.
These two essays are building blocks for the new economics of infor­
mation. They are about an issue leading to a major change in the world
economy, one which Arrow anticipated in his work many years ago. I
called this change the "knowledge revolution," because I believe the
most important input to production now is knowledge, rather than

capital and labor as in an industrial society, or land, as in an agricultural
society. Knowledge can be encoded in books or on electronic equipment
but it is mostly held in human brains and is thus often called human
capital. Information is not the same as knowledge. Information is the
medium in which knowledge is processed, stored, and communicated.
Knowledge is the content. And it is the content, aided by radical tech­
nological changes in the medium, that is driving change today.
The transition from the industrial to the knowledge society is not
even, but it is deep and swift. One may say that we are undergoing a


10

G. Chichilnisky

social and economic revolution which matches the impact of the agri­
cultural and industrial revolutions. I like to call it the knowledge revolu­
tion.4 Information technology is the most obvious manifestation of this
change, but the real change is in human knowledge, its creation and dis­
tribution, and the corresponding changes in the organization of society.
Knowledge has always been the force driving change in the world
economy. However, by releasing the constraints on the ability to repro­
duce, store, and communicate knowledge, information technology fuels
knowledge today as never before. Information fuels the engine of eco­
nomic progress, knowledge. The dynamics in the world economy today
is in computers and software, in telecommunications and biotechnology,
in entertainment and financial markets. It is not, as was previously
thought, a transformation from industrial production to services. It is
a transformation from a resource-intensive to a knowledge-intensive
economy. This revolution can lead to the advent of the knowl­

edge society, a society global in nature, deeply innovative in and de­
pendent on the use of human knowledge and, it can be argued,
conservative in environmental use: a society centered on human capital
where diversity is the foundation of innovation and where knowledge is
power.
The first part of this book is about knowledge, uncertainty and infor­
mation, and the challenges which they pose to economic theory today.
Uncertainty is lack of information. As Arrow said, "What information
does do is reduce uncertainty." Thus information and uncertainty are two
sides of the same coin.
The problem of uncertainty is part and parcel of the human condi­
tion. It originates in the fact that time is a dimension in which we are
short. Humans live only for a few years and cannot travel across time. In
geometrical terms, we are "flat" in the time dimension. Because we
cannot observe well through time, we cannot predict. Due to this lack of
information, we are uncertain.
The short span of a human's life contrasts with the long life of the
human species. Humans fit into their species as cells fit into an organism.
We are important parts of a larger animal and even as the parts die, the
whole survives and grows. The part and the whole share common inter­
ests but on occasion they have contrasting goals and needs.
All this creates a fascinating tension often perceived in economic
organizations. It is the tension between decentralization, the pursuit of
4 See also G. Chichilnisky, The Knowledge Revolution, Columbia University Discussion

Paper 1995 and Journal of International Trade and Economic Development, 7(4):39-54,
1996.


Introduction

11

the individual interest, and centralization, the pursuit of the interests of
the whole society. Sometimes they meet and sometimes they pull apart.
One can say that an essential feature of human societies is the ten­
sion between the interests of the individual and those of the group.
Economics inherits the tension between individual interests and social
interests. Centralization and decentralization, markets and planning are
examples. Kenneth Arrow's work illustrates this well. Starting from his
work on social choice and individual values, he moved swiftly toward the
study of that quintessentially decentralized organization, the competitive
market. Throughout he kept his eyes firmly on the fundamental issues of
uncertainty and information. Both are at the root of the tension between
individuals and society.
In this book each author reflects on an aspect of the uncertainty­
information axis, which, as I argued above, is simply a representation of
the tug-of-war between the individual, whose life is short and whose
capacities to predict are limited, and society, which exists in a more atem­
poral world.
Each writer has a close connection with Kenneth Arrow through life
and work, and reflects on the aspects that most deeply touched him or
her. Each contributor offers a scientific contribution in the spirit of a first
step toward a new theoretical development. Each seeks a better under­
standing of how the economy works. The essays are not just technical but
often profound. It is a pleasure for me as an editor to offer this book in
celebration of Kenneth Arrow's contributions.
The first part of the book deals with markets and information, and is
followed by the other side of the coin: markets and uncertainty. There
are several chapters dealing with "endogenous uncertainty," uncertainty

partly caused by nature and lack of information, and partly by human
action. Discussed minimally for several years, this interesting subject was
introduced formally by Partha Dasgupta and Geoffrey Heal5 in the
context of development paths where present actions alter the environ­
ment and thus future productivity, and treated informally by Mordecai
Kurz in a comment on the Kester-Stigum model.6 Optimal growth paths
with endogenous uncertainty were first studied by Heal.7 The first theo5 P. Dasgupta and G. Heal, Economic Theory and Exhaustible Resources, Cambridge

University Press, 1979.
6 Kurz, The Kesten-Stigum Model and the Treatment of Uncertainty in Equilibrium
Theory, in M. Balch, D. McFadden, and S. Wu (eds.) , Essays in Economic Behavior under
Uncertainty, North Holland, 1974.
7 G. Heal, Economics and Climate: A Framework for Policy Design under Uncertainty, in
K. Smith and Ann Dryden (eds.) , Advances in Applied Macroeconomics, Greenwich:
J.A.I. Press, 151-8.


12

G. Chichilnisky

rems on the existence of a general equilibrium in markets with endoge­
nous uncertainty are in Chichilnisky and Wu,8 Chichilnisky, Dutta, and
Heal,9 and Chichilnisky. 10 Several chapters on the subject are included
in this book and are discussed below.
Jacques Dreze's contribution is an insightful discussion of uncertainty,
starting from Arrow's 1953 paper to the most recent literature on
endogenous uncertainty. Dreze's chapter is useful because it discusses
several ways in which the general equilibrium theory of markets has
incorporated uncertainty and lack of information. He discusses tempo­

rary equilibrium models of markets in which forward markets are not
active and expectations about prices are used to make decisions. Dreze
includes a short but interesting discussion linking this with the theory of
general equilibrium with incomplete markets, in which certain markets
are not open.
Frank Hahn's chapter presents a model of a two-period economy
where traders take into consideration that there are several possible
equilibrium prices in the second period. This contrasts with the "rational
expectations" literature in that here expectations about the second
period equilibrium prices are a set-valued, as opposed to a single-valued,
function. Hahn shows that this leads to rather different behavior. In par­
ticular, if rational agents predict correctly the set of possible market
clearing prices in the second period, the economy will never reach an
equilibrium.
My own chapter takes a step in formalizing Arrow-Debreu markets
to include uncertainty about prices. Aware of our uncertainty, we intro­
duce markets for hedging against unfavorable consequences of price
changes. I introduce formally and discuss the concept of endogenous
uncertainty which is caused by a combination of nature and human
actions. Price uncertainty is a typical example of endogenous uncertainty.
But how to hedge against the risks that we ourselves cause? Not per­
fectly. We introduce new markets, markets where the securities hedge
against endogenous risks. This is precisely the role of derivative markets,
which hedge against the negative consequences of changes in crucial
indices. I define a concept of general equilibrium in which the state space
and the asset markets are defined as part of the equilibrium. Traders do
G. Chichilnisky and H. M. Wu, Financial Innovation and Endogenous Default in
Incomplete Asset Markets, Stanford Institute for Theoretical Economics Technical Report
No. 50, 1991.
9 G. Chichilnisky, J. Dutta, and G. Heal, Price Uncertainty and Derivative Securities,

Working Paper, Columbia Business School, 1993.
10 G. Chichilnisky, Markets with Endogenous Uncertainty: Theory and Policy, Theory and
Decision, 1996, 99-131.
8


Introduction

13

not know the equilibrium prices a priori. An equilibrium consists of a
state space, the corresponding asset markets, and prices yielding fully
insured and Pareto efficient allocations which clear the markets. The
essay proves the existence of a market equilibrium building on recent
results in Chichilnisky, Dutta, and Heal (1993).
Following the work of J acques Dreze, Frank Hahn, and myself, the
chapter by Ho-Mou Wu and Peter Huang studies a general equilibrium
model of an economy where traders also have uncertainty about prices.
Using a somewhat different approach, the authors discuss how investors
can hedge against spot price uncertainty by trading in complete markets
for European options when they know the equilibrium price correspon­
dence, and when they do not. They discuss in general terms what condi­
tions may be needed to ensure the existence of equilibrium.
Chichilnisky and Heal's chapter deals with markets facing unknown
risks and suggests how a new type of instrument can hedge these risks
efficiently. The essay is concerned with individual risks whose frequencies
are unknown, perhaps because they are relatively new - such as the health
effects of a recently discovered environmental hazard. Opinions may be
widely different about how the population is affected, and there are no
reliable actuarial data. Under these conditions, we study financial instru­

ments that suffice to reach efficient allocations of risk bearing. The
problem is formalized in a general equilibrium economy with incomplete
markets. Introducing simultaneously an array of mutual insurance poli­
cies to cover individual risks and security markets for the correlated part
of the risks leads parsimoniously to an efficient allocation. The results explained less formally in a previous essay by the same authors11 - suggest
the creation of derivative instruments called "catastrophe futures." These
instruments came into existence soon after our first article was published,
and are now traded in the Chicago Board of Trade. This chapter also antic­
ipates the emergence of another instrument, a hybrid combining insur­
ance and security elements, called "catastrophe bundles," which is now
coming to existence. The results anticipated the recent trend for securiti­
zation in the insurance and reinsurance industries worldwide.
Turning the coin over, we pass on to the subject of markets with imper­
fect information. The next chapters deal with this issue. Ned Phelps pre­
sents a model of intertemporal equilibrium with unemployment based
on the maximization of expected lifetime utility when workers and man­
agers have imperfect, differential information. In this setting, an enter­
prise is a firm in the sense that it offers continuing employment to every
11

Chichilnisky and Heal, Global Environmental Risks, Journal of Economic Pespectives,
1994.