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 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 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 Economics 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 Information and the organization of industry Kenneth J Arrow 19 Equilibrium in an economy with information goods Vladimir I Danilov, Gleb A Koshevoy, and Alexandr I Sotskov 26 Section II Uncertainty and finance The formulation of uncertainty: Prices and states Jacques H Dreze 45 A remark on incomplete market equilibrium Frank Hahn 67 Existence and optimality of a general equilibrium with endogenous uncertainty Graciela Chichilnisky 72 Market equilibrium with endogenous price uncertainty and options Peter H Huang and Ho-Mou Wu 97 Catastrophe futures: Financial markets for unknown risks Graciela Chichilnisky and Geoffrey Heal v 120 v1 Contents Section III Market externalities and justice 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 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 Hammond 17 Redistribution by a representative democracy and distributive justice under uncertainty Peter Coughlin 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 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 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 372 P Coughlin where, as before, (} is the group that voter i is in and k is the index for the "other" candidate Once the assumption that unobservable factors enter into the voters' choices has been cast in this form, it becomes clear that for the selection probabilities for a given voter i to be fully specified, the only thing to be added at this point is an appropriate assumption about the distribution of the random variable f.;c('ljJc) - f.;k( 'ljJk) Since we are using the logit model here, we are specifically assuming that this random variable has a logistic distribution With the candidate expectations now under consideration, a unique electoral equilibrium exists and is the pair of candidate positions ('!jJj,'!jJ!) at which '!jJj 'ljJ!, and their common position maximizes (using the notation defined in Section 3) the following weighted sum of the voters' Bernoulli utility functions on the set of feasible income distributions:5 = (5.3) This conclusion implies that the income distribution which maximizes (5.3) is the income distribution that can be expected in any representa­ tive democracy in which the assumptions in Section and this section's assumption about the candidates' expectations are satisfied Explicitly solving for the maximum of (6.4)6 reveals that the income distribution that can be expected is one in which the amount that a group j will get will be influenced by whether (again, making use of the nota­ tion introduced in Section 3) the inequality f3e g ( (}) � -·Y> k 2, l;ee /31; g(s) (5.4) I holds for the group The equilibrium income distribution itself can be described as follows First, if the inequality in (5.4) does not hold for a given group (that is, the income level on the left-hand side of (5.4) does not exceed the legal minimum for the group), then the corresponding constraint Se ::::: ke becomes binding; the group, therefore, gets what it is required to get by law - and nothing more Second, for each remaining group (that is, for each group for whom the income level on the left-hand side of (5.4) exceeds kj), the income that it will get is se f3e/3· g(e)( ) l;2,e A 1; g s = · · [ Y See Coughlin ( 1992, pp 38, 52-7) - 2, k1; 1;eB ] See Coughlin (1992, pp 54-6) (5.5) Redistribution and distributive justice under uncertainty 373 Thus the proportion of the remaining income that will go to that group is the "normalized" product of the coefficient /3i from its utility function and its size (that is, the ratio of /3i g(j) to the sum Lee A {/311 · g( ti)}) One important implication of these results is that (this time around) the relevant portion of Aranson's statement quoted at the end of the preceding section is the portion that applies when an electoral equilib­ rium exists As a consequence, this time around, his statement tells us that the income distribution the candidates select can be interpreted as what is in the public interest, as revealed by the democratic process This implication follows in particular because (since an electoral equilibrium exists) the model is one in which the outcome does not "exhibit stochastic variety and, on occasion, internal inconsistency" and, hence, is free of the characteristics which Buchanan (1974) argued are inappropriate for an institution that is going to carry out redistribution These results also have another important implication Kenneth Arrow wrote: · In the prescription of economic policy normative questions of distributive justice inevitably arise The implicit basis of economic policy judgment is some version of utilitarianism (1985, p 140) Amartya Sen similarly observed: [I]n traditional welfare economics, when the notion of justice has been invoked, it has typically been seen only as a part of a bigger exercise, viz., that of social welfare maximization (1987, p 1039) Solving (5.3) maximizes a Benthamite social welfare function (in partic­ ular, one which uses the voters' utility functions on the set of possible income distributions) Therefore, solving (5.3) is clearly an identifiable and defensible principle of justice Therefore, since a representative democracy will select an income distribution which maximizes (5.3), a representative democracy selects an income which reflects an identifiable and defensible principle of justice Conclusion This chapter has investigated whether Public Choice Theory leads us inexorably to the conclusion that, as Brennan and Buchanan (1985) sug­ gested, redistribution via government in a representative democracy does not reflect an identifiable and defensible principle of distributive justice I addressed this normative question in the context of the positive 374 P Coughlin models of representative democracy developed in the Public Choice literature The first step in the analysis is the specification of a model of redis­ tribution in a representative democracy The first major conclusion is about the model obtained by assuming that voting is fully determined by the voters' preferences on income distributions In this first case, redistribution by representative democracies does not reflect an identifiable and defensible principle of justice, as in the conclusions reached by Brennan and Buchanan (1985) The second major conclu­ sion is for the alternative model of representative democracy where candidates are uncertain about the choices voters will make and use a logit model for voters' choices In this alternative case, redistribution via government does reflect an identifiable and defensible principle of justice Finally, returning to the central question in this chapter: The second major conclusion clearly implies that the answer is "No, Public Choice Theory does not inexorably lead us to the conclusion that redistribution via government in a representative democracy fails to reflect any identifiable and defensible principle of justice." It is now clear that the Public Choice literature does not support any sweeping normative assessment that either declares that redistribution via government in a representative democracy always reflects an identifiable and defensible principle of distributive justice or declares that it always fails to so Rather, any such assessment necessarily fails to reflect accurately either what happens when "on the one hand" voting is fully determined by the voters' preferences on income distributions or when "on the other hand" political candidates are uncertain about the choices voters will make and, therefore, use an econometric model (such as a logit model) of voter choice behavior References Aranson, P 1981 American Government: Strategy and Choice, Cambridge, MA: Winthrop Publishers Arrow, K 1963 Social Choice and Individual Values 2nd ed New York: Wiley Arrow, K 1969 Tullock and an existence theorem Public Choice, 6:105-1 Arrow, K 1970 Essays in the Theory of Risk Bearing Amsterdam: North­ Holland Arrow, K 1973 General economic equilibrium: Purpose, analytic techniques, col­ lective choice Les Prix Nobel en 1972, Stockholm: Nobel Foundation, pp 253-72 Arrow, K 1974 The Limits of Organization, New York: Norton Redistribution and distributive justice under uncertainty 375 Arrow, K 1981 Optimal and voluntary income distribution In Economic Welfare and the Economics of Soviet Socialism, ed S Rosefielde Cambridge, UK: Cambridge University Press, pp 267-88 Arrow, K 1985 Distributive justice and desirable ends of economic activity In Issues in Contemporary Macroeconomics & Distribution, ed G Feiwel Albany: State University of New York Press, pp 134-56 Brennan, G., and J Buchanan 1984 Voter choice: Evaluating political alterna­ tives American Behavioral Scientist, 28:185-201 Brennan, G., and J Buchanan 1985 The Reason of Rules: Constitutional Political Economy Cambridge, UK: Cambridge University Press Broome, J 1988 Review of The Reason of Rules: Constitutional Political Economy by Geoffrey Brennan and James Buchanan Economica, 55:282-3 Buchanan, J 1954 Individual choice in voting and the market Journal ofPolitical Economy, 62:334-43 Buchanan, J 1974 Who should distribute what in a Federal system? In Redistribution Through Public Choice, ed H Hochman and G Peterson New York: Columbia University Press, pp 22-42 Buchanan, J 1975 The Limits of Liberty: Between Anarchy and Leviathan Chicago: University of Chicago Press Buchanan, J 1977 Freedom in Constitutional Contract College Station: Texas A&M Press Buchanan, J 1984 Politics without romance: A sketch of positive Public Choice Theory and its normative implications In The Theory of Public Choice II, ed J Buchanan and R Tollison Ann Arbor: University of Michigan Press, pp 1-22 Buchanan, J., and G Tullock 1962 The Calculus of Consent Ann Arbor: University of Michigan Press Coughlin, P 1992 Probabilistic Voting Theory Cambridge, UK: Cambridge University Press Enelow, J., and M Hinich 1984 The Spatial Theory of Voting Cambridge, UK: Cambridge University Press Lindbeck, A 1985 Redistribution policy and the expansion of the public sector Journal of Public Economics, 28:309-28 Lindbeck, A., and J Weibull 1987 Balanced-budget redistribution as the outcome of political competition Public Choice, 52:273-97 McFadden, D 1982 Qualitative response models In Advances in Econometrics, ed W Hildenbrand Cambridge, UK: Cambridge University Press, pp 1-37 Mueller, D 1976 Public choice: A survey Journal of Economic Literature, 14:395 433 Mueller, D 1979 Public Choice Cambridge UK: Cambridge University Press Mueller, D 1989 Public Choice II Cambridge, UK: Cambridge University Press Ordeshook, P 1986 Game Theory and Political Theory Cambridge, UK: Cambridge University Press Phelps, E 1987 Distributive justice In The New Pa/grave: A Dictionary of Economics, Volume , ed J Eatwell et al London: Macmillan, pp 886-8 Sen, A 1970 Collective Choice and Social Welfare San Francisco: Holden-Day Sen, A 1973 On Income Inequality Oxford: Clarendon 376 P Coughlin Sen,A 1974 Rawls versus Bentham: An axiomatic examination of the pure redis­ tribution problem Theory and Decision, 4, pp 301-10 Sen, A 1987 Justice The New Palgrave: A Dictionary of Economics, Volume 2, ed., J Eatwell et al London: Macmillan, pp 1039-43 Sen, A 1990 Justice: Means versus freedom Philosophy and Public Affairs, 19, pp 11-21 Shubik, M 1984 A Game Theoretic Approach to Political Economy Cambridge, MA: MIT Press Tullock, G 1983 Economics of Income Redistribution Boston: Kluwer Author index Aliprantis, C D., 115, 116 Allen, B., 52, 54 Allen, F., 236 Anderson, R M., 353 Aranson, P., 369 Argote, L., 179 Arrow, K J., 26, 27n3, 45, 46, 47, 53, 56, 60, 64, 67, 76, 97, 98, 99, 101, 102, 103, 104, 106, 17, 122, 144, 166, 206n7, 235, 301, 305n2, 322, 328, 329, 332, 334, 335, 362, 366nl, 367, 373 Arthur, W B., 193n4 Aumann, R J., 100n3 Balch, M., l ln5 Barro, R J., 309n8 Baumol, W J., 307n6 Becker, G S., 24, 148n4 Bernheim, B D., 309n9 Berns, A., 183 Bewley, T., 101, 353 Bisin, A., 236 Blanchard, 0., 157n8, 158 Bliss, C J., 355 Brandenburger, A., 100n3 Brennan, G., 363-70, 373-4 Broome, John, 364 Brown, D J., 14, 115, 16, 214n9 Bryant, W D A., 335 Buchanan, J M., 363-70, 373-4 Burkinshaw, 0., 16 Calvo, G A., 146, 148, 310, 350 Cass, D., 68, 102, 122, 254 Champsaur, P., 206n7 Chari, V V., 355 377 Chichilnisky, G., 10n3, 12, 13, 46, 57, 61, 62, 64, 68, 73n3, 74n4, 75, 76, 80, 89nll, 91, 92, 94, 95, 98, 100, 101, 102, 110, 121, 122, 131, 193n4 Choquet, G., 172 Clark, C W., 255 Clower, R W., 219 Cordella, T., 323 Coughlin, P., 368n2, 369, 371 Cournot, A A., 20 Crutchfield, J A., 255 Danilov, V I., 26, 27, 34, 35, 38 Dasgupta, P S., l ln4, 95, 167nl, 254 David, P A., 193n3, 203n6, 214n8 Debreu, G., 47, 53, 73n2, 75, 97, 98, 105, 106, 113, 127, 328, 329, 332, 352 Diamond, P., 332 Dierker, E., 127, 135n9 Dixit, A., 351, 356 Dreze, J., 48n6, 60n15, 61n16, 206n7 Dryden, A., lln6 Duffie, D., 97, 236, 352 Durlauf, S N., 236 Dutta, J., 12, 13, 46, 64, 73n3, 74n4, 75, 80, 89nl l , 91, 92, 94, 95, 98, 100, 101, 110 Enelow, J., 365, 368n3 Epple, D., 179 Farrell, J., 192, 193, 202, 204 Feldman, M., 353 Fischer, S., 350 Fisher, A., 305n2 Fisher, Irving, 352 378 �uthor index Foley, D., 238, 241, 245, 247 Fudenberg, D., 167nl Gabriel, P., 38 Gale, D M., 236, 353 Gary, M R., 129 Geanakoplos, J., 49n9, 50-2, 56, 60, 61, 112 Gilles, C., 353 Gollier, C., 61n16 Gordon, H S., 255 Grandmont, J M., 49n10, 50-2, 60, 61, 322 Gratzer, G., 26, 28, 36 Greenstein, S., 203n6, 214n8 Hahn, F., 46, 57, 61, 62, 63, 74n4, 75, 76, 94, 95, 101, 110, 236nl, 238, 328, 332 Hakansson, N H., 103 Haller, H., 220 Halmos, P., 78 Hammond, P J., 330-1, 351, 356 Hardin, G., 255, 259 Harrison, J M., 58 Hart, 0., 236, 239-40 Heal, G M., llnn4, 6, 12, 13, 46, 64, 73n3, 74n4, 75, 76, 80, 89nll , 91, 92, 94, 95, 98, 100, 101, 102, 110, 121, 131, 206n7, 214n9, 239, 254 Heller, W P., 8, 236, 237nn3,4, 250 Hendricks, K., 218 Henrotte, P., 95, 16 Henry, Cl., 206n7 Hicks, J., 45, 99, 232, 352 Hinich, M., 365, 368n3 Hoon, H T., 145, 146 Hotelling, H., 254 Huang, C., 100 Huang, P H., 112, 113 Hurwicz, L., 206n7, 301 Intriligator, M., 328nl Jevons, W S., 219, 223 Johansson, P.-0., 255 Johnson, D S., 129 Jordan, J S., 54 Judd, K., 353 Kaneko, M., 330-1 Karp, L., 355 Katz, M., 192, 193, 202, 203n6, 214n8 Klein, D., 355 Koopmans, T., 254, 315n15 Koshevoy, G A., 34, 35 Kotlikoff, L., 309n9 Kreps, D., 58, 100 Krutilla, J., 305n2 Ku, B I., 59, 112 Kurz, M., l ln5, 46, 56, 59, 68, 94, 99, 100, 101, 116, 117 Kydland, F., 350 Lawler, E., 221, 230 Lindbeck, A., 365, 367 Linhart, P B., 168, 176 Littlechild, S C., 192 Lofgren, K.-G., 255 Lovasz, L., 38 Lucas, R E., 352, 355 McFadden, D., l ln5, 322 McKenzie, L., 323 Magill, M., 51, 56, 59, 60, 61 Majumdar, M., 166, 189 Makarov, V L., 26 Makowski, L., 236, 239, 244 Maler, K.-G., 254 Malinvaud, E., 122, 123, 124n4, 125 Marschak, J., 45 Marshall, Alfred, 20 Mas-Colell, A., 103, 116 Maskin, E., 355 Meade, J., 312n12 Meadows, D., 306n3 Milgrom, P., 247n8 Mill, John Stuart, 20 Mirrlees, J., 332 Modigliani, F., 309n9 Morgenstern, 0., 338 Mueller, D., 365, 368, 369 Munro, G R., 255 Negishi, T., 109, 111 Neveu, J., 172 Newbery, D., 355 Norman, V., 351, 356 Author index Oates, W., 307n6 Ordeshook, P., 368n3, 370 Oren, S S., 192 Ostroy, J M., 219, 236, 239, 244 Peles, Y C., 168n2 Pesendorfer, W., 236 Phelps, E S., 144, 145, 146, 148, 149, 362 Piccione, M., 218 Pigou, A C., 254 Polemarchakis, H., 59, 112 Prescott, E C., 350, 352 Presman, E L., 189n7 Radner, R., 47, 53, 54, 166, 168, 176, 189 Rahi, R., 236 Ramsey, F P., 254 Roberts, J., 247n8 Rogawski, J., 219 Rogers, C A., 355 Rohlfs, J., 192, 201-2, 209 Rosenstein-Rodan, P., 236 Ross, S., 102, 111, 15 379 Staiger, R W., 355 Starr, R M., 8, 218, 219 Starrett, D A., 8, 236, 237n4, 305nl, 310, 312nnl2,13 Stiglitz, J., 147, 149, 167nl Stigum, Marcia, 50 Stinchcombe, M B., 218, 220nl Stokey, N L., 352, 355 Streufert, P., 74n4 Svensson, L E 0., 59, 60, 101, 116 Swinkels, J., 74n4 Tabellini, M., 355 Tahvonen, 0., 255 Tan, G., 218 Teplitz, C J., 180 Tesfatsion, L., 331, 350, 351, 358 Tintner, G., 45 Tirole, J., 167nl Tobin, J., 218, 231, 232 Tsomocos, D P., 102 Tullock, G., 363, 367 Uzawa, H., 254, 255, 273, 301, 303 Saloner, G., 192, 193, 202, 204 Salop, S C., 145 Samuelson, P A., 322, 335 Savage, L J., 46n3, 97 Schaefer, M B., 255 Scitovsky, T., 236 Scott, A D., 255 Selten, R., 330, 338 Sempere, J., 351 Sen, A., 356, 363, 364, 366nl, 373 Shafer, \V., 51, 56, 59, 60, 61 Shapiro, C., 147, 149, 192, 193, 202, 203n6, 214n8 Shell, K., 68 Shiller, R J., 98nl, 17 Shubik, M., 219, 367, 368n3 Smith, Adam, 20 Smith, K., l ln6 Smith, S A., 192 Sonnenschein, H., 51nll, 56n14 Sotskov, A I., 34, 35 Vanzandt, T., 168, 176 Ventura, L., 323 von Neumann, J., 338 \Valras, Leon, 217-18 \Veibull, Jorgen, 365 \Verner, J., 14 \Veyl, Herman, 3nl \Vicksell, K., 255 \Vooders, M H., 330-1 \Vu, H.-M., 12, 68, 95, 98, 99, 100, 101, 102, 112, 13, 116, 122 \Vu, S., l ln5 Young, A., 177n6 Zame, W R., 16 Zellner, A., 255 Zisman, M., 38 Subject index agents: in Arrow-Debreu economy, 67; called marketmakers, 237-9, 242-6, 250-1; information partition by, 53-4; in overlapping generations with sequential allocations model, 352-4; in process of equilibria with transfers, 354-5; in sequence economy, 67 airline industry: cost minimizing structure of routes in, 218 19; valueadded networks in reservation systems, 192 allocation of goods: autarkic and world competitive equilibrium, 322-7; in consumer-producer coalition, 30-1; in Walrasian economy, 80n9 Arrow-Debreu economy: applying intertemporal models to, 329-30; equilibrium in, 126-7; futures markets in, 101; inability to hedge price risks in, 73-9; informational role of prices in, 53; market game with redistribution, 334-5; price expectations in, 67; with price uncertainty, 10-11, 31, 75-95; as sequential model of uncertainty, 97; simple market game, 332-4; uncertainty in, 72-9 Arrow-Debreu equilibrium allocation, 132-8 Arrow futures market, 236-7 auctioneer: in Arrow-Debreu economy, 77; in economy with price uncertainty, 77-8, 87; Walrasian, 74 autarky, domestic, 322-7 bandwagon effects, 192-3, 204 Black-Scholes option pricing model, 111 380 capital: social and institutional, 253-4; social overhead capital, 253 capital, natural See also stock of natural capital: dynamic model of, 255; optimum investment in, 280-6; as part of social overhead capital, 253 catastrophe futures and bundles, 13, 131 centralization, 10-1 1, 14 commodities: allocation and reallocation in autarkic and world trade scenarios, 322-7; in resource allocation under certainty and uncertainty, 45-6; as state-contingent claims, 91-2 commodity markets, Arrow-Debreu, 100-1 commons, global: measurement of, 308-9; as nonexcludable good, 307-8; population crowding externality on, 309-10 competition, perfect and monopolistic, 239 complexity theory, 129 consumers: of information goods, 28 5; in market formation model, 241-2 consumption: state-dependent utility of, 55 contracts: insurance, 50, 61; mutual insurance contracts, 13, 127-31, 137-8; price-dependent, 58-60 coordination: options market as substitute for, 111; sunspots as devices for, 68 coordination failure: conditions in market equilibrium for, 247-50; in market innovation models, 236 costs See also transaction costs: average and marginal cost pricing, 175, 195-201, 205-9, 214; in choice of optimal policy related to new Subject index costs (cont.) technology, 167-90; fixed and marginal in bilateral trade, 225-33 critical mass: effect in economically viable VAN, 192-3, 204; idea of, 192-3, 204; network price and market share, 205-9; in noncooperative game, 204; PCMs in interconnection issues, 209-11 ; price at formation of, 201; private (PCM) and social (SCM) under different pricing systems, 194-201; subsidies to attain, 214 decentralization: agents with local information, 238-9; coordination failure with, 237; of information, 235-6; networks as decentralized organizations, 14; tension between centralization and, 10-11 derivatives: catastrophe futures, 13; market for, 12 discounting: social rate of discount, 312-16; zero discounting, 314-16 dynamic optimality problem, 254 economies, continuum: agents' lack of power to influence prices, 344; redistribution in, 344-50; subgame imperfections in, 350-2 economy L: defined, 80-1; equilibrium of, 86-93; financial structure of, 83-4; price system and utilities for, 85-6; structure of uncertainty in, 81-4 electoral competition: under simple majority rule (Brennan and Buchanan), 367-8; voting preferences, 368 70 employment: in intertemporal model of shirking, 264-80 equilibria, multiple: of Arrow-Debreu economy, 67; of Arrow economy with securities, 67; L-complete economy, 69-70; economies with, 62-4; in securities markets, 68 equilibrium See also Nash equilibrium: market equilibrium concept, 51; sunspots in, 68; two-period general competitive model (Arrow), 97-8 381 equilibrium, general See general equilibrium; general equilibrium with price uncertainty (GEPU); temporary general equilibrium (TGE) exchange, efficient, 224-5 expectations See also rational expectations: with choice of prices for market clearing, 74; formation under GEI or TGE, 55-6; in market equilibrium concept, 51; multivalued, 74; price-dependent, 52-6; related to market clearing, 144; related to price in Arrow's theorem, 67; related to spot prices, 54-5; set-valued, 12; TGE model, 49-51 externalities: arising from natural environment or social structure, 16; in consumption and production of social overhead capital, 254, 273-80; pecuniary, 312-13; of population crowding, 307-10; social cost measurement, 16-17; static and dynamic, 254, 274-6; of trading activity, 16 firms: definitions of, 22-4; in economic theory, 23; information base of, 14, 23; in intertemporal model of shirking, 147, 153-5; as loci of knowledge and claims to wealth, 19, 23-5; role in economic theory, 23 forecasts: based on current information, 53 general equilibrium: core of, 30-1; existence of, 31-5; with incomplete markets (GEI), 13, 49-52, 60-1; intertemporal model, 254; model of information goods transactions, 27-42; with price-contingent contracts, 58-60; with price uncertainty, 110-11 general equilibrium with price uncertainty (GEPU): in model of agents without structural knowledge, 113-16; in model of economy with price uncertainty, 107-8; in model with complete option markets, 108 1; in model with incomplete options markets, 111-13 382 Subject index government: choice of income distribution made by, 363; coordination role, 240; criterion for intervention by, 316-20; as manager of social overhead capital, 255-6; policy in sequential models, 354-5; role in efficiency theorems of welfare economics, 350-2 human capital, firm-specific, 24 incentive-wage models, 162-3 income distribution: by government, 363, 367-70; justice principle in, 362-3; model of, 365-8; policy decided in electoral competition, 367-70; in simple continuum economy, 344-50; voting preferences in determining, 368-70 information: asymmmetric, 20, 144-5; base embedded in firms ' employees, 24; decentralized, 235-7; as determinant of production, 24-5; as economic commodity, 8-9, 19-22; in the firm, 14; imperfect, 143-4; in market formation equilibrium model, 237-9; for marketmaker, 239-46; price­ dependent, 53-4; in prices, 53; private, 238-9; as property, 21-2; relation to knowledge, 9-10; relation to uncertainty, 10-11 ; signals in, 53-4; uses of technical, 21 information goods: allocation of, 9; buying and selling, 27; difference from ordinary goods, 26; distributive lattices of, 31-7; summed as a semilattice, 26; summed in general equilibrium model, 27-9 information partition, 53, 56 information theory of value, 9, 19, 26 infrastructure, social: in dynamic model of social overhead capital, 286-95; as part of social overhead capital, 253, 255; as social overhead capital, 26773 innovation: incentives for and diffusion of, 22 institutions: maintaining social overhead capital, 254-5; resource allocation through private, 255 insurance contracts: in catastrophe bundles, 61; securitization of some, 13, 121 interconnection: common standards for VANs, 174-5; intuition behind, 209-11 justice, distributive See also income distribution: Arrow on, 362, 373; related to electoral process (Buchanan and Brennan), 364; when government redistributes, 363 knowledge: diffusion of, 21-2; embodiment of, 22; firms as loci of, 19, 23-4; human, 10; price uncertainty with and without structural, 103-13; relation to information, 9-10 knowledge revolution, 9-10 lattices, distributive See also semilattice: functions on, 38-40; geometrical realization and triangulation of, 37-8; of information goods, 31-5; ordered sets, 35-7 learning by doing, 166; in decision to implement technologies, 166-8; model, 168-71; under optimal and extreme policies, 171-6 mapping: in Arrow's paradigm, 98; from events to prices, 54-5, 98 market clearing: choice of prices for, 74; for labor market equilibrium, 144-5; in neoclassical theory, 144; verification in Arrow-Debreu economy, 130; verification in E1 economy, 130 market equilibrium concept, market formation equilibrium, competitive and monopolistic, 247, 249 market formation equilibrium model: competitive and monopolistic, 246; consumers and producers in, 241-2; marketmakers in, 237-9, 242-6 market games: agent demands in noncooperative Arrow-Debreu, 329; with redistribution, 334-5; simple Arrow-Debreu, 332-4; two-period intertemporal economy, 17-18, 330-2 Subject index marketmakers: in equilibrium model of market formation, 237-9, 242 6, 250-1; in monopolistic and competitive markets, 244 6; partial equilibrium market research of, 239; in perfect competition, 245 6, 251 markets See also commodity markets, Arrow-Debreu; information goods; securities markets; spot markets: catastrophe futures in, 12, 131; clearing in economies with multiple equilibria, 108-10; competitive, 16; economizing on, 47; factors influencing emergence of, 15-16; failure of, 143-4, 235; hedging against uncertainty, 12, 29-31; hedging with endogenous uncertainty, 72-93; with imperfect information, 13-14; incomplete, 49; missing, 15, 235-7, 239-40, 247-51; observabiity of states in, 48; open, inactive, and closed, 235-7; Pareto-efficient and inefficient, 240-1, 247-51; in perfect and monopolistic competition, 23949; simultaneous, 78; spot, 47; in temporary equilibrium, 12, 49-50; for unknown risks, 127 money: emergence in network of Walrasian trading posts, 228-33; use in network of trading posts, 15, 219-24; use of a single, 218-19, 233 moral hazard: related to employer and unemployment, 145 Nash equilibrium: equilibria corresponding to Walrasian equilibria, 329-30, 336-44; equilibria in market game with redistribution, 335; network usage, 201-4 networks See also value-added networks (VANs): average cost pricing for, 195-7; comparison of average and marginal pricing, 198-200; cost to provide product of, 193-5; as decentralized organizations, 14; externalities between users, 192; interconnection, 209-11; marginal cost pricing for, 197-8 network users: differentiation among, 211-14; Nash equilibrum in patterns of use, 201-4; in single and multiple 383 vendor noncooperative games, 203-4; strategy to ensure increasing numbers of, 205-9 noncooperative game See Nash equilibrium NP completeness concept, 129, 132 observability: of prices, 52-3; of states, 48 optimum economic growth theory, 254 optimum theory of environmental quality, 254 options: as insurance against endogenous price uncertainty, 102-13; price uncertainty with complete options market, 108-11; role in hedging against endogenous price uncertainty, 102-3; trading in model of economy with price uncertainty, 104-8 options markets: consumption allocation of complete and incomplete, 108-13; incomplete, 59 60, 105 6; price uncertainty with complete and incomplete, 108-13; as substitute for coordination of expectations, 1 ; as substitutes for spot markets, 58 Pareto efficiency: conditions for inefficient markets, 239-41; with equilibrium in market formation model, 237; with open market equilibrium, 236-9; of risk allocation, 125-7 Pareto inefficiency: complete markets with transaction costs, 240-1, 247, 249-51; with endogenous missing markets, 235 PCM (private critical mass) See critical mass Pontryagin's Maximum Principle, 298303 population crowding, 16-17, 307-10 price allocation: in complete options market with price uncertainty, 108-11; in incomplete options market with price uncertainty, 111-13 prices See also pricing system; spot prices: choice for market clearing, 74; informational role in resource allocation, 53 6; nominal and noncompetitive, 60-1; noncompetitive prices in TGE and GEi theory, 384 Subject index prices (cont.) 107; observability of, 52-4; perfect foresight about, 98; Walrasian auction, 74 prices, market-clearing: determined in Arrow-Debreu economy, 77-9; in economy with price uncertainty, 77-87; spot, 46-8 price uncertainty: assets to hedge against, 78; in economy with layered sets of states, 78-93; endogenous and exogenous, 12, 101-2; general equilibrium with (GEPU), 107-11 ; hedging in Arrow-Debreu markets, 73-95; layers of, 30; meaning of, 99-102; model of economy with, 104-8; model of economy with complete and incomplete options market, 108-13; resolution in economy L, 33; with and without structural knowledge, 102-16 pricing system: average cost pricing, 195-7, 205-9; in information goods market, 29-30; marginal cost pricing, 196-8; private and social critical mass corresponding to, 194-201; resource allocation with average and marginal cost pricing, 195-201, 214 producers: of information goods, 28-35 production: information as determinant of, 24-5; knowledge as input to, 9; learning by doing model, 176-90; uses of technical information in, 21; using one of two technologies, 166-71 profit: in choice of optimal policy related to new technology, 167-90 property, common See also commons, global: social overhead capital as, 254; tragedy of the commons, 259 property rights: related to information, 21-2 public choice theory, 364-74 Ramsey-Cass-Koopmans utility integral, 269, 281, 290 rational expectations: Arrow 's position, 98nl; equilibrium, 51 resource allocation: in Arrow-Debreu framework, 129-30; under certainty, 45; dynamic model of natural environment, 256-67; dynamic model of social infrastructure of social overhead capital, 267-73; in dynamic model of social overhead capital, 286-98; informational role of prices in theory of, 53; intertemporal, 254; of scarce resources of the environment, 254-5; sequential, 352-4; uncertainty in, 46 risk allocation See also options; options markets: of endogenous risk, 99; insurance pools as, 121; by securities markets, 102 risks See also price uncertainty: Arrow's model used in hedging against, 102; changes in expectations with, 74; hedging unknown, 120-1; individual, 13; insurance on known, 121-2; markets for unknown, 127-8; new, 120; role of catastrophe futures in allocation of unknown, 131-2; sharing in price-dependent contracts, 58-60 Russell paradox, 72, 77-9, 102 Savage states: of nature, 67-8, 74-5, 80-1; uncertainty in, 68 SCM (social critical mass) See critical mass securities See also catastrophe futures and bundles; markets; options; prices; spot prices: in Arrow economy, 67; catastrophe futures and bundles as, 13, 131; hedging against risks by shifting income, 102; statistical, 123, 127-31, 135-8 securities markets: allocation of and hedging against risk in, 102; model of incomplete, 68; multiple equilibria in, 68 semilattice, 218 shirking: intertemporal equilibrium model of, 146-61; model with asymmetric information, 145 social overhead capital: categories of, 253; competitive equilibrium under, 295-8; dynamic model of natural environment as, 256-67; externalities in consumption and production of, Subject index 385 social overhead capital (cont.) 273-80; externalities in theory of 254· ' general dynamic model of, 286- social rate of discount: in applied welfare economics, 313-14; in context of population crowding, 16-17; equity considerations related to, 313-14; zero discounting, 314-16 social utility function: of structure of natural capital, 281 spot markets: in economies with multiple equilibria, 108-10; equilibrium model of economy with price uncertainty, 105-7; options markets as substitutes for, 104 spot prices: general equilibrium with incomplete markets, 95; in GEPU, 107-8; hedging against uncertainty in, 13; influence of options markets on, 103; known, 47; market-clearing, 46-8 standards adoption model: networks in, 202-3 state of the economy: social state of, 122-4, 134-6, 138; statistical state of, 122-6, 136-8 states: Arrow's concept of, 46; concept of, 46, 49; in environment of uncertainty, 46, 97-8; within layers of uncertainty, 73-4, 77-9; observability of, 48; price­ dependent, 56-7; statistical and social ' 132-8 states of nature: Arrow 's, 97-100; Savage, 67-8 states of the environment: as an event, 54; Arrow 's concept of uncertain, 45-6 state space: of equilibrium, 12-13; of price uncertainty in Arrow-Debreu market' 72; Savage, 67-8 stock of natural capital: consumption and rates of depletion and regeneration, 258-62, 280 ; imputed price over time, 260 ; levels in dynamic model, 265-7; rate of change in dynamic model of natural capital, 256-67; rate of regeneration, 281 stock of social infrastructure: consumption of and change in, 268-9; depletion and increase in dynamic model of social infrastructure, 267-8; imputed price of, 269-73 cJ sunspots, 68-71 technologies: decision to implement production of one of two 166-8· ' formal statement of deci ion to implement one of two 168-71· information technolo y, 10; le rning curves of two different, 167-8; mixing two technologies based on profit function, 14, 167; optimal and extreme policies in implementation decision for, 165, 171-6, 188-9; profit stream as function of price and technology, 167 temporary general equilibrium (TGE): model of, 49-50; money in, 60-1; theory of, 50-2 trade: in country in isolation, 322-7; gains in utility with international ' 322-7·' Pareto gains from, 322-7 trade, bilateral: arrangement using trading posts model, 224-5; efficient arrangement of, 224-5; for given pairs of equilibrium prices, 217-19; monetary and nonmonetary, 219-24; monetary structure, 218; organized for given equilibrium prices, 217 trading structure: choice of monetary instrument for trading posts, 218-24; in Walrasian trading posts, 217-18 tragedy of the commons, 259 transaction costs: in bilateral trading structure, 219; including information processing, 58; monetary trade in conduct of transactions, 15; Pareto inefficiency in complete markets with, 240-3, 247, 249-51 transfer, intergenerational: dynasty model, 309-10; life-cycle model, 309-12 transfers, domestic: balancing across individuals, 322; for Pareto gains, 322-3 ; � � uncertainty See �/so price uncertainty; _ nsks: alternative states of the environment in, 45-6; in date-event state, 46; hedging two types of, 120 2; with layered sets of states, 79-93; layers of, 72-3, 77-9; relation of information to, 10 1; structure in economy L, 386 Subject index uncertainty (cont.) 33 6; in terms of exogenous states of nature (Arrow), 99-101 uncertainty, endogenous: defined, 11; faced by economic agents (Kurz), 101-2; literature on, 46-7; motivating, 73-4; role of options in hedging against, 102-4; source of, 101 uncertainty, exogenous: difference from endogenous uncertainty, 101; hedging for efficent allocation of risk, 102-4; and incomplete options markets, 112; options in state-contingent markets for, 103-4; source of, 101 unemployment: equilibrium rate of, 144; in intertemporal model of shirking, 13-14, 264-80 utility: with autarkic and international trade, 322-7; price-dependent, 55 6; social utility function of natural capital, 281; state-dependent, 55; von Neumann-Morgenstern, 125 value: of a firm, 21-2; information theory of, 26; set-valued expectations, 10 value-added networks (VANs): airline reservation systems as, 192; average cost pricing solution, 175; with diverse set of users, 211-13; emergence of markets through, 14-15; with identical users, 200-211; Nash equilbrium usage patterns, 202-9; as natural monopoly, 191-2, 202-3, 213-14; price and market share, 205-9; Reuters FX monitor and SWIFT as examples of, 191-2 voters: in model of income distribution, 365-8; selection probability in electoral competition, 367-70; self-interest of (Brennan and Buchanan), 368-72 voting: determined by distributional preferences, 368-72; individual choice behavior in, 370-3; redistribution by majority, 363 Walrasian equilibria: of Arrow-Debreu economy, 330, 333-4; intertemporal, 336-8; in market game with redistribution, 335; Nash equilibria correponding to, 329-30, 336-44; standard definition of, 328; subgame perfect equilibrium in intertemporal, 338-44 welfare economics: efficiency theorems of, 328-9, 350, 354; in market formation, 247-51; social rate of discount in applied, 312-13; zero discounting, 314-16 ... 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... lack of information As Arrow said, "What information does is reduce uncertainty. " Thus information and uncertainty are two sides of the same coin The problem of uncertainty is part and parcel of. . .Kenneth J Arrow Markets, information, and uncertainty Essays in economic theory in honor of Kenneth J Arrow Edited by GRACIELA CHICHILNISKY Columbia