A unified treatment of finite and infinite economies: limited arbitrage is necessary and sufficient for the existence of equilibrium and the core

Summary. A single condition, limited arbitrage, is shown to be necessary and sufficient for the existence of a competitive equilibrium and the core in economies with any number of markets, finite or infinite, with or without short sales. This extends earlier results of Chichilnisky [8] for finite economies. This unification of finite and infinite economies is achieved by proving that in Hilbert spaces limited arbitrage is necessary and sufficient for the compactness of the Pareto frontier. Limited arbitrage has also been shown to be necessary and sufficient for a resolution of the social choice paradox [9], [10], [12], [13], [14]. Received: August 4, 1995; revised version: April 11, 1997     

Identification of consumers’ preferences when their choices are unobservable

Summary. We provide conditions under which the heterogenous, deterministic preferences of consumers in a pure exchange economy can be identified from the equilibrium manifold of the economy. We extend those conditions to consider exchange economies, with two commodities, where consumers preferences are random. For the latter, we provide conditions under which consumers heterogenous random preferences can be identified from the joint distribution of equilibrium prices and endowments. The results can be applied to infer consumers preferences when their demands are unobservable.Received: 8 May 2003, Revised: 14 September 2004, JEL Classification Numbers: D12, D51.I am very grateful to an anonymous referee, Donald Brown, and Daniel McFadden for their detailed comments and insightful suggestions. Section 2 of this paper is joint work with Donald J. Brown; it is included here for publication with his permission. Those results were presented at the 1990 Workshop on Mathematical Economics at the University of Bonn, the 1992 SITE Workshop on Empirical Implications of General Equilibrium Models at Stanford University, and, more recently, at the June 2000 Conference in Honor of Rolf Mantel, in Buenos Aires, Argentina. The comments of the participants at those conferences and workshops are much appreciated. The research presented in this paper was supported by NSF Grants SES-8900291, SBR-9410182, and SES-0241858. This paper is dedicated to Marcel K. Richter, who has inspired much of my research.     

Endogenous market segmentation with heterogeneous agents

Summary. An explanation is provided for the evolution of segmented marketplaces in a pairwise exchange economy. Large traders operating in a pairwise exchange market prefer to meet other similar traders, because this enables them to trade their endowments in a smaller number of encounters. Large and small traders, however, cannot be distinguished a priori, and the existence of the small traders imposes a negative externality on the large traders. We show that, under conditions which are not very restrictive, establishing a separate market (perhaps with an entry fee) designated for the large traders induces the two types of traders to segment themselves. However, this segmentation is not necessarily welfare improving. Received: January 12, 2001; revised version: July 17, 2002 RID="*" ID="*" I wish to thank the participants in the Friday Theory Workshop at the University of Sydney, and the participants at the 17th Australian Theory Workshop at the University of Melbourne for comments and discussion. John Hillas and Stephen King pointed out an omission in an earlier version, and Catherine de Fontenay and Hodaka Morita made extensive comments on earlier drafts. This work was initiated while I was a short-term visitor at the University of Southern California.     

Balanced cycles in an OLG model with a continuum of finitely-lived individuals

This paper studies the intertemporal equilibrium of a barter economy populated with a continuum of finitely-lived overlapping generations. Assuming isoelastic preferences and zero endowments at the beginning and the end of the individuals’ life-span, it proves the existence of an Hopf bifurcation and provides sufficient conditions on parameters for its occurrenceThe authors would like to thank an anonymous referee, Alain Venditti and Francesco Ricci for helpful comments and suggestions     

A Model of Financial Markets with Endogenously Correlated Rational Beliefs

This paper studies how communication amongst agents influences the equilibria of a financial economy. We set up a standard overlapping generations model with assets, while allowing for heterogeneous beliefs. The paper explicitly describes how communication causes the beliefs of the agents to be correlated. In particular, it is shown that communication may generate large fluctuations even if the unconditional probability beliefs themselves are independent. Because of the complex nature of the problem, we use simulations to examine the characteristics of the equilibria Part of the results presented in this paper is based on my Ph.D. thesis at Stanford University. I gratefully acknowledge the inspiration obtained from innumerable discussions with Mordecai Kurz about this subject over the years. Also, I appreciate comments from Kenneth J. Arrow and Peter J. Hammond as well as from the participants of the workshop at Stanford University, University of Tokyo and the 1st Illinois workshop in Economic Theory (University of Illinois at Urbana-Champaign) and the anonymous referee     

A theory of capital gains taxation and business turnover

We present a theory concerning the realization of capital gains where ownership and control are linked as in Holmes and Schmitz (J. Pol. Econ. 103: 1005–1038, 1995). The model developed is a version of a Lucas-tree economy in which the productivity of a technology depends on the ownership of the technology. The existence and uniqueness of equilibrium follow from the Contraction Mapping Theorem. The theory implies that impediments to asset trading, such as capital gains taxation, negatively affect production efficiency. Moreover, we calibrate the model economy to U.S. data on small-business turnover and find that indexing deductions for inflation is capable of increasing capital-gains tax revenues. We thank an anonymous referee for helpful comments, and well as Tom Holmes, Ed Prescott, Jim Schmitz and Neil Wallace for insightful conversations. Cavalcanti is grateful for financial support from CNPq, as well as the hospitality from the University of Toronto during his visiting appointment at the Department of Economics in 2006. Erosa acknowledges the support from the Institute for Policy Analysis at the University of Toronto and the Social Sciences and Humanities Research Council of Canada.     

Existence of equilibria for economies with externalities and a measure space of consumers

Summary. This paper considers an exchange economy with a measure space of agents and consumption externalities, which take into account two possible external effects on consumers preferences: dependence upon prices and dependence upon other agents consumption. We first consider a model with a general externality mapping and we then treat the particular case of reference coalition externalities, in which the preferences of each agent a are influenced by prices and by the global or the mean consumption of the agents in finitely many (exogenously given) reference coalitions associated with agent a. Our paper provides existence results of equilibria in both models when consumers have transitive preferences. It extends in exchange economies the standard results by Aumann [2], Schmeidler [16], Hildenbrand [12], and previous results by Greenberg et al. [11] for price dependent preferences, Schmeidler [17] for fixed reference coalitions and Noguchi [15] for a more particular concept of reference coalitions. We also mention related results obtained independently by Balder [4].Received: 25 May 2004, Revised: 19 October 2004, JEL Classification Numbers: D62, D51, H23. Correspondence to: Bernard CornetThis paper has benefited from comments and valuable discussions with Erik Balder, Stefan Balint, Jean-Marc Bonnisseau, Alessandro Citanna, Gael Giraud, Filipe Martins-da-Rocha, Jean-Philippe Médecin, Jean-François Mertens, Nicholas Yannelis and an anonymous referee.     

Fair social orderings

In a model of private good allocation, we construct social orderings which depend only on ordinal non-comparable information about individual preferences. In order to avoid Arrovian-type impossibilities, we let those social preferences take account of the shape of individual indifference curves. This allows us to introduce equity and cross-economy robustness properties, inspired by the theory of fair allocation. Combining such properties, we characterize two families of fair social orderings. We thank E. Maskin, A. Sen, W. Thomson, B. Tungodden and an anonymous referee for comments, and seminar participants at the Indian Statistical Institute-Delhi, the Norwegian School of Economics (Bergen), the University of Caen, the University of Rochester, and the University of Cergy-Pontoise. Financial Support from European TMR Network Living Standards, Inequality and Taxation Contract ERBFMXCT 980248 is gratefully acknowledged.     

Edgeworth's conjecture with infinitely many commodities: commodity differentiation

Summary. Convergence of the cores of finite economies to the set of Walrasian allocations as the number of agents grows has long been taken as one of the basic tests of perfect competition. The present paper examines this test in the most natural model of commodity differentiation: the commodity space is the space of nonnegative measures, endowed with the topology of weak convergence. In Anderson and Zame [12], we gave counterexamples to core convergence in L ¹, a space in which core convergence holds for replica economies and core equivalence holds for continuum economies; in addition, we gave a core convergence theorem under the assumption that traders' utility functions exhibit uniformly vanishing marginal utility at infinity. In this paper, we provide two core convergence results for the commodity differentiation model. A key technical virtue of this space is that relatively large sets (in particular, closed norm-bounded sets) are compact. This permits us to invoke a version of the Shapley-Folkman Theorem for compact subsets of an infinite-dimensional space. We show that, for sufficiently large economies in which endowments come from a norm bounded set, preferences satisfy an equidesirability condition, and either (i) preferences exhibit uniformly bounded marginal rates of substitution or (ii) endowments come from an order-bounded set, core allocations can be approximately decentralized by prices. Received: July 29, 1996; revised version: January 14, 1997     

An exchange economy can have an empty α-core

Summary Yannelis has shown that under very mild conditions on preferences, a 2-agent exchange economy has a nonempty -core [4, Corollary 4.2]. The purpose of the present paper is to demonstrate that an exchange economy with three or more agents can have an empty -core. Hence, Yannelis' result would not extend to three or more agents. Examples are provided with and without free disposal, and all preferences are described by linear utility functions. These results are compared with those of Scarf [3], who proved the existence of an -core solution for a large class ofn-person games. The comparison is carried out on two levels. First, since Scarf [3] and Yannelis [4] use different definitions for the -core of an exchange economy, we compare these definitions. Second, the present results show that a natural extension of Scarf's theorem forn-person games fails if certain feasibility constraints are incorporated.I am grateful to Nicholas Yannelis, Atsushi Kajii, Stephan Krasa, and an anonymous referee for their comments, and to a second anonymous referee whose suggestion substantially simplified the 3-agent example.     

Evolutionary choice of markets

We consider an economy where a finite set of agents can trade on one of two asset markets. Due to endogenous participation the markets may differ in the liquidity they provide. Traders have idiosyncratic preferences for the markets, e.g.due to differential time preferences for maturity dates of futures contracts. For a broad range of parameters we find that no trade, trade on both markets (individualization) as well as trade on one market only (standardization) is supported by a Nash equilibrium. By contrast, whenever the number of traders becomes large, the evolutionary process selects a unique stochastically stable state which corresponds to the equilibrium with two active markets and coincides with the welfare maximizing market structure. We are grateful to Thorsten Hens, Fernando Vega-Redondo and a referee for valuable comments. We also thank seminar participants at the University of Zurich, the CES research seminar at the University of Munich, the Koc University in Istanbul as well as conference participants at the SAET conference in Ischia, the ESEM in Lausanne and the ESF workshop on Behavioural Models in Economics and Finance in Vienna. A first version of the paper was written while Marc Oliver Bettzüge was visiting the Institute for Empirical Research in Economics at the University of Zurich. Financial Support by the Swiss Banking Institute and by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK) is gratefully acknowledged. The NCCR FINRISK is a research program supported by the Swiss National Science Foundation.     

Asset price volatility and trading volume with rational beliefs

Summary. This paper develops a model of speculative trading in a large economy with a continuum of investors. In our model the investors are assumed to have diverse beliefs which are rational in the sense of being compatible with observed data. We demonstrate the existence of price amplification effects and show that the equilibrium prices can be higher or lower than the rational expectation equilibrium price. It is also shown that trading volume is positively related to the directions of price changes. Moreover, we study how asset price volatility and trading volume are influenced by belief structures, short selling constraints and the amount of fund available for investment.Received: 23 January 2003, Revised: 30 April 2003, JEL Classification Numbers: D84, G12.We are grateful to Professors Mordecai Kurz, Kenneth Arrow, Kenneth Judd, Carsten Nielsen, Maurizio Motolese, Mark Garmaise, Jean-Michel Grandmont, Peter Hammond, Karl Shell, Jan Werner and participants of the Society for the Advancement of Economic Theory (SAET) Conference and Stanford Institute of Theoretical Economics (SITE) Conference for many helpful suggestions. Correspondence to: H.-M. Wu     

Share Ownership and Employee Attitudes: Some Evidence from China''s Postprivatization Rural Industry

In this paper, we report the impacts of share ownership on employee attitudes in China's privatized rural industries based on a survey administered in the Provinces of Jiangsu and Shandong. Our results indicate that, in general, employee shareholders have higher levels of job satisfaction, perceive greater degrees of participation in enterprise decision-making, display stronger organizational commitment, and have more positive attitudes towards the privatization process than nonshareholders in privatized firms. J. Comp. Econ., June 2002 30(4), pp. 812–835. Department of Economics, University of Winnipeg, Winnipeg, Manitoba, Canada; Economics Program, University of Northern British Columbia, Prince George, British Columbia, Canada; and Department of Economics, University of British Columbia, Vancouver, British Columbia, Canada. © 2002 Association for Comparative Economic Studies. Published by Elsevier Science (USA). All rights reserved.Journal of Economic Literature Classification Numbers: P3, P2, J5.     

Dynamic price formation in a futures market via double auctions

Summary We report an exploratory study of the process of price formation in a speculative market in the absence of liquidity traders. Traders exchange a futures contract because they interpret information differently. We formulate trading as a sequence of anonymous double auctions and introduce a notion of bounded rationality in which traders use approximate models of market response in forming their bids. We prove existence of a perfect equilibrium in the sequential anonymous auctions game, and show that the equilibrium has a no-regret property. After learning the market price, a trader regrets neither the bid that he made nor the position that he holds. We show that trading volume is related to changes in the distribution of information in the economy. We also show that volume and expected change in price are related to two different attributes of the pattern of private information flow. Fundamentally, no particular relationship between the time series of these variables is always valid for all futures contracts. This point is emphasized by an example.I am thankful for useful comments made by Avraham Beja, James Gammil, Chi-fu Huang, David Scharfstein and three anonymous referees. Financial support from Stanford Graduate School Faculty Fellowship is gratefully acknowledged.     

Stochastic equilibria with incomplete financial markets

We demonstrate the existence of equilibria with incomplete financial markets for stochastic economies whose information structure is given by an event tree, restricting attention to purely financial securities, those paying in units of account (e.g., “dollars”). Financial markets may be incomplete: some consumption streams may be impossible to obtain by any trading strategy. Securities may be individually precluded from trade at arbitrary states and dates. Sufficient conditions for the existence of stochastic equilibria are: continuous, convex, strictly monotonic preferences and strictly positive aggregate endowments. These conditions are weakened. A corollary states that any regime of security prices precluding arbitrage can be embedded in an equilibrium.     

On the theory of east-west trade under uncertainty

Taking the final stage of the existing socialist economy as the labormanaged economy, this paper establishes a model of East-West trade between a capitalist economy and a labor-managed economy, both of which face asymmetric technological uncertainty. The model reflects the facts that the securities markets for firms' ownership shares exist only in the capitalist economy and that the firm's objective function in the capitalist economy is different from that in the labor-managed economy. It also considers the existence of international forward markets for commodities as international risk-sharing arrangements. Thus, the paper shows that all the basic theorems in traditional trade theory (Factor Price Equalization, Heckscher-Ohlin, Stolper-Samuelson and Rybczynski) carry over to the uncertain environments characterized by different types of economies.This is the final version of the paper, the first draft of which was presented at the 1987 annual meeting of the Japanese Association of International Economics. An earlier version has recently appeared in my book,Competition, Monopoly and International Trade Under Uncertainty (written in Japanese, Tokyo: Asian Economic New Press 1989). I wish to thank professors H. E. Leland, S. Fujino, H. Eguchi, M. Ohyama, K. Otaka, M. Ogawa, T. Ohsawa, K. Fukao, M. Nishijima and two anonymous referees for their helpful comments. Any remaining errors, however, are my responsibility.     

Computing equilibria in finance economies with incomplete markets and transaction costs

Summary. Transaction costs on financial markets may have important consequences for volumes of trade, asset pricing, and welfare. This paper introduces an algorithm for the computation of equilibria in the general equilibrium model with incomplete asset markets and transaction costs. We show that economies with transaction costs can be analyzed with differentiable homotopy techniques and thus in the same framework as frictionless economies despite the existence of non-differentiabilities of agents asset demand functions and the existence of locally non-unique equilibria. We introduce an equilibrium selection concept into the computation of economic equilibria that picks out a specific equilibrium in the presence of a continuum of equilibria.Received: 2 December 2002, Revised: 15 November 2004, JEL Classification Numbers: C61, C62, C63, C68, D52, D58, G11, G12. Correspondence to: P. Jean-Jacques HeringsThis research started when Jean-Jacques Herings enjoyed the generous hospitality of the Cowles Foundation for Research in Economics at Yale University. His research has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organisation for Scientific Research. We thank audiences at Stanford University, UC San Diego, and Venice for discussions on the subject. We are very grateful to an anonymous referee for very helpful comments on an earlier draft.     

Sustainable markets with short sales

Market objectives can conflict with long-term goals. Behind the conflict is the impatience axiom introduced by T. Koopmans to describe choices over time. The conflict is resolved here by introducing a new concept, sustainable markets. These differ from Arrow-Debreu markets in that traders have sustainable preferences and no bounds on short sales. Sustainable preferences are sensitive to the basic needs of the present without sacrificing the needs of future generations and embody the essence of sustainable development (Chichilnisky in Soc Choice Welf 13(2):231–257, 1996a; Res Energy Econ 73(4):467–491, 1996b). Theorems 1 and 2 show that limited arbitrage is a necessary and sufficient condition describing diversity and ensuring the existence of a sustainable market equilibrium where the invisible hand delivers sustainable as well as efficient solutions (Chichilnisky in Econ Theory 95:79–108, 1995; Chichilnisky and Heal in Econ Theory 12:163–176, 1998). In sustainable markets prices have a new role: they reflect both the value of instantaneous consumption and the value of the long-run future. The latter are connected to the independence of the axiom of choice at the foundations of mathematics (Godel 1940).     

Nash and Walras equilibrium via Brouwer

Summary. The existence of Nash and Walras equilibrium is proved via Brouwer's Fixed Point Theorem, without recourse to Kakutani's Fixed Point Theorem for correspondences. The domain of the Walras fixed point map is confined to the price simplex, even when there is production and weakly quasi-convex preferences. The key idea is to replace optimization with “satisficing improvement,” i.e., to replace the Maximum Principle with the “Satisficing Principle.” Received: July 9, 2001; revised version: February 25, 2002 RID="*" ID="*" I wish to thank Ken Arrow, Don Brown, and Andreu Mas-Colell for helpful comments. I first thought about using Brouwer's theorem without Kakutani's extension when I heard Herb Scarf's lectures on mathematical economics as an undergraduate in 1974, and then again when I read Tim Kehoe's 1980 Ph.D dissertation under Herb Scarf, but I did not resolve my confusion until I had to discuss Kehoe's presentation at the celebration for Herb Scarf's 65th birthday in September, 1995. RID="*" ID="*"Correspondence to: C. D. Aliprantis     

Status-seeking behavior,the evolution of income inequality,and growth

Using an overlapping generations model, this paper investigates the implications of status-seeking behavior, induced by preferences for relative income, for the evolution of income inequality. When average income rises, an individual’s marginal utility of their own income may increase (keeping up with the Joneses, or KUJ), or decrease (running away from the Joneses, or RAJ). It is shown that income inequality is shrinking over time in the KUJ economy, whereas it is expanding in the RAJ economy. We also explore the implications for long-run growth and inequality, in the existence of both KUJ and RAJ agents. I am truly grateful to Koichi Futagami for his encouragement and guidance in writing this paper. I have benefitted from comments by an anonymous referee, Been-Lon Chen, Giacomo Corneo, Akiomi Kitagawa, Kazuo Mino, Kazuhiro Yuki, and seminar participants at Osaka University, the 2006 Japanese Economic Association Autumn Meeting at Osaka City University, the Far Eastern Meeting of Econometric Society 2007 at Taipei, SER Conference 2007 at Singapore, and the European Meeting of Econometric Society 2007 at Budapest. All remaining errors are, of course, my own. The financial support from JSPS Research Fellowships for Young Scientists is greatly acknowledged.