Money,price dispersion and welfare

Summary. We introduce heterogeneous preferences into a tractable model of monetary search to generate price dispersion, and then examine the effects of money growth on price dispersion and welfare. With buyers search intensity fixed, we find that money growth increases the range of (real) prices and lowers welfare as agents shift more of their consumption to less desirable goods. When buyers search intensity is endogenous, multiple equilibria are possible. In the equilibrium with the highest welfare level, money growth reduces welfare and increases the range of prices, while having ambiguous effects on search intensity. However, there can be a welfare-inferior equilibrium in which an increase in money growth increases search intensity, increases welfare, and reduces the range of prices.Received: 25 July 2003, Revised: 12 December 2003JEL Classification Numbers: E31, D60.B. Peterson, S. Shi: We thank Gabriele Camera, Aleksander Berentsen and an anonymous referee for useful suggestions. We have also received valuable comments from the participants of the workshop at Michigan State, the Purdue Conference on Monetary Theory (2003) and the Midwest Macro Meeting (Chicago, 2003). Shi gratefully acknowledges financial support from the Bank of Canada Fellowship and the Social Sciences and Humanities Research Council of Canada. The opinion expressed here is the authors own and does not reflect the view of the Bank of Canada.Correspondence to: S. Shi     

Cournot–Nash equilibria in continuum games with non-ordered preferences

In the usual framework of continuum games with externalities, we substantially generalize Cournot–Nash existence results [Balder, A unifying approach to existence of Nash equilibria, Int. J.Game Theory 24 (1995) 79–94; On the existence of Cournot–Nash equilibria in continuum games, J. Math. Econ. 32 (1999) 207–223; A unifying pair of Cournot–Nash equilibrium existence results, J. Econ. Theory 102 (2002) 437–470] to games with possibly non-ordered preferences, providing a continuum analogue of the seminal existence results by Mas-Colell [An equilibrium existence theorem without complete or transitive preferences, J. Math. Econ. 1 (1974) 237–246], Gale and Mas-Colell [An equilibrium existence theorem for a general model without ordered preferences, J. Math. Econ. 2 (1975) 9–15], Shafer and Sonnenschein [Equilibrium in abstract economies without ordered preferences, J. Math. Econ. 2 (1975) 345–348], Borglin and Keiding [Existence of equilibrium actions and of equilibrium: a note on the “new” existence theorems, J. Math. Econ. 3 (1976) 313–316] and Yannelis and Prabhakar [Existence of maximal elements and equilibria in linear topological spaces, J. Math. Econ. 12 (1983) 233–245].     

Ambiguity aversion and the absence of indexed debt

Summary. Following the seminal works of Schmeidler (1989), Gilboa and Schmeidler (1989), roughly put, an agents subjective beliefs are said to be ambiguous if the beliefs may not be represented by a unique probability distribution, in the standard Bayesian fashion, but instead by a set of probabilities. An ambiguity averse decision maker evaluates an act by the minimum expected value that may be associated with it. In spite of wide and long-standing support among economists for indexation of loan contracts there has been relatively little use of indexation, except in situations of extremely high inflation. The object of this paper is to provide a (theoretical) explanation for this puzzling phenomenon based on the hypothesis that economic agents are ambiguity averse. The paper considers a general equilibrium model based on Magill and Quinzii (1997) with ambiguity averse agents, where both nominal and indexed bond contracts are available for trade and all relevant prices are determined endogenously. We obtain conditions which prompt an endogenous cessation of trade in indexed bonds: i.e., conditions under which there is no trade in indexed bonds in any equilibrium; only nominal bonds are traded.Received: 7 April 2003, Revised: 8 March 2004, JEL Classification Numbers: D81, E31, D52, E44.Correspondence to: Sujoy MukerjiWe thank seminar members at Birkbeck, Oxford, Paris I, Southampton and Tel Aviv, the audience at the 00 European Workshop on General Equilibrium Theory, and especially, E.Dekel, I. Gilboa, D. Schmeidler and A. Pauzner for helpful comments. The first author acknowledges financial assistance from an Economic and Social Research Council of U.K. Research Fellowship (# R000 27 1065). The second author thanks financial support from the French Ministry of Research (Action Concertée Incitative).     

Coalitional instability of the distributive Lindahl equilibrium

Summary Bergstrom [3] has showed that the Lindahlian approach to the analysis of public goods may also be used to analyze a model of wide-spread externalities in which agents have preferences defined on allocations rather than on individual commodity bundles. He has provided versions of the first and second welfare theorem for adistributive Lindahl equilibrium and also presented sufficient conditions for its existence. However, we shall show that, in contrast to Foley's [4] result on the core stability of a Lindahl equilibrium, a distributive Lindahl equilibrium need not satisfy coalitional stability. We will provide a robust example in which the unique, distributive Lindahl equilibrium does not belong to the -core defined either as in Scarf [11] or as in Yannelis [12].I would like to thank F. Canova, R. Serrano, M. Spagat, R. Vohra at Brown University, P. C. Padoan at University of Rome and an anonymous referee for their comments. I am also grateful to the participants at the Third Annual MeetingColloquia on Economic Research at I.G.I.E.R. in Milan, Italy, and to the participants at the Citibank Workshop in Economic Theory at Brown University.     

Convergence of the Aumann–Davis–Maschler and Geanakoplos bargaining sets

Summary. Geanakoplos [17] defined a notion of bargaining set, and proved that his bargaining set is approximately competitive in large finite transferable utility (TU) exchange economies with smooth preferences. Shapley and Shubik [26] showed that the Aumann–Davis–Maschler bargaining set is approximately competitive in replica sequences of TU exchange economies with smooth preferences. We extend Geanakoplos result to nontransferable utility (NTU) exchange economies without smooth preferences, and we extend the Shapley and Shubik result to non-replica sequences of NTU exchange economies with smooth preferences.Received: November 11, 1996This revised version was published online in February 2005 with corrections to the cover date.     

On the existence of pure-strategy equilibria in large games

Over the years, several formalizations and existence results for games with a continuum of players have been given. These include those of Schmeidler [D. Schmeidler, Equilibrium points of nonatomic games, J. Stat. Phys. 4 (1973) 295-300], Rashid [S. Rashid, Equilibrium points of non-atomic games: Asymptotic results, Econ. Letters 12 (1983) 7-10], Mas-Colell [A. Mas-Colell, On a theorem by Schmeidler, J. Math. Econ. 13 (1984) 201-206], Khan and Sun [M. Khan, Y. Sun, Non-cooperative games on hyperfinite Loeb spaces, J. Math. Econ. 31 (1999) 455-492] and Podczeck [K. Podczeck, On purification of measure-valued maps, Econ. Theory 38 (2009) 399-418]. The level of generality of each of these existence results is typically regarded as a criterion to evaluate how appropriate is the corresponding formalization of large games.In contrast, we argue that such evaluation is pointless. In fact, we show that, in a precise sense, all the above existence results are equivalent. Thus, all of them are equally strong and therefore cannot rank the different formalizations of large games.     

Coalitions, agreements and efficiency

If agents negotiate openly and form coalitions, can they reach efficient agreements? We address this issue within a class of coalition formation games with externalities where agents’ preferences depend solely on the coalition structure they are associated with. We derive Ray and Vohra's [Equilibrium binding agreements, J. Econ. Theory 73 (1997) 30-78] notion of equilibrium binding agreements using von Neumann and Morgenstern [Theory of Games and Economic Behavior, Princeton University Press, Princeton, 1944] abstract stable set and then extend it to allow for arbitrary coalitional deviations (as opposed to nested deviations assumed originally). We show that, while the extended notion facilitates the attainment of efficient agreements, inefficient agreements can nevertheless arise, even if utility transfers are possible.     

Consumption externalities, rental markets and purchase clubs

Summary. A premise of general equilibrium theory is that private goods are rival. Nevertheless, many private goods are shared, e.g., through borrowing, through co-ownership, or simply because one persons consumption affects another persons wellbeing. I analyze consumption externalities from the perspective of club theory, and argue that, provided consumption externalities are limited in scope, they can be internalized through membership fees to groups. Two important applications are to rental markets and purchase clubs, in which members share the goods that they have individually purchased.Received: 2 June 2003, Revised: 8 March 2004, JEL Classification Numbers: D11, D62.This paper was supported by the U.C., Berkeley Committee on Research, and the Institute of Economics, University of Copenhagen. I am grateful to Birgit Grodal for her collaboration on the theory that underlies this paper, and for her helpful and motivating comments about these particular extensions. I also thank Hal Varian, Doug Lichtman, Steve Goldman, Karl Vind, anonymous referees, and members of the Berkeley Microeconomics Seminar for discussion.     

Duplication, Growth and ‘Total Return Economics’

Maintenance consumption is an expense recovered in product prices, yet also a source of taste satisfaction which must be exhausted, rather than reinvested, from the capital affording it. This riddle is solved in the duplication rules: the cost of maintenance consumption is recovered in pay and prices, but an equal flow is exhausted from the human capital of the worker earning the pay. The rules impact tradition in several ways. If output is defined in principle as value added, then it cannot also be described as consumption plus net investment without double-counting the maintenance consumption recovered in prices. Also rate of return in the stationary state is not zero, but is the rate sufficient to offset the exhaustion of individual human capital. The rules lead to new insights into economic return, and support an argument that all growth at the scale of closure is due to productivity gain rather than to thrift.     

Giffen goods and market making

Summary. This paper shows that information effects per se are not responsible for the Giffen goods anomaly affecting traders demands in multi asset noisy, rational expectations equilibrium markets. The role that information plays in traders strategies also matters. In a market with risk averse, uninformed traders, informed agents have a dual trading motive: speculation and market making. The former entails using prices to assess the effect of error terms; the latter requires employing them to disentangle noise traders demands within aggregate orders. In a correlated environment this complicates the signal extraction problem and may generate upward sloping demand curves. Assuming (i) that competitive, risk neutral market makers price the assets or that (ii) uninformed traders risk tolerance coefficient grows unboundedly, removes the market making component from informed traders demands rendering them well behaved in prices.Received: 30 April 2002, Revised: 3 December 2003, JEL Classification Numbers: G100, G120, G140.Support from the Barcelona Economics Program of CREA and the Ente per gli Studi Monetari e Finanziari Luigi Einaudi, are gratefully acknowledged. I thank Anat Admati, Jordi Caballé, Giacinta Cestone, and Xavier Vives for useful suggestions. The comments provided by the Associate Editor and an anonymous referee greatly improved the papers exposition.     

Market equilibrium with heterogeneous recursive-utility-maximizing agents

Summary The paper by C. Ma [1] contains several errors. First, statement and proof of Theorem 2.1 on the existence of intertemporal recursive utility function as a unique solution to the Koopmans equation must be amended. Several additional technical conditions concerning the consumption domain, measurability of certainty equivalent and utility process need to be assumed for the validity of the theorem. Second, the assumptions for Theorem 3.1 need to be amended to include the Feller's condition that, for any bounded continuous functionf C(S × ⁿ ₊), (f(S_t+1, )¦s_t =s) is bounded and continuous in (s, ). In addition, for Theorem 3.1, the pricep, the endowmente and the dividend rate as functions of the state variables S are assumed to be continuous.The Feller's condition for Theorem 3.1 is to ensure the value function to be well-defined. This condition needs to be assumed even for the expected additive utility functions (See Lucas [2]). It is noticed that, under this condition, the right hand side of equation (3.5) in [1] defines a bounded continuous function ins and. The proof of Theorem 3.1 remains valid with this remark in place.A correct version of Theorem 2.1 in [1] is stated and proved in this corrigendum. Ozaki and Streufert [3] is the first to cast doubt on the validity of this theorem. They point out correctly that additional conditions to ensure the measurability of the utility process need to be assumed. This condition is identified as conditionCE ₄ below. In addition, I notice that, the consumption space is not suitably defined in [1], especially when a unbounded consumption set is assumed. In contrast to what claimed in [3], I show that the uniformly bounded consumption setX and stationary information structure are not necessary for the validity of Theorem 2.1.I would like to thank Hiroyuki Ozaki and Peter Streufert for pointing out correctly some mistakes made in the original article. Comments and suggestions from an anonymous referee are gratefully appreciated. Financially support from SSHRC of Canada is acknowledged.     

Information and size of coalitions

We consider a set of asymmetrically informed agents, where the information of each trader is susceptible of being altered when she becomes a member of a coalition. For this, we consider a general rule that depending on the coalition, a signal (or an information partition) is assigned to each member of the coalition. We set examples showing that Grodal’s (Econometrica 40:581–583, 1972), Schmeidler’s (Econometrica 40:579–580, 1972) and Vind’s (Econometrica 40:585–586, 1972) core characterizations of a continuum economy may fail in this general informational setting. However, under mild assumptions on the rule, we extend Schmeidler’s and Vind’s results to economies that allocate information to agents in each coalition according to the rule. We then focus on information mechanisms based on the size of coalitions and provide a general characterization result for the corresponding cores. Moreover, we pay close attention to the rule that assigns the shared information to each member of specific coalitions. We prove that the resulting cores are exactly the same independently of whether arbitrarily small or large coalitions share information.     

Factor price equalization beyond a “cubic” world

Summary. The importance of factor price equalization (FPE) is widely recognized in economics. The FPE theorem states that, absent any factor intensity reversal, factor prices are equal across countries with identical technologies and product mixes. In a two-factor-two-good-two-country Heckscher-Ohlin model this is equivalent to countries factor endowments being contained in the diversification cone defined by goods factor intensities. This paper identifies a condition, stated in terms of the allocation of factor endowments across countries relative to the demand for and the factor intensities of goods, that is necessary and sufficient for FPE in a world with arbitrary number of countries, goods and factors.Received: 16 July 2004, Revised: 10 January 2005, JEL Classification Numbers: F1.     

Shiftable Externalities: A Market Solution

In this paper we propose a regulatory scheme for what has become known as shiftable externalities (Not In My Backyard type garbage location problemswhere the externality is characterized by the absence of jointness in supply).The scheme facilitates the establishment of a market for the externality, and it isfeasible for a wider class of regulation problems and more information efficientthan the other regulatory schemes that have been proposed for this type ofexternality. Finally, we show that it is possible to decentralize the participationdecision so as to take account of verification costs.     

Stochastically independent randomization and uncertainty aversion

Summary.   This paper proposes a preference-based condition for stochastic independence of a randomizing device in a product state space. This condition is applied to investigate some classes of preferences that allow for both independent randomization and uncertainty or ambiguity aversion (a la Ellsberg). For example, when imposed on Choquet Expected Utility (CEU) preferences in a Savage framework displaying uncertainty aversion in the spirit of Schmeidler [27], it results in a collapse to Expected Utility (EU). This shows that CEU preferences that are uncertainty averse in the sense of Schmeidler should not be used in settings where independent randomization is to be allowed. In contrast, Maxmin EU with multiple priors preferences continue to allow for a very wide variety of uncertainty averse preferences when stochastic independence is imposed. Additionally, these points are used to reexamine some recent arguments against preference for randomization with uncertainty averse preferences. In particular, these arguments are shown to rely on preferences that do not treat randomization as a stochastically independent event. Received: February 10, 2000; revised version: March 30, 2000     

Almost-objective uncertainty

Summary. Every subjective state space with Euclidean structure contains almost-objective events which arbitrarily closely approximate the properties of objectively uncertain events for all individuals with event-smooth betting preferences - whether or not they are expected utility, state-independent, or probabilistically sophisticated. These properties include unanimously agreed-upon revealed likelihoods, statistical independence from other subjective events, probabilistic sophistication over almost-objective bets, and linearity of state-independent and state-dependent expected utility in almost-objective likelihoods and mixtures. Most physical randomization devices are based on events of this form. Even in the presence of state-dependence, ambiguity, and ambiguity aversion, an individuals betting preferences over almost-objective events are based solely on their attitudes toward objective risk, and can fully predict (or be predicted from) their behavior in an idealized casino.Received: 17 July 2003, Revised: 12 November 2003, JEL Classification Numbers: D81.I am grateful to Kenneth Arrow, Erik Balder, Hoyt Bleakley, Richard Carson, Eddie Dekel, Larry Epstein, Clive Granger, Simon Grant, Peter Hammond, Jean-Yves Jaffray, Edi Karni, Peter Klibanoff, Duncan Luce, John Pratt, Chris Tyson, Uzi Segal, Peter Wakker, Joel Watson, Nicholas Yannelis, anonymous referees and especially Ted Groves and Joel Sobel for helpful comments. This material is based upon work supported by the National Science Foundation under Grant No. 9870894.     

On the characterization of excess demand functions

Summary. In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras law and zero homogeneity of Marshallian demand functions.Received: 25 November 2002, Revised: 11 March 2004, JEL Classification Numbers: D11.Marwan Aloqeili: I would like to thank an anonymous referee for helpful comments.     

Endogenous fluctuations in unionized economies with productive externalities

Summary. We discuss the effects of unions on steady-state multiplicity and welfare, and on the existence of endogenous fluctuations. We consider an OG economy with productive capital externalities and we focus on underemployment equilibria. We find that for wide regions in the parameter space, including an arbitrarily small degree of externalities and a Cobb-Douglas technology, unions increase steady state employment and welfare, and local indeterminacy (sunspots) emerges. Moreover with a CES technology multiplicity of steady states is only possible in the presence of unions. Our results also show that the role of unions in shaping local dynamics and bifurcations depends on technology (externalities and factors substitutability).Received: 16 January 2002, Revised: 18 March 2004, JEL Classification Numbers: E32, J51, D60, D62. Correspondence to: Leonor ModestoThis paper is a much revised version of our former working paper Unions, Increasing Returns and Endogenous Fluctuations. Financial support from Fundação para a Ciência e Tecnologia under the POCTI, is gratefuly acknowledged.     

What is an ‘endogenous state space’?

Summary. In the literature on choice under unforeseen contingencies, the decision maker behaves as if she aggregates possible instances of future rankings indexed by a set S. The set S is interpreted as a subjective state space even though subsequent rankings need not conform to any one of the aggregated utilities. This paper proposes a definition for a subjective state space under unforeseen contingencies that is topologically unique, derives its existence from preference primitives as opposed to the representation of preferences, and does not commit to an interpretation in which states correspond to future realized rankings. The definition topologically concurs with and extends the identification of the essentially unique subjective state space due to Dekel, Lipman and Rustichini [4].Received: 28 October 2003, Revised: 13 October 2004, JEL Classification Numbers: D11, D81, D91.I thank Eddie Dekel, Alan Kraus, Bart Lipman, Chris Shannon, and the referee for some helpful remarks.     

Stable Coalition Structures with Externalities

This paper argues that the sign of external effects of coalition formation provides a useful organizing principle in examining economic coalitions. In many interesting economic games, coalition formation creates eithernegativeexternalities orpositiveexternalities for nonmembers. Examples of negative externalities are research coalitions and customs unions. Examples of positive externalities include output cartels and public goods coalitions. I characterize and compare stable coalition structures under the following three rules of coalition formation: the Open Membership game of Yi and Shin (1995), the Coalition Unanimity game of Bloch (1996), and the Equilibrium Binding Agreements of Ray and Vohra (1994).Journal of Economic LiteratureClassification Numbers: C72, C71.