The graph of Lindahl correspondence as the unique von Neumann-Morgenstern abstract stable set

In this paper, we consider a continuum economy with a finite number of types of agent, and several private and public goods. The main result of the paper is that the graph of the equal-treatment Lindahl equilibria mapping is the unique abstract stable set with respect to the dominance relation in economies with crowding effects introduced by Vasil'ev et al. in 1995. The external stability of this mapping implies that, for any equal-treatment allocation x in , that is not a Lindahl equilibrium, there exists a subeconomy of such that one of its equal-treatment Lindahl allocations blocks x. This result is a counterpart of the theorem of Mas-Colell for Aumann's atomless market with private goods.     

A topological invariant for competitive markets

This paper summarizes the concepts of global cones and limited arbitrage introduced in Chichilnisky (Economic Theory, 1995, 5, 79–108), and the corresponding results establishing that limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium and for the compactness of Pareto frontier (announced in Chichilnisky (American Economic Review, 1992, 84, 427–434, and Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189–207). Using the same global cones I extend my earlier results to encompass ‘mixed economies’ based on Chichilnisky (CORE Discussion Paper No. 9527, 1995). I introduce a topological invariant for competitive markets which deepens the concept of limited arbitrage. This invariant encodes exact information on the equilibria and on the social diversity of the economy and all its subeconomies, and predicts a failure of effective demand.     

Generic properties of the core and equilibria of pure exchange economies

We show that for an open dense set of markets with a continuum of traders the number of equilibrium allocations [which by the celebrated theorem of ^{Aumann (Econometrica. 1964, 32. 39–50)} coincide with the core allocations for such markets are finite. This presents a limiting case result that complements similar asymptotic theorems for cores of large economies proved by ^{Bewley (Econometrica 1973, 41, 425–454)}, and ^{Dierker (Journal of Mathematical Economics 1975, 2. 155–169)}. If we require that the measure on the space of agents be one with a finite number of atoms of equal weight, our reasoning recovers the classical results obtained by ^{Debreu (Econometrica. 1970. 38, 387–392)} for economies with a finite number of agents.     

Financial market equilibria with cumulative prospect theory

The paper first shows that financial market equilibria need not to exist if agents possess cumulative prospect theory preferences with piecewise-power value functions. This is due to the boundary behavior of the cumulative prospect theory value function, which might cause an infinite short-selling problem. But even when a non-negativity constraint on final wealth is added, non-existence can occur due to the non-convexity of CPT preferences, which might cause discontinuities in the agents’ demand functions. This latter observation also implies that concavification arguments which has been used in portfolio allocation problems with CPT preferences do not apply to our general equilibrium setting with finite many agents. Existence of equilibria is established when non-negativity constraints on final wealth are imposed and there is a continuum of agents in the market. However, if the original prospect theory is used instead of cumulative prospect theory, then other discontinuity problems can cause non-existence of market equilibria even in this case.     

Myopia and monetary equilibria

In an infinitely lived, representative individual economy, important properties of competitive equilibria, such as determinacy and the non-existence of monetary equilibria, are not robust to the introduction of myopia. An individual is myopic if, at each date, he plans consumption only for that date and few periods that immediately follow; that is, his planning horizon, n, is finite. Equilibria with myopia can display real indeterminacy and allow for monetary as well as non-monetary steady states; thus, they share some of the features of equilibria in economies of overlapping generation. The equilibrium price dynamics (but not the consumption dynamics) of an exchange economy with extreme myopia, n = 1, are identical to the dynamics of an overlapping generation economy with two-period lives.     

Stochastic processes of temporary equilibria

It is the aim of the paper to study within the framework of an ‘overlapping generation model’ the evolution of temporary equilibria. At date t, there are ‘newborn’ agents and ‘old’ agents who were born in previous periods; the old agents hold cash balances (fiat money) that they carried over from the previous period. At the beginning of period t, all agents receive a random endowment of consumption goods. Then the agents exchange these endowments and money on spot markets at date t (trading in future markets is not considered). Once a temporary equilibrium is reached, the economy move to the next date. Agents who were born at date t then become old and meet agents born at period t+1.It is shown that the evolution of temporary equilibria in this model leads to analyse the ergodic properties of a certain class of Markov processes with stationary transition probability.     

On endogenous economic regulation

This paper presents a model in which in each of a succession of time periods the State and the private economy interact to determine rules under which the private agents will operate in the next period, and rules and resources that constrain interventions of the State in the next period. The set of State institutions, called regulators, that are the instruments of State intervention is endogenously determined in each period. The model is a multiperiod game consisting of two phases. The first is a (noncooperative) game played by private economic agents in each period, the rules for which are given by the regulators in the preceding period. The second phase is political. In each period the private agents acting politically determine the legal and budgetary constraints under which the regulators will operate in the next period, and thereby determine the noncooperative game to be played in the next period. Formal entities in the model allow a wide variety of regulatory instruments and transfer payments to be represented.     

Regularity and robustness in monotone Bayesian games

This paper defines regular and weakly regular equilibria for monotone Bayesian games with one-dimensional actions and types. It analyzes the robustness of equilibria with respect to perturbations. It also proves an index theorem and provides applications to uniqueness of equilibrium.     

A new necessary condition for Nash implementation

In this paper we formulate a family of conditions called `B_k-monotonicity' that are necessary for Nash implementation, where k is a natural number that indexes a particular condition, and where the condition only becomes more restrictive as k increases. B_k-monotonicity is in general a stricter condition than Maskin monotonicity, and can be used to show that certain social choice correspondences that satisfy Maskin monotonicity cannot be Nash implemented.     

A profit-center game with incomplete information

Profit centers in a firm in multidivisional form agree in the ex ante stage upon a plan about their joint production and profit imputation. The plan is executed in the subsequent two periods of the interim stage: the setup period and the manufacturing period. In the setup period, each center has its private information, but a part of its information is revealed to the other centers through its action. Based on the information endogenously pooled this way, the centers take another round of actions in the manufacturing period. A core plan is defined as a Bayesian incentive-compatible plan of the grand coalition of profit centers, upon which no coalition can improve using its Bayesian incentive-compatible plan. A core plan is called full-information revealing if each center fully reveals its private information in the setup period. Three existence theorems for a full-information revealing core plan are established. The first two theorems impose alternative conditions on returns to scale: (1) the neoclassical convex technology, and (2) increasing returns to scale. In case (2), a stronger condition than Scarf's distributiveness is imposed on the total production set. The third theorem is based on a specific supplier-customer relationship among the divisions. Received: 13 October 1997 / Accepted: 26 July 1999     

Efficiency and information aggregation in auctions with costly information

Consider an auction in which k identical objects are sold to n > k bidders who each have a value for one object which can have both private and common components to it. Private information concerning the common component of the object is not exogenously given, but rather endogenous and bidders face a cost to becoming informed. If the cost of information is not prohibitively high, then the equilibrium price in a uniform price auction will not aggregate private information, in contrast to the costless information case. Moreover, for a wide class of auctions if the cost of information is not prohibitively high then the objects can only be allocated in a weakly efficient sense, and then only if the equilibrium proportion of endogenously informed agents is vanishing as the economy grows. In spite of these results, it is shown that there is a mechanism for which there exist equilibria and for which (weak) efficiency is achieved as the economy grows in the face of endogenous information acquisition.Received: 6 August 2001, Accepted: 27 July 2002, JEL Classification: C72, D44, D82Financial support under NSF grant SBR-9507912 is gratefully acknowledged. I thank Valentina Bali for conversations out of which this project grew, and Larry Ausubel for a very helpful discussion of an early version of this paper at the 1998 summer meetings of the Econometric Society from which I have borrowed in structuring the exposition of the paper. I also thank Andy Postlewaite, Jeroen Swinkels, and an associate editor and anonymous referee for helpful comments and suggestions on earlier drafts.     

The elasticity of derived demand, factor substitution, and product demand: Corrections to Hicks' formula and Marshall's Four Rules

The concept of the elasticity of substitution between capital and labor, introduced by John Hicks and Joan Robinson over 75 years ago, has had important implications in labor economics and several areas of economic inquiry. In his The Theory of Wages (1932/1963), Hicks developed a formula that has proven very useful in relating the substitution elasticity to the derived demand for productive factors, the distribution of factor incomes, and Marshall's Four Rules. This short paper shows that the original and subsequent derivations of Hicks' celebrated formula contained a slip (that factor shares are independent of the substitution elasticity and therefore constant), presents a new derivation and a corrected formula, and demonstrates that, with the corrected formula, Marshall's First Rule based on the substitution elasticity is no longer generally valid.     

General consumption constraints and regular economies

In the spirit of Smale’s work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowments. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has a finite number of equilibria, which locally depend on endowments and possibility functions in a continuous manner.     

Financial reforms and money demand: Evidence from 20 developing countries

The effects of financial reforms on money demand (M1) are analysed with estimates for two sets of sub-samples and two break dates for twenty developing Asian and African countries. In all cases, the magnitude of income elasticity does not change significantly when compared with sub-samples and whole sample periods. Using CUSUM and CUSUMSQ tests, we find that the demand for money functions in our selected countries are temporally stable and therefore the respective monetary authorities may target money supply as the conduct of monetary policy.     

Bargaining: separately or together?

This paper explores conditions under which economic agents will want to bargain collectively instead of individually with a common third party—when, for example, two firms (or unions), who are bargaining with the same, indispensable, outside party, will want to merge and bargain as one. I use a non-cooperative sequential bargaining model to analyze this question. Previous work has shown that agents prefer to bargain collectively if they are substitutes for each other in production. This result, however, depends on an exogenously fixed sequence of bargaining. I allow the bargaining sequence to be determined endogenously and investigate how incentives for collective bargaining vary with heterogeneity when delay is costly. The previous results are not robust when the agents are substitutes. In particular, substitute agents prefer individual to collective bargaining if they are heterogeneous and sufficiently patient. In the presence of transaction costs, substitutability of agents is no longer the sole determinant of collectivization. Rather, the degree of heterogeneity in production, in conjunction with the degree of substitutability between agents determine the incentives for collective action.     

Geodesics on the equilibrium manifold

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.     

Implementation in generalized matching problems

We search for (Nash) implementable solutions on a class of one-to-one matching problems which includes both the housing market (Shapley and Scarf, Journal of Mathematical Economics, 1974, 1, 23–28) and marriage problems (Gale and Shapley, American Mathematical Monthly, 1962, 69, 9–15). We show that the core correspondence is implementable. We show, furthermore, that any solution that is Pareto efficient, individually rational, and implementable is a supersolution of the core correspondence. That is, the core correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable. A corollary of independent interest in the context of the housing market is that the core correspondence is the only single-valued solution that is Pareto efficient, individually rational, and implementable.     

Arbitrage, equilibrium, and gains from trade: A counterexample

We present a counterexample to a theorem due to Chichilnisky (Bulletin of the American Mathematical Society, 1993, 29, 189–207; American Economic Review, 1994, 84, 427–434). Chichilnisky's theorem states that her condition of limited arbitrage is necessary and sufficient for the existence of an equilibrium in an economy with unbounded short sales. Our counterexample shows that the condition defined by Chichilnisky is not sufficient for existence of equilibrium. We also discuss difficulties in Chichilnisky (Economic Theory, 1995, 5, 79–107).     

E-stability and stability of adaptive learning in models with private information

The paper demonstrates how the E-stability principle introduced by Evans and Honkapohja [2001. Learning and Expectations in Macroeconomics. Princeton University Press, Princeton, NJ] can be applied to models with heterogeneous and private information in order to assess the stability of rational expectations equilibria under learning. The paper extends already known stability results for the Grossman and Stiglitz [1980. On the impossibility of informationally efficient markets. American Economic Review 70, 393–408] model to a more general case with many differentially informed agents and to the case where information is endogenously acquired by optimizing agents. In both cases it turns out that the rational expectations equilibrium of the model is inherently E-stable and thus locally stable under recursive least squares learning.     

The not-so-secret-agent: Professional monitors,hierarchies and implementation

Abstract. It is well-known that, when agents in an organization possess private information that is unverifiable by an outside party, games where agents simply announce their information can have multiple equilibria that may impede the successful implementation of the organization's objectives. We show that the introduction of a professional monitor (e.g. auditor, regulator, supervisor) can help to destroy the “bad' equilibria when agents have private information but have incomplete info rmation about others' information. Received: 21 May 1998 / Accepted: 26 May 2000