Pareto improving price regulation when the asset market is incomplete

Summary. Incomplete asset markets cause competitive equilibria to be constrained suboptimal and provides scope for Pareto improving interventions. In this paper, we examine how intervention in prices in asset or spot commodity markets serves this purpose. We show that, if fix-price equilibria behave sufficiently regularly near Walrasian equilibria, Pareto improving price regulation is generically possible. An advantage of price regulation, contrasted with interventions in individuals asset portfolios, is that it operates anonymously, on market variables.Received: 12 August 2002, Revised: 10 July 2003, JEL Classification Numbers: D45, D52, D60.Earlier and longer versions were circulated as Discussion Paper No. 9841 (June, 1998), CORE, Université Catholique de Louvain, and Working Paper No. 01-31 (2001), Department of Economics, Brown University.The research of Herings was made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences and a grant of the Netherlands Organization for Scientific Research (NWO); while this paper was being written, he enjoyed the generous hospitality of the Cowles Foundation.John Geanakoplos and Hamid Sabourian asked questions that clarified a number of points in earlier drafts of the paper. An anonymous referee made comments that were insightful and helpful.     

Generic inefficiency of equilibria in the general equilibrium model with incomplete asset markets and infinite time

Summary. We consider a Lucas asset-pricing model with heterogeneous agents, exogenous labor income, and a finite number of exogenous shocks. Although agents are infinitely lived, endowments and dividends are time-invariant functions of the exogenous shock alone and are thus restricted to lie in a finite-dimensional space; genericity analysis can be conducted on sets of zero Lebesgue measure. When financial markets are incomplete, that is, there are fewer financial securities than shocks, we show that generically in individual endowments all competitive equilibria are Pareto inefficient. Received: November 22, 1999; revised version: March 4, 2002 RID="*" ID="*" We are grateful to an anonymous referee for very insightful comments on earlier drafts.     

Planning under market socialism when iteration is incomplete

If an iterative planning procedure is cut short due to time shortage, the plan must be set subject to information gaps. But the nature of these gaps depends on which iterative procedure was used. For the case of Lange's model, Weitzman's “prices versus quantities” framework is redeveloped for the particular information gaps then found. With one good, the optimal quantity signal comes from the expected supply-demand intersection, but an optimal price signal lies between this intersection and the price from the last stage of iteration. When there are many goods, however, we cannot be so specific.     

A social welfare function characterizing competitive equilibria of incomplete financial markets

A classic characterization of competitive equilibria views them as feasible allocations maximizing a weighted sum of utilities. It has been applied to establish fundamental properties of the equilibrium notion, such as existence, determinacy, and computability. However, it fails for economies with missing financial markets.We give such a characterization for economies with a single commodity and missing financial markets, by an amended social welfare function. Its parameters capture both the relative importance of households welfare, through the classic welfare weights, as well as the disagreements among them as to the value of the missing markets.As a by-product, we identify the dimension of the set of interior equilibrium allocations.     

Belief-free equilibria in games with incomplete information: Characterization and existence

We generalize the results of Hörner and Lovo (2009) [15] to N-player games with arbitrary information structure. First, we characterize the set of belief-free equilibrium payoffs under low discounting as the set of feasible payoffs that are individually rational, jointly rational, and incentive compatible. Second, we provide necessary and sufficient conditions on the information structure for this set to be non-empty.     

The set of sunspot equilibria in economies with incomplete financial markets: variable asset prices

Summary. I consider the set of equilibria of two-period economies with S extrinsic states of nature in the second period and I assets with linearly independent nominal payoffs. Asset prices are variable. If the number of agents is greater than (S-I), the payoff matrix is in general position and S 2I, the set of equilibrium allocations generically (in utility function space) contains a smooth manifold of dimension (S-1). Moreover, the map from states o f nature to equilibrium allocations (restricted to this manifold) is one-to-one at each equilibrium. Received: February 23, 1998; revised version: June 1, 2000     

Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach

We consider a general equilibrium model of a private ownership economy with consumption and production externalities. Utility functions and production technologies may be affected by the consumption and production activities of all other agents in the economy. We use homotopy techniques to show that the set of competitive equilibria is non-empty and compact. Fixing the externalities, the assumptions on utility functions and production technologies are standard in a differentiable framework. Competitive equilibria are written in terms of first order conditions associated with agents’ behavior and market clearing conditions, following the seminal paper of Smale (J Math Econ 1:1–14, 1974). The work of adapting the homotopy approach to economies with externalities on the production side is non-trivial and it requires some ingenious adjustments, because the production technologies are not required to be convex with respect to the consumption and production activities of all agents.     

Non-existence of recursive equilibria on compact state spaces when markets are incomplete

This paper analyzes one-good exchange economies with two infinitely lived agents and incomplete markets. It is shown that there are no recursive (Markov) equilibria for which borrowing (debt) constraints never bind if the state space of exogenous and endogenous variables is a compact subset of . Moreover, for large enough (but finite) borrowing limits, no recursive equilibrium with compact state space exists. These non-existence results hold for any economy satisfying the following standard assumptions: preferences are additively separable across time and states; the one-period utility function is time- and state-independent and unbounded from below; endowments are bounded and follow a Markov chain with stationary transition matrix; there is some idiosyncratic risk and no aggregate risk.     

Non-equivalence of uniqueness of equilibria in complete and in incomplete market models

This paper contains two examples to prove the non-equivalence of uniqueness of competitive equilibria in complete and in incomplete market models. They show that even if an equilibrium is unique for complete markets, this property can be violated for incomplete markets, and vice versa.     

The existence and computation of competitive equilibria in markets with an indivisible commodity

This paper considers an exchange economy called a generalized assignment market, in which sellers and buyers trade one indivisible commodity possibly with product differentiation for a perfectly divisible commodity. The existence of a competitive equilibrium in this economy is proved using Kakutani's fixed point theorem. This existence theorem is applied to a production economy in which sellers are formulated as producers with convex cost functions. Two examples of housing markets are provided and their competitive equilibria are numerically calculated.     

On the existence of involuntary unemployment equilibria

Conclusion We have proved the existence of equilibria implying involuntary unemployment of labour in non-competitive economies with fixed wage rate. We notice that model (II) and its extensions have not been presented as aninterpretation of Keynes' theory. We may define them as Keynesian models only in the sense that they admit involuntary unemployment equilibrium, which concept is basic to Keynes' theory. In any case, we think that these models are a first step in the development of more realistic microeconomic foundations for short-run macroeconomic theory.A first draft of this paper was presented in December 1972 at the Institute of Political Economy, Faculty of Economics and Banking, Siena University.     

On the generic existence of Radner equilibria when there are as many securities as states of nature

We show that for a special class of economies with a sequence of markets, parametrized by the vector of initial endowments, Radner equilibria exist generically.     

Undecidability of the existence of pure Nash equilibria

Summary. The purpose of this paper is to show that for any positive integer n, there exists no algorithm which decides for each non-cooperative n-person game in strategic form with partially computable payoff functions whether it has a pure Nash equilibrium or not.Received: 20 March 2002, Revised: 23 April 2003, JEL Classification Numbers: C72.The author thanks the Referee and the Associate Editor for offering critical comments on this paper, which is dedicated to his brother Konstantinos Efstathiou Sofronidis.     

Sufficient conditions for the existence of sunspot equilibria

This paper reports on conditions on agents' preferences and endowments sufficient to guarantee the existence of sunspot equilibria in a simple overlapping generations model of pure exchange. Sunspot equilibria are those in which uncertainty extrinsic to the economy operates through expectations to yield a fulfilled expectations competitive equilibrium in which the extrinsic randomness has real effects on prices and allocations. The paper also provides necessary and sufficient conditions for these equilibria to have agents trading in a fixed stock of valued fiat money. The condition derived can be interpreted as requiring that intertemporal income effects appropriately dominate substitution effects.     

A forecasting model for the market of competitive products

The classic way of performing a market forecast for industrial products implies an econometric analysis of the historical data of consumption and their projections into the future. The present work illustrates a fresh approach to the problem; the demand for the product under study is evaluated in a mathematical model which takes into consideration the technological and commercial characteristics of this product and correlates it with competitive and substitutive products. Competitiveness is measured by assigning merit scores to the characteristics of the different products, and calculating the relevant “weights of importance” on the basis of the historical consumptions. Forecasts of consumption are made by estimating the future scores of the characteristics and extrapolating the weights of importance. An example of complete application of the model to the textile market in Italy is included.     

A direct test of hyperbolic discounting using market asset data

This paper introduces a framework that generalizes exponential discounting in a net present value model by including a quasi-hyperbolic discount parameter in the asset valuation equation. Using observed market asset data, a statistically significant quasi-hyperbolic parameter is obtained, thus rejecting exponential discounting.     

Some theorems on the existence of competitive equilibrium

The purpose of this paper is to point out a relationship between theorems on the existence of competitive equilibrium in economies with externalities, and recent results (pioneered by A. Mas-Colell) on the existence of equilibrium for economies in which consumer preferences are neither complete nor transitive. This observation leads both to a substantial strengthening of the theorem on the existence of equilibrium with externalities, and at the same time to a revealing perspective on the Mas-Colell theorem.     

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.     

On the generic existence of fully revealing price equilibria

In an asset trading model, the generic existence of rational expectations equilibrium established by Radner requires an assumption which is not shown to be generic. A regularity condition is imposed on the relative risk aversion of the utility function to eliminate the assumption.