Characterizing C2 aggregate excess demand functions

Summary. We integrate and sharpen two characterizations of aggregate excess demand functions: we obtain Mas-Colell's (1977) equilibrium invariance, and strengthen Geanakoplos' (1984) weakly concave utility functions to strictly concave ones. Our proofs modify and extend Geanakoplos' utility-construction. We note two applications: a sharper characterization of equilibrium price sets (cf. Mas-Colell (1977)), and a basis for the studies of computable economies (Richter and Wong (1996)). Received: July 29, 1996; revised version: February 20, 1997     

Monotone risk aversion

Summary. This paper defines decreasing absolute risk aversion in purely behavioral terms without any assumption of differentiability and shows that a strictly increasing and risk averse utility function with decreasing absolute risk aversion is necessarily differentiable with an absolutely continuous derivative. A risk averse utility function has decreasing absolute risk aversion if and only if it has a decreasing absolute risk aversion density, and if and only if the cumulative absolute risk aversion function is increasing and concave. This leads to a characterization of all such utility functions. Analogues of these results also hold for increasing absolute and for increasing and decreasing relative risk aversion.Received: 31 January 2003, Revised: 15 January 2004, JEL Classification Numbers: D81.The views, thoughts and opinions expressed in this paper are those of the author in his individual capacity and should not in any way be attributed to Morgan Stanley or to Lars Tyge Nielsen as a representative, officer, or employee of Morgan Stanley.     

Securely implementable social choice functions in divisible and nonexcludable public good economies with quasi‐linear utility functions

This paper studies the possibility of secure implementation (Saijo et al., 2007) in divisible and nonexcludable public good economies with quasi‐linear utility functions. In these economies, although Saijo et al. (2007) showed that the Groves mechanisms (Groves, 1973) are securely implementable when the valuation functions of the public good are (i) differentiable, concave, and (ii) identified with a real number, respectively, this paper shows the following negative result: securely implementable social choice functions are dictatorial or constant when the valuation functions of the public good are strictly increasing and strictly concave.     

The scope of satisfactory mechanisms for the provision of public goods

This paper establishes the existence of satisfactory public-good provision mechanisms when utilities are nonseparable. The assumptions used to obtain this result are: (1) that the public good is continuously variable; (2) that utility functions are parametrically representable and twice continuously differentiable; and (3) that the provision rule is a strictly increasing function of the reported marginal rates of substitution between the public good and the private good. The satisfactory mechanisms derived are all augmented Groves mechanisms and are equivalent to Groves mechanisms if, and only if, each consumer's utility function is additive in income.     

Product R&D Investment Policies in an International Duopoly

This study analyzes the optimal product R&D investment policies of a developed and a developing country in an international Cournot duopoly where firms from these two countries compete through endogenous quality–quantity decisions. We explore a new international trade model by using demand functions derived from utility functions. We find that the optimal product R&D investment policies for both countries are subsidies. This study counters a finding that used Hotelling‐type demand functions and it partially modifies another result that adopted the same demand functions but with an international Bertrand duopoly.     

Strategy-proof allocation mechanisms for pure public goods economies when preferences are monotonic

Summary. A fundamental problem in public finance is that of allocating a␣given budget to financing the provision of public goods (education, transportation, police, etc.). In this paper it is established that when␣admissible preferences are those representable by continuous and increasing utility functions, then strategy-proof allocation mechanisms whose (undominated) range contains three or more outcomes are dictatorial on the set of profiles of strictly increasing utility functions, a dense subset of the domain in the topologies commonly used in this context. If admissible utility functions are further restricted to be strictly increasing, or if mechanisms are required to be non-wasteful, then strategy-profness leads to (full) dictatorship. Received: August 14, 1995; revised version: September 25, 1997     

Continuity of the equilibrium price density and its uses in peak-load pricing

Summary. With as the commodity space, the equilibrium price density is shown to be a continuous function of the commodity characteristics. The result is based on symmetry ideas from the Hardy-Littlewood-Pólya theory of rearrangements. It includes, but is not limited to, the case of symmetric (rearrangement-invariant) production costs and additively separable consumer utility. Examples arise in continuous-time utility pricing, e.g., electricity pricing. In this context, a continuously varying price has two uses. First, it precludes demand jumps that would arise from discontinuous switches from one price rate to another. Second, in the problems of operating and valuing hydroelectric and pumped-storage plants (studied elsewhere), price continuity guarantees that their capacities (viz., the reservoir and the converter), the energy stocks, and in the case of hydro also the river flows, have well-defined marginal values.Received: 9 May 2001, Revised: 8 July 2004, JEL Classification Numbers: C62, D51, D58, L94. Correspondence to: Anthony HorsleyPart of this work (CentER DP 9014) was completed at the Center for Economic Research, Tilburg University, whose financial support is gratefully acknowledged. The extension to storage was supported by ESRC grant R000232822. We also thank the referee and the editor for their comments.     

Evolution of Interdependent Preferences in Aggregative Games

We study the evolution of preference interdependence in aggregative games which are symmetric with respect to material payoffs but asymmetric with respect to player objective functions. We identify a class of aggregative games whose equilibria have the property that the players with interdependent preferences (who care not only about their own material payoffs but also about their payoffs relative to others) earn strictly higher material payoffs than do the material payoff maximizers. Implications of this finding for the theory of preference evolution are discussed. Journal of Economic Literature Classification Numbers: C72, D62.     

Competitive equilibrium when preferences change over time

Summary. We show the existence of a competitive equilibrium in an economy with many consumers whose preferences may change over time. The demand correspondence of an individual consumer is determined by the set of subgame-perfect equilibrium outcomes in his intrapersonal game. For additively separable preferences with concave period utility functions that are unbounded above, this demand correspondence will satisfy the usual boundary conditions. Whenever consumers can recall their own mixed actions, this correspondence is convex-valued. This ensures the existence of a symmetric competitive equilibrium.Received: 29 July 2004, Revised: 17 November 2004, JEL Classification Numbers: D51, D91, C73. Correspondence to: Thomas MariottiWe thank Michele Piccione for useful comments and suggestions. The views expressed herein are those of the authors and not necessarily those of the Federal Reserve Bank of Minneapolis or the Federal Reserve System.     

Differentiable Technology,the Curvature of the Profit Function,and the Response of Supply to Own-Price Changes

The author establishes a property of supply for a competitive firm: Assuming differentiability of the production frontier, linearly independent price vectors have disjoint image sets under the supply mapping. This property supports the main results. First, the author drew a simple proof of McFadden's proposition that differentiability of the production frontier is necessary and sufficient for strict quasiconvexity of the profit function. This proposition rules out linearity of the profit function on any subset of price domain, in turn ruling out supply and input- demand functions that are constant and have zero values for all price effects. Second, for discrete price changes, own-price effects in supply are strictly positive, assuming a differentiable technology. In this context, strict convexity of the production set is irrelevant. The author indicates implications for cost and demand theory.     

Logconcavity versus Logconvexity: A Complete Characterization

This paper provides a complete characterization of logconcavity, an increasingly popular concept in the economics of uncertainty and information. New and known results are proven without assuming that density functions are differentiable. A systematic comparison between logconcavity and logconvexity is made and the source of the asymmetries between the two is investigated. The key difference is that logconcavity is preserved under one-sided integrations regardless of the types of distribution supports. This property, however, does not hold for logconvexity. Logconcavity for multivariate distributions is also discussed.Journal of Economic LiteratureClassification Number: D80.     

Disaggregation of excess demand under additive separability

A differentiable function satisfying Walras' law and homogeneity of degree zero can be disaggregated, at a point, into excess demand functions, each derived by the maximization of a regular and additively separable utility function subject to the budget constraint.     

Remarks concerning concave utility functions on finite sets

Summary. A direct construction of concave utility functions representing convex preferences on finite sets is presented. An alternative construction in which at first directions of supergradients (prices) are found, and then utility levels and lengths of those supergradients are computed, is exhibited as well. The concept of a least concave utility function is problematic in this context.Received: 28 November 2002, Revised: 28 June 2004, JEL Classification Numbers: D11, C60.I am indebted to an anonymous referee, Marcel K. Richter and Kam-Chau Wong, for many valuable remarks and suggestions.     

Bargaining with revoking costs

A simple two stage bilateral bargaining game is analyzed. The players simultaneously demand shares of a unit size pie. If the demands add up to more than one, the players simultaneously choose whether to stick to their demand or accept the other?s offer. While both parties sticking to their offers leads to an impasse, accepting a lower share than the original demand is costly for each party. The set of pure strategy subgame perfect equilibria of the game is characterized for continuously differentiable payoff and cost functions, strictly increasing in the pie share and the amount conceded, respectively. Higher cost functions are shown to improve bargaining power. The limit equilibrium prediction of the model, as the cost functions are made arbitrarily high, selects a unique equilibrium in the Nash Demand Game that corresponds to a Proportional Bargaining Solution of Kalai (1977).     

Achieving efficiency with manipulative bargainers

Two agents bargain over the allocation of a bundle of divisible commodities. After strategically reporting utility functions to a neutral arbitrator, the outcome is decided by using a bargaining solution concept chosen from a family that includes the Nash and the Raiffa–Kalai–Smorodinsky solutions. When reports are restricted to be continuous, strictly increasing and concave, it has been shown that this kind of “distortion game” leads to inefficient outcomes. We study the distortion game originated when agents are also allowed to claim non-concave utility functions. Contrasting with the previous literature, any interior equilibrium outcome is efficient and any efficient allocation can be supported as an equilibrium outcome of the distortion game. In a similar fashion to the Nash demand game we consider some uncertainty about the opponent's features to virtually implement the Nash bargaining solution.     

Optimal financial investments for non-concave utility functions

We prove a formula for the computation of optimal financial investments in an expected utility framework with arbitrary (not necessarily concave) utility functions. This extends classical results on optimal financial investments for strictly concave utility functions and is of importance particularly for applications of prospect theory where the utility function has a convex-concave shape.     

Decision theories and probabilistic insurance: an experimental test

This paper reports the results of an experiment in which probabilistic insurance, as proposed by Kahneman and Tversky (1979), is compared both with full insurance and no insurance. The experimental results conform to the intuitive prediction that risk-averse agents who are indifferent between full insurance and no insurance, will prefer full insurance to probabilistic insurance and probabilistic insurance to no insurance. The first conclusion is incompatible with the predictions of expected utility theory, and the second with Kahneman and Tversky's prospect theory. We also show that Loomes and Sudgen's regret theory can easily accommodate these intuitive results. JEL Classification: C91, D81. We are most grateful to Graham Loomes and two anonymous referees for their very helpful comments. Financial support from the Ministerio de Ciencia y Tecnología, under project BEC2001-0535, and from the Generalitat Valenciana under project GRUPOS03/086, is gratefully acknowledeged.     

On optimal cycles in dynamic programming models with convex return function

Summary. In this paper we study the behavior of optimal paths in dynamic programming models with a strictly convex return function. Such a model has been investigated in Dawid and Kopel (1997) who assume that the growth of a renewable resource is governed by a piecewise linear function. We prove that in their model the optimal cycles undergo the following qualitative changes or bifurcations: a cycle of period n“bifurcates” into a cycle of period n+1 for increasing elasticity of the return function. We also show that under the assumption of a concave differentiable growth function the qualitative properties of the optimal policy remain valid: oscillating behavior is optimal. Furthermore, we demonstrate numerically that the period of a cyclic optimal path increases if the convexity of the return function (measured by the elasticity) increases. Received: January 22, 1997; revised version: October 13, 1997     

Risk preference and productivity measurement under output price uncertainty

This paper deals with joint estimation of production and risk preference functions in the presence of output price uncertainty. We use quadratic production and utility functions under the assumption that producers maximize expected utility of anticipated profit. A panel data on Norwegian salmon farms is used for this purpose. Empirical results show that all salmon farmers are risk averse. Relative risk premium (the implicit cost of private risk bearing) is found to be about 15% of mean profit. We also find rapid technological change taking place (3.75% per year) in the salmon farming industry. First version received: February 2000/Final version received: February 2001