Institutions, Equilibria and Efficiency

Frontmatter

1. Birgit Grodal: A Friend to Her Friends

Andreu Mas-Colell

2. On the Definition of Differentiated Products in the Real World

Summary

This paper proposes an abstract model of commodity differentiation that incorporates manufacturing imprecision and dimensioning and tolerancing standards. The potential consistency of such a model based on engineering consideration is analyzed. For a large pure exchange economy, competitive equilibria exist and are Pareto optimal. Production issues such as the derived demand for intermediate products, continuity of cost functions, and product selection and technology issues such as mass customization, agile manufacturing, and manufacturability are discussed.

Beth Allen

3. Equilibrium Pricing of Derivative Securities in Dynamically Incomplete Markets

Summary

We develop a method of assigning unique prices to derivative securities, including options, in the continuous-time finance model developed in Raimondo [47]. In contrast with the martingale method of valuing options, which cannot distinguish among infinitely many possible option pricing processes for a given underlying securities price process when markets are dynamically incomplete, our option prices are uniquely determined in equilibrium in closed form as a function of the underlying economic data.

Robert M. Anderson, Roberto C. Raimondo

4. Adaptive Contracting: The Trial-and-Error Approach to Outsourcing

Summary

Adaptive contracting occurs when a principal experiments with the delegation of authority through leaving contracts incomplete. We highlight two potential benefits of adaptive contracting: First, the delegation of authority can be advantageous even if the agent acts opportunistically, since expected private benefits will be shared between the parties through price negotiation. Second, the principal extracts information from experimenting with delegation of authority and we identify a positive option value embodied in the principal’s ability to extend or withdraw the delegated authority in future contracting periods.

Morten Bennedsen, Christian Schultz

5. Monetary Equilibria over an Infinite Horizon

Summary

Money provides liquidity services through a cash-in-advance constraint. The exchange of commodities and assets extends over an infinite horizon under uncertainty and a sequentially complete asset market. Monetary policy sets the path of rates of interest and accommodates the demand for balances through open market operations or loans. A public authority, which, most pertinently, inherits a strictly positive public debt, raises revenue from taxes and seignorage, and it distributes possible budget surpluses to individuals through transfers. Competitive equilibria exist, under mild solvency conditions. But, for a fixed path of rates of interest, there is a non-trivial multiplicity of equilibrium paths of prices of commodities. Determinacy requires that, subject to no-arbitrage and in addition to rates of interest, the prices of state-contingent revenues be somehow determined.

Gaetano Bloise, Jacques H. Drèze, Herakles M. Polemarchakis

6. Do the Wealthy Risk More Money? An Experimental Comparison

Summary

Are poor people more or less likely to take money risks than wealthy folks? We find that risk attraction is more prevalent among the wealthy when the amounts of money at risk are small (not surprising, since ten dollars is a smaller amount for a wealthy person than for a poor one), but, interestingly, for the larger amounts of money at risk the fraction of the nonwealthy displaying risk attraction actually exceeds that of the wealthy. We also replicate our previous finding that many people display risk attraction for small money amounts, but risk aversion for large ones.

Antoni Bosch-Domènech, Joaquim Silvestre

7. Are Incomplete Markets Able to Achieve Minimal Efficiency?

Summary

We consider economies with incomplete markets, one good per state, two periods, t=0, 1, private ownership of initial endowments, a single firm, and no assets other than shares in this firm. In Dierker, Dierker, Grodal (2002), we give an example of such an economy in which all market equilibria are constrained inefficient. In this paper, we weaken the concept of constrained efficiency by taking away the planner’s right to determine consumers’ investments. An allocation is called minimally constrained efficient if a planner, who can only determine the production plan and the distribution of consumption at t=0, cannot find a Pareto improvement. We present an example with arbitrarily small income effects in which no market equilibrium is minimally constrained efficient.

Egbert Dierker, Hildegard Dierker, Birgit Grodal

8. A Competitive Model of Economic Geography

Summary

Most of the literature argues that competitive analysis has nothing interesting to say about location. This paper argues, to the contrary, that a competitive model can have something interesting to say about location, provided that locations are not identical and transportation costs are not zero. To do this, it constructs a competitive intertemporal general equilibrium model and applies it to a suggestive example of migration.

Bryan Ellickson, William Zame

9. The Organization of Production, Consumption and Learning

Summary

This paper provides an extension of general equilibrium theory that incorporates the actions of individuals both as demanders and suppliers of goods and as members of firms, schools, social groups, and contractual relationships. The central notion of the paper is a group: a collection of individuals associated with one another for some purpose. The model takes as primitive an exogenous set of group types, interpretable as (potential) firms, schools, social groups, contracts etc. The types of schools and firms that materialize in equilibrium, as well as the way that agents acquire skills, are determined endogenously in a competitive market, as are the contracts they enter into, and the production and consumption of private commodities. Equilibrium exists and the core coincides with the set of equilibrium states. Examples and Applications illustrate the flexibility and power of the framework.⁴

Bryan Ellickson, Birgit Grodal, Suzanne Scotchmer, William R. Zame

10. Household Inefficiency and Equilibrium Efficiency

Summary

Collective consumption decisions taken by the members of a household may prove inefficient. The impact on market performance depends on whether household inefficiencies are caused by inefficient net trades with the market or by inefficient distribution of resources within households. Inefficient net trades might be consistent with global efficiency. Inefficient internal distribution always results in inefficient equilibrium allocations. This leads us to consider competitive forces as disciplinary device for households. Competition of households for both resources and members can eliminate or reduce inefficient internal distribution.

Hans Gersbach, Hans Haller

11. Equilibrium with Arbitrary Market Structure

Summary

Fifty years ago Arrow [1] introduced contingent commodities and Debreu [4] observed that this reinterpretation of a commodity was enough to apply the existing general equilibrium theory to uncertainty and time. This interpretation of general equilibrium theory is the Arrow-Debreu model. The complete market predicted by this theory is clearly unrealistic, and Radner [10] formulated and proved existence of equilibrium in a multiperiod model with incomplete markets.

In this paper the Radner result is extended. Radner assumed a specific structure of markets, independence of preferences, indifference of preferences, and total and transitive preferences. All of these assumptions are dropped here. We — like Radner — keep assumptions implying compactness.

Birgit Grodal, Karl Vind

12. 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.

P. Jean-Jacques Herings, Herakles Polemarchakis

13. On Behavioral Heterogeneity

Summary

An index of “behavioral heterogeneity” for every finite population of households is defined. It is shown that the higher the index of behavioral heterogeneity the less sensitive depends the aggregate consumption expenditure ratio upon prices. As a consequence, a high index implies a tendency for the Jacobian of aggregate demand to have a dominant negative diagonal.

Werner Hildenbrand, Alois Kneip

14. Learning of Steady States in Nonlinear Models when Shocks Follow a Markov Chain

Summary

Local convergence results for adaptive learning of stochastic steady states in nonlinear models are extended to the case where the exogenous observable variables follow a finite Markov chain. The stability conditions for the corresponding nonstochastic model and its steady states yield convergence for the stochastic model when shocks are sufficiently small. The results are applied to asset pricing and to an overlapping generations model. Large shocks can destabilize learning even if the steady state is stable with small shocks. Relationship to stationary sunspot equilibria are also discussed.

Seppo Honkapohja, Kaushik Mitra

15. The Evolution of Conventions under Incomplete Information

Summary

We formulate an evolutionary learning process with trembles for static games of incomplete information. For many games, if the amount of trembling is small, play will be in accordance with the games’ (strict) Bayesian equilibria most of the time supporting the notion of Bayesian equilibrium. Often the process will select a specific equilibrium. For two specific games of economic interest we characterize this selection. The first is an extension to incomplete information of the prototype strategic conflict known as “Chicken”. The second is an incomplete information bilateral monopoly, which is also an extension to incomplete information of Nash’s demand game, or a simple version of the so-called sealed bid double auction. The examples reveal that equilibrium selection by evolutionary learning may well be in favor of Bayesian equilibria where some types of players fail to coordinate, so that the equilibrium outcomes are inefficient.

Mogens Jensen, Birgitte Sloth, Hans Jøgen Whitta-Jacobsen

16. Group Formation with Heterogeneous Feasible Sets

Summary

In this paper we consider a model of group formation where group of individuals may have different feasible sets. We focus on two polar cases, increasing returns, when the set of feasible alternatives increases if a new member joins the group, and decreasing returns, when a new member has an opposite effect and reduces the number of alternatives available for the enlarged group. We consider two notions, stability and strong stability of group structures, that correspond to Nash and Strong Nash equilibrium of the associated non-cooperative game. We prove existence results for various classes of environments and also investigate the link between dimensionality of feasible sets and the existence of stable structures.

Michel Le Breton, Shlomo Weber

17. 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.

Lars Tyge Nielsen

18. Will Democracy Engender Equality?

Summary

Many suppose that democracy is an ethos which requires, inter alia, a degree of economic equality among citizens. In contrast, we conceive of democracy as ruthless electoral competition between groups of citizens with different interests, who are organized into parties. We inquire whether such competition, which we assume to be concerned with distributive matters, will engender economic equality in the long run. Society is modeled as OLG, and each generation competes politically over educational finance and tax policy; the policy space is infinite dimensional. A political equilibrium concept is proposed which determines the membership of two parties endogenously, and their proposed policies in political competition. One party wins the election (stochastically). This process determines the evolution of the distribution of human capital. We show that, whether the limit distribution of human capital is an equal one depends upon the nature of intra-party bargaining and the degree of inequality in the original distribution.

John E. Roemer

19. 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 person’s consumption affects another person’s 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.

Suzanne Scotchmer

20. Core-Equivalence for the Nash Bargaining Solution

Summary

Core equivalence and shrinking of the core results are well known for economies. The present paper establishes counterparts for bargaining economies, a specific class of production economies (finite and infinite) representing standard two-person bargaining games and their continuum counterparts as coalition production economies. Thereby we get core equivalence of the Nash solution. The results reconfirm the Walrasian approach to Nash bargaining of Trockel (1996). Moreover we establish the same speed of convergence as is known from Debreu (1975) and Grodal (1975) for replicated pure exchange economies and for regular purely competitive sequences of economies, respectively.

Walter Trockel

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