The Effectiveness of Distributive Policy in a Competitive Economy

I consider an abstract social system made of individual owners endowed with nonpaternalistic interdependent preferences, who interact by means of individual gifts and by exchanges on competitive markets. The existence of equilibrium is established. I identify the set of allocations that are decentralizable in the sense that they are general equilibria for some vectors of market prices and initial endowments. This set is characterized in a simple way from the social endowment and individual market and distributive preferences. Decentralizable allocations are all accessible to distributive policy, unless public transfers are confined to some neighborhood of 0. In the latter case, distributive policy remains free to perform local redistributions of wealth across the components of the graph of equilibrium gifts.     

Comparing competition and collusion: a numerical approach

Summary. Collusion is a serious problem in many procurement auctions. In this research, I study a model of first price sealed bid procurement auctions with asymmetric bidders. I demonstrate that the equilibrium to the model is unique and describe three algorithms that can be used to compute the inverse equilibrium bid functions. I then use the computational algorithms to compare competitive and collusive bidding. The algorithms are useful for structural estimation of auction models and for assessing the damages from bid-rigging. Received: January 14, 2000; revised version: February 28, 2001     

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     

Ecological Transfers in Non-Human Communities Parallel Economic Markets in a General Equilibrium Ecosystem Model

Synopsis: The oft-cited analogies between ecological and economic systems are exploited to develop a many-species model of population dynamics. In economies, markets are the fundamental institutions in which the interaction of demands and supplies determine the quantities and prices of goods. However, economic markets are not appropriate for ecological communities, because markets rely on voluntary exchange, whereas plants and animals engage in involuntary transfers of biomass. A properly defined counterpart to markets based on biomass transfers permits a general equilibrium model of predator/prey and competitive interactions in a many-species community. Functional response from optimal foraging and predation risk provide the demand and supply, respectively, in the biomass transfers. Energy per unit time is scarce and predators and prey make optimum choices with respect to functional response and risk avoidance based on required energy expenditures. The energy expenditures are similar to economic prices: they determine foraging strategies and are beyond the control of the predators and prey, yet they are determined by the aggregate choices of all predators and prey and by population densities. The energies acquired from foraging are used in a new way to construct difference equations that determine the population dynamics. This revised version was published online in July 2006 with corrections to the Cover Date.     

ON THE GAME‐THEORETIC FOUNDATIONS OF COMPETITIVE SEARCH EQUILIBRIUM*

We provide a unified directed search framework with general production and matching specifications that encompass most of the existing literature. We prove the existence of subgame perfect Nash equilibria in pure firm strategies in a finite version of the model. We use this result to derive a more complete characterization of the equilibrium set for the finite economy and to extend convergence results as the economy becomes large to general production and matching specifications. The latter extends the microfoundations for the standard market utility assumption used in competitive search models with a continuum of agents to new environments.     

Uncertainty and insurance in strategic market games

Summary. For perfectly competitive economies under uncertainty, there is a well-known equivalence between a formulation with contingent goods and one with state-specific securities followed by spot markets for goods. In this paper, I examine whether this equivalence carries over to a particular form of imperfect competition. Specifically, I look at three Shapley-Shubik strategic market games: one with contingent commodities, one with Arrow securities traded under imperfect competition and one with Arrow securities traded under perfect competition. First I compare the feasibility constraints of these three games. Then I compare their equilibrium sets. As in Peck and Shell (1989), the only common equilibria between the first and the second game are those which involve no transfer of income across states. However, if the securities markets are competitive, then the set of equilibria of the contingent commodities game and the securities game coincide. Received: June 16, 1997; revised version: April 30, 1998     

The complete removal of individual uncertainty: multiple optimal choices and random exchange economies

Summary. The aim of this paper is to develop some measure-theoretic methods for the study of large economic systems with individual-specific randomness and multiple optimal actions. In particular, for a suitably formulated continuum of correspondences, an exact version of the law of large numbers in distribution is characterized in terms of almost independence, which leads to several other versions of the law of large numbers in terms of integration of correspondences. Widespread correlation due to multiple optimal actions is also shown to be removable via a redistribution. These results allow the complete removal of individual risks or uncertainty in economic models where non-unique best choices are inevitable. Applications are illustrated through establishing stochastic consistency in general equilibrium models with idiosyncratic shocks in endowments and preferences. In particular, the existence of “global” solutions preserving microscopic independence structure is shown in terms of competitive equilibria for the cases of divisible and indivisible goods as well as in terms of core for a case with indivisible goods where a competitive equilibrium may not exist. An important feature of the idealized equilibrium models considered here is that standard results on measure-theoretic economies are now directly applicable to the case of random economies. Some asymptotic interpretation of the results are also discussed. It is also pointed out that the usual unit interval [0,1] can be used as an index set in our setting, provided that it is endowed together with some sample space a suitable larger measure structure. Received: September 14, 1998; revised version: January 6, 1999     

Time Consistent Optimal Redistribution Policy in an Overlapping Generations Model

This paper analyzes optimal redistribution policy in a two‐period version of the overlapping generations model with heterogeneous individuals and asymmetric information between the government and the private sector. The government of the first period determines redistribution transfers for the first period but is not able to set the policy variables for the second period. With respect to savings the paper considers two scenarios: In the first scenario savings are observable and the government can set individual savings levels in addition to redistributive transfers. In the second scenario savings and capital incomes are not observable. In both cases the redistribution equilibrium is not second‐best efficient.     

Regular Distributive Social Systems

I consider abstract social systems where individual owners make gifts according to their preferences on the distribution of wealth in the context of a noncooperative equilibrium. I define a condition of regularity and a condition of strong regularity of these social systems. I prove notably that: regularity is generic, and implies the local uniqueness of equilibrium and the uniqueness of status quo equilibrium; strong regularity is nongeneric, implies that an equilibrium exists for all initial distributions of wealth, whenever an equilibrium exists for one of them, and implies the connectedness of the range of the equilibrium correspondence. These properties have strong implications for distributive theory and policy, summarized in a general hypothesis of perfect substitutability of private and public transfers. The formulation and discussion of this hypothesis lead to a general assessment of the explanatory power of the theory.     

Risk and evolution

Summary. I examine a Knightian (1921) model of risk using a general equilibrium model of investment and trade. A population of agents with various preference types can choose between a safe production technology and a risky production technology. In addition, the distribution of types of agents changes through a standard evolutionary dynamic. For a given population distribution, the equilibrium is in general inefficient, however, by allowing the population distribution to change in response to market generated rewards, the population will converge to one where the equilibrium is efficient and where the population as a whole behaves as if all agents were risk neutral. Received: November 7, 1996; revised version: October 20, 1997     

Bertrand vs. Cournot equilibrium with risk averse firms and cost uncertainty

Summary. In an oligopoly game with cost uncertainty and risk averse firms, we show that Bertrand and Cournot equilibrium have different convergence properties when the market is replicated. The Cournot equilibrium price converges to the competitive price. Under very typical and somewhat general conditions, the highest Bertrand equilibrium price converges to one higher than the competitive equilibrium. We also give examples to show how to compute the limit of the highest Bertrand equilibrium prices and illustrate the ideas of the proof. We explore conditions under which the supply curve is upward sloping, a useful condition for our results. Received: April 20, 2000; revised version: May 10, 2001     

The bargaining set of a large economy with differential information

Summary. We study the Mas-Colell bargaining set of an exchange economy with differential information and a continuum of traders. We established the equivalence of the private bargaining set and the set of Radner competitive equilibrium allocations. As for the weak fine bargaining set, we show that it contains the set of competitive equilibrium allocations of an associated symmetric information economy in which each trader has the “joint information” of all the traders in the original economy, but unlike the weak fine core and the set of fine value allocations, it may also contain allocations which are not competitive in the associated economy. Received: February 15, 1999; revised version: August 9, 1999     

Exchange economies with asymmetric information: competitive equilibrium and core

Summary. A replica theorem is shown to hold for exchange economies with asymmetric information. In a replicated exchange economy with asymmetric information the set of all core elements with equal treatment is nonempty, but it is in general only a subset of the core. Nevertheless, the replica theorem and the presence of at least one core element with equal treatment suffice to show existence of a competitive quasi-equilibrium. Conditions on the initial endowments and the communication system are given to ensure that every competitive quasi-equilibrium is a competitive equilibrium.Received: 24 February 2003, Revised: 3 July 2003JEL Classification Numbers: C70, D50, D82.I thank an anonymous referee whose comments led to an improvement of the paper.     

International Trade and the Environment: Theoretical and Policy Linkages

I review and extend three approaches to trade and environmental policies: competitive general equilibrium, oligopoly and monopolistic competition. The first two have surprisingly similar implications: deviations from first-best rules are justified only by constraints on policy choice (which motivates what I call a “single dividend” approach to environmental policy), and taxes and emissions standards differ in ways which reflect the Le Chatelier principle. I also show how environmental taxes may lead to a catastrophic relocation of industry in the presence of agglomeration effects, although not necessarily if there is a continuum of industries which differ in pollution intensity. *An earlier version was presented as an invited plenary lecture to the European Association for Environmental and Resource Economics Conference, Oslo, 1999.     

The Arrow-Debreu model: How math can hide a fatal conceptual error

I argue that math, like love, can cover a multitude of sins, and I use the neoclassical object of adoration, the Arrow-Debreu model, as the case in point. It is commonplace that the Arrow-Debreu (AD) model of general equilibrium does not describe the real world, but it is equally commonplace to accept it as representing the pure logic of the competitive capitalist economy in an idealized world free of transactions costs. I show that the AD model fails even as an idealized model; it actually mistakes the logic of pure capitalism. Unlike McKenzie’s model of idealized general equilibrium under constant returns to scale, Arrow and Debreu claim to have shown the existence of competitive equilibrium under decreasing returns to scale and positive pure profits. The AD model (again unlike the McKinzie model) needs to assign the profits to individuals and this is done using the notion of “ownership of the production set.” But this notion suffers from a fatal ambiguity. If Arrow and Debreu interpret it to mean “ownership of a corporation” then a simple argument in the form “labor can hire capital or capital can hire labor” defeats the alleged necessity of assigning residual claimancy to the corporation. A given corporation may or may not end up exploiting a set of production opportunities (represented by a production set) depending on whether it hires in labor and undertakes production or hires out its capital to others (all by assumption at the parametrically given prices). In the latter case, residual claimancy is elsewhere. There is no such property right as “ownership of a production set” in a private property market economy. The legal party which purchases or already owns all the inputs used up in production has the defensible legal claim on the outputs: there is no need to also “purchase the production set.” At any set of prices that allow positive pure profits, anyone in the idealized AD model could bid up the price of the inputs and thus try to reap a smaller but still positive profit. Therefore,pace Arrow and Debreu, there could be no equilibrium with positive pure profits. In the Appendix, the property rights fallacy that afflicts the AD model is shown to also afflict orthodox capital theory and corporate finance theory.     

Price dynamics in overlapping generations environments

Summary This work examines the existence, uniqueness and computation of competitive equilibria in a class of overlapping generations environments. This set of environments represents a broad generalization of the overlapping generations model considered by Aliprantis and Plott [1]. Two types of results are presented in this paper. First, some general characteristics of perfect foresight competitive equilibrium price paths are developed for economies with finite or countably infinite time horizons and agents with finite lifetimes. The results establish the conditions leading to locally monotonic and locally stable equilibrium prices given arbitrarily many exogenous parameter shifts. Second, these results are strengthened when consideration is focused on a single parametric shift in a finite economy. Existence of a unique equilibrium price path is established. A simple set of rules are given to facilitate computation of this price path for any given shift.The authors wish to express their thanks to Donald Brown, Diego Moreno, Charles Plott, Vernon Smith, and Mark Walker for their comments and suggestions regarding this research.     

Learning buyers' valuation distribution in posted-price selling

Summary. For his proof of the existence of a general competitive equilibrium Abraham Wald assumed a strictly pseudomonotone inverse market demand function or, equivalently, that market demand satisfies the Weak Axiom of Revealed Preference. It is well known that more recent existence theorems do not need this assumption. In order to clarify its role in Wald's proof, the question of existence of an equilibrium for a modified version of the Walras-Cassel model is reduced to the solvability of a related variational inequality problem. In general, the existence of a solution to such a problem can only be proved by advanced mathematical methods. We provide an elementary induction proof which demonstrates the essence of Abraham Wald's famous contribution. Received: July 22, 1997; revised version: December 11, 1997     

On Efficient Child Making

This paper is devoted to the study of the Pareto-efficiency of the competitive equilibrium for an overlapping generations economy with endogenous fertility. Pareto-efficiency needs a reformulation when fertility is endogenous. Then it is proved that a competitive equilibrium that converges in over-accumulation is non-Pareto-efficient. However, we provide an example in which a competitive equilibrium that converges in under-accumulation is non-Pareto-efficient. Finally, we give a general condition that ensures the Pareto-efficiency of the competitive equilibrium. This paper was presented at the conference “Irregular Growth”: Beyond Balanced Growth” , Paris, June 2003. The current version of this paper was completed after Philippe Michel’s sudden death. Bertrand Wigniolle wants to express his deep sorrow for the loss of a close friend and an excellent economist, from whom he learned a lot over the years. The authors would like to thank Tapan Mitra for helpful comments. They also are grateful to Claire Loupias, who began to think with them on the subject and to an anonymous referee for useful suggestions and improvements.     

Growth in economies with non convexities: sunspots and lottery equilibria

Summary. We investigate the relation between lotteries and sunspot allocations in a dynamic economy where the utility functions are not concave. In an intertemporal competitive economy, the household consumption set is identified with the set of lotteries, while in the intertemporal sunspot economy it is the set of measurable allocations in the given probability space of sunspots. Sunspot intertemporal equilibria whenever they exist are efficient, independently of the sunspot space specification. If feasibility is, at each point in time, a restriction over the average value of the lotteries, competitive equilibrium prices are linear in basic commodities and intertemporal sunspot and competitive equilibria are equivalent. Two models have this feature: Large economies and economies with semi-linear technologies. We provide examples showing that in general, intertemporal competitive equilibrium prices are non-linear in basic commodities and, hence, intertemporal sunspot equilibria do not exist. The competitive static equilibrium allocations are stationary, intertemporal equilibrium allocations, but the static sunspot equilibria need not to be stationary, intertemporal sunspot equilibria. We construct examples of non-convex economies with indeterminate and Pareto ranked static sunspot equilibrium allocations associated to distinct specifications of the sunspot probability space.Received: 25 August 2003, Revised: 16 March 2004, JEL Classification Numbers: D84, D90.Correspondence to: Paolo SiconolfiWe thank Herakles Polemarchakis for helpful conversations on the topic. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556.     

Collusion and Information Exchange

Antitrust authorities view that exchange of individual firms’ sales data is more anti‐competitive than that of aggregate sales data. In this paper, I survey antitrust implications of such inter‐firm information exchange. I argue that both types of information exchange are anti‐competitive under some circumstances. More precisely, I compare profits when each type of information exchange is allowed to that when firms can only observe their own sales (Stigler’s secret price‐cutting model), and the former is bigger than the latter. I also provide a general method to bound the equilibrium profits without such information exchange.