Equilibrium, Trade, and Capital Accumulation

The paper summarizes the author's principal contributions to economic theory: (1) one of the first rigorous proofs of the existence of competitive equilibrium; (2) existence of competitive equilibrium with weakened assumptions; (3) the minimum income approach to demand theory; (4) tatonnement stability with weak gross substitutes; (5) a general theory of comparative advantage; (6) factor price equalization with attention to factor supplies; and (7) turnpike theory allowing for von Neumann facets and neighbourhood convergence.
JEL Classification Number: B10     

Nonconvexity,efficiency and equilibrium in exhaustible resource depletion

We consider the problem of efficiency and existence of a competitive equilibrium in exhaustible resource markets where extraction costs are nonconvex. Nonconvexity is shown to imply that (1) (efficient) extraction ceases to the left of the minimum efficient scale, i.e., where average costs exceed marginal costs; and (2) a competitive equilibrium does not exist. Introduction of a backstop technology (which induces a flat portion of the industry demand curve) restores both existence and efficiency, provided that the backstop price is sufficiently low. If firms face even a small amount of uncertainty regarding their rivals' stocks, a backstop technology is sufficient to restore existence of competitive equilibrium, even if the backstop price is very high. In this case, however, the competitive equilibrium is not efficient.     

Existence of equilibrium in the Helpman–Krugman model of international trade with imperfect competition

Helpman and Krugman (Market structure and foreign trade. Increasing returns, imperfect competition, and the international economy. MIT Press, Cambridge, 1985) provide a synthesis of the traditional factor proportions theory of international trade and the theory of international trade due to the exploitation of scale economies in imperfectly competitive markets. They derive illuminating results about trade patterns and gains from trade, among other things, leaving unanswered the question of existence of equilibrium, however. The central significance of their characterization of properties of free trade equilibria with inter-industry and intra-industry trade calls for an analysis of existence of equilibrium. This is the object of the present paper. We prove the existence of equilibrium for the integrated multi-sector multi-factor Helpman–Krugman economy without national borders. Well-known conditions ensure that the world economy under free trade reproduces this equilibrium and thus establishes existence of a free trade equilibrium. Since an equilibrium of the integrated economy is not necessarily unique, the same holds true for a free trade equilibrium.     

A competitive equilibrium for a warm-glow economy

The warm-glow model (Andreoni in J Political Econ 97:1447–1458, 1989; Econ J 100:464–477, 1990) of public goods provision has received widespread interest, yet surprisingly most attention has focused on the voluntary contribution equilibrium of the model, and only very little attention has been devoted to the competitive equilibrium. In this paper, we introduce the concept of competitive equilibrium for a warm-glow economy (henceforth, warm-glow equilibrium) and establish both existence and welfare properties. The warm-glow equilibrium concept may prove to be very useful to the normative and positive theory of public goods provision. First, it is a price-based mechanism achieving efficient outcomes. Second, not only could the warm-glow equilibria outcomes serve as a point of reference to measure free-riding and welfare loss but also, as suggested by Bernheim and Rangel (Behavioral Economics and Its Applications, 2007), in large economies they may be approximated by Walrasian equilibria outcomes.     

Value theory with personalized trading

This paper extends existing general equilibrium theory to describe the competitive production and allocation of “personalized commodities:” commodities with only one potential buyer or seller. The basic, novel theoretic possibility introduced into value theory with the introduction of personalized trading—the trading of personalized commodities—is that price discrimination over quantity may occur under perfect competition. Theorems on the existence and optimality of competitive equilibria under discriminatory pricing are proved.     

Competitive equilibria of economies with a continuum of consumers and aggregate shocks

This paper studies competitive equilibria of a production economy with aggregate productivity shocks. There is a continuum of consumers who face borrowing constraints and individual labor endowment shocks. The dynamic economy is described in terms of sequences of aggregate distributions. The existence of competitive equilibrium is proven and a recursive characterization is established. In particular, it is shown that for any competitive equilibrium, there is a payoff equivalent competitive equilibrium that is generated by a suitably defined recursive equilibrium.     

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.     

Indeterminate Balanced Growth under Habit Persistence and Fiscal Policies

This paper studies a dynamic general equilibrium model with habit persistence in preferences and fiscal policies of taxation and expenditures. Preference takes a subtractive form of habits (the marginal rate of substitution between the agent's own consumption and habit stocks is constant), and technology is linear in aggregate capital (the economy grows without a limit in the long run). We find a continuum of competitive equilibrium paths in conjunction with a unique balanced growth path in the growing economy, in which habits represent both envy/jealousy and altruism/admiration. In addition, in the social optimum under second-best fiscal policies, we show the existence of indeterminacy in transitional allocations along with a unique balanced growth path. Thus, we find that the introduction of habits influences the patterns of the transitional paths but has no impact on the balanced growth path in either competitive or social optimum allocations. The second-best fiscal policy, therefore, restores the socially optimal balanced growth rate but fails to select the unique transitional path among multiple competitive equilibrium paths in the imperfectly competitive economy.     

Dissertation Abstract: Decision-Theoretic Models of Market Equilibration

There has been a surprising dearth of decision-theoretic approaches to market equilibration within the extended Arrow-Debreu-McKenzie framework. While game theory is replete with learning and evolutionary models in which Nash equilibria are not necessarily the only stable states of a game, general equilibrium theorists have generally been content to accept the attainment of competitive equilibrium as a matter of faith. The first two chapters of this dissertation advance the study of behaviorally plausible models of market equilibration. First, we develop the epsilon-intelligent competitive equilibrium algorithm. According to this model, the actions of minimally sophisticated agents based on local information will lead an exchange economy to approximate competitive equilibrium in a larger set of economics than Walras’ tatonnement. The algorithm also supports a behavioral interpretation of Negishi’s existence proof of competitive equilibrium. The second chapter is an empirical analysis of laboratory markets designed to test the extent to which human behavior is consistent with the algorithm’s behavioral restrictions, and suggest alternative hypotheses. The chief finding is that while subjects sufficiently sophisticated to consistently secure competitive utility for themselves exist, the majority are satisficers who follow small modifications of a simple utility-improvement rule.While general equilibrium theory has lacked a behaviorally plausible foundation of price equilibration, behavioral economic models typically ignore general equilibrium implications. In the third chapter of this dissertation, I present the surprising result that loss aversion and diminishing sensitivity for gains imply a greater redistribution of endowments than when otherwise identical preferences are reference-independent. The result is surprising because loss aversion was developed in part to account for the status quo bias, whereby people tend to value a good more when it is in their possession than when it is not. One might reasonably suspect trade to be inhibited by this bias. The counter-intuitive result is driven by the fact that, given the axiomatization of loss aversion and diminishing sensitivity for gains, the acquisition of some quantity of a good increases one’s taste for that good, thus perpetuating a taste for more trade.     

BORK'S PARADOX: STATIC VS. DYNAMIC EFFICIENCY IN ANTITRUST ANALYSIS

Judge Robert Bork holds two opposing attitudes towards perfect competition. It is a highly useful economic model for illustrating allocative efficiency, but it is a defective policy model because it deliberately omits productive efficiency. He reconciles these attitudes by combining perfectly competitive allocative efficiency with dynamically competitive productive efficiency in his analysis.
However, these two kinds of competition do not readily mix. One is a static equilibrium concept, the other a dynamic disequilibrium concept. One assumes perfect knowledge and the absence of change; the other assumes imperfect knowledge, learning, and continual flux. Each kind of competition is built on assumptions which, if true, would preclude the existence of the other.
Bork's policy conclusions require the simultaneous existence of both kinds of competition. If he drops dynamic competition from the analysis, a much more stringent antitrust policy is called for. If he drops static competition, economic theory does not justify even his strictures against mergers and cartels.     

Stability and Turnpike Theorems in Dynamic Competitive Equilibrium

This study reviews the main results in the literature on the integration of competitive equilibrium theory and optimal growth theory, in particular those concerning the convergence of an equilibrium path to a stationary state (stability theorems).
JEL Classification Numbers: C6, D9.     

Optimal steady-state in stationary consumption-loan type models

We consider a stationary overlapping generations economy, and prove that an optimal steady state exists. We show that if a government intervention is needed in order to implement the optimal steady state as a competitive equilibrium, it is necessary only in a finite number of periods. If the interest rate associated with the optimal steady state equals the population rate of growth, some outside money may be required in order to make the competitive equilibrium follow the optimal steady state. We show that our existence result enables us to construct Pareto optimal competitive equilibria in some important cases.     

Equilibrium theory with asymmetric information and with infinitely many commodities

The traditional deterministic general equilibrium theory with infinitely many commodities cannot cover economies with private information constraints on the consumption sets. We bring the level of asymmetric information equilibrium theory at par with that of the deterministic one. In particular, we establish results on equilibrium existence for exchange economies with asymmetric (differential) information and with an infinite dimensional commodity space. Our new equilibrium existence theorems include, as a special case, classical results, e.g. Bewley [Existence of equilibria in economies with infinitely many commodities, J. Econ. Theory 4 (1972) 514-540] or Mas-Colell [The price equilibrium existence problem in topological vector lattices, Econometrica 54 (1986) 1039-1053].     

Experts against adverse selection: A note on the existence of equilibrium with costly appropriable information

The existence of competitive equilibrium in Laffont's (J. Econ. Theory10 (1975)) model of adverse selection with costly information is studied. The existence of an equilibrium with finite prices is demonstrated without unusual restrictions on preferences or the technology of information production. This is made possible by changing the way in which the behaviour of information producing agents is modelled, and allowing for some public information.     

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.     

Rationality without Transitivity

In this article rational choice behavior is investigated without assuming transitivity or completeness of the underlying preferences. These standard properties are replaced by a property concerning dominant alternatives. This permits the existence of preference cycles among alternatives which are dominated, while still ensuring the existence of a rational choice correspondence. We will also realize that some rational choice rules still hold in this context. Further we will see that in equilibrium analysis the existence of a competitive equilibrium follows when transitivity and completeness is replaced by this domination property.     

Monetary equilibrium in an overlapping generations model with productive capital

Summary We study perfect foresight competitive equilibrium in an overlapping generations model with productive capital and a fixed nominal stock of money. We obtain almost-complete characterizations of (a) the existence of a monetary equilibrium from an arbitrary initial capital stock, and (b) the existence of anefficient monetary equilibrium from an arbitrary initial capital stock. When the initial capital stock is no larger than the golden rule stock, the necessary and sufficient condition for both (a) and (b) is the dynamic inefficiency (in the sense of Malinvaud) of the autarkic (or nonmonetary) equilibrium from the same initial stock. However, this condition, though necessary, isnot sufficient for the existence of a monetary equilibrium when the initial stock exceeds the golden rule stock (and still more conditions are needed for anefficient monetary equilibrium to exist). We provide characterizations for these cases, and as corollaries obtain examples in which (a) the nonmonetary equilibrium is inefficient but no monetary equilibrium exists, and (b) monetary equilibria exist but no efficient monetary equilibrium does.We are grateful to a co-editor and an anonymous referee for comments that greatly improved the exposition in the paper.     

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.     

Bargaining, binding contracts, and competitive wages

In a model where many workers bargain with one firm and sign binding contracts, we show existence of a stationary subgame perfect equilibrium. If the production function satisfies decreasing returns, each worker receives a share of his marginal product (treating all other workers as employed) in equilibrium. Thus, wages are competitive. This is in contrast to Stole and Zweibel (1996, Rev. Econ. Stud. 63, 375–410), who assume that contracts are non-binding and find that the payoff of a worker is a weighted average of the inframarginal contributions. Hence, binding contracts imply lower wages than non-binding contracts.     

Spatial monopolistic competition versus spatial monopoly

This paper compares the equilibrium firm output, market area, price of services, and level of net benefits in monopolistically competitive spatial equilibrium versus the multiplant monopolists spatial equilibrium. Through a computer simulation, it is found that the welfare comparisons depend on population density—the monopolists equilibrium is superior to the monopolistically competitive equilibrium in high density areas and vice versa, contrary to traditional economic theory in which distance is assumed costless.