General Equilibrium Theory and Market Efficiency
 Irreducibility, Resource Relatedness, and Survival in Equilibrium with Individual NonConvexities in R. Becker, M. Boldrin, R. Jones, and W. Thomson (eds.) General Equilibrium, Growth, and Trade II: The Legacy of Lionel W. McKenzie (San Diego: Academic Press, 1993), ch. 4, pp. 73–115.
Abstract:
Standard results in general equilibrium theory, such as existence and the second efficiency and core equivalence theorems, are most easily proved for compensated equilibria. A new condition establishes that, even with individual nonconvexities, in compensated equilibrium any agent with a cheaper feasible net trade is also in uncompensated equilibrium. Some generalizations of McKenzie’s irreducibility assumption are then presented. They imply that (almost) no agent is at a cheapest point, so the easier and more general results for compensated equilibria become true for uncompensated equilibria. Survival of all consumers in uncompensated equilibrium also depends on satisfying an additional assumption that is similar to irreducibility. PDF file of preprint

Walrasian Equilibrium without Survival: Equilibrium, Efficiency, and Remedial Policy (with Jeffrey L. Coles) in K. Basu, P.K. Pattanaik, and K. Suzumura (eds.) Choice, Welfare and Development: A Festschrift in Honour of Amartya K. Sen (Oxford: Oxford University Press, 1995), ch. 3, pp. 32–64.
Abstract:
Standard general equilibrium theory excludes starvation by assuming that everybody can survive without trade. Because trade cannot harm consumers, they can therefore also survive with trade. Here this assumption is abandoned, and equilibria in which not everybody survives are investigated. A simple example is discussed, along with possible policies which might reduce starvation. Thereafter, for economies with a continuum of agents, the usual results are established — existence of equilibrium, the two fundamental efficiency theorems of welfare economics, and core equivalence. Their validity depends on some special but not very stringent assumptions needed to deal with natural nonconvexities in each consumer’s feasible set. PDF file of preprint

“The Efficiency Theorems and Market Failure,” in A.P. Kirman (ed.) Elements of General Equilibrium Analysis (Oxford: Basil Blackwell, 1998) ch. 6, pp. 211–260. PDF file of preprint

Efficiency with NonConvexities: Extending the ÔScandinavian Consensus’ Approaches (with Antonio Villar) Scandinavian Journal of Economics 100 (1998), 11–32; also in T.M. Andersen and K.O. Moene (eds.) Public Policy and Economic Theory (Oxford: Blackwell, 1998), pp. 11–32.
Abstract:
There are two distinct “Scandinavian consensus” approaches to public good supply, both based on agents’ willingness to pay. A Wicksell–Foley public competitive equilibrium arises from a negative consensus in which no change of public environment, together with associated taxes and subsidies which finance it, will be unanimously approved. Alternatively, in a Lindahl or valuation equilibrium, charges for the public environment induce a positive consensus. To allow general nonconvexities to be regarded as aspects of the public environment, we extend recent generalizations of these equilibrium notions and prove counterparts to both the usual fundamental efficiency theorems of welfare economics.
PDF file of preprint

Valuation Equilibrium Revisited (with Antonio Villar) in A. Alkan, C.D. Aliprantis, and N.C. Yannelis (eds.) Current Trends in Economics: Theory and Applications: Proceedings of the Third International Meeting of the Society for the Advancement of Economic Theory (Berlin: Springer, 1999), pp. 201–214.
Abstract:
This paper extends the notion of valuation equilibrium which applies to market economies involving the choice of a public environment. Unlike some other recent work, it is assumed here that consumers and firms evaluate alternative environments taking market prices as given (hence this notion is closer to that of competitive equilibria). It is shown that valuation equilibria with balanced tax schemes yield efficient allocations and that efficient allocations can be decentralized as valuation equilibria, with tax schemes that may be unbalanced.

(with Antonio Villar) “Efficiency and Core Properties of Valuation Equilibrium with Increasing Returns,” Instituto Valenciano de Investigaciones Económicas, WPAD 200124. PDF file

Competitive Market Mechanisms as Social Choice Procedures University of Warwick, Economics Research Paper No. 804 (2007); to appear in K.J. Arrow, A.K. Sen and K. Suzumura (eds.) Handbook of Social Choice and Welfare, Vol. II (Amsterdam: NorthHolland).
Abstract:
A competitive market mechanism is a prominent example of a nonbinary social choice rule, typically defined for a special class of economic environments in which each social state is an economic allocation of private goods, and individuals' preferences concern only their own personal consumption. This chapter begins by discussing which Pareto efficient allocations can be characterized as competitive equilibria with lumpsum transfers. It also discusses existence and characterization of such equilibria without lumpsum transfers. The second half of the chapter focuses on continuum economies, for which such characterization results are much more natural given that agents have negligible influence over equilibrium prices. PDF file