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Markets, Arbitrage and Social Choices

Chichilnisky, Graciela

The paper establishes a clear connection between equilibrium theory and social choice theory by showing that, for a well defined social choice problem, the conditions which are necessary and sufficient to establish existence of a competitive equilibrium. We define a condition of limited arbitrage on the preferences and the endowments of an Arrow-Debreu economy. This bounds the utility gains that the traders can afford from their initial endowments. Theorem 2 proves that limited arbitrage is necessary and sufficient for the existence of a social choice rule which allocates society's resources among individuals in a manner which depends continuously and anonymously on their preferences over allocations, and which respects unanimity. Limited arbitrage is also necessary and sufficient for the existence of a competitive equilibrium in the Arrow-Debreu economy, with or without bounds on short sales, Theorem 7. Theorem 4 proves that any market allocation can be achieved as a social choice allocation, i.e. an allocation which is maximal among all feasible allocations according to a social preference defined via a social choice rule which is continuous, anonymous and respects unanimity.



More About This Work

Academic Units
Department of Economics, Columbia University
Department of Economics Discussion Papers, 649
Published Here
February 17, 2011


December 1992.