Academic Commons


Limited Arbitrage Is Necessary and Sufficient for the Existence of a Competitive Equilibrium

Chichilnisky, Graciela

A condition of limited arbitrage is defined on the endowments and the preferences of the traders in an Arrow-Debreu economy. It bounds the diversity of the traders in the economy, and the gains from trade which they can afford from initial endowments. Theorem 1 shows that limited arbitrage is necessary and sufficient for the existence of a competitive equilibrium, when consumption sets are either positive orthants or the whole euclidean space. The results apply therefore to market economies with or without bounds on short sales. Theorem 6 establishes that an Arrow-Debreu economy has a competitive equilibrium if and only if every subeconomy with N + 1 traders does, where N is the number of commodities. Limited arbitrage has been shown elsewhere to be equivalent to the contractibility of spaces of preferences, and therefore, by the results of Chichilnisky and Heal [12], to be necessary and sufficient for the existence of social choice rules defined on individual preferences over allocations, rules which are continuous, anonymous and respect unanimity.



More About This Work

Academic Units
Department of Economics, Columbia University
Department of Economics Discussion Papers, 650
Published Here
February 17, 2011


December 1992.