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A Unified Treatment of Finite and Infinite Economies: Limited Arbitrage Is Necessary and Sufficient for the Existence of Equilibrium and the Core

Graciela Chichilnisky and Geoffrey Heal
Economic Theory
Vol. 12, No. 1 (Jul., 1998), pp. 163-176
Published by: Springer
Stable URL: http://www.jstor.org/stable/25055114
Page Count: 14
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A Unified Treatment of Finite and Infinite Economies: Limited Arbitrage Is Necessary and Sufficient for the Existence of Equilibrium and the Core
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Abstract

A single condition, limited arbitrage, is shown to be necessary and sufficient for the existence of a competitive equilibrium and the core in economies with any number of markets, finite or infinite, with or without short sales. This extends earlier results of Chichilnisky [8] for finite economies. This unification of finite and infinite economies is achieved by proving that in Hilbert spaces limited arbitrage is necessary and sufficient for the compactness of the Pareto frontier. Limited arbitrage has also been shown to be necessary and sufficient for a resolution of the social choice paradox [9], [10], [12], [13], [14].

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