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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| Authors: | Graciela Chichilnisky Geoffrey Heal |
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| Institution: | (1) Departments of Applied Mathematics, Statistics and Economics and Program on Information and Resources, Columbia University, Earth Institute, 405 Low Library, New York, NY 10027, USA, US;(2) Graduate School of Business and Program on Information and Resources, Earth Institute, Columbia University, New York, NY 10027, USA, US |
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| Abstract: | Summary. 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].
Received: August 4, 1995; revised version: April 11, 1997 |
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| Keywords: | JEL Classification Numbers: D50 D51 G10 |
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