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

Economic Theory, Vol. 12, Iss. 1, 1998

Posted: 4 Oct 1998

See all articles by Graciela Chichilnisky

Graciela Chichilnisky

Columbia University

Geoffrey M. Heal

Columbia University - Columbia Business School, Finance; National Bureau of Economic Research (NBER)

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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], and for the non-emptiness of the core.

JEL Classification: D50, D51, G10

Suggested Citation

Chichilnisky, Graciela and Heal, Geoffrey M., A Unified Treatment of Finite and Infinite Economies: Limited Arbitrage is Necessary and Sufficient for the Existence of Equilibrium and the Core. Economic Theory, Vol. 12, Iss. 1, 1998, Available at SSRN: https://ssrn.com/abstract=113629

Graciela Chichilnisky

Columbia University ( email )

3022 Broadway
New York, NY 10027
United States
212 678 1148 (Phone)
212 678 0405 (Fax)

HOME PAGE: http://www.chilchilnisky.com

Geoffrey M. Heal

Columbia University - Columbia Business School, Finance ( email )

3022 Broadway
New York, NY 10027
United States
212-854-6459 (Phone)
212-316-9219 (Fax)

HOME PAGE: http://www.gsb.columbia.edu/faculty/gheal/

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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