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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

Author

Listed:
  • Graciela Chichilnisky

    (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)

  • Geoffrey Heal

    (Graduate School of Business and Program on Information and Resources, Earth Institute, Columbia University, New York, NY 10027, USA)

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].

Suggested Citation

  • Graciela Chichilnisky & Geoffrey Heal, 1998. "A unified treatment of finite and infinite economies: limited arbitrage is necessary and sufficient for the existence of equilibrium and the core," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 163-176.
    • Handle: RePEc:spr:joecth:v:12:y:1998:i:1:p:163-176
    Note: Received: August 4, 1995; revised version: April 11, 1997
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    Citations

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    Cited by:

    1. Geoffrey Heal, 2017. "Price Uncertainty and Price-Contingent Securities," NBER Working Papers 23723, National Bureau of Economic Research, Inc.
    2. Zdzisław Naniewicz, 2007. "Pseudomonotonicity and Economic Equilibrium Problem in Reflexive Banach Space," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 436-466, May.

    More about this item

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

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