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Determinacy of Competitive Equilibria in Economies with Many Commodities

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  • Chris Shannon

    (University of California, Berkeley)

Abstract

This paper provides a framework for establishing the determinacy of equilibria in general equilibrium models with infinitely many commodities and a finite number of consumers and producers. The paper defines a notion of regular economy for such models and gives sufficient conditions on the excess savings equations characterizing equilibria under which regular economies have a finite number of equilibria, each of which is locally stable with respect to perturbations in exogenous parameters, and under which regular economies are generic. For the case of sequence economies in which there are countably many commodities, such as discrete time models or markets with countably many assets, the paper develops sufficient conditions on preferences and technologies for these generic determinacy conclusions to hold. These arguments build on the intuition that these economies can be thought of as the limit of economies with a large finite number of commodities, and conclude that the sharp predictions of generic determinacy in economies with finitely many commodities carry over to economies with countably many commodities under one additional assumption, which prohibits goods from becoming perfect substitutes asymptotically.

Suggested Citation

  • Chris Shannon, 1996. "Determinacy of Competitive Equilibria in Economies with Many Commodities," GE, Growth, Math methods 9610002, EconWPA.
  • Handle: RePEc:wpa:wuwpge:9610002
    Note: 53pp
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    References listed on IDEAS

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    1. Bezalel Peleg & Menahem E. Yaari, 1973. "On the Existence of a Consistent Course of Action when Tastes are Changing," Review of Economic Studies, Oxford University Press, vol. 40(3), pages 391-401.
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    Cited by:

    1. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    2. Covarrubias Enrique, 2010. "Regular Infinite Economies," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 10(1), pages 1-21, July.
    3. DEMICHELIS, Stefano & POLEMARCHAKIS, Heracles, 2000. "Life-span and the determinacy of equilibrium in economies of overlapping generations," CORE Discussion Papers 2000034, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. H. Polemarchakis & S. Demichelis, 2002. "Frequency of Trade and the Determinancy of Equilibrium Paths: Logarithmic Economies of Overlapping Generations Under Certainty," Working Papers 2002-16, Brown University, Department of Economics.

    More about this item

    JEL classification:

    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General

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