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A Note on the Size of Determinacy and Indeterminacy

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  • Julio Davila

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

It is shown in this note that in an incomplete markets economy with uncountably many states of the world there may be uncountably many isolated equilibria as well as uncountably many non-isolated equilibria. Moreover, both subsets can be simultaneously of second category. Therefore, none of the subsets can be considered negligible with respect to the other, neither from a cardinality point of view nor from a topological one. Unfortunately, this fact prevents from claiming that these economies may have "typically" determinate equilibria – even though uncountably many of them – as would have been desirable for comparative statics exercises.

Suggested Citation

  • Julio Davila, 1998. "A Note on the Size of Determinacy and Indeterminacy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00286028, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00286028
    DOI: 10.1007/s001990050219
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    Cited by:

    1. Monteiro, Paulo Klinger & Pascoa, Mario R., 2000. "Discreteness of equilibria in incomplete markets with a continuum of states," Journal of Mathematical Economics, Elsevier, vol. 33(2), pages 229-237, March.

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    Keywords

    determinacy; incomplete markets;

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