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On the existence of approximated equilibria in discontinuous economies

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  • Bich, Philippe
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    Abstract

    In this paper, we prove an existence theorem for approximated equilibria in a class of discontinuous economies. The existence result is a direct consequence of a discontinuous extension of Brouwer’s fixed point Theorem (1912), and is a refinement of several classical results in the standard general equilibrium with incomplete markets (GEI) model. [Brouwer, L.E.J., 1912. Über Abbildung von Mannigfaltigkeiten. Mathematische Annalen 71, 97–115.] As a by-product, we get the first existence proof of an approximated equilibrium in the GEI model, without perturbing the asset structure nor the endowments. Our main theorem rests on a new topological structure result for the asset equilibrium space and may be of interest by itself.

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    Bibliographic Info

    Paper provided by Université Paris-Dauphine in its series Open Access publications from Université Paris-Dauphine with number urn:hdl:123456789/6191.

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    Date of creation: 2005
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    Publication status: Published in Journal of Mathematical Economics (2005) v.41, p.463-481
    Handle: RePEc:ner:dauphi:urn:hdl:123456789/6191

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    Related research

    Keywords: General equilibrium; Incomplete markets; Discontinuity; Fixed point;

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    1. repec:hal:journl:halshs-00287677 is not listed on IDEAS
    2. Bich, Philippe, 2006. "On the orientability of the asset equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 452-470, August.
    3. Vincenzo Scalzo, 2011. "Existence of Equilibrium Prices for Discontinuous Excess Demand Correspondences," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 5(2), pages 203-210, August.

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