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On the pseudo-equilibrium manifold in semi-algebraic economies with real financial assets

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  • Arias-R., Omar Fdo.

Abstract

The aim of this paper is to prove that if the consumption set of an economy with incomplete financial markets is semi-algebraic, then the corresponding pseudo-equilibrium manifold is also semi-algebraic. For this, we proceed by constructing an incomplete financial economy with real assets and semi-algebraic utility functions. Then, we show that the spot-equilibrium set and the pseudo-equilibrium set are smooth semi-algebraic manifolds. We extent this results by showing that the pseudo-equilibrium natural projection is a semi-algebraic diffeomorphism in each regular point of the semi-algebraic pseudo-equilibrium manifold. It is directly related with the local determinacy of pseudo-equilibrium.

Suggested Citation

  • Arias-R., Omar Fdo., 2014. "On the pseudo-equilibrium manifold in semi-algebraic economies with real financial assets," MPRA Paper 54297, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:54297
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    File URL: https://mpra.ub.uni-muenchen.de/54297/1/MPRA_paper_54297.pdf
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    References listed on IDEAS

    as
    1. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    2. Blume, Lawrence E & Zame, William R, 1994. "The Algebraic Geometry of Perfect and Sequential Equilibrium," Econometrica, Econometric Society, vol. 62(4), pages 783-794, July.
    3. Kubler, Felix & Schmedders, Karl, 2010. "Competitive equilibria in semi-algebraic economies," Journal of Economic Theory, Elsevier, vol. 145(1), pages 301-330, January.
    4. Zhou, Yuqing, 1997. "Genericity Analysis on the Pseudo-Equilibrium Manifold," Journal of Economic Theory, Elsevier, vol. 73(1), pages 79-92, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    semi-algebraic; finance; spot-equilibrium; pseudo-equilibrium;

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D52 - Microeconomics - - General Equilibrium and Disequilibrium - - - Incomplete Markets

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