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An algebraic index theorem for non-smooth economies

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  • GIRAUD, Gaël

Abstract

In this paper, we prove an existence theorem for equilibria in production economies with increasing returns, which generalizes the classic results on this topic. In particular, we eliminate both the free-disposal assumptions and any smoothness requirements on the boundary of the production sets. For this purpose, we propose a new definition of the topological degree for non-convex-valued correspondences defined on non-smooth topological manifolds.

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Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 2000016.

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Date of creation: 00 Mar 2000
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Handle: RePEc:cor:louvco:2000016

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Related research

Keywords: Non-smooth production; topological degree; local homology; increasing returns.;

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References

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  1. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
  2. Hamano, Tadashi, 1994. "On the existence of equilibria without convexity or free disposal on production technologies," Journal of Mathematical Economics, Elsevier, vol. 23(6), pages 565-583, November.
  3. Kamiya, Kazuya, 1988. "Existence and uniqueness of equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 149-178, April.
  4. DEBREU, Gérard, . "Economies with a finite set of equilibria," CORE Discussion Papers RP -67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Mclennan, A., 1989. "Approximation Of Contractible Valued Correspondences By Functions," Papers 252, Minnesota - Center for Economic Research.
  6. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April.
  7. Jouini, Elyès, 1992. "An index theorem for nonconvex production economies," Economics Papers from University Paris Dauphine 123456789/5638, Paris Dauphine University.
  8. Jouini, Elyes, 1992. "Existence of equilibria in nonconvex economies without free disposal," Economics Letters, Elsevier, vol. 38(1), pages 37-42, January.
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Citations

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Cited by:
  1. Gaël Giraud & Cécile Renouard, 2011. "In search of an alternative to shareholder value maximization," Documents de travail du Centre d'Economie de la Sorbonne 11038, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Antoine Mandel, 2007. "An index formula for production economies with externalities," Documents de travail du Centre d'Economie de la Sorbonne b07026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  3. Antoine Mandel, 2009. "Changes in the firms behavior after the opening of markets of allowances," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00633355, HAL.
  4. Antoine Mandel, 2007. "An Index Formula for Production Economies with Externalities," Post-Print halshs-00155775, HAL.
  5. Antoine Mandel, 2007. "Changes in the firms behavior after the opening of an allowance market," Post-Print halshs-00155783, HAL.
  6. Hans-Jürgen Salchow, 2005. "Non-existence of equilibria with free elimination," Cahiers de la Maison des Sciences Economiques b05057, Université Panthéon-Sorbonne (Paris 1).
  7. Gaël Giraud & Cécile Renouard, 2011. "In search of an alternative to shareholder value maximization," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00611712, HAL.
  8. Enrique Covarrubias, 2011. "The Number of Equilibria of Smooth Infinite Economies," Working Papers 2011-02, Banco de México.
  9. Giraud, Gaël & Renouard, Cécile, 2011. "In search of an alternative to shareholder value maximization," ESSEC Working Papers WP1108, ESSEC Research Center, ESSEC Business School.
  10. repec:hal:journl:halshs-00634648 is not listed on IDEAS
  11. Salchow, Hans-Jurgen, 2006. "An essay on the state of economic science," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 653-660, September.
  12. Gaël Giraud & Cécile Renouard, 2011. "In search of an alternative to shareholder value maximization," Post-Print hal-00609153, HAL.

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