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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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File URL: http://alfresco.uclouvain.be/alfresco/download/attach/workspace/SpacesStore/d5372426-8652-4186-bbb3-4969698cf14a/coredp_2000_16.pdf
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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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Keywords: Non-smooth production; topological degree; local homology; increasing returns.;

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References

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  1. McLennan, Andrew, 1991. "Approximation of contractible valued correspondences by functions," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 591-598.
  2. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April.
  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, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  5. 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.
  6. Jouini, Elyès, 1992. "An index theorem for nonconvex production economies," Economics Papers from University Paris Dauphine 123456789/5638, Paris Dauphine University.
  7. BONNISSEAU, Jean-Marc & CORNET, Bernard, . "Existence of equilibria when firms follow bounded losses pricing rules," CORE Discussion Papers RP -814, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  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," Post-Print hal-00609153, HAL.
  2. repec:hal:cesptp:hal-00633355 is not listed on IDEAS
  3. repec:hal:journl:halshs-00155783 is not listed on IDEAS
  4. Giraud, Gaël & Renouard, Cécile, 2011. "In search of an alternative to shareholder value maximization," ESSEC Working Papers WP1108, ESSEC Research Center, ESSEC Business School.
  5. repec:hal:journl:halshs-00195903 is not listed on IDEAS
  6. repec:hal:journl:halshs-00155775 is not listed on IDEAS
  7. repec:hal:cesptp:halshs-00195903 is not listed on IDEAS
  8. repec:hal:cesptp:halshs-00155775 is not listed on IDEAS
  9. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany.
  10. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
  11. 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.
  12. repec:hal:journl:halshs-00634648 is not listed on IDEAS
  13. Antoine Mandel, 2009. "Changes in the firms behavior after the opening of markets of allowances," Economic Theory, Springer, vol. 40(1), pages 1-25, July.
  14. repec:hal:cesptp:halshs-00611712 is not listed on IDEAS
  15. Hans-Jürgen Salchow, 2005. "Non-existence of equilibria with free elimination," Cahiers de la Maison des Sciences Economiques b05057, Université Panthéon-Sorbonne (Paris 1).
  16. Salchow, Hans-Jurgen, 2006. "An essay on the state of economic science," Journal of Mathematical Economics, Elsevier, vol. 42(6), pages 653-660, September.

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