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An Algebraic Index Theorem for Non-smooth Economies

  • Gaël Giraud

    ()

    (BETA - Bureau d'Economie Théorique et Appliquée - Université de Strasbourg - UL - Université de Lorraine - CNRS - Centre National de la Recherche Scientifique)

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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Paper provided by HAL in its series Post-Print with number hal-00460314.

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Date of creation: Dec 2001
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Publication status: Published in Journal of Mathematical Economics, Elsevier, 2001, 36 (4), pp.255-269. <10.1016/S0304-4068(01)00074-X>
Handle: RePEc:hal:journl:hal-00460314
DOI: 10.1016/S0304-4068(01)00074-X
Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00460314
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  1. Jouini, Elyes, 1992. "Existence of equilibria in nonconvex economies without free disposal," Economics Letters, Elsevier, vol. 38(1), pages 37-42, January.
  2. Kamiya, Kazuya, 1988. "Existence and uniqueness of equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 149-178, April.
  3. Mclennan, A., 1989. "Approximation Of Contractible Valued Correspondences By Functions," Papers 252, Minnesota - Center for Economic Research.
  4. 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).
  5. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April.
  6. repec:dau:papers:123456789/5638 is not listed on IDEAS
  7. 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.
  8. 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).
  9. Jouini, Elyes, 1992. "An index theorem for nonconvex production economies," Journal of Economic Theory, Elsevier, vol. 57(1), pages 176-196.
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