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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
Date of revision:
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
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  1. 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.
  2. Bonnisseau, J.-M. & Cornet, B., 1986. "Existence of equilibria when firms follow bounded losses pricing rules," CORE Discussion Papers 1986007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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).
  4. Jouini, Elyes, 1992. "Existence of equilibria in nonconvex economies without free disposal," Economics Letters, Elsevier, vol. 38(1), pages 37-42, January.
  5. repec:dau:papers:123456789/5638 is not listed on IDEAS
  6. KAMIYA, Kazuya, 1987. "Existence and uniqueness of equilibria with increasing returns," CORE Discussion Papers 1987040, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Jouini, Elyes, 1992. "An index theorem for nonconvex production economies," Journal of Economic Theory, Elsevier, vol. 57(1), pages 176-196.
  8. McLennan, Andrew, 1991. "Approximation of contractible valued correspondences by functions," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 591-598.
  9. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April.
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