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An algebra index theorem for non-smooth economies

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Author Info
GIRAUD, Ga‘l
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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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: 01 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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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Existence and Stability Conditions of Equilibrium
D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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  1. Kamiya, Kazuya, 1988. "Existence and uniqueness of equilibria with increasing returns," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 149-178, April. [Downloadable!] (restricted)
  2. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April. [Downloadable!] (restricted)
  3. 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. [Downloadable!] (restricted)
  4. 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. [Downloadable!] (restricted)
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  5. McLennan, Andrew, 1991. "Approximation of contractible valued correspondences by functions," Journal of Mathematical Economics, Elsevier, vol. 20(6), pages 591-598. [Downloadable!] (restricted)
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