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An index formula for production economies with externalities

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  • Antoine Mandel

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

Abstract

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)L−1 where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00634648.

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Date of creation: 22 Jul 2008
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Publication status: Published, Journal of Mathematical Economics, 2008, 44, 1385-1397
Handle: RePEc:hal:cesptp:halshs-00634648

Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00634648
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Keywords: General equilibrium theory ; Existence of equilibrium ; Increasing returns ; Externalities ; Degree theory;

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  1. Bonnisseau, J.M., 1995. "Existence of Equilibria in Economies with Externalities and Non Convexities," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 95.45, Université Panthéon-Sorbonne (Paris 1).
  2. Bonnisseau, J.M. & Medecin, J.-P., 2000. "Existence of Marginal Pricing Equilibria in Economies with Externalities and Non Convexities," Papiers d'Economie Mathématique et Applications, Université Panthéon-Sorbonne (Paris 1) 2000.84, Université Panthéon-Sorbonne (Paris 1).
  3. Bonnisseau, Jean-Marc, 1992. "Existence of equilibria in the presence of increasing returns : A synthesis," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 441-452.
  4. Monique Florenzano, 2008. "General equilibrium," Documents de travail du Centre d'Economie de la Sorbonne, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne b08005, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  5. GIRAUD, Gaël, 2000. "An algebraic index theorem for non-smooth economies," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 2000016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  6. Dierker, Egbert, 1993. "Regular economies," Handbook of Mathematical Economics, Elsevier, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 17, pages 795-830 Elsevier.
  7. 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.
  8. del Mercato, Elena L., 2006. "Existence of competitive equilibria with externalities: A differential viewpoint," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 525-543, August.
  9. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, Elsevier, vol. 4(2), pages 180-199, April.
  10. Jouini, Elyès, 1992. "An index theorem for nonconvex production economies," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/5638, Paris Dauphine University.
  11. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
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Cited by:
  1. Covarrubias, Enrique, 2008. "The number of equilibria of smooth infinite economies with separable utilities," MPRA Paper 11099, University Library of Munich, Germany.
  2. 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 hal-00633355, HAL.
  3. repec:hal:journl:halshs-00155783 is not listed on IDEAS

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