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Existence of equilibria with a tight marginal pricing rule

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  • Bonnisseau, J.-M.
  • Cornet, B.

Abstract

This paper deals with the existence of marginal pricing equilibria when it is defined by using a new and tighter normal cone introduced by B. Cornet and M.O. Czarnecki. The main interest of this new definition of the marginal pricing rule comes from the fact that it is more precise in the sense that the set of prices satisfying the condition is smaller than the one given by the Clarke's normal cone. The counterpart is that it is not convex valued, which leads to some mathematical difficulties in the existence proof. The result is obtained through an approximation argument under the same assumptions as in the previous existence results.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 44 (2008)
Issue (Month): 7-8 (July)
Pages: 613-624

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Handle: RePEc:eee:mateco:v:44:y:2008:i:7-8:p:613-624

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  1. repec:hal:journl:halshs-00194881 is not listed on IDEAS
  2. Jean-Marc Bonnisseau & Alexandrine Jamin, 2003. "Equilibria with increasing returns : sufficient conditions on bounded production allocations," Cahiers de la Maison des Sciences Economiques, Université Panthéon-Sorbonne (Paris 1) b05045, Université Panthéon-Sorbonne (Paris 1), revised Jun 2005.
  3. Jean-Marc Bonnisseau & Bernard Cornet & Marc-Olivier Czarnecki, 2006. "The Marginal Pricing Rule Revisited," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers), HAL halshs-00113332, HAL.
  4. BONNISSEAU, Jean-Marc & CORNET, Bernard, . "Existence of equilibria when firms follow bounded losses pricing rules," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -814, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Khan, M Ali, 1999. " The Mordukhovich Normal Cone and the Foundations of Welfare Economics," Journal of Public Economic Theory, Association for Public Economic Theory, Association for Public Economic Theory, vol. 1(3), pages 309-38.
  6. Bonnisseau, J.-M. & Cornet, B., 1986. "Fixed-point theorems and Morse’s lemma for Lipschitzian functions," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1986028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Cornet, B., 1984. "Existence of equilibria in economies with increasing returns," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1984007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  8. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, Econometric Society, vol. 43(1), pages 1-29, January.
  9. Bonnisseau, J.-M. & Cornet, B., 1988. "Existense of marginal cost pricing equilibria: the nonsmooth case," CORE Discussion Papers, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) 1988015, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Jouini, Elyes, 1989. "A remark on Clarke's normal cone and the marginal cost pricing rule," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 18(1), pages 95-101, February.
  11. Bonnisseau, Jean-Marc, 1992. "Existence of equilibria in the presence of increasing returns : A synthesis," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 21(5), pages 441-452.
  12. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 17(2-3), pages 103-118, April.
  13. Jouini, Elyès, 1990. "Functions with constant generalized gradients," Economics Papers from University Paris Dauphine, Paris Dauphine University 123456789/5646, Paris Dauphine University.
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Cited by:
  1. M Ali Khan, 2007. "Perfect Competition," Microeconomics Working Papers 22207, East Asian Bureau of Economic Research.
  2. Khan, M. Ali Khan, 2007. "Perfect Competition," MPRA Paper 2202, University Library of Munich, Germany.

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