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Existence of equilibria with a tight marginal pricing rule

Author

Listed:
  • Jean-Marc Bonnisseau

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Bernard Cornet

    (Department of economics, University of Kansas - KU - University of Kansas [Lawrence], CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

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.

Suggested Citation

  • Jean-Marc Bonnisseau & Bernard Cornet, 2008. "Existence of equilibria with a tight marginal pricing rule," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00187216, HAL.
    • Handle: RePEc:hal:cesptp:hal-00187216
    DOI: 10.1016/j.jmateco.2007.03.001
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    References listed on IDEAS

    as
    1. Cornet, B., 1984. "Existence of equilibria in economies with increasing returns," LIDAM Discussion Papers CORE 1984007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Cornet, Bernard, 1988. "General equilibrium theory and increasing returns : Presentation," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 103-118, April.
    3. M. Ali Khan, 1999. "The Mordukhovich Normal Cone and the Foundations of Welfare Economics," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(3), pages 309-338, July.
    4. 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.
    5. 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.
    6. J. M. Bonnisseau & A. Jamin, 2008. "Equilibria with Increasing Returns: Sufficient Conditions on Bounded Production Allocations," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(6), pages 1033-1068, December.
    7. repec:dau:papers:123456789/5649 is not listed on IDEAS
    8. Jean-Marc Bonnisseau & Bernard Cornet & Marc-Olivier Czarnecki, 2007. "The marginal pricing rule revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 579-589, December.
    9. Bonnisseau, J.-M. & Cornet, B., 1986. "Fixed-point theorems and Morse’s lemma for Lipschitzian functions," LIDAM Discussion Papers CORE 1986028, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. repec:dau:papers:123456789/5646 is not listed on IDEAS
    11. Khan, M Ali, 1999. "The Mordukhovich Normal Cone and the Foundations of Welfare Economics," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 1(3), pages 309-338.
    12. Bonnisseau, Jean-Marc & Cornet, Bernard, 1990. "Existence of Marginal Cost Pricing Equilibria: The Nonsmooth Case," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 31(3), pages 685-708, August.
    13. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
    14. Jouini, Elyes, 1989. "A remark on Clarke's normal cone and the marginal cost pricing rule," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 95-101, February.
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    Cited by:

    1. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.

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    More about this item

    Keywords

    General economic equilibrium; Increasing returns; Marginal pricing rule; Existence;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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