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Existence of marginal pricing equilibria in economies with externalities and non-convexities

Author

Listed:
  • Jean-Marc Bonnisseau

    () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Jean-Philippe Medecin

    () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a general equilibrium model with externalities and non-convexities in production. The consumption sets, the preferences of the consumers and the production possibilities are represented by set-valued mappings to take into account possibility of external effects. There is no convexity assumption on the correspondences of production. We propose a definition of the marginal pricing rule, which generalizes the one used in the model without externality and, which satisfies a continuity assumption with respect to the external effect. We prove the existence of general equilibria under assumptions which allow us to encompass together the works on economies with externalities and convex conditional production sets, and those on marginal pricing equilibria in economies without externalities. We provide examples to illustrate the definition of the marginal pricing rule and to show the difference with the standard case.

Suggested Citation

  • Jean-Marc Bonnisseau & Jean-Philippe Medecin, 2001. "Existence of marginal pricing equilibria in economies with externalities and non-convexities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00187219, HAL.
  • Handle: RePEc:hal:cesptp:hal-00187219
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00187219
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    References listed on IDEAS

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    1. Cornet, B., 1984. "Existence of equilibria in economies with increasing returns," CORE Discussion Papers 1984007, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Moriguchi, Chiaki, 1996. "Two-part marginal cost pricing in a pure fixed cost economy," Journal of Mathematical Economics, Elsevier, vol. 26(3), pages 363-385.
    3. 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.
    4. Guesnerie, Roger, 1975. "Pareto Optimality in Non-Convex Economies," Econometrica, Econometric Society, vol. 43(1), pages 1-29, January.
    5. Kamiya, Kazuya, 1988. "On the survival assumption in marginal (cost) pricing," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 261-273, April.
    6. Beato, Paulina & Mas-Colell, Andreu, 1985. "On marginal cost pricing with given tax-subsidy rules," Journal of Economic Theory, Elsevier, vol. 37(2), pages 356-365, December.
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    Citations

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    Cited by:

    1. Fuentes, Matías N., 2011. "Existence of equilibria in economies with externalities and non-convexities in an infinite-dimensional commodity space," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 768-776.
    2. Cuong Van & Frank Page & Myrna Wooders, 2007. "Risky arbitrage, asset prices, and externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 33(3), pages 475-491, December.
    3. Elena L. Mercato & Vincenzo Platino, 2017. "Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach," Journal of Economics, Springer, vol. 121(1), pages 75-98, May.
    4. Elena L. Del Mercato & Vincenzo Platino, 2016. "Private ownership economies with externalities and existence of competitive equilibria: A differentiable approach," Post-Print halshs-01164015, HAL.
    5. Antoine Mandel, 2009. "Changes in the firms behavior after the opening of markets of allowances," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 1-25, July.
    6. Jean-Marc Bonnisseau & Matías Fuentes, 2018. "Market failures and equilibria in Banach lattices," Documents de travail du Centre d'Economie de la Sorbonne 18037, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    7. Holmberg, Pär & Tangerås, Thomas & Ahlqvist, Victor, 2018. "Central- versus Self-Dispatch in Electricity Markets," Working Paper Series 1257, Research Institute of Industrial Economics, revised 27 Mar 2019.
    8. Elena L. Mercato & Vincenzo Platino, 2017. "On the regularity of smooth production economies with externalities: competitive equilibrium à la Nash," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 287-307, January.
    9. Antoine Mandel, 2007. "An Index Formula for Production Economies with Externalities," Post-Print halshs-00155775, HAL.
    10. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
    11. Elena L. Del Mercato & Vincenzo Platino, 2016. "On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash," Post-Print halshs-01162039, HAL.

    More about this item

    Keywords

    General equilibrium; External effects; Non-convex set-valued mappings; Marginal pricing; Clarke's normal cone;

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms

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