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Existence of Equilibria in Economies with Externalities and Nonconvexities

Author

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  • Jean-Marc Bonnisseau

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We consider a general equilibrium model of an economy in which the production possibilities, the consumption sets and the preferences of the consumers are represented by set-valued mappings which depend on the environment to take into account the possibility of external effect. In order to encompass all kinds of nonconvexities, we do not put any convexity assumption either on the graph of the set-valued mapping which describes the technological possibilities or on the production set for a given environment. The firms are instructed to set their prices according to general pricing rules which may depend on the production plans of other producers and on consumption plans. We report an existence result of general equilibria. As in the model without external effects, the key hypotheses are bounded loss and survival assumptions. Nevertheless, we also assume that the set-valued mappings which describe the fundamentals of the economy are lower semi-continuous and have a closed graph. Our framework is sufficiently large to generalize previous works on the existence of competitive equilibria with externalities when the firms have convex production sets and on the existence of equilibria with general pricing rule without externality.

Suggested Citation

  • Jean-Marc Bonnisseau, 1997. "Existence of Equilibria in Economies with Externalities and Nonconvexities," Post-Print hal-00176205, HAL.
  • Handle: RePEc:hal:journl:hal-00176205
    DOI: 10.1023/A:1008658403530
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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. Bonnisseau, Jean-Marc & Iehle, Vincent, 2007. "Payoff-dependent balancedness and cores," Games and Economic Behavior, Elsevier, vol. 61(1), pages 1-26, October.
    3. 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.
    4. repec:dau:papers:123456789/89 is not listed on IDEAS
    5. Nizar Allouch & Myrna Wooders, 2017. "On the nonemptiness of approximate cores of large games," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 191-209, January.
    6. Jean-Marc Bonnisseau & Antoine Mandel & Yann Toma & François-Guy Trébulle, 2015. "Penser le changement climatique," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01496167, HAL.
    7. 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.
    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. Vincenzo Platino, 2021. "Externalities in private ownership production economies with possibility functions. An existence result," Metroeconomica, Wiley Blackwell, vol. 72(3), pages 509-525, July.
    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. Jean-Marc Bonnisseau & Vincent Iehlé, 2007. "Payoff-dependent balancedness and cores (revised version)," UFAE and IAE Working Papers 678.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
    12. Jean-Marc Bonnisseau & Matías Fuentes, 2020. "Market Failures and Equilibria in Banach Lattices: New Tangent and Normal Cones," Journal of Optimization Theory and Applications, Springer, vol. 184(2), pages 338-367, February.

    More about this item

    Keywords

    general equilibria; external effects; bounded loss; survival assumptions; nonconvexity; set-valued mapping;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C68 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computable General Equilibrium Models

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