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Existence of equilibria for economies with externalities and a measure space of consumers

Author

Listed:
  • Bernard Cornet

    (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, KU - University of Kansas [Lawrence])

  • Mihaela Topuzu

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

Abstract
This paper considers an exchange economy with a measure space of agents and consumption externalities, which take into account two possible external effects on consumersrsquo preferences: dependence upon prices and dependence upon other agentsrsquo consumption. We first consider a model with a general externality mapping and we then treat the particular case of reference coalition externalities, in which the preferences of each agent a are influenced by prices and by the global or the mean consumption of the agents in finitely many (exogenously given) reference coalitions associated with agent a. Our paper provides existence results of equilibria in both models when consumers have transitive preferences. It extends in exchange economies the standard results by Aumann [2], Schmeidler [16], Hildenbrand [12], and previous results by Greenberg et al. [11] for price dependent preferences, Schmeidler [17] for fixed reference coalitions and Noguchi [15] for a more particular concept of reference coalitions. We also mention related results obtained independently by Balder [4].

Suggested Citation

  • Bernard Cornet & Mihaela Topuzu, 2005. "Existence of equilibria for economies with externalities and a measure space of consumers," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00287686, HAL.
    • Handle: RePEc:hal:cesptp:hal-00287686
    DOI: 10.1007/s00199-004-0576-3
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    References listed on IDEAS

    as
    1. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, vol. 37(4), pages 578-585, October.
    3. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    4. SCHMEIDLER, David, 1970. "Fatou's lemma in several dimensions," LIDAM Reprints CORE 46, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. GREENBERG, Joseph & SHITOVITZ, Benyamin & WIECZOREK, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," LIDAM Reprints CORE 361, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    6. Balder, Erik J., 2000. "Incompatibility of Usual Conditions for Equilibrium Existence in Continuum Economies without Ordered Preferences," Journal of Economic Theory, Elsevier, vol. 93(1), pages 110-117, July.
    7. Hildenbrand, Werner, 1970. "Existence of Equilibria for Economies with Production and a Measure Space of Consumers," Econometrica, Econometric Society, vol. 38(5), pages 608-623, September.
    8. Khan, M. Ali & Vohra, Rajiv, 1984. "Equilibrium in abstract economies without ordered preferences and with a measure space of agents," Journal of Mathematical Economics, Elsevier, vol. 13(2), pages 133-142, October.
    9. HILDENBRAND, Werner, 1970. "Existence of equilibria for economies with production and a measure space of consumers," LIDAM Reprints CORE 79, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Greenberg, Joseph & Shitovitz, Benyamin & Wieczorek, Andrzej, 1979. "Existence of equilibria in atomless production economies with price dependent preferences," Journal of Mathematical Economics, Elsevier, vol. 6(1), pages 31-41, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
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    Cited by:

    1. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 123-147, July.
    2. Ericson Richard E. & Kung Fan-chin, 2015. "Fundamental Non-convexity and Externalities: A Differentiable Approach," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(1), pages 49-62, January.
    3. Noguchi, Mitsunori, 2009. "Price-dependent consumption externalities and non-existence of equilibria," Journal of Mathematical Economics, Elsevier, vol. 45(3-4), pages 205-211, March.
    4. Christian Pietro & Maria Gabriella Graziano & Vincenzo Platino, 2022. "Social loss with respect to the core of an economy with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 487-508, April.
    5. Balder, Erik J., 2008. "More on equilibria in competitive markets with externalities and a continuum of agents," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 575-602, July.
    6. Sebastián Cea-Echenique & Carlos Hervés-Beloso & Juan Pablo Torres-Martínez, 2012. "Endogenous Information: The Role of Sequential Trade and Financial Participation," Working Papers wp361, University of Chile, Department of Economics.
    7. Nieto-Barthaburu, Augusto, 2021. "Competitive General Equilibrium with network externalities," Journal of Mathematical Economics, Elsevier, vol. 94(C).
    8. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    9. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    10. Correia-da-Silva, João & Hervés-Beloso, Carlos, 2008. "Subjective expectations equilibrium in economies with uncertain delivery," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 641-650, July.
    11. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 419-432, February.
    12. Kung, Fan-chin, 2008. "Voluntary contributions to multiple public goods in a production economy with widespread externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1364-1378, December.
    13. Noguchi, Mitsunori, 2006. "Mean consumption representation of consumption externalities," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 301-310, May.

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    More about this item

    Keywords

    Equilibrium; Externalities; Reference coalitions; Measure space of agents; Equilibrium.;
    All these keywords.

    JEL classification:

    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • H23 - Public Economics - - Taxation, Subsidies, and Revenue - - - Externalities; Redistributive Effects; Environmental Taxes and Subsidies

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