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

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  • Bernard Cornet

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  • Mihaela Topuzu

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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 consumers’ preferences: dependence upon prices and dependence upon other agents’ 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]. Copyright Springer-Verlag Berlin/Heidelberg 2005

Suggested Citation

  • Bernard Cornet & Mihaela Topuzu, 2005. "Existence of equilibria for economies with externalities and a measure space of consumers," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(2), pages 397-421, August.
  • Handle: RePEc:spr:joecth:v:26:y:2005:i:2:p:397-421 DOI: 10.1007/s00199-004-0576-3
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    References listed on IDEAS

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    1. Schmeidler, David, 1969. "Competitive Equilibria in Markets with a Continuum of Traders and Incomplete Preferences," Econometrica, Econometric Society, pages 578-585.
    2. 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.
    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. 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.
    5. 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.
    6. 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.
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    Citations

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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), pages 123-147.
    2. 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.
    3. 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.
    4. 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.
    5. M. Ali Khan, 2007. "Perfect Competition," PIDE-Working Papers 2007:15, Pakistan Institute of Development Economics.
    6. Noguchi, Mitsunori, 2009. "Existence of Nash equilibria in large games," Journal of Mathematical Economics, Elsevier, vol. 45(1-2), pages 168-184, January.
    7. Joao Correia-da-Silva & Carlos Hervés-Beloso, 2005. "Subjective Expectations Equilibrium in Economies with Uncertain Delivery," FEP Working Papers 190, Universidade do Porto, Faculdade de Economia do Porto.
    8. 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.
    9. 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.
    10. Noguchi, Mitsunori, 2006. "Mean consumption representation of consumption externalities," Mathematical Social Sciences, Elsevier, vol. 51(3), pages 301-310, May.
    11. 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.

    More about this item

    Keywords

    Externalities; Reference coalitions; Measure space of agents; Equilibrium.;

    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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