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On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash

Author

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  • Elena L. del Mercato

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

  • Vincenzo Platino

    () (DiSES - Department of Economics and Statistics - University of Naples Federico II)

Abstract

We consider a general equilibrium model of a private ownership economy with consumption and production externalities. The choices of all agents (households and firms) may affect utility functions and production technologies. The allocation of a competitive equilibrium is a Nash equilibrium. We provide an example showing that, under standard assumptions, competitive equilibria are indeterminate in an open set of the household's endowments. We introduce the model with firms' endowments, in the spirit of Geanakoplos, Magill, Quinzii and Drèze (1990). In our model, firms' endowments impact the technologies and the marginal productivities of the other firms. We then prove that these economies are generically regular in the space of endowments of households and firms.

Suggested Citation

  • 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.
  • Handle: RePEc:hal:journl:halshs-01162039
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01162039v2
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    References listed on IDEAS

    as
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    Cited by:

    1. 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.
    2. 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.
    3. Christian Pietro & Maria Gabriella Graziano & Vincenzo Platino, 0. "Social loss with respect to the core of an economy with externalities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 0, pages 1-22.
    4. Michael Zierhut, 2021. "Generic regularity of differentiated product oligopolies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 71(1), pages 341-374, February.

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    More about this item

    Keywords

    regular economies; externalities; competitive equilibrium à la Nash; private ownership economies;
    All these keywords.

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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