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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 - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - 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 = Università degli studi di Napoli 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. Next, we consider a new version of this model, with firms' endowments in the spirit of Geanakoplos et al. (J Math Econ 19:113–151, 1990). In our model, firms' endowments impact the technologies of the other firms. We then prove that, generically in the space of endowments of households and firms, each economy has a finite number of competitive equilibria and each competitive equilibrium is locally a differentiable map of the fundamental parameters.

Suggested Citation

  • Elena L. del Mercato & Vincenzo Platino, 2017. "On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash," PSE-Ecole d'économie de Paris (Postprint) hal-01438970, HAL.
    • Handle: RePEc:hal:pseptp:hal-01438970
    DOI: 10.1007/s00199-016-1029-5
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    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

    private ownership economies; competitive equilibrium à la Nash; regular economies; externalities;
    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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