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

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  • Elena L. Mercato

    () (Université Paris 1 Panthéon-Sorbonne and Centre d’Economie de la Sorbonne)

  • Vincenzo Platino

    () (University of Naples Federico II and CSEF)

Abstract

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. 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.
  • Handle: RePEc:spr:joecth:v:63:y:2017:i:1:d:10.1007_s00199-016-1029-5
    DOI: 10.1007/s00199-016-1029-5
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    References listed on IDEAS

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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. 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.
    3. Elena L. del Mercato & Vincenzo Platino, 2016. "Private ownership economies with externalities and existence of competitive equilibria: A differentiable approach," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01164015, HAL.
    4. Elena L. Del Mercato & Vincenzo Platino, 2016. "Private ownership economies with externalities and existence of competitive equilibria: A differentiable approach," Post-Print halshs-01164015, HAL.

    More about this item

    Keywords

    Externalities; Production economies; Competitive equilibrium; Nash equilibrium; Regular economies;

    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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