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An index formula for production economies with externalities

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  • Antoine Mandel

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

We prove that the degree of the equilibrium correspondence of an economy with increasing returns and external effects is equal to (−1)L−1 where L is the dimension of the space of goods. This allows us to infer existence, finiteness and uniqueness results.

Suggested Citation

  • Antoine Mandel, 2008. "An index formula for production economies with externalities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00634648, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00634648
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00634648
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    References listed on IDEAS

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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. del Mercato, Elena L., 2006. "Existence of competitive equilibria with externalities: A differential viewpoint," Journal of Mathematical Economics, Elsevier, vol. 42(4-5), pages 525-543, August.
    3. Jouini, Elyes, 1992. "An index theorem for nonconvex production economies," Journal of Economic Theory, Elsevier, vol. 57(1), pages 176-196.
    4. GIRAUD, Gaël, 2000. "An algebraic index theorem for non-smooth economies," LIDAM Discussion Papers CORE 2000016, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    10. Bonnisseau, J.M., 1995. "Existence of Equilibria in Economies with Externalities and Non Convexities," Papiers d'Economie Mathématique et Applications 95.45, Université Panthéon-Sorbonne (Paris 1).
    11. Starrett, David A., 1972. "Fundamental nonconvexities in the theory of externalities," Journal of Economic Theory, Elsevier, vol. 4(2), pages 180-199, April.
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    13. Kehoe, Timothy J, 1980. "An Index Theorem for General Equilibrium Models with Production," Econometrica, Econometric Society, vol. 48(5), pages 1211-1232, July.
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    15. Jouini, Elyes, 1992. "An index theorem for nonconvex production economies," Journal of Economic Theory, Elsevier, vol. 57(1), pages 176-196.
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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. Covarrubias, Enrique, 2013. "The number of equilibria of smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 49(4), pages 263-265.
    3. Antoine Mandel, 2007. "Changes in the firms behavior after the opening of an allowance market," Documents de travail du Centre d'Economie de la Sorbonne b07027, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Antoine Mandel, 2009. "Changes in the firms behavior after the opening of markets of allowances," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(1), pages 1-25, July.
    5. 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.
    6. Vincenzo Platino, 2021. "Externalities in private ownership production economies with possibility functions. An existence result," Metroeconomica, Wiley Blackwell, vol. 72(3), pages 509-525, July.

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    More about this item

    Keywords

    Existence of equilibrium; Increasing returns; Externalities; Degree theory; General equilibrium theory;
    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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