IDEAS home Printed from https://ideas.repec.org/p/hal/cesptp/halshs-01162039.html
   My bibliography  Save this paper

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

Author

Listed:
  • Elena L. del Mercato

    () (PSE - Paris School of Economics, CES - Centre d'économie de la Sorbonne - UP1 - Université 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01162039, HAL.
  • Handle: RePEc:hal:cesptp:halshs-01162039
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01162039v2
    as

    Download full text from publisher

    File URL: https://halshs.archives-ouvertes.fr/halshs-01162039v2/document
    Download Restriction: no

    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. John Geanakoplos & H M Polemchakis, 2008. "Pareto Improving Taxes," Levine's Working Paper Archive 122247000000002219, David K. Levine.
    3. 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.
    4. Cass, David & Siconolfi, Paolo & Villanacci, Antonio, 2001. "Generic regularity of competitive equilibria with restricted participation," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 61-76, September.
    5. Smale, S., 1974. "Global analysis and economics IIA : Extension of a theorem of Debreu," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 1-14, March.
    6. Villanacci, Antonio & Zenginobuz, Ünal, 2012. "Subscription equilibrium with production: Non-neutrality and constrained suboptimality," Journal of Economic Theory, Elsevier, vol. 147(2), pages 407-425.
    7. Atsushi Kajii & Antonio Villanacci & Alessandro Citanna, 1998. "Constrained suboptimality in incomplete markets: a general approach and two applications," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 11(3), pages 495-521.
    8. Geanakoplos, John & Polemarchakis, H.M., 2008. "Pareto improving taxes," Journal of Mathematical Economics, Elsevier, vol. 44(7-8), pages 682-696, July.
    9. Citanna, A. & Polemarchakis, H.M. & Tirelli, M., 2006. "The taxation of trades in assets," Journal of Economic Theory, Elsevier, vol. 126(1), pages 299-313, January.
    10. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    11. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 44(1), pages 123-147, July.
    12. Bonnisseau, Jean-Marc & Medecin, Jean-Philippe, 2001. "Existence of marginal pricing equilibria in economies with externalities and non-convexities," Journal of Mathematical Economics, Elsevier, vol. 36(4), pages 271-294, December.
    13. Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-236.
    14. repec:hal:journl:halshs-00634648 is not listed on IDEAS
    15. Hervé Crès & Mich Tvede, 2013. "Production externalities: internalization by voting," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 53(2), pages 403-424, June.
    16. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
    17. 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.
    18. Antonio Villanacci & Ünal Zenginobuz, 2006. "Pareto improving interventions in a general equilibrium model with private provision of public goods," Review of Economic Design, Springer;Society for Economic Design, vol. 10(3), pages 249-271, December.
    19. Villanacci, Antonio & Zenginobuz, E.Unal, 2005. "Existence and regularity of equilibria in a general equilibrium model with private provision of a public good," Journal of Mathematical Economics, Elsevier, vol. 41(4-5), pages 617-636, August.
    20. Jean-Jacques Laffont, 1988. "Fundamentals of Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121271.
    21. Allen, Beth, 1981. "Utility perturbations and the equilibrium price set," Journal of Mathematical Economics, Elsevier, vol. 8(3), pages 277-307, October.
    22. Antoine Mandel, 2008. "An index formula for production economies with externalities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00634648, HAL.
    23. Antoine Mandel, 2007. "An Index Formula for Production Economies with Externalities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00155775, HAL.
    24. Bruce C. Greenwald & Joseph E. Stiglitz, 1986. "Externalities in Economies with Imperfect Information and Incomplete Markets," The Quarterly Journal of Economics, Oxford University Press, vol. 101(2), pages 229-264.
    25. Geanakoplos, J. & Magill, M. & Quinzii, M. & Dreze, J., 1990. "Generic inefficiency of stock market equilibrium when markets are incomplete," Journal of Mathematical Economics, Elsevier, vol. 19(1-2), pages 113-151.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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

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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:hal:cesptp:halshs-01162039. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD). General contact details of provider: https://hal.archives-ouvertes.fr/ .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.