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Private ownership economies with externalities and existence of competitive equilibria: A differentiable approach

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Abstract

We consider a general equilibrium model of a private ownership economy with consumption and production externalities. Utility functions and production technologies may be affected by the consumption and production activities of all other agents in the economy. We use differential techniques to show that the set of competitive equilibria is non-empty and compact. Fixing the externalities, the assumptions on utility functions and production technologies are standard in a differentiable framework. Competitive equilibria are written in terms first-order conditions associated with agents' behavior and market clearing conditions, following the seminal work by Smale (1974). Adapting differential techniques to economies with externalities is non trivial and it requires some ingenious adjustments, because the production technologies are not required to be convex with respect to the consumption and production activities of all agents

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  • Elena L. del Mercato & Vincenzo Platino, 2015. "Private ownership economies with externalities and existence of competitive equilibria: A differentiable approach," Documents de travail du Centre d'Economie de la Sorbonne 15034, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  • Handle: RePEc:mse:cesdoc:15034
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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, December.
    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. 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.
    4. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
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    6. 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.
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    8. 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.
    9. Jean-Jacques Laffont, 1988. "Fundamentals of Public Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262121271.
    10. 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.
    11. Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
    12. Bonnisseau, Jean-Marc & del Mercato, Elena L., 2008. "General consumption constraints and regular economies," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1286-1301, December.
    13. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    14. 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.
    15. Balasko, Yves, 2015. "Wealth concerns and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 92-101.
    16. Ericson Richard E. & Kung Fan-chin, 2015. "Fundamental Non-convexity and Externalities: A Differentiable Approach," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 15(1), pages 1-14, January.
    17. Smale, S., 1974. "Global analysis and economics III : Pareto Optima and price equilibria," Journal of Mathematical Economics, Elsevier, vol. 1(2), pages 107-117, August.
    18. repec:hal:journl:halshs-00634648 is not listed on IDEAS
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    Cited by:

    1. 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.
    2. Vincenzo Platino, 2019. "Externalities in Private Ownership Production Economies with Possibility Functions. An Existence Result," CSEF Working Papers 549, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy.
    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. 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.

    More about this item

    Keywords

    Externalities; private ownership economy; competitive equilibrium; differentiable approach;

    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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