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Existence of competitive equilibria with externalities: A differential viewpoint

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  • del Mercato, Elena L.

Abstract

We consider a class of pure exchange economies with externalities. Each consumption set is described by a function called possibility function which depends on the individual initial endowment. Moreover, each possibility function, as well as each utility function, depends on the consumptions of all households. Our definition of competitive equilibrium with externalities includes as a particular case the classical definition. Using homotopy arguments, under differentiability and boundary conditions, we show that for all economies the set of equilibria is non-empty and compact. This work is the first step to encompass externalities in the global analysis of equilibria.
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  • 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.
  • Handle: RePEc:eee:mateco:v:42:y:2006:i:4-5:p:525-543
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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, November.
    2. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
    3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    4. Monique Florenzano, 2007. "General equilibrium," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00250167, HAL.
    5. 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.
    6. 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.
    7. 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).
    8. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Some theorems on the existence of competitive equilibrium," Journal of Economic Theory, Elsevier, vol. 11(1), pages 83-93, August.
    9. Jean-Marc Bonnisseau & Jorge Rivera Cayupi, 2003. "The equilibrium manifold with boundary constraints on the consumption sets," Estudios de Economia, University of Chile, Department of Economics, vol. 30(2 Year 20), pages 225-240, December.
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    Citations

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    Cited by:

    1. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 123-147.
    2. Elena L. Mercato & Vincenzo Platino, 2017. "Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach," Journal of Economics, Springer, pages 75-98.
    3. repec:hal:journl:halshs-01164015 is not listed on IDEAS
    4. Dimitrios Xefteris & Nicholas Ziros, 2017. "Strategic vote trading under complete information," University of Cyprus Working Papers in Economics 03-2017, University of Cyprus Department of Economics.
    5. del Mercato, Elena L., 2006. "Existence of competitive equilibria with externalities: A differential viewpoint," Journal of Mathematical Economics, Elsevier, pages 525-543.
    6. 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.
    7. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, pages 1385-1397.
    8. Balasko, Yves, 2015. "Wealth concerns and equilibrium," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 92-101.
    9. Bonnisseau, Jean-Marc & del Mercato, Elena L., 2008. "General consumption constraints and regular economies," Journal of Mathematical Economics, Elsevier, pages 1286-1301.
    10. 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.

    More about this item

    JEL classification:

    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory
    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

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