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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. The consumption set and the preferences of each household depend on his initial endowment and on the actions of the other households. We give a definition of competitive equilibrium with externalities which includes as particular case the classical definition. Under differentiability and boundary conditions, we show that for all economies there exist competitive equilibria with strictly positive consumptions and prices. Our approach is based on homotopy arguments in differential topology, where it is possible describe equilibria in terms of first order conditions and market clearing conditions.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 42 (2006)
Issue (Month): 4-5 (August)
Pages: 525-543

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Handle: RePEc:eee:mateco:v:42:y:2006:i:4-5:p:525-543

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Web page: http://www.elsevier.com/locate/jmateco

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References

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  1. Wayne Shafer & Hugo Sonnenschein, 1974. "Some Theorems on the Existence of Competitive Equilibrium," Discussion Papers 103, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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. 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).
  4. 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.
  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. repec:hal:cesptp:halshs-00250167 is not listed on IDEAS
  7. Jean-Marc Bonnisseau & Jorge Rivera Cayupi, 2002. "The equilibrium manifold with Boundary constraints on the Consumption sets," Working Papers wp196, University of Chile, Department of Economics.
  8. Monique Florenzano, 2008. "General equilibrium," Documents de travail du Centre d'Economie de la Sorbonne b08005, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  9. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
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Citations

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Cited by:
  1. Antoine Mandel, 2007. "An index formula for production economies with externalities," Documents de travail du Centre d'Economie de la Sorbonne b07026, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. repec:hal:journl:halshs-00257731 is not listed on IDEAS
  3. repec:hal:journl:halshs-00159638 is not listed on IDEAS
  4. Jean-Marc Bonnisseau & Elena Mercato, 2010. "Externalities, consumption constraints and regular economies," Economic Theory, Springer, vol. 44(1), pages 123-147, July.
  5. 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.
  6. 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.
  7. 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.

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