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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. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  2. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-92, May.
  3. 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.
  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. 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).
  7. 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.
  8. 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.
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Cited by:
  1. Jean-Marc Bonnisseau & Elena L. Del Mercato, 2008. "Externalities, consumption constraints and regular economies," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00257731, HAL.
  2. Antoine Mandel, 2008. "An index formula for production economies with externalities," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00634648, HAL.
  3. 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.
  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.

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