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Existence of competitive equilibria with externalities : a differential viewpoint

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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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04078.pdf
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Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04078.

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Length: 33 pages
Date of creation: Sep 2004
Date of revision:
Handle: RePEc:mse:wpsorb:b04078
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  1. 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.
  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. Shafer, Wayne & Sonnenschein, Hugo, 1975. "Equilibrium in abstract economies without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(3), pages 345-348, December.
  4. 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.
  5. 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.
  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. 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.
  8. DEBREU, Gérard, . "Economies with a finite set of equilibria," CORE Discussion Papers RP -67, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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