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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. 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.
  2. 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).
  3. Wayne Shafer & Hugo Sonnenschein, 1974. "Equilibrium in Abstract Economies Without Ordered Preferences," Discussion Papers 94, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Elena Laureana Del Mercato, 2004. "Existence of competitive equilibria with externalities : a differential viewpoint," Cahiers de la Maison des Sciences Economiques b04078, Université Panthéon-Sorbonne (Paris 1).
  5. 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.
  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. 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.
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Citations

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Cited by:
  1. Jean-Marc Bonnisseau & Elena L. del Mercato, 2008. "Externalities, Consumption Constraints and Regular Economies," CSEF Working Papers 195, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 01 Dec 2009.
  2. repec:hal:journl:halshs-00159638 is not listed on IDEAS
  3. repec:hal:cesptp:halshs-00634648 is not listed on IDEAS
  4. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
  5. 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.
  6. Elena Laureana Del Mercato, 2004. "Existence of competitive equilibria with externalities : a differential viewpoint," Cahiers de la Maison des Sciences Economiques b04078, Université Panthéon-Sorbonne (Paris 1).

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