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Regular economies with non-ordered preferences

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  • Bonnisseau, Jean-Marc

Abstract

We consider exchange economies with non-ordered preferences and externalities. Under continuity and boundary conditions, we prove an index formula, which implies the existence of equilibria for all initial endowments, and the upper semi-continuity of the Walras correspondence. We then posit a differentiability assumption on the preferences. It allows us to prove that the equilibrium manifold is a nonempty differentiable sub-manifold of an Euclidean space. We define regular economies as the regular values of the natural projection. We show that the set of regular economies is open, dense and of full Lebesgue measure. From the index formula, one deduces that a regular economy has a finite odd number of equilibria, and, for each of them, the implicit function theorem implies that there exists a local differentiable selection. So, even with only non-ordered preferences and externalities, exchange economies have nice properties for equilibrium analysis.
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  • Bonnisseau, Jean-Marc, 2003. "Regular economies with non-ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 39(3-4), pages 153-174, June.
  • Handle: RePEc:eee:mateco:v:39:y:2003:i:3-4:p:153-174
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    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702, March.
    2. Gale, D. & Mas-Colell, A., 1975. "An equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 2(1), pages 9-15, March.
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    9. Gale, D. & Mas-Colell, A., 1979. "Corrections to an equilibrium existence theorem for a general model without ordered preferences," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 297-298, December.
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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), vol. 44(1), pages 123-147, July.
    2. Yves Balasko & Mich Tvede, 2010. "General equilibrium without utility functions: how far to go?," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 45(1), pages 201-225, October.
    3. Jacques Dreze, 2016. "Existence and multiplicity of temporary equilibria under nominal price rigidities," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 62(1), pages 279-298, June.
    4. Elena L. Mercato & Vincenzo Platino, 2017. "Private ownership economies with externalities and existence of competitive equilibria: a differentiable approach," Journal of Economics, Springer, vol. 121(1), pages 75-98, May.
    5. repec:hal:journl:halshs-01164015 is not listed on IDEAS
    6. Renou, Ludovic & Schlag, Karl H., 2014. "Ordients: Optimization and comparative statics without utility functions," Journal of Economic Theory, Elsevier, vol. 154(C), pages 612-632.
    7. repec:eee:mateco:v:75:y:2018:i:c:p:84-92 is not listed on IDEAS
    8. Elena L. Mercato & Vincenzo Platino, 2017. "On the regularity of smooth production economies with externalities: competitive equilibrium à la Nash," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 63(1), pages 287-307, January.
    9. repec:spr:joptap:v:168:y:2016:i:2:d:10.1007_s10957-015-0805-x is not listed on IDEAS
    10. Mandel, Antoine, 2008. "An index formula for production economies with externalities," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1385-1397, December.
    11. Shikhman, V. & Nesterov, Yu. & Ginsburgh, V., 2018. "Power method tâtonnements for Cobb–Douglas economies," Journal of Mathematical Economics, Elsevier, vol. 75(C), pages 84-92.

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