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Structural stability, Morse's lemma and singular economies

Author

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  • Elvio Accinelli

    (UASLP, Facultad de Economía San Luis Potosí, México)

Abstract

In this paper we consider economies whose consumption spaces are subsets of a Hilbert space with non-empty interior, and we introduce the Negishi approach to characterize the social equilibria of these economies. Using Morse's lemma, we analyze the main characteristics of two-agents-economies, and classify them. We show that the characteristics of \similar economies", in the sense introduced in [Debreu,G. (1970)], can be very di®erent from the structural stability point of view. Finally, we show that the useful mathematical de¯nition of structural stability is not enough to characterize structural stability in economics.

Suggested Citation

  • Elvio Accinelli, 2007. "Structural stability, Morse's lemma and singular economies," Documentos de Trabajo (working papers) 0607, Department of Economics - dECON.
    • Handle: RePEc:ude:wpaper:0607
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    File URL: https://hdl.handle.net/20.500.12008/2072
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    References listed on IDEAS

    as
    1. Elvio Accinelli & Alfredo Piria & Martín Puchet, 2003. "Taste And Singular Economies," Remef - Revista Mexicana de Economía y Finanzas Nueva Época REMEF (The Mexican Journal of Economics and Finance), Instituto Mexicano de Ejecutivos de Finanzas, IMEF, vol. 2(1), pages 35-48, Marzo 200.
    2. Elvio Accinelli, 1994. "Existence and uniqueness of the competitive equilibrium for infinite dimensional economies," Estudios de Economia, University of Chile, Department of Economics, vol. 21(2 Year 19), pages 313-326, December.
    3. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    4. Elvio Accinelli & Martín Puchet Anyul, 2005. "Can Catastrophe Theory Become a New Tool in Understanding Singular Economies?," Lecture Notes in Economics and Mathematical Systems, in: Jacek Leskow & Lionello F. Punzo & Martín Puchet Anyul (ed.), New Tools of Economic Dynamics, chapter 6, pages 95-109, Springer.
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    Cited by:

    1. Elvio Accinelli Gamba & Leobardo Plata Pérez, 2008. "Crisis sociales y singularidades. Los fundamentos microeconómicos de las crisis sociales," Ensayos Revista de Economia, Universidad Autonoma de Nuevo Leon, Facultad de Economia, vol. 0(2), pages 49-88, November.

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    More about this item

    Keywords

    Structural stability; Morse functions; singular economies;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General

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