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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

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    1. 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.
    2. Chichilnisky, Graciela & Zhou, Yuqing, 1998. "Smooth infinite economies," Journal of Mathematical Economics, Elsevier, vol. 29(1), pages 27-42, January.
    3. 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.
    4. 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.
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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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