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Can Catastrophe Theory Become a New Tool in Understanding Singular Economies?

In: New Tools of Economic Dynamics

Author

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  • Elvio Accinelli

    (U. de la República Montevideo, Uruguay and UAM-X)

  • Martín Puchet Anyul

    (Fac. de Economía UNAM)

Abstract

Summary The aim of this paper is to show that economic systems must be characterized by their possible singularities rather than by their regularities. Changes in parameters of a regular economy imply only small changes in the optimal choice of the agents, i.e. the economic system is structurally stable, and they are consistent with one another minor changes. But in a singular economy, small changes in parameters affect the choice of the agents in a relevant way. The equilibria, after and before the changes, are radically different states, i.e. the economic system is structurally unstable. Catastrophe theory and Morse theory are used here to characterize singular economies. These are classical theories in mathematics but nevertheless, they are new tools to help understand the behavior of an economic system. Also the approach of Negishi is followed, and this allows us to consider in a unified way economies with finitely or infinitely many goods.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lnechp:978-3-540-28444-4_6
    DOI: 10.1007/3-540-28444-3_6
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    Cited by:

    1. Elvio Accinelli, 2007. "Structural stability, Morse's lemma and singular economies," Documentos de Trabajo (working papers) 0607, Department of Economics - dECON.

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