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From singularity theory to finiteness of Walrasian equilibria

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  • Castro, Sofia B.S.D.
  • Dakhlia, Sami
  • Gothen, Peter B.

Abstract

The main result of this paper states that there exists a residual subset of the set of critical economies whose associated equilibria are finite in number. We also show that this subset does not contain any open set and therefore the result is the best possible for our choice of topology (compact-open topology). The proof rests on results and concepts from singularity theory.

Suggested Citation

  • Castro, Sofia B.S.D. & Dakhlia, Sami & Gothen, Peter B., 2013. "From singularity theory to finiteness of Walrasian equilibria," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 169-175.
    • Handle: RePEc:eee:matsoc:v:66:y:2013:i:2:p:169-175
    DOI: 10.1016/j.mathsocsci.2013.03.002
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    References listed on IDEAS

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    1. Mas-Colell, Andreu, 1977. "On the equilibrium price set of an exchange economy," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 117-126, August.
    2. Castro, Sofia B.S.D. & Dakhlia, Sami & Gothen, Peter B., 2010. "Direct perturbations of aggregate excess demand," Journal of Mathematical Economics, Elsevier, vol. 46(4), pages 562-571, July.
    3. Debreu, Gerard, 1970. "Economies with a Finite Set of Equilibria," Econometrica, Econometric Society, vol. 38(3), pages 387-392, May.
    4. Mas-Colell, Andreu & Nachbar, John H., 1991. "On the finiteness of the number of critical equilibria, with an application to random selections," Journal of Mathematical Economics, Elsevier, vol. 20(4), pages 397-409.
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