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A note on the structural stability of the equilibrium manifold

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  • Loi, Andrea
  • Matta, Stefano

Abstract

In a smooth pure exchange economy with fixed total resources we investigate whether the smooth selection property holds when endowments are redistributed across consumers through a continuous (non local) redistribution policy. We show that if the policy is regular then there exists a unique continuous path of equilibrium prices which support it. If singular economies are involved in the redistribution, then an analogous result can be obtained if the singular policy is the projection of a path transversal to the set of critical equilibria.

Suggested Citation

  • Loi, Andrea & Matta, Stefano, 2009. "A note on the structural stability of the equilibrium manifold," MPRA Paper 15507, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:15507
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    File URL: https://mpra.ub.uni-muenchen.de/15507/1/MPRA_paper_15507.pdf
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    References listed on IDEAS

    as
    1. Mas-Colell,Andreu, 1990. "The Theory of General Economic Equilibrium," Cambridge Books, Cambridge University Press, number 9780521388702.
    2. Dierker, Egbert, 1993. "Regular economies," Handbook of Mathematical Economics, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 17, pages 795-830, Elsevier.
    3. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
    4. Garratt, Rod & Goenka, Aditya, 1995. "Income redistributions without catastrophes," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 441-455.
    5. 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.
    6. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-569, May.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Andrea Loi & Stefano Matta, 2012. "Structural stability and catastrophes," Economics Bulletin, AccessEcon, vol. 32(4), pages 3378-3385.
    2. Loi, Andrea & Matta, Stefano, 2009. "Evolution paths on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 854-859, December.
    3. Stefano Matta, 2021. "A note on local uniqueness of equilibria: How isolated is a local equilibrium?," Papers 2103.04968, arXiv.org.
    4. Loi, Andrea & Matta, Stefano, 2015. "Increasing complexity in structurally stable models: An application to a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 57(C), pages 20-24.

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    More about this item

    Keywords

    Equilibrium manifold; regular equilibria; catastrophes; structural stability; smooth selection of prices;
    All these keywords.

    JEL classification:

    • D50 - Microeconomics - - General Equilibrium and Disequilibrium - - - General
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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