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Minimality and uniqueness of equilibrium

Author

Listed:
  • Loi, Andrea
  • Matta, Stefano

Abstract

In this paper we propose the following conjecture: the equilibrium manifold E(r) ⊂ RLM−1, where L is the number of goods and M the number of consumers, is a minimal submanifold if and only if the price is unique for every economy. We show the validity of this conjecture for an arbitrary number of goods and two consumers and for an arbitrary number of consumers and two goods under the assumption that the normal vector field of E(r) is constant outside a compact subset.

Suggested Citation

  • Loi, Andrea & Matta, Stefano, 2019. "Minimality and uniqueness of equilibrium," MPRA Paper 98055, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:98055
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    File URL: https://mpra.ub.uni-muenchen.de/106178/1/MPRA_paper_106178.pdf
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    References listed on IDEAS

    as
    1. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
    2. Loi, Andrea & Matta, Stefano, 2018. "Curvature and uniqueness of equilibrium," Journal of Mathematical Economics, Elsevier, vol. 74(C), pages 62-67.
    3. Loi, Andrea & Matta, Stefano, 2011. "Catastrophes minimization on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 47(4), pages 617-620.
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    Citations

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    Cited by:

    1. Giménez, Eduardo L., 2022. "Offer curves and uniqueness of competitive equilibrium," Journal of Mathematical Economics, Elsevier, vol. 98(C).

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    More about this item

    Keywords

    Equilibrium manifold; uniqueness of equilibrium; minimal submanifold.;
    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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