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Geodesics on the equilibrium manifold

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  • Loi, Andrea
  • Matta, Stefano

Abstract

We show the existence of a Riemannian metric on the equilibrium manifold such that a minimal geodesic connecting two (sufficiently close) regular equilibria intersects the set of critical equilibria in a finite number of points. This metric represents a solution to the following problem: given two (sufficiently close) regular equilibria, find the shortest path connecting them which encounters the set of critical equilibria in a finite number of points. Furthermore, this metric can be constructed in such a way to agree, outside an arbitrary small neighborhood of the set of critical equilibria, to any given metric with economic meaning.

Suggested Citation

  • Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
    • Handle: RePEc:eee:mateco:v:44:y:2008:i:12:p:1379-1384
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    References listed on IDEAS

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    1. Andrea Loi & Stefano Matta, 2016. "On the topology of the set of critical equilibria," International Journal of Economic Theory, The International Society for Economic Theory, vol. 12(2), pages 107-126, June.
    2. Andrea Loi & Stefano Matta & Daria Uccheddu, 2023. "Uniqueness of equilibrium and redistributive policies: a geometric approach to efficiency," Papers 2308.03706, arXiv.org.
    3. Loi, Andrea & Matta, Stefano, 2009. "Evolution paths on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 854-859, December.
    4. Andrea Loi & Stefano Matta, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Papers 2102.09827, arXiv.org.
    5. Loi, Andrea & Matta, Stefano, 2019. "Minimality and uniqueness of equilibrium," MPRA Paper 98055, University Library of Munich, Germany.
    6. Loi, Andrea & Matta, Stefano, 2011. "Catastrophes minimization on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 47(4), pages 617-620.
    7. Loi, Andrea & Matta, Stefano, 2021. "Minimal entropy and uniqueness of price equilibria in a pure exchange economy," Journal of Mathematical Economics, Elsevier, vol. 97(C).

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