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Evolution paths on the equilibrium manifold

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  • Loi, Andrea
  • Matta, Stefano

Abstract

In a pure exchange smooth economy with fixed total resources, we define the length between two regular equilibria belonging to the equilibrium manifold as the number of intersection points of the evolution path connecting them with the set of critical equilibria. We show that there exists a minimal path according to this definition of length.

Suggested Citation

  • Loi, Andrea & Matta, Stefano, 2009. "Evolution paths on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 45(12), pages 854-859, December.
    • Handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:854-859
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    References listed on IDEAS

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    1. repec:ebl:ecbull:v:4:y:2006:i:30:p:1-9 is not listed on IDEAS
    2. Balasko, Yves, 1979. "A geometric approach to equilibrium analysis," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 217-228, December.
    3. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
    4. Stefano Matta, 2005. "A riemannian metric on the equilibrium manifold," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-7.
    5. 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.
    6. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
    7. Stefano Matta & Andrea Loi, 2006. "A Riemannian metric on the equilibrium manifold: the smooth case," Economics Bulletin, AccessEcon, vol. 4(30), pages 1-9.
    8. Loi, Andrea & Matta, Stefano, 2009. "A note on the structural stability of the equilibrium manifold," MPRA Paper 15507, University Library of Munich, Germany.
    9. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-569, May.
    10. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-912, Sept.-Nov.
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    Cited by:

    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. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
    3. Andrea Loi & Stefano Matta, 2012. "Structural stability and catastrophes," Economics Bulletin, AccessEcon, vol. 32(4), pages 3378-3385.
    4. 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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    More about this item

    Keywords

    Equilibrium manifold Regular economies Critical equilibria Catastrophes Jordan-Brouwer separation theorem;

    JEL classification:

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

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