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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.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Mathematical Economics.

Volume (Year): 45 (2009)
Issue (Month): 12 (December)
Pages: 854-859

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Handle: RePEc:eee:mateco:v:45:y:2009:i:12:p:854-859

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Web page: http://www.elsevier.com/locate/jmateco

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

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  1. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, Econometric Society, vol. 46(3), pages 557-69, May.
  2. Dierker, Egbert, 1993. "Regular economies," Handbook of Mathematical Economics, Elsevier, in: K. J. Arrow & M.D. Intriligator (ed.), Handbook of Mathematical Economics, edition 4, volume 2, chapter 17, pages 795-830 Elsevier.
  3. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(12), pages 1379-1384, December.
  4. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(1), pages 1-8, October.
  5. repec:ebl:ecbull:v:4:y:2006:i:30:p:1-9 is not listed on IDEAS
  6. Loi, Andrea & Matta, Stefano, 2009. "A note on the structural stability of the equilibrium manifold," MPRA Paper 15507, University Library of Munich, Germany.
  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. Stefano Matta, 2005. "A riemannian metric on the equilibrium manifold," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-7.
  9. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  10. Balasko, Yves, 1979. "A geometric approach to equilibrium analysis," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 6(3), pages 217-228, December.
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Cited by:
  1. Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 44(12), pages 1379-1384, December.
  2. Andrea Loi & Stefano Matta, 2012. "Structural stability and catastrophes," Economics Bulletin, AccessEcon, vol. 32(4), pages 3378-3385.
  3. Loi, Andrea & Matta, Stefano, 2011. "Catastrophes minimization on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 47(4), pages 617-620.

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