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Geodesics on the equilibrium manifold

  • Loi, Andrea
  • Matta, Stefano

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.

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

Volume (Year): 44 (2008)
Issue (Month): 12 (December)
Pages: 1379-1384

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Handle: RePEc:eee:mateco:v:44:y:2008:i:12:p:1379-1384
Contact details of provider: Web page: http://www.elsevier.com/locate/jmateco

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  1. Yves Balasko, 2004. "The equilibrium manifold keeps the memory of individual demand functions," Economic Theory, Springer, vol. 24(3), pages 493-501, October.
  2. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-69, May.
  3. Chiappori, P. -A. & Ekeland, I. & Kubler, F. & Polemarchakis, H. M., 2004. "Testable implications of general equilibrium theory: a differentiable approach," Journal of Mathematical Economics, Elsevier, vol. 40(1-2), pages 105-119, February.
  4. Balasko, Yves, 1979. "A geometric approach to equilibrium analysis," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 217-228, December.
  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. repec:ebl:ecbull:v:4:y:2006:i:30:p:1-9 is not listed on IDEAS
  7. Brown, Donald J & Matzkin, Rosa L, 1996. "Testable Restrictions on the Equilibrium Manifold," Econometrica, Econometric Society, vol. 64(6), pages 1249-62, November.
  8. Garratt, Rod & Goenka, Aditya, 1995. "Income redistributions without catastrophes," Journal of Economic Dynamics and Control, Elsevier, vol. 19(1-2), pages 441-455.
  9. repec:ebl:ecbull:v:4:y:2005:i:7:p:1-7 is not listed on IDEAS
  10. Andrea, Loi & Stefano, Matta, 2006. "Evolution paths on the equilibrium manifold," MPRA Paper 4694, University Library of Munich, Germany.
  11. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  12. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
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