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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.

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Bibliographic Info

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

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

Related research

Keywords: Equilibrium manifold Regular equilibria Catastrophes Riemannian metric Geodesics Income redistribution;

References

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  1. 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, Elsevier, vol. 40(1-2), pages 105-119, February.
  2. Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, Econometric Society, vol. 43(5-6), pages 907-12, Sept.-Nov.
  3. Donald J. Brown & Rosa L. Matzkin, 1995. "Testable Restrictions on the Equilibrium Manifold," Cowles Foundation Discussion Papers, Cowles Foundation for Research in Economics, Yale University 1109, Cowles Foundation for Research in Economics, Yale University.
  4. Balasko, Yves, 1979. "A geometric approach to equilibrium analysis," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 6(3), pages 217-228, December.
  5. Yves Balasko, 2004. "The equilibrium manifold keeps the memory of individual demand functions," Economic Theory, Springer, Springer, vol. 24(3), pages 493-501, October.
  6. Garratt, Rod & Goenka, Aditya, 1995. "Income redistributions without catastrophes," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 19(1-2), pages 441-455.
  7. Andrea, Loi & Stefano, Matta, 2006. "Evolution paths on the equilibrium manifold," MPRA Paper 4694, University Library of Munich, Germany.
  8. repec:ebl:ecbull:v:4:y:2006:i:30:p:1-9 is not listed on IDEAS
  9. Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, Elsevier, vol. 58(1), pages 1-8, October.
  10. repec:ebl:ecbull:v:4:y:2005:i:7:p:1-7 is not listed on IDEAS
  11. Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, Econometric Society, vol. 46(3), pages 557-69, May.
  12. 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.
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Cited by:
  1. Loi, Andrea & Matta, Stefano, 2009. "Evolution paths on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, Elsevier, vol. 45(12), pages 854-859, December.
  2. 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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