Evolution paths on the equilibrium manifold
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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- Loi, Andrea & Matta, Stefano, 2009. "A note on the structural stability of the equilibrium manifold," MPRA Paper 15507, University Library of Munich, Germany.
- Balasko, Yves, 1978. "Economic Equilibrium and Catastrophe Theory: An Introduction," Econometrica, Econometric Society, vol. 46(3), pages 557-569, May.
- Loi, Andrea & Matta, Stefano, 2008. "Geodesics on the equilibrium manifold," Journal of Mathematical Economics, Elsevier, vol. 44(12), pages 1379-1384, December.
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- 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.
- Stefano Matta & Andrea Loi, 2006. "A Riemannian metric on the equilibrium manifold: the smooth case," Economics Bulletin, AccessEcon, vol. 4(30), pages 1-9.
- Balasko, Yves, 1979. "A geometric approach to equilibrium analysis," Journal of Mathematical Economics, Elsevier, vol. 6(3), pages 217-228, December.
- Balasko, Yves, 1992. "The set of regular equilibria," Journal of Economic Theory, Elsevier, vol. 58(1), pages 1-8, October.
- Balasko, Yves, 1975. "The Graph of the Walras Correspondence," Econometrica, Econometric Society, vol. 43(5-6), pages 907-912, Sept.-Nov.
- Stefano Matta, 2005. "A riemannian metric on the equilibrium manifold," Economics Bulletin, AccessEcon, vol. 4(7), pages 1-7.
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