Evolution paths on the equilibrium manifold

Andrea, Loi and Stefano, Matta (2006): Evolution paths on the equilibrium manifold.

Abstract

In a pure exchange smooth economy with fixed total resources, we de- fine 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.

• Item Type: MPRA Paper
• Institution: University of Cagliari
• Language: English
• Keywords: Equilibrium manifold; regular economies; critical equilibria; catastrophes; Jordan-Brouwer separation theorem
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General

References

[1] Y. Balasko, The graph of the Walras correspondence, Econometrica, 43 (1975), 907-912. [2] Y. Balasko, Economic equilibrium and catastrophe theory: an introduction, Econo- metrica, 46 (1978), 557-569. [3] Y. Balasko, Geometric approach to equilibrium analysis, J. of Mathematical Eco- nomics 6 (1979), 217-228. [4] Y. Balasko, Foundations of the Theory of General Equilibrium, Academic Press, Boston (1988). [5] Y. Balasko, The set of regular equilibria, J. of Economic Theory 58 (1992), 1-8. [6] E. Dierker, Regular Economies, Chap.17 in Handbook of Mathematical Economics, vol.I I, edited by K. Arrow and M. Intriligator. Amsterdam: North-Holland(1982). [7] V. Guillemin and A. Pollack, Differential Topology, Prentice Hall, Englewood Cliffs (1974). [8] E.L. Lima, The Jordan-Brouwer separation theorem for smooth hypersurfaces, Am. Math. Monthly 95 (1988), 39-42. [9] A. Loi, S. Matta, A Riemannian metric on the equilibrium manifold: the smooth case, Economics Bulletin 4 No. 30 (2006), 1-9. [10] S. Matta, A Riemannian metric on the equilibrium manifold, Economics Bulletin 4 No. 7 (2005), 1-7. [11] H. Samelson, Orientability of Hypersurfaces in Rn , Proc. Am. Math. Soc. 22 (1969), 301-302.