A note on the structural stability of the equilibrium manifold

Loi, Andrea and Matta, Stefano (2009): A note on the structural stability of the equilibrium manifold.

Abstract

In a smooth pure exchange economy with fixed total resources we investigate whether the smooth selection property holds when endowments are redistributed across consumers through a continuous (non local) redistribution policy. We show that if the policy is regular then there exists a unique continuous path of equilibrium prices which support it. If singular economies are involved in the redistribution, then an analogous result can be obtained if the singular policy is the projection of a path transversal to the set of critical equilibria.

• Item Type: MPRA Paper
• Language: English
• Keywords: Equilibrium manifold, regular equilibria, catastrophes, structural stability, smooth selection of prices
• Subjects: D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D50 - General; D - Microeconomics > D5 - General Equilibrium and Disequilibrium > D51 - Exchange and Production Economies

References

Balasko, Y., 1978, Economic equilibrium and catastrophe theory: an introduction, Econometrica 46, 557-569.

Balasko, Y., 1988, Foundations of the Theory of General Equilibrium, Academic Press, Boston.

Balasko, Y., 1992, The set of regular equilibria, Journal of Economic Theory 58, 1-8.

Dierker, E., 1982, Regular Economies, Chap.17 in Handbook of Mathematical Economics, vol.II, edited by K. Arrow and M. Intriligator (North-Holland, Amsterdam).

Garratt, R. and A. Goenka, 1995, Income redistributions without catastrophes, Journal of Economic Dynamics and Control 19, 441-455.

Kehoe, T.J., 1985, The comparative statics properties of tax models, Canadian Journal of Economics XVIII No. 2, 314-334

Loi, A. and S. Matta, 2007, Evolution paths on the equilibrium manifold, mimeo, available at http://mpra.ub.uni-muenchen.de/4694/

Loi, A. and S. Matta, 2008, Geodesics on the equilibrium manifold, Journal of Mathematical Economics, 44, 1379-1384.

Mas-Colell, A., 1985, The Theory of General Economic Equilibrium, a Differentiable Approach. Cambridge University Press, Cambridge.

Mas-Colell, A. and J.H. Nachbar, 1991, On the finiteness of the number of critical equilibria with an application to random selections, Journal of Mathematical Economics, 20, 397-409.

Massey, W.S., 1990, Algebraic Topology: an Introduction. Springer - Verlag, New York.