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Determinacy of equilibria of smooth infinite economies

Covarrubias, Enrique (2008): Determinacy of equilibria of smooth infinite economies.

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Abstract

This paper deals with generic determinacy of equilibria for infinite dimensional consumption spaces. Our work could be seen as an infinite-dimensional analogue of Dierker and Dierker (1972), by characterising equilibria of an economy as a zero of the aggregate excess demand, and studying its transversality. In this case, we can use extensions of the transversality density theorem. Assuming separable utilities, we give a new proof of generic determinacy of equilibria. We define regular price systems in this setting and show that an economy is regular if and only if its associated excess demand function only has regular equilibrium prices. We also define the infinite equilibrium manifold and show that it has the structure of a Banach manifold.

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