A Generalization of the Implicit Function Theorems
Facultad de Economía de la Universidad Autónoma de San Luís Potosí
November 24, 2009
In this work we show that it is possible to extend the classical implicit function theorem to mappings defined in a cartesian product of two convex subsets, not necessarily open, included in the cartesian product of two Banach spaces, in to another Banach space. We apply this theorem to show that the excess utility function for an economy with infinitely many commodities is a differentiable mapping.
Number of Pages in PDF File: 8
Keywords: Implicit Function Theorem's, Banach spaces, excess
JEL Classification: C60
Date posted: December 2, 2009 ; Last revised: September 12, 2011