A Generalization of the Implicit Function Theorems
8 Pages Posted: 2 Dec 2009 Last revised: 12 Sep 2011
Date Written: 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.
Keywords: Implicit Function Theorem's, Banach spaces, excess
JEL Classification: C60
Suggested Citation: Suggested Citation