Stability results in the framework of Shephard's lemma for non differentiable functions

Abstract

We present a version of a well known result in the context of consumer theory (Shephard's Lemma) for a non regular convex case, where the usual derivative is replaced by the subdifferential. Then, starting from some results concerning a suitable type of continuity of the subdifferential operator of a convex function, we are able to get a sort of stability under suitable perturbation of the data.