Structural stability in economies on Banach's spaces

In this paper we analyze, from the Negishi approach the concepts of structurally stable and structurally unstable economies on Banach's spaces. With this purpose we formalize the intuitive concept of similar economies. We show that in certain cases similar (or neighboring) economies can show no similar behaviors when small modifications of their tastes (defined by utility functions) or their endowments are considered. This happen in the cases of structurally unstable economies. The structurally stable and unstable concepts in economics are strongly related with the corresponding mathematical concepts, but they are no the same. We introduce a more adequate definition to economics. The Negishi approach allows us to work in a unified way in the cases of finite or infinite dimensional economies.