Structural Stability in Economies on Banach's Spaces

In this paper from the Negishi approach we analyze the concepts of structurally stable and structurally unstable economies on Banach's spaces. With this object 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. These happens in the cases of structurally unstable economies. The structural 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 allow us to work in an unified way in the cases of finite or infinite dimensional economies