Possibility functions and regular economies

In the spirit of Smale's work, we consider pure exchange economies with general consumption sets. In this paper, the consumption set of each household is described in terms of a function called possibility function. The main innovation comes from the dependency of each possibility function with respect to the individual endowment. We prove that, generically in the space of endowments and possibility functions, economies are regular. A regular economy has only a finite number of equilibria which locally depend on endowments and possibility functions in a continuous manner.