Externalities, Consumption Constraints and Regular Economies

We consider a general model of pure exchange economies with consumption externalities. Households may have different consumption sets and each consumption set is described by a function called the possibility function. Utility and possibility functions depend on the consumptions of all households. Showing by means of an example that basic assumptions are not enough to guarantee generic regularity, we provide sufficient conditions for generic regularity in the space of endowments and possibility functions.