Existence of competitive equilibria with externalities: A differential viewpoint

We consider a class of pure exchange economies with externalities. Each consumption set is described by a function called possibility function which depends on the individual initial endowment. Moreover, each possibility function, as well as each utility function, depends on the consumptions of all households. Our definition of competitive equilibrium with externalities includes as a particular case the classical definition. Using homotopy arguments, under differentiability and boundary conditions, we show that for all economies the set of equilibria is non-empty and compact. This work is the first step to encompass externalities in the global analysis of equilibria.