Externalities in private ownership production economies with possibility functions. An existence result

We consider a private ownership production economy with consumption and production externalities. Each household is characterized by a consumption set described by a possibility function, an endowment of commodities, and preferences described by a utility function. Each firm is owned by households and it is characterized by technology described by a transformation function. The choices of all agents (households and firms) affect individual consumption sets, individual preferences, and production technologies. Describing equlibria in terms of first-order conditions and market clearing conditions, and using a homotopy approach, under differentiability and boundary conditions, we prove the non-emptiness and the compactness of the set of competitive equilibria with consumptions and prices strictly positive.