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.