On the regularity of smooth production economies with externalities: Competitive equilibrium à la Nash

We consider a general equilibrium model of a private ownership economy with consumption and production externalities. The choices of all agents (households and firms) may affect utility functions and production technologies. The equilibrium notion blends Arrow-Debreu with Nash, that is, agents (households and firms) maximize their goals by taking as given both commodity prices and choices of every other agent in the economy. We provide an example showing that under standard assumptions, such economies may have infinitely many equilibria. We present our model with firms' endowments following Geanakoplos, Magill, Quinzii and Drèze (1990). Firms' endowments consist of amounts of commodities held by the firms to generate receipts from sales of initially-held stocks of commodities and claims from debts, subsidies and taxes expressible in terms of them. We prove that almost all economies are regular in the space of endowments of households and firms