A note on the Drèze’s criterion for large capitalist firms.

The paper extends the Drèze's Criterion [Investment under private ownership : optimality, equilibrium and stability, in «Allocation under Uncertainty ; Equilibrium and Optimality», Wiley, New York, 1974, p.129] for firms to non-smooth and non-convex technologies and to non-ordered preferences for the consumers. Technically, the proofs follow the lines of Guesnerie [Pareto Optimality in Non-convex Economies, in Econometrica, 43, p. 1-31, (1975)]. Using recent tools of non-smooth analysis, we exhibit the first-order-necessary conditions for constrained Pareto optimal allocations. The Drèze's criterion for firms is recovered, but the profit maximization is replaced by a first-order- necessary condition for optimality, together with other relations between state prices and consumptions. A new stock-market equilibrium is formalized. We show that stock holders buy nothing but stocks of a firm that maximize his expected profit with respect to his own shadow price.