Existence and optimality of social equilibrium with many convex and nonconvex firms

This paper analyzes the existence of efficient equilibrium allocations in an economy with many convex and non-convex firms. A Social Equilibrium is defined as a price vector and an allocation satisfying the following properties: a) Consumers satisfy their preferences, subject to their budget constraints; b,l) Convex firms maximize profits at given prices; b,2) Non-convex firms maximize profits at given prices, subject to an input constraint; and c) All markets clear. We show that, under suitable assumptions, a Pareto Optimal Social Equilibrium does exist. This result can be interpreted as defining a regulation policy yielding efficient outcomes, which consists of imposing constraints on the availability of some inputs for the non-convex firms, and let them act in the market as (constrained) profit maximizers.