Equilibrium with Non-Convex Firms

General equilibrium models face serious difficulties in the presence of nonconvex technologies, when there are finitely many firms and non-convexities are not negligible. Such difficulties are both analytical and theoretical and are mainly concerned with the fact that the supply correspondence may not be convex-valued or even defined, so that the existence of competitive equilibrium will typically fail. This implies that, if we want to analyze a general equilibrium model allowing for non-convex technologies, we must permit the firms to follow more general rules of behaviour, and suitably re-define the equilibrium notion. This will imply, however, that the identification between equilibrium and optimum will no longer hold (the Invisible Hand Theorem now splits into two halves). Thus, the existence of equilibria under nonconvex technologies, and the analysis of their properties of optimality now become two very different questions.