Economic Problems With Constraints: How Efficiency Relates To Equilibrium

We consider situations, in which socially important goods (like transportation capacity or hospital beds) are supplied by independent economic agents. There is also a regulator that believes that constraining the goods delivery is desirable. The regulator can compute a constrained Pareto-efficient solution to establish optimal output levels for each agent. We suggest that a coupled-constraint equilibrium (also called a "generalized" Nash or "normalized" equilibrium à la Rosen) may be more relevant for market economies than a Pareto-efficient solution. We examine under which conditions the latter can equal the former. We illustrate our findings using a coordination problem, in which the agents' outputs depend on externalities. It becomes evident that the correspondence between an efficient and equilibrium solutions cannot be complete if the agents' activities generate both negative and positive externalities at the same time.