Public Sector Rationing and Private Sector Selection

We study the interaction between a public sector and a private sector in the provision of a private good. Under a limited budget, the public supplier uses a rationing policy. A private ?rm may supply the good to those consumers who are rationed by the public system. Consumers have di¤erent amounts of wealth, and costs of providing the good to them vary. We consider two information regimes: First, the public supplier observes only wealth information; second, the public supplier observes both wealth and cost information. The public supplier chooses a rationing policy based on its information; simultaneously, the private firm, observing only cost but not wealth information, chooses a pricing policy. In the first information regime, there is a continuum of equilibria; in each, rich consumers are rationed, and the private firm sells to these rationed consumers at high prices. In the second regime, there is a unique equilibrium. The public supplier allocates the good to consumers according to a cost-e¤ectiveness rule. In the equilibrium, rationed consumers have high costs relative to the bene?t, and the rationing rule is the same as if the private market were inactive.