Public Sector Rationing and Private Sector Selection

We study the interaction between nonprice public rationing and prices in the private market. Under a limited budget, the public supplier uses a rationing policy. A private firm may supply the good to those consumers who are rationed by the public system. Consumers have different amounts of wealth, and costs of providing the good to them vary. We consider two regimes. First, the public supplier observes consumers’ wealth information; second, the public supplier observes both wealth and cost information. The public supplier chooses a rationing policy, and, simultaneously, the private firm, observing only cost but not wealth information, chooses a pricing policy. In the first regime, there is a continuum of equilibria. The Pareto dominant equilibrium is a means-test equilibrium: poor consumers are supplied while rich consumers are rationed. Prices in the private market increase with the budget. In the second regime, there is a unique equilibrium. This exhibits a cost-effectiveness rationing rule; consumers are supplied if and only if their costbenefit ratios are low. Prices in the private market do not change with the budget. Equilibrium consumer utility is higher in the cost-effectiveness equilibrium than the means-test equilibrium. Acknowledgement: We thank many seminar and conference participants for their comments and suggestions. We also thank the editor John Conley and two referees for their advice. Various parts of the research here were done while the authors were at the Universidad Carlos III de Madrid; we are grateful to their hospitality. The first author received partial financial support from the Italian Fulbright Foundation.