Optimal public rationing : price response and cost effectiveness

Abstract

We study optimal public rationing of an indivisible good and private sector price response. Consumers differ in their wealth and cost of provisions. Due to a limited budget, some consumers must be rationed. Public rationing determines the characteristics of consumers who seek supply from the private sector, where a firm sets prices based on consumer cost information and in response to the rationing rule. We consider two inforrmation regimes. In the first, the public supplier rations consumers according to their wealth information. In equilibrium, the public supplier must ration both rich and poor consumers. Supplying all poor consumers would leave only rich consumers in the private market, and the firm would react by setting a high price. Rationing some poor consumers is optimal, and implements price reduction in the private market. In the second information regime, the public supplier rations consumes according to consumer wealth and cost information. In equilibrium, rationing is based on cost-effectiveness and consumers are allocated the good if and only if their costs are below a threshold.