We study optimal public rationing of an indivisible good and private sector price responses. Consumers differ in their wealth and costs 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 consumers' cost information and in response to the rationing rule. We consider two information 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 consumers according to consumers' wealth and cost information. In equilibrium, consumers are allocated the good if and only if their costs are below a threshold. Wealth information is not used. Rationing based on cost results in higher equilibrium total consumer surplus than rationing based on wealth. [Authors]