We consider the problem of how to regulate a monopolistic firm whose costs are unknown to the regulator. The regulator's objective is to maximize a linear social welfare function of the consumer's surplus and the firm's profit. In the optimal regulatory policy, prices and subsidies are designed as functions of the firm's cost report so that expected social welfare is maximized, subject to the constraints that the firm has nonnegative profit and has no incentive to misrepresent its costs. We explicitly derive the optimal policy and analyze its properties.