Regulating a Monopolist with Unknown Demand and Cost Functions

We consider the design of regulatory policy when the regulator is imperfectly informed about both the firm's cost function and the demand function it faces. To some extent the optimal policy here is the natural "combination" of the optimal policies when there is uncertainty only about either demand or cost. Important qualitative differences also exist, however. For example, it may be optimal to set prices below marginal cost, and the pricing authority delegated to the firm may be more limited when there is uncertainty about both cost and demand.