Optimal Rewards for Economic Regulation

Suppose several production units or firms must be regulated when costs and benefits are uncertain. Pollution might be a specific example, although there are many others. Given that firms must bear their own costs, the regulators want to transmit a schedule of revenues to each unit which in some expected value sense elicits an optimal response. What makes this problem intriguing is that while benefits are typically a nonseparable function of all the firms' outputs, it seems realistic to require that the revenue function to be received by a given unit must depend in some well-defined way on its individual actions alone. Two control modes often used in regulation are "prices" and "quantitites." These can be viewed as special cases of revenue functions. Prices are a linear function of output. Quantities might be described as a quadratic loss function of deviations from target, accompanied by a heavy-penalty weight. Although these two control modes are frequently treated as mutually exclusive regulatory strategies, it is highly unlikely that either extreme is optimal. In the class of all objective functions, what is the best revenue schedule? This paper is devoted to formalizing the question, giving a precise answer (at least for an important special case), and analyzing the answer. Roughly speaking, in an optimal policy the center transmits to each firm a "price term" plus a weighted "quantity term," the weight depending in a well-defined way on specific features of the underlying situation. Such a result can be interpreted as providing a reasonable justification for regulation based on both price incentives and quantity targets.