Regulating a Monopolist with Unknown Costs

Abstract

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 of the consumers' 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. IN THEIR CLASSIC PAPERS Dupuit [2] and Hotelling [5] considered pricing policies for a bridge that had a fixed cost of construction and zero marginal cost. They demonstrated that the pricing policy that maximizes consumer well-being is to set price equal to marginal cost and to provide a subsidy to the supplier equal to the fixed cost, so that a firm would be willing to provide the bridge. This first-best solution is based on a number of informational assumptions. First, the demand is assumed to be known to both the regulator and to the firm. While the assumption of complete information may be too strong, the assumption that information about demand is as available to the regulator as it is to the firm does not seem unnatural. A second informational assumption is that the regulator has complete information about the cost of the firm or at least has the same information about cost as does the firm. This assumption is unlikely to be met in reality, since the firm would be expected to have better information about costs than would the regulator. As Weitzman has stated, An essential feature of the regulatory environment I am trying to describe is uncertainty about the exact specification of each firm's cost function. In most cases even the managers and engineers most closely associated with production will be unable to precisely specify beforehand the cheapest way to generate various hypothetical output levels. Because they are yet removed from the production process, the regulators are likely to be vaguer still about a firm's cost function [12, p. 684]. As this observation suggests, it is natural to expect that a firm would have better information regarding its costs than would a regulator. The purpose of this paper is to develop an optimal regulatory policy for the case in which the regulator does not know the costs of the firm. One strategy that a regulator could use in the absence of full information about costs is to give the firm the title to the total social surplus and to delegate the pricing decision to the firm. In pursuing its own interests, which would then be to maximize the total social surplus, the firm would adopt the same marginal cost pricing strategy that the regulator would have imposed if the regulator had