problem in the theory of regulation. In this paper, we develop a simple but general concept of return based on an equilibrium model of production under uncertainty. We propose regulatory behavior which will induce firms to make efficient input choices, while at the same time guaranteeing returns. * Regulation is a common phenomenon in natural monopolies, those industries with decreasing average costs. Optimal resource use in such industries dictates that output be provided by a single firm, but this easily leads to inefficient monopolistic practices by firms in the absence of regulation. Effective regulation, however, requires that meaningful regulatory objectives be specified and rules devised for their implementation. While economic theory provides appropriate objectives and behavioral rules when there is no uncertainty, the presence of uncertainty is central to the knottiest problems of regulation. And until recently, economic theory had little to say about optimal production in the presence of uncertainty. A particularly crucial problem facing regulatory agencies is an appropriate definition of a fair rate of return. The legal guideline for regulation, based on the Hope decision, requires that regulatory policies provide a return to the equity holder commensurate with returns on investments with corresponding risks.' Under certainty, this guideline is well-defined: equity holders should receive the riskless rate of return which prevails throughout the economy. Under uncertainty, the guideline is much less clear. Often corresponding risks are not present. And if they are present, they usually are associated with other regulated firms, leaving a simul