Journal Article A Note on the Concavity of the Mean-Variance Problem Get access David Sibley David Sibley Yale University Search for other works by this author on: Oxford Academic Google Scholar The Review of Economic Studies, Volume 42, Issue 3, July 1975, Pages 479–481, https://doi.org/10.2307/2296861 Published: 01 July 1975

A framework of optimal pricing decisions combined with simple load management is designed for a public utility self-rationing strategy that will optimize prices under risk and improve on other schemes in the literature. This approach has the advantages of not resorting to restrictive assumptions, allows the firm to accomplish solvency without relying on additional schemes, avoids the difficulty of excess demand, and requires minimum information about consumer preferences. The authors recommend further research that includes multiple periods, analyzes more flexible and more sophisticated techniques, and that can be extended to cover peak-load pricing. 15 references. (DCK)

We consider optimal nonuniform pricing schedules, where the price depends upon the amount purchased. Such schedules are regularly used by public utilities and other services. Welfare-optimal nonuniform prices are related to the theory of optimal uniform prices developed by Ramsey. We characterize situations in which upward or downward discontinuities in pricing schedules are optimal. Our results are applicable to a number of related problems, including optimal taxation, insurance, and incentives.

This paper provides necessary and sufficient conditions for it to be optimal to base decisions on estimates of the parameters that characterize a decision problem (e.g., profit maximization with an estimated price elasticity of demand). We show that the separation of parameter estimation from decision making generally yields lower utility than an integrated approach which takes account of estimation uncertainty. We evaluate the decision in the parameter estimation method and show that the resulting utility loss can be substantial. MANY ACTUAL DECISIONS are based on statistical estimates of parameters that help to characterize the decision environment. For example, a firm maximizing the expected utility of profit might find that its input and output decisions depend on unknown parameters of its demand function. Econometric estimates of such parameters might then be derived and utilized in making these decisions. The first purpose of this paper is to rigorously investigate whether it is correct to make decisions in this manner; in general, it is not. The second purpose is to investigate the decis'ion bias in decisions based on commonly employed parameter estimates. We will determine, for example, whether a price setting monopolist is mistakenly setting prices too high or too low when he bases his pricing decision on the maximum likelihood estimate of his demand equation. Finally, we provide a detailed numerical example to show that basing decisions on conventional parameter estimates can lead to large losses of utility. In Section 2, we introduce all notation, explain the procedure commonly used when basing decisions on values of unknown underlying parameters, and exhibit the decision-theoretic correct alternative procedure. When the optimal decisions under these two procedures are identical, we call the proper. We use the term summary value to refer not only to standard parameter estimates but to any single substituted for an unknown parameter in order to make decisions. This generalized concept is necessary because a that is appropriate for making decisions, in a sense defined below, need not have any of the properties of conventional parameter estimators. In Section 3, we derive under general assumptions necessary and sufficient conditions for the existence of proper values that are independent of the decision maker's utility function, U( ). This independence restriction is