Firms that provide capacity to meet randomly fluctuating demand typically will not be producing on the efficient frontier of their production possibilities sets. Consequently, the standard dual theory of cost and production is inapplicable. This article provides an alternative that leaves most of the theory intact provided that firms are viewed as producing the probability of providing service rather than an explicit produced output. As an application we show that for a telecommunications firm facing a network externality it is quite possible to find something that looks like negative marginal cost.
"The di@alty which arises is that trafic offered is not the same as trajjk canied. " Littlechild (1979) The standard theory of cost and production requires that production occur on the boundary of the production possibilities set. For price-taking, profit-maximizing firms in a nonstochastic environment, this result follows from profit-maximizing behavior; for output and price-taking firms, this is an assumption that seems at least reasonable. However, when demand is random and when firms are required to provide service to all demanders, as is the case in telecommunications, something has to give. The choices are limited to either efficiency or universal provision of service. In regulated industries, it is usually efficiency that is slighted. In such cases one must then wonder at the extent to which dual functional forms, concepts and ideas, each of which require efficiency, can be used to model firm behavior. This paper presents a reformulation of production theory to account for the situation and applies it in determining appropriate functional forms for cost functions in telecommunications firms. In particular, I look carefully at situations where observed output or demand is below capacity or maximum-producible output. While my primary concern is the provision of telecommunications services, the theory should apply to other public services such as those provided by not-for-profit hospitals or fire departments.
*The opinions expressed in this paper are those of the author alone and do not necessarily represent the opinions of GTE or any of its subsidiaries. I'd like to thank Rip Viscusi, Dave Salant, Glenn Woroch, and Larry Cole for various comments. To Roger Tobin, my coauthor on other parts of this study, I give a particular thanks.