Peak-Load Pricing of Telephone Calls

Abstract

Because of the complex network structure of a telephone system, it is not immediately apparent what constitutes the marginal cost of a telephone call. This paper develops a mathematical programming model based upon the maximization of producers' plus consumers' surplus subject to capacity constraints for each item of equipment at each time of day. An optimal peak-load pricing (and investment) structure results from the Kuhn-Tucker conditions: namely, that the price of a call is set equal to the sum of the marginal opportunity costs (given by the dual variables) of the capacities utilized. The model is illustrated using cost and demand data relevant to a simple network centered on Chicago, and suggests that present prices are considerably above marginal costs, especially on long-distance, high-density routes.