A Mathematical Formulation of the Peak-Load Pricing Problem

This paper formulates peak-load pricing problems using mathematical micromodels. The optimal strategy chosen for the public utility is that of maximizing the social satisfaction derived from services provided. The notion of consumers' surplus is used, and period demands are assumed to be both independent and dependent. The case of dependent demands, a heretofore unsolved problem, is handled using the line-integral calculus. Several specific models are analyzed, with both capacity constraints and profit constraints being considered. In some models it is shown that prices should depend on marginal operating costs but not on marginal capacity costs. Trade-offs between these marginal costs are explored in the peak-load pricing context. In other models the relationships of price with both demand elasticities and marginal costs are developed. Several of the existing peak-load pricing models of the literature can be shown to be subcases of models developed herein.