Optimal peak load pricing with time-additive consumer preferences

Abstract

The formulation of socially optimal pricing policies for non-storable goods with cyclical demand is by now a classical problem of applied welfare economics. Applications may be found in a diverse range of industries, notably transportation, electric power, and telecommunications. This paper departs from the received theory of peak load pricing’ in three respects. Instead of the usual discrete periodization, the problem is formulated in continuous time. Second, the traditi,onal consumers’ plus producers’ surplus welfare criterion is replaced by a time-additive utility functional which serves to rank preferentially alternative consumption paths. And third, the familiar fixed-proportions production technology is replaced by a more plausible neoclassical technology.* This formalism is used to derive simple rules for optimal consumption policies for both price-taking and technology-constrained institutional contexts. First-best pricing policies which induce consumers to choose the optimal, technology-constrained consumption paths are then given. When instantaneous utility varies’smoothly in time, the optimal pricing policy is shown also to vary smoothly with time. The problem of approximating the optimal smooth pricing policies by pure-jump pricing policies is treated. And optimal investment rules are also given. A parametric example is presented to illustrate the general results. An empirically viable specification of the time-additive utility functional is briefly introduced. And results are summarized in a concluding section.