Optimal water pricing and storage with cyclical supply and demand

Optimal storage of a naturally renewable, seasonally varying resource is considered where demand is price sensitive and seasonal and social resources are required for storage and processing prior to consumption. The particular application is water supply, where the demand and supply fluctuations are generally out of phase. Using a Lagrangian analytical framework, net willingness to pay is maximized subject to fundamental constraints that characterize water supply and storage. The purpose of this work is to integrate the literatures of peak load pricing and optimal reservoir planning and operation, noting that price is both an active form of ‘soft’ demand management and an effective information signal for efficient allocation of (nonwater) resources in the management of water supply. Results indicate that although demand is assumed to vary continuously with time, the optimal rate structure is approximated by a policy in which the price of water is adjusted at only a few points in the cycle. In contrast with the usual discrete time model, the duration of each subperiod of constant pricing is endogenously determined. It is also shown that owing to the introduction of storage, off‐peak prices as well as the peak season price may be held above marginal operating costs, thereby bearing part of the capacity costs.