Continuity of the equilibrium price density and its uses in peak-load pricing

Summary. With as the commodity space, the equilibrium price density is shown to be a continuous function of the commodity characteristics. The result is based on symmetry ideas from the Hardy-Littlewood-Pólya theory of rearrangements. It includes, but is not limited to, the case of symmetric (rearrangement-invariant) production costs and additively separable consumer utility. Examples arise in continuous-time utility pricing, e.g., electricity pricing. In this context, a continuously varying price has two uses. First, it precludes demand jumps that would arise from discontinuous switches from one price rate to another. Second, in the problems of operating and valuing hydroelectric and pumped-storage plants (studied elsewhere), price continuity guarantees that their capacities (viz., the reservoir and the converter), the energy stocks, and in the case of hydro also the river flows, have well-defined marginal values.Received: 9 May 2001, Revised: 8 July 2004, JEL Classification Numbers: C62, D51, D58, L94. Correspondence to: Anthony HorsleyPart of this work (CentER DP 9014) was completed at the Center for Economic Research, Tilburg University, whose financial support is gratefully acknowledged. The extension to storage was supported by ESRC grant R000232822. We also thank the referee and the editor for their comments.