Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when $L^{\infty}$ is the commodity space, is weakened to allow applications to continuous-time problems, and especially to peak-load pricing when the users' utility and production functions are Mackey continuous. A general form for production sets with the required property is identified, and examples are given of technologies which meet the weakened but not the original condition: these include industrial use and storage of cyclically priced goods. This gives a framework for settling Boiteux's conjecture on the shifting-peak problem. To make clear the restriction implicit in Mackey continuity, we interpret it as interruptibility of demand; and we point out that, without this assumption, the equilibrium can feature pointed peaks with singular, instantaneous capacity charges. The general equilibrium results are supplemented by results for prices supporting individual consumer or producer optima.