The formal theory of pricing and investment for electricity
The Thesis develops the framework of competitive equilibrium in infinite-dimensional commodity and price spaces, and applies it to the problems of electricity pricing and investment in the generating system. Alternative choices of the spaces are discussed for two different approaches to the price singularities that occur with pointed output peaks. Thermal generation costs are studied first, by using the mathematical methods of convex calculus and majorisation theory, a.k.a. rearrangement theory. Next, the thermal technology, pumped storage and hydroelectric generation are studied by duality methods of linear and convex programming. These are applied to the problems of operation and valuation of plants, and of river flows. For storage and hydro plants, both problems are approached by shadow-pricing the energy stock, and when the given electricity price is a continuous function of time, the plants' capacities, and in the case of hydro also the river flows, are shown to have definite and separate marginal values. These are used to determine the optimum investment. A short-run approach to long-run equilibrium is then developed for pricing a differentiated good such as electricity. As one tool, the Wong-Viner Envelope Theorem is extended to the case of convex but nondifferentiable costs by using the short-run profit function and the profit-imputed values of the fixed inputs, and by using the subdifferential as a multi-valued, generalised derivative. The theorem applies readily to purely thermal electricity generation. But in general the short-run approach builds on solutions to the primal-dual pair of plant operation and valuation problems, and it is this framework that is applied to the case of electricity generated by thermal, hydro and pumped-storage plants. This gives, as part of the long-run equilibrium solution, a sound method of valuing the fixed assets-in this case, the river flows and the sites suitable for reservoirs.