The Short-run Approach to Long-run Equilibrium in Competitive Markets ― A General Theory With Application to Peak-load Pricing With Storage

The authors present a new formal framework forfinding the long-run competitive market equilibrium through short-runequilibria by exploiting the operating policies and plant valuations. This“short-run approach” develops ideas of Boiteux and Koopmans. Applied to the peak-load pricing of electricity generated bythermal, hydro and pumped-storage plants, it gives a sound and practical methodof valuing the fixed assets—in this case, the river flows and the geologicalsites suitable for reservoirs. Its main mathematical basis is the producer’sshort-run profit maximization programme and its dual; their solutions haverelatively simple forms that can greatly ease the fixed-point problem ofsolving for the general equilibrium. Since the optimal values (profit and costfunctions) are usually nondifferentiable—this is so when there are joint costsof production such as capacity constraints—nonsmooth calculus is employed toresolve long-standing discrepancies between textbook theory and industrialreality by giving subdifferential extensions of basic results ofmicroeconomics, including the Wong-Viner Envelope Theorem.

Anthony Horsley (1939--2006) was a Britishmathematical economist and a nuclear physicist who in the 1960s worked for theU.K. Atomic Energy Authority (becoming then its youngest ever Senior ScientificOfficer) and for the Council for Scientific Policy. Later, devoting himself to academicresearch and teaching, he worked on the theory and applications of competitiveequilibrium at the University of Sussex, Oxford University and, from 1979 untilretirement and untimely death, the London School of Economics. A Renaissancemind, he also had a keen interest in literature, history and politics. Hereceived a Ph. D. in Mathematical Physics from the University of Birmingham anda D. Phil. in Economics from the University of Oxford.

Andrew J. Wrobel (b. 1955) is a Polish-bornmathematical economist. He has worked at the Institute of Computer Science inWarsaw and, as a Senior Research Fellow, at the London School of Economics andthe Catholic University of Brabant in Tilburg. His main research, joint withAnthony Horsley, is on the theory of competitive equilibrium and itsapplications to the electricity supply industry. Educated in Warsaw, and inBonn and London on postgraduate grants from the Studienstiftung des deutschenVolkes and the LSE, he holds an M.A. in Mathematics from the University ofWarsaw and a Ph.D. in Economics from the University of London.