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Efficiency Rents of Storage Plants in Peak-Load Pricing, II: Hydroelectricity - (Now published as Efficiency rents of hydroelectric storage plants in continuous-time peak-load pricing, in The Current State of Economic Science, by S B Dahiya (ed.), vol.1, pp.453-480 (Spellbound Publications, Rohtak, 1999)

  • Anthony Horsley
  • Andrew J Wrobel

Duality methods of linear and convex programming are applied to impute definite marginal values to the fixed inputs of a hydroelectric plant from the operating profit. Our earlier analysis of pumped storage (of energy and other cyclically priced goods) is thus extended to valuation of an external inflow to the reservoir. Given a continuous time-of-use price for electricity, the profit-imputed hydro values are uniquely determined - unlike the corresponding values imputed from fuel savings for a mixed hydro-thermal system. In particular the water inflow is assigned a unique, time-dependent shadow price. The short-run profit is then differentiable in all the fixed inputs, so that unique and separate marginal values can be imputed to the reservoir and the turbine capacities (despite their perfect complementarity). The two rents can be expressed in terms of the shadow price for water (which determines the optimal storage policy). In particular, the unit reservoir rent equals the total positive variation of the shadow price over the cycle. Evaluation of profit-imputed rents is shown to be useful not only to a profit-maximising industry but also to a public utility aiming to price its outputs at long-run marginal cost and to optimise its capital stock on the basis of purely short-run calculations. In addition we verify the production set properties that are needed to incorporate such a storage problem into a continuous-time model of general competitive equilibrium with the space of bounded functions of time as the commodity space.

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Paper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Theoretical Economics Paper Series with number 372.

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Date of creation: Oct 1999
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Handle: RePEc:cep:stitep:372
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  1. repec:cep:stitep:/1996/301 is not listed on IDEAS
  2. Littlechild, S C, 1970. "Marginal-cost Pricing with Joint Costs," Economic Journal, Royal Economic Society, vol. 80(318), pages 323-35, June.
  3. repec:cep:stitep:/1996/299 is not listed on IDEAS
  4. Tjalling C. Koopmans, 1957. "Water Storage Policy in a Simplified Hydroelectric System," Cowles Foundation Discussion Papers 26, Cowles Foundation for Research in Economics, Yale University.
  5. Horsley, A. & Wrobel, A.J., 1990. "The Existence of an Equilibrium Density for Marginal Cost Prices, and the Solution to the Shifting-Peak Problem," Discussion Paper 1990-12, Tilburg University, Center for Economic Research.
  6. Horsley, Anthony & Wrobel, A. J. & Van Zandt, Timothy, 1998. "Berge's maximum theorem with two topologies on the action set," Economics Letters, Elsevier, vol. 61(3), pages 285-291, December.
  7. Anthony Horsley, 1982. "Electricity Pricing for Large Supply Systems," STICERD - Theoretical Economics Paper Series 48, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  8. repec:cep:stitep:/1991/232 is not listed on IDEAS
  9. Horsley, A. & Wrobel, A., 1990. "The Closedness Of The Free-Disposal Hull Of A Production Set," Papers 9013, Tilburg - Center for Economic Research.
  10. Bewley, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," Journal of Economic Theory, Elsevier, vol. 4(3), pages 514-540, June.
  11. repec:cep:stitep:/1991/231 is not listed on IDEAS
  12. repec:cep:stitep:/1996/300 is not listed on IDEAS
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