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Efficiency Rents of Pumped-Storage Plants and their Uses for Operation and Investment Decisions

  • Anthony Horsley
  • Andrew J Wrobel

We apply duality methods of linear and convex programming to the problems of operation and rental valuation of facilities for conversion and storage of cyclically priced goods, e.g. , energy. Both problems are approached by shadow-pricing the stock (which is a purely intermediate commodity); and if the given market price p for the final good is a continuous function of time, then the stock's shadow price function ? is shown to be unique (and continuous). Therefore, despite being perfect Allen-Hicks complements, the plant's capacities have definite and separate marginal values, which are expressed in terms of ? (and p). In particular, the unit reservoir rent equals the total positive variation of ? over the cycle. The optimal storage policy is also given in terms of ? and p). The marginal capacity values are used to determine the optimum investment. The framework can accommodate related storage problems (such as hydroelectric generation).

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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 405.

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Date of creation: Nov 2000
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Handle: RePEc:cep:stitep:405
Contact details of provider: Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

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  1. Anthony Horsley & Andrew J. Wrobel, 1999. "Efficiency rents of storage plants in peak-load pricing, ii: hydroelectricity," LSE Research Online Documents on Economics 19342, London School of Economics and Political Science, LSE Library.
  2. Anthony Horsley & Andrew J. Wrobel, 2001. "Continuity of the equilibrium price density and its uses in peak-load pricing," LSE Research Online Documents on Economics 19330, London School of Economics and Political Science, LSE Library.
  3. Anthony Horsley & Andrew J. Wrobel & Timothy Van Zandt, 1998. "Berge's maximum theorem with two topologies on the action set," LSE Research Online Documents on Economics 19358, London School of Economics and Political Science, LSE Library.
  4. repec:cep:stitep:/1996/301 is not listed on IDEAS
  5. D.T. Nguyen, 1976. "The Problems of Peak Loads and Inventories," Bell Journal of Economics, The RAND Corporation, vol. 7(1), pages 242-248, Spring.
  6. Gravelle, H S E, 1976. "The Peak Load Problem with Feasible Storage," Economic Journal, Royal Economic Society, vol. 86(342), pages 256-77, June.
  7. Anthony Horsley & Andrew J. Wrobel, 2000. "The short-run approach to LRMC pricing for multiple outputs with nondifferentiable costs," LSE Research Online Documents on Economics 19338, London School of Economics and Political Science, LSE Library.
  8. Anthony Horsley & Andrew J Wrobel, 1996. "Efficiency Rents of Storage Plants in Peak-Load Pricing, I: Pumped Storage," STICERD - Theoretical Economics Paper Series 301, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. Anthony Horsley & Andrew J. Wrobel, 2002. "Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time," Economic Theory, Springer, vol. 20(3), pages 503-537.
  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. Pyatt, Graham, 1978. "Marginal Costs, Prices and Storage," Economic Journal, Royal Economic Society, vol. 88(352), pages 749-62, December.
  12. 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.
  13. Anthony Horsley & Andrew J Wrobel, 1999. "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 ," STICERD - Theoretical Economics Paper Series 372, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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