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Efficiency rents of pumped-storage plants and their uses for operation and investment decisions

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  • Horsley, Anthony
  • Wrobel, Andrew J.

Abstract

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Dynamics and Control.

Volume (Year): 27 (2002)
Issue (Month): 1 (November)
Pages: 109-142

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Handle: RePEc:eee:dyncon:v:27:y:2002:i:1:p:109-142

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Web page: http://www.elsevier.com/locate/jedc

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References

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  1. Pyatt, Graham, 1978. "Marginal Costs, Prices and Storage," Economic Journal, Royal Economic Society, vol. 88(352), pages 749-62, December.
  2. 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.
  3. 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.
  4. 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.
  5. Anthony Horsley & Andrew J Wrobel, 2001. "Continuity of the Equilibrium Price Density and its Uses in Peak-Load Pricing," STICERD - Theoretical Economics Paper Series 417, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. 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.
  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. 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.
  9. Anthony Horsley & Andrew J Wrobel, 1996. "Efficiency Rents of Storage Plants in Peak-Load Pricing, I: Pumped Storage," STICERD - Theoretical Economics Paper Series /1996/301, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  10. Gravelle, H S E, 1976. "The Peak Load Problem with Feasible Storage," Economic Journal, Royal Economic Society, vol. 86(342), pages 256-77, June.
  11. 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.
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Cited by:
  1. Bjarne Steffen & Christoph Weber, 2011. "Efficient storage capacity in power systems with thermal and renewable generation," EWL Working Papers 1104, University of Duisburg-Essen, Chair for Management Science and Energy Economics, revised Aug 2011.
  2. Anthony Horsley & Andrew J Wrobel, 2005. "The Wong-Viner Envelope Theorem for subdifferentiable functions," STICERD - Theoretical Economics Paper Series /2005/489, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  3. Crampes, Claude & Moreaux, Michel, 2010. "Pumped storage and cost saving," Energy Economics, Elsevier, vol. 32(2), pages 325-333, March.
  4. Anthony Horsley & Andrew J Wrobel, 2001. "Continuity of the Equilibrium Price Density and its Uses in Peak-Load Pricing," STICERD - Theoretical Economics Paper Series 417, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  5. Anthony Horsley & Andrew J Wrobel, 2005. "A Practical Short-run Approach to Market Equilibrium," STICERD - Theoretical Economics Paper Series /2005/488, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. Horsley, Anthony & Wrobel, Andrew J., 2007. "Profit-maximizing operation and valuation of hydroelectric plant: A new solution to the Koopmans problem," Journal of Economic Dynamics and Control, Elsevier, vol. 31(3), pages 938-970, March.
  7. Anthony Horsley & Andrew J Wrobel, 2005. "Characterizations of long-run producer optima and the short-runapproach to long-run market equilibrium: a general theory withapplications to peak-load pricing," STICERD - Theoretical Economics Paper Series /2005/490, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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