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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)

Author

Listed:
  • Anthony Horsley
  • Andrew J Wrobel

Abstract

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.

Suggested Citation

  • 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.
  • Handle: RePEc:cep:stitep:372
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    File URL: http://sticerd.lse.ac.uk/dps/te/te372.pdf
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    References listed on IDEAS

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    1. Horsley, Anthony & Wrobel, Andrzej J, 1991. "The Closedness of the Free-Disposal Hull of a Production Set," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 386-391, October.
    2. repec:cep:stitep:300 is not listed on IDEAS
    3. Horsley, A. & Wrobel, A., 1990. "The Existence Of An Equilibrium Density For Marginal Cost Prices, And The Solution To The Shifting-Peak Problem," Papers 9012, Tilburg - Center for Economic Research.
    4. Anthony Horsley & Andrew J Wrobel, 1996. "The Wong-Viner Envelope Theorem or Nonsmooth Joint Costs, Rental Valuation and the Short-Run Approach to Long-Run Equilibrium," STICERD - Theoretical Economics Paper Series /1996/299, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. repec:cep:stitep:299 is not listed on IDEAS
    6. Anthony Horsley & Andrew J Wrobel, 1991. "Marginal Analysis and Bewley Equilibria: The Use of Subgradients," STICERD - Theoretical Economics Paper Series 231, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. 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.
    8. 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.
    9. Littlechild, S C, 1970. "Marginal-cost Pricing with Joint Costs," Economic Journal, Royal Economic Society, vol. 80(318), pages 323-335, June.
    10. repec:cep:stitep:/1991/232 is not listed on IDEAS
    11. 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.
    12. Anthony Horsley & Andrew J Wrobel, 1996. "Uninterruptible Consumption, Concentrated Charges, and Equilibrium in the Commodity Space of Continuous Functions," STICERD - Theoretical Economics Paper Series /1996/300, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. repec:cep:stitep:301 is not listed on IDEAS
    14. 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.
    15. repec:cep:stitep:/1991/231 is not listed on IDEAS
    16. 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.
    17. Horsley, Anthony & Wrobel, Andrew J., 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.
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    Citations

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    Cited by:

    1. 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.
    2. Anthony Horsley & Andrew J Wrobel, 2000. "The Short-Run Approach to LRMC Pricing for Multiple Outputs with Nondifferentiable Costs," STICERD - Theoretical Economics Paper Series 393, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Horsley, Anthony & Wrobel, Andrew J., 2002. "Efficiency rents of pumped-storage plants and their uses for operation and investment decisions," Journal of Economic Dynamics and Control, Elsevier, vol. 27(1), pages 109-142, November.

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