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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)

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  • 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.

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File URL: http://sticerd.lse.ac.uk/dps/te/te372.pdf
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Bibliographic Info

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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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp

Related research

Keywords: storage hydro; rental valuation; peak-load pricing; linear programming.;

References

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  1. Horsley, A. & Wrobel, A., 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.
  2. Littlechild, S C, 1970. "Marginal-cost Pricing with Joint Costs," Economic Journal, Royal Economic Society, vol. 80(318), pages 323-35, June.
  3. Horsley, A. & Wrobel, A., 1990. "The Closedness Of The Free-Disposal Hull Of A Production Set," Papers 9013, Tilburg - Center for Economic Research.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Anthony Horsley & Andrew J Wrobel, 1991. "Price Singularities: Representation vs. Exclusion - (Now published as 'Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time', in Economic Theory, vol. 2," STICERD - Theoretical Economics Paper Series /1991/232, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  9. 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.
  10. 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.
  11. Anthony Horsley & Andrew J Wrobel, 1991. "Marginal Analysis and Bewley Equilibria: The Use of Subgradients," STICERD - Theoretical Economics Paper Series /1991/231, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  12. 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.
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Cited by:
  1. Anthony Horsley & Andrew J. Wrobel, 2000. "Efficiency rents of pumped-storage plants and their uses for operation and investment decisions," LSE Research Online Documents on Economics 19336, London School of Economics and Political Science, LSE Library.
  2. Anthony Horsley & Andrew J. Wrobel, 2005. "Characterizations of long-run producer optima and the short-run approach to long-run market equilibrium: a general theory with applications to peak-load pricing," LSE Research Online Documents on Economics 19307, London School of Economics and Political Science, LSE Library.
  3. 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.
  4. 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.

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