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Efficiency Rents of Storage Plants in Peak-Load Pricing, I: Pumped Storage

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  • Anthony Horsley
  • Andrew J Wrobel

Abstract

Programming methods are given for rental valuation of storage and conversion facilities in cyclical, continuous-time pricing problems, e.g. pumped storage of electricity. By identifying the points of differentiability of the short-run profit function, unique and separate marginal values can be imputed to the different capital inputs, even though these are perfect complements (which, with multiple outputs, does not entail fixed input proportions). The short-run (profit-maximising) operation problem has a dual that gives the shadow prices of the stored intermediate good. Formulae for the quasi-rents are derived in terms of the shadow prices. In particular, the unit reservoir rent is shown to be equal to the total positive variation of the shadow price over the cycle. This is unique if the (given) market price for the final good is continuous over time. The shadow prices also determine the optimal storage policy. It is also shown, by studying input requirement functions, that continuous-time problems of this kind can be incorporated into a model of general competitive equilibrium with the space of bounded functions as the commodity space.

Suggested Citation

  • 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.
    • Handle: RePEc:cep:stitep:/1996/301
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    Cited by:

    1. Anthony Horsley & Andrew Wrobel, 2005. "Continuity of the equilibrium price density and its uses in peak-load pricing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 839-866, November.
    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. 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. Anthony Horsley & Andrew J Wrobel, 1999. "The Density Form of Equilibrium Prices in Continuous Time and Boiteuxs Solution to the Shifting-Peak Problem- (Now published as Boiteuxs solution to the shifting-peak problem and the equilibrium price," STICERD - Theoretical Economics Paper Series 371, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    5. 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.
    6. 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 490, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Ilak, Perica & Rajšl, Ivan & Krajcar, Slavko & Delimar, Marko, 2015. "The impact of a wind variable generation on the hydro generation water shadow price," Applied Energy, Elsevier, vol. 154(C), pages 197-208.
    8. Perica Ilak & Slavko Krajcar & Ivan Rajšl & Marko Delimar, 2014. "Pricing Energy and Ancillary Services in a Day-Ahead Market for a Price-Taker Hydro Generating Company Using a Risk-Constrained Approach," Energies, MDPI, vol. 7(4), pages 1-26, April.
    9. Perica Ilak & Ivan Rajšl & Josip Đaković & Marko Delimar, 2018. "Duality Based Risk Mitigation Method for Construction of Joint Hydro-Wind Coordination Short-Run Marginal Cost Curves," Energies, MDPI, vol. 11(5), pages 1-12, May.
    10. Andrew J. Wrobel, 2020. "Bounded topologies on Banach spaces and some of their uses in economic theory: a review," Papers 2005.05202, arXiv.org, revised Sep 2020.

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