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

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  • Anthony Horsley
  • Andrew J Wrobel

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).

Suggested Citation

  • Anthony Horsley & Andrew J Wrobel, 2000. "Efficiency Rents of Pumped-Storage Plants and their Uses for Operation and Investment Decisions," STICERD - Theoretical Economics Paper Series 405, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stitep:405
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    1. Horsley, Anthony & Wrobel, Andrew J., 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.
    2. 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.
    3. repec:cep:stitep:301 is not listed on IDEAS
    4. 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;Society for the Advancement of Economic Theory (SAET), vol. 20(3), pages 503-537.
    5. 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.
    6. 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.
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    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, 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.
    10. 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.
    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.
    12. Horsley, Anthony & Wrobel, Andrew J., 1999. "The density form of equilibrium prices in continuous time and Boiteux's solution to the shifting-peak problem," LSE Research Online Documents on Economics 19344, London School of Economics and Political Science, LSE Library.
    13. Pyatt, Graham, 1978. "Marginal Costs, Prices and Storage," Economic Journal, Royal Economic Society, vol. 88(352), pages 749-762, December.
    14. 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.
    15. 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.
    16. BEWLEY, Truman F., 1972. "Existence of equilibria in economies with infinitely many commodities," LIDAM Reprints CORE 122, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Steffen, Bjarne & Weber, Christoph, 2016. "Optimal operation of pumped-hydro storage plants with continuous time-varying power prices," European Journal of Operational Research, Elsevier, vol. 252(1), pages 308-321.
    2. Durmaz, Tunç, 2016. "Precautionary Storage in Electricity Markets," Discussion Papers 2016/5, Norwegian School of Economics, Department of Business and Management Science.
    3. Carsten Helm & Mathias Mier, 2020. "Steering the Energy Transition in a World of Intermittent Electricity Supply: Optimal Subsidies and Taxes for Renewables Storage," ifo Working Paper Series 330, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    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.
    5. Carsten Helm & Mathias Mier, 2018. "Subsidising Renewables but Taxing Storage? Second-Best Policies with Imperfect Pricing," Working Papers V-413-18, University of Oldenburg, Department of Economics, revised Oct 2018.
    6. 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.
    7. Crampes, Claude & Moreaux, Michel, 2009. "Pumped Storage and Energy Saving," TSE Working Papers 09-073, Toulouse School of Economics (TSE).
    8. Dunguo Mou, 2019. "Pumped storage hydro power’s function in the electricity market under the electricity deregulation background in China – A case study of Fujian province," Energy & Environment, , vol. 30(6), pages 951-968, September.
    9. Dunguo Mou, 2018. "Wind Power Development and Energy Storage under China’s Electricity Market Reform—A Case Study of Fujian Province," Sustainability, MDPI, vol. 10(2), pages 1-20, January.
    10. Helm, Carsten & Mier, Mathias, 2021. "Steering the energy transition in a world of intermittent electricity supply: Optimal subsidies and taxes for renewables and storage," Journal of Environmental Economics and Management, Elsevier, vol. 109(C).
    11. Tsitakis, D. & Xanthopoulos, S. & Yannacopoulos, A.N., 2006. "A closed-form solution for the price of cross-commodity electricity derivatives," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 543-551.
    12. Steffen, Bjarne & Weber, Christoph, 2013. "Efficient storage capacity in power systems with thermal and renewable generation," Energy Economics, Elsevier, vol. 36(C), pages 556-567.
    13. Horsley, Anthony & Wrobel, Andrew J., 2005. "A practical short-run approach to market equilibrium," LSE Research Online Documents on Economics 19313, London School of Economics and Political Science, LSE Library.
    14. Tchai Tavor & Limor Dina Gonen & Uriel Spiegel, 2019. "Optimal Pricing and Capacity Under Well-Defined and Well-Known Deterministic Demand Fluctuations," Review of European Studies, Canadian Center of Science and Education, vol. 11(2), pages 1-15, December.
    15. 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.
    16. Crampes, Claude & Moreaux, Michel, 2010. "Pumped storage and cost saving," Energy Economics, Elsevier, vol. 32(2), pages 325-333, March.
    17. Helm, Carsten & Mier, Mathias, 2019. "Subsidising Renewables but Taxing Storage? Second-Best Policies with Imperfect Carbon Pricing," VfS Annual Conference 2019 (Leipzig): 30 Years after the Fall of the Berlin Wall - Democracy and Market Economy 203539, Verein für Socialpolitik / German Economic Association.
    18. Anthony Horsley & Andrew J Wrobel, 2005. "The Wong-Viner Envelope Theorem for subdifferentiable functions," STICERD - Theoretical Economics Paper Series 489, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    19. 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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    More about this item

    Keywords

    Pumped storage; peak-load pricing; marginal values; linear programming;
    All these keywords.

    JEL classification:

    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities
    • D46 - Microeconomics - - Market Structure, Pricing, and Design - - - Value Theory
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • L95 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Gas Utilities; Pipelines; Water Utilities
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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