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Continuity of the Equilibrium Price Density and its Uses in Peak-Load Pricing

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  • Anthony Horsley
  • Andrew J Wrobel

Abstract

With L8 as the commodity space, the equilibrium price density is shown to be a continuous function of the commodity characteristics. The result is based on symmetry ideas from the Hardy-Littlewood-Pólya theory of rearrangements; and it includes, but is not limited to, the case of symmetric (rearrangement-invariant) production costs and additively separable consumer utility. For continuous-time peak-load pricing of, e.g., electricity, this allows the inclusion of storage and of cross-price dependent demands. In this context a continuously varying price has two uses. First, it excludes the demand jumps that arise from discontinuous switches from one price rate to another. Second, in the operation and valuation of hydroelectric and pumped-storage plants (studied elsewhere), price continuity guarantees that their capacities (viz., the reservoir and the converter), the energy stocks and, in the case of hydro also the river flows, have well-defined marginal values.

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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 417.

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Date of creation: May 2001
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Handle: RePEc:cep:stitep:417

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

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Keywords: Price density; continuous-time peak-load pricing; pumped storage.;

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References

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  1. 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.
  2. 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.
  3. Richard, Scott F., 1989. "A new approach to production equilibria in vector lattices," Journal of Mathematical Economics, Elsevier, vol. 18(1), pages 41-56, February.
  4. Larry E. Jones, 1982. "A Competitive Model of Commodity Differentiation," Discussion Papers 526, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  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 & Andrew J. Wrobel, 2002. "Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time," Economic Theory, Springer, vol. 20(3), pages 503-537.
  7. 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.
  8. 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.
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Citations

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Cited by:
  1. 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.
  2. 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.
  3. 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.
  4. Anthony Horsley & Andrew J. Wrobel, 2005. "The Wong-Viner envelope theorem for subdifferentiable functions," LSE Research Online Documents on Economics 19309, London School of Economics and Political Science, LSE Library.
  5. 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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