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Continuity of the equilibrium price density and its uses in peak-load pricing

  • Anthony Horsley


  • Andrew Wrobel

With $L^{\infty}$ 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. It includes, but is not limited to, the case of symmetric (rearrangement-invariant) production costs and additively separable consumer utility. Examples arise in continuous-time utility pricing, e.g., electricity pricing. In this context, a continuously varying price has two uses. First, it precludes demand jumps that would arise from discontinuous switches from one price rate to another. Second, in the problems of operating and valuing 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. Copyright Springer-Verlag Berlin/Heidelberg 2005

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Article provided by Springer in its journal Economic Theory.

Volume (Year): 26 (2005)
Issue (Month): 4 (November)
Pages: 839-866

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Handle: RePEc:spr:joecth:v:26:y:2005:i:4:p:839-866
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  1. 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.
  2. Jones, Larry E, 1984. "A Competitive Model of Commodity Differentiation," Econometrica, Econometric Society, vol. 52(2), pages 507-30, March.
  3. 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.
  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, vol. 20(3), pages 503-537.
  5. Anthony Horsley & Andrew J Wrobel, 1996. "Uninterruptible Consumption, Concentrated Charges, and Equilibrium in the Commodity Space of Continuous Functions," STICERD - Theoretical Economics Paper Series 300, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  6. repec:cep:stitep:/1996/300 is not listed on IDEAS
  7. repec:cep:stitep:/1996/301 is not listed on IDEAS
  8. 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.
  9. 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.
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