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Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

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  • Anthony Horsley

    ()
    (Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

  • Andrew J. Wrobel

    ()
    (Department of Economics, London School of Economics, Houghton Street, London WC2A 2AE, UK)

Abstract

Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when $L^{\infty}$ is the commodity space, is weakened to allow applications to continuous-time problems, and especially to peak-load pricing when the users' utility and production functions are Mackey continuous. A general form for production sets with the required property is identified, and examples are given of technologies which meet the weakened but not the original condition: these include industrial use and storage of cyclically priced goods. This gives a framework for settling Boiteux's conjecture on the shifting-peak problem. To make clear the restriction implicit in Mackey continuity, we interpret it as interruptibility of demand; and we point out that, without this assumption, the equilibrium can feature pointed peaks with singular, instantaneous capacity charges. The general equilibrium results are supplemented by results for prices supporting individual consumer or producer optima.

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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 20 (2002)
Issue (Month): 3 ()
Pages: 503-537

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Handle: RePEc:spr:joecth:v:20:y:2002:i:3:p:503-537

Note: Received: February 16, 2000; revised version: July 7, 2001
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Related research

Keywords: Price density; Continuous-time peak-load pricing.;

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Cited by:
  1. Anthony Horsley & Andrew J. Wrobel, 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.
  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. 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, Elsevier, vol. 31(3), pages 938-970, March.
  4. Anthony Horsley & Andrew Wrobel, 2005. "Continuity of the equilibrium price density and its uses in peak-load pricing," Economic Theory, Springer, Springer, vol. 26(4), pages 839-866, November.

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