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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 density in continuous time, in Economic Theory, vol. 20 (2002), pp.503-537.)

Author

Listed:
  • Anthony Horsley
  • Andrew J Wrobel

Abstract

Bewley's condition on production sets, imposed to ensure the existence of an equilibrium price density when L? 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 function are Mackey continuous. A general form of the 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. General equilibrium results are supplemented by those for prices supporting individual consumer or producer optima. Also, 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.

Suggested Citation

  • 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.
  • Handle: RePEc:cep:stitep:371
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    File URL: http://sticerd.lse.ac.uk/dps/te/te371.pdf
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    References listed on IDEAS

    as
    1. Back, Kerry, 1988. "Structure of consumption sets and existence of equilibria in infinite-dimensional spaces," Journal of Mathematical Economics, Elsevier, vol. 17(1), pages 89-99, February.
    2. repec:cep:stitep:300 is not listed on IDEAS
    3. repec:cep:stitep:/1992/246 is not listed on IDEAS
    4. 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.
    5. Horsley, Anthony & Wrobel, Andrzej J, 1991. "The Closedness of the Free-Disposal Hull of a Production Set," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(4), pages 386-391, October.
    6. Horsley, A. & Wrobel, A.J., 1990. "The Existence of an Equilibrium Density for Marginal Cost Prices, and the Solution to the Shifting-Peak Problem," Discussion Paper 1990-12, Tilburg University, Center for Economic Research.
    7. 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.
    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.
    9. repec:cep:stitep:301 is not listed on IDEAS
    10. 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.
    11. 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.
    12. Gerard Debreu, 1961. "New Concepts and Techniques for Equilibrium Analysis," Cowles Foundation Discussion Papers 129, Cowles Foundation for Research in Economics, Yale University.
    13. 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.
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