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

A. Horsley, A.J. Wrobel

    Research output: Contribution to journalArticleScientificpeer-review

    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 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.
    Original languageEnglish
    Pages (from-to)503-537
    Number of pages34
    JournalEconomic Theory
    Volume20
    Issue number3
    DOIs
    Publication statusPublished - 2002

    Fingerprint

    Equilibrium price
    Continuous time
    General equilibrium
    Utility function
    Continuity
    Commodities
    Production function
    Charge
    Peak-load pricing

    Keywords

    • price density
    • continuous-time peak-load pricing

    Cite this

    @article{0f4de12158894a08b191ce4d1b358518,
    title = "Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time",
    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 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.",
    keywords = "price density, continuous-time peak-load pricing",
    author = "A. Horsley and A.J. Wrobel",
    note = "DP 9012 Pagination: 34",
    year = "2002",
    doi = "10.1007/s001990100226",
    language = "English",
    volume = "20",
    pages = "503--537",
    journal = "Economic Theory",
    issn = "0938-2259",
    publisher = "Springer New York",
    number = "3",

    }

    Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time. / Horsley, A.; Wrobel, A.J.

    In: Economic Theory, Vol. 20, No. 3, 2002, p. 503-537.

    Research output: Contribution to journalArticleScientificpeer-review

    TY - JOUR

    T1 - Boiteux's solution to the shifting-peak problem and the equilibrium price density in continuous time

    AU - Horsley, A.

    AU - Wrobel, A.J.

    N1 - DP 9012 Pagination: 34

    PY - 2002

    Y1 - 2002

    N2 - 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 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.

    AB - 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 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.

    KW - price density

    KW - continuous-time peak-load pricing

    U2 - 10.1007/s001990100226

    DO - 10.1007/s001990100226

    M3 - Article

    VL - 20

    SP - 503

    EP - 537

    JO - Economic Theory

    JF - Economic Theory

    SN - 0938-2259

    IS - 3

    ER -