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Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints

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  • Holmberg, Pär

    (Department of Economics)

Abstract

Producers submit committed supply functions to a procurement auction, e.g. an electricity auction, before the uncertain demand has been realized. In the Supply Function Equilibrium(SFE), every firm chooses the bid maximizing his expected profit given the bids of the competitors. In case of asymmetric producers with general cost functions, previous work has shown that it is very difficult to find valid SFE. This paper presents a new numerical procedure that can solve the problem. It comprises numerical integration and an optimization algorithm that searches an end-condition. The procedure is illustrated by an example with three asymmetric firms.

Suggested Citation

  • Holmberg, Pär, 2005. "Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2005:12, Uppsala University, Department of Economics.
  • Handle: RePEc:hhs:uunewp:2005_012
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    References listed on IDEAS

    as
    1. E. J. Anderson & A. B. Philpott, 2002. "Using Supply Functions for Offering Generation into an Electricity Market," Operations Research, INFORMS, vol. 50(3), pages 477-489, June.
    2. Edward J. Anderson & Xinmin Hu, 2008. "Finding Supply Function Equilibria with Asymmetric Firms," Operations Research, INFORMS, vol. 56(3), pages 697-711, June.
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    10. von der Fehr, Nils-Henrik Morch & Harbord, David, 1993. "Spot Market Competition in the UK Electricity Industry," Economic Journal, Royal Economic Society, vol. 103(418), pages 531-546, May.
    11. Holmberg, Pär, 2008. "Game-theoretical, Strategic forward Contracting in the Electricity Market," Working Paper Series 756, Research Institute of Industrial Economics.
    12. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
    13. Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics.
    14. Green, Richard J & Newbery, David M, 1992. "Competition in the British Electricity Spot Market," Journal of Political Economy, University of Chicago Press, vol. 100(5), pages 929-953, October.
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    16. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Supply function equilibrium; uniform-price auction; numerical integration; oligopoly; asymmetry; capacity constraint; wholesale electricity market;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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