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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. Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics.
    3. Edward J. Anderson & Xinmin Hu, 2008. "Finding Supply Function Equilibria with Asymmetric Firms," Operations Research, INFORMS, vol. 56(3), pages 697-711, June.
    4. Day, Christopher J & Bunn, Derek W, 2001. "Divestiture of Generation Assets in the Electricity Pool of England and Wales: A Computational Approach to Analyzing Market Power," Journal of Regulatory Economics, Springer, vol. 19(2), pages 123-141, March.
    5. Severin Borenstein & James Bushnell & Christopher R. Knittel, 1999. "Market Power in Electricity Markets: Beyond Concentration Measures," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 65-88.
    6. 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.
    7. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
    8. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    9. Green, Richard J, 1996. "Increasing Competition in the British Electricity Spot Market," Journal of Industrial Economics, Wiley Blackwell, vol. 44(2), pages 205-216, June.
    10. Par Holmberg, 2007. "Supply Function Equilibrium with Asymmetric Capacities and Constant Marginal Costs," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 55-82.
    11. Newbery, D.M., 1991. "Capacity-Constrained Supply Function Equilibria: Competition and Entry in the Electricity Spot Market and Competition and Regulation in English Electricity Industry," Cambridge Working Papers in Economics 9208, Faculty of Economics, University of Cambridge.
    12. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    13. Bolle, Friedel, 1992. "Supply function equilibria and the danger of tacit collusion : The case of spot markets for electricity," Energy Economics, Elsevier, vol. 14(2), pages 94-102, April.
    14. Ross Baldick & Ryan Grant & Edward Kahn, 2004. "Theory and Application of Linear Supply Function Equilibrium in Electricity Markets," Journal of Regulatory Economics, Springer, vol. 25(2), pages 143-167, March.
    15. 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.
    16. Aleksandr Rudkevich & Max Duckworth & Richard Rosen, 1998. "Modeling Electricity Pricing in a Deregulated Generation Industry: The Potential for Oligopoly Pricing in a Poolco," The Energy Journal, International Association for Energy Economics, vol. 0(Number 3), pages 19-48.
    17. Holmberg, Pär, 2008. "Game-theoretical, Strategic forward Contracting in the Electricity Market," Working Paper Series 756, Research Institute of Industrial Economics.
    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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