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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. 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.
    2. Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics.
    3. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-1277, November.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
    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. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    12. 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.
    13. Holmberg, Pär, 2008. "Game-theoretical, Strategic forward Contracting in the Electricity Market," Working Paper Series 756, Research Institute of Industrial Economics.
    14. 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.
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    Cited by:

    1. repec:eee:ecolet:v:166:y:2018:i:c:p:50-55 is not listed on IDEAS
    2. Kamiński, Jacek, 2012. "The development of market power in the Polish power generation sector: A 10-year perspective," Energy Policy, Elsevier, vol. 42(C), pages 136-147.
    3. Hallberg, Daniel, 2006. "Cross-national differences in income poverty among Europe´s 50+," Working Paper Series 2006:14, Uppsala University, Department of Economics.
    4. Holmberg, Pär, 2005. "Comparing Supply Function Equilibria of Pay-as-Bid and Uniform-Price Auctions," Working Paper Series 2005:17, Uppsala University, Department of Economics.
    5. Ollikka, Kimmo & Tukiainen, Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.
    6. Berg, Lennart & Berger, Tommy, 2005. "The Q theory and the Swedish housing market –an empirical test," Working Paper Series 2005:19, Uppsala University, Department of Economics.
    7. Johansson, Fredrik & Klevmarken, Anders, 2006. "Explaining the size and nature of response in a survey on health status and economic standard," Working Paper Series 2006:2, Uppsala University, Department of Economics.
    8. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
    9. Newbery, D, 2008. "Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability," Cambridge Working Papers in Economics 0848, Faculty of Economics, University of Cambridge.
    10. Yasui, Yuta & Haraguchi, Junichi, 2018. "Supply function equilibria and nonprofit-maximizing objectives," Economics Letters, Elsevier, vol. 166(C), pages 50-55.
    11. Per Engstrom & Bertil Holmlund, 2009. "Tax evasion and self-employment in a high-tax country: evidence from Sweden," Applied Economics, Taylor & Francis Journals, vol. 41(19), pages 2419-2430.
    12. Hunt Allcott, 2012. "The Smart Grid, Entry, and Imperfect Competition in Electricity Markets," NBER Working Papers 18071, National Bureau of Economic Research, Inc.
    13. Genc, Talat S. & Reynolds, Stanley S., 2011. "Supply function equilibria with capacity constraints and pivotal suppliers," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 432-442, July.
    14. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    15. Alexander Vasin & Marina Dolmatova & Gerhard-Wilhelm Weber, 2016. "Supply function equilibria for uniform price auction in oligopolistic markets," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(4), pages 819-831, December.
    16. Li, Gong & Shi, Jing & Qu, Xiuli, 2011. "Modeling methods for GenCo bidding strategy optimization in the liberalized electricity spot market–A state-of-the-art review," Energy, Elsevier, vol. 36(8), pages 4686-4700.
    17. Reihani, Ehsan & Motalleb, Mahdi & Thornton, Matsu & Ghorbani, Reza, 2016. "A novel approach using flexible scheduling and aggregation to optimize demand response in the developing interactive grid market architecture," Applied Energy, Elsevier, vol. 183(C), pages 445-455.
    18. Jie Chen, 2006. "The Dynamics of Housing Allowance Claims in Sweden: A Discrete Time-Hazard Analysis," European Journal of Housing Policy, Taylor and Francis Journals, vol. 6(1), pages 1-29, April.
    19. Ramteen Sioshansi & Shmuel Oren, 2007. "How good are supply function equilibrium models: an empirical analysis of the ERCOT balancing market," Journal of Regulatory Economics, Springer, vol. 31(1), pages 1-35, February.
    20. Holmberg, Pär & Newbery, David, 2010. "The supply function equilibrium and its policy implications for wholesale electricity auctions," Utilities Policy, Elsevier, vol. 18(4), pages 209-226, December.
    21. repec:spr:joptap:v:152:y:2012:i:1:d:10.1007_s10957-011-9879-2 is not listed on IDEAS

    More about this item

    Keywords

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

    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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