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Supply Function Equilibrium in Electricity Spot Markets with Contracts and Price Caps

Author

Listed:
  • E. J. Anderson

    (University of New South Wales)

  • H. Xu

    (University of Southampton)

Abstract

In electricity wholesale markets, generators often sign long term contracts with purchasers of power in order to hedge risks. In this paper, we consider a market where demand is uncertain, but can be represented as a function of price together with a random shock. Each generator offers a smooth supply function into the market and wishes to maximize his expected profit, allowing for his contract position. We investigate supply function equilibria in this setting, using a model introduced by Anderson and Philpott. We study first the existence of a unique monotonically increasing supply curve that maximizes the objective function under the constraint of limited generation capacity and a price cap, and discuss the influence of the generator’s contract on the optimal supply curve. We then investigate the existence of a symmetric Nash supply function equilibrium, where we do not have to assume that the demand is a concave function of price. Finally, we identify the Nash supply function equilibrium which gives rise to the generators’ maximal expected profit.

Suggested Citation

  • E. J. Anderson & H. Xu, 2005. "Supply Function Equilibrium in Electricity Spot Markets with Contracts and Price Caps," Journal of Optimization Theory and Applications, Springer, vol. 124(2), pages 257-283, February.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:2:d:10.1007_s10957-004-0924-2
    DOI: 10.1007/s10957-004-0924-2
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    References listed on IDEAS

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    1. Von Der Fehr, N.H.M. & Harbord, D., 1992. "Long-Tern Contracts and Imperfectly Competitive Spot Markets : A Study of U.K. Electricity Industry," Memorandum 1992_014, Oslo University, Department of Economics.
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    Cited by:

    1. 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.
    2. Denis Claude & Mabel Tidball, 2022. "Taking firms’ margin targets seriously in a model of competition in supply functions," Working Papers hal-03548797, HAL.
    3. Razeghi, Ghazal & Brouwer, Jack & Samuelsen, Scott, 2016. "A spatially and temporally resolved model of the electricity grid – Economic vs environmental dispatch," Applied Energy, Elsevier, vol. 178(C), pages 540-556.
    4. Brown, David P. & Eckert, Andrew, 2021. "Analyzing firm behavior in restructured electricity markets: Empirical challenges with a residual demand analysis," International Journal of Industrial Organization, Elsevier, vol. 74(C).
    5. Anderson, Edward J. & Hu, Xinmin, 2008. "Forward contracts and market power in an electricity market," International Journal of Industrial Organization, Elsevier, vol. 26(3), pages 679-694, May.
    6. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
    7. Holmberg, Pär & Willems, Bert, 2015. "Relaxing competition through speculation: Committing to a negative supply slope," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 236-266.
    8. Javad Khazaei & Golbon Zakeri & Shmuel S. Oren, 2017. "Single and Multisettlement Approaches to Market Clearing Under Demand Uncertainty," Operations Research, INFORMS, vol. 65(5), pages 1147-1164, October.
    9. Haikel Khalfallah & Vincent Rious, 2013. "A game theoretical analysis of the design options of the real-time electricity market," Post-Print halshs-00816355, HAL.
    10. Robert Wilson, 2008. "Supply Function Equilibrium in a Constrained Transmission System," Operations Research, INFORMS, vol. 56(2), pages 369-382, April.
    11. Joseph Mullins & Liam Wagner & John Foster, 2010. "Price Spikes in Electricity Markets: A Strategic Perspective," Energy Economics and Management Group Working Papers 05, School of Economics, University of Queensland, Australia.
    12. T. S. Genc, 2009. "Discriminatory Versus Uniform-Price Electricity Auctions with Supply Function Equilibrium," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 9-31, January.
    13. Safarzynska, Karolina & van den Bergh, Jeroen C.J.M., 2011. "Industry evolution, rational agents and the transition to sustainable electricity production," Energy Policy, Elsevier, vol. 39(10), pages 6440-6452, October.
    14. Par Holmberg, 2011. "Strategic Forward Contracting in the Wholesale Electricity Market," The Energy Journal, , vol. 32(1), pages 169-202, January.
    15. Edward J. Anderson & Xinmin Hu, 2012. "Asymmetric Supply Function Equilibria with Forward Contracts," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 198-224, January.
    16. Dali Zhang & Huifu Xu & Yue Wu, 2010. "A two stage stochastic equilibrium model for electricity markets with two way contracts," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 1-45, February.

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