Abstract
We consider a supply function equilibrium (SFE) model of interaction in an electricity market. We assume a linear demand function and consider a competitive fringe and several strategic players having capacity limits and affine marginal costs. The choice of SFE over Cournot equilibrium and other models and the choice of affine marginal costs is reviewed in the context of the existing literature. We assume that bid rules allow affine or piecewise affine non-decreasing supply functions by firms and extend results of Green and Rudkevitch concerning the linear SFE solution. An incentive compatibility result is proved. We also find that a piecewise affine SFE can be found easily for the case where there are non-negativity limits on generation. Upper capacity limits, however, pose problems and we propose an ad hoc approach. We apply the analysis to the England and Wales electricity market, considering the 1996 and 1999 divestitures. The piecewise affine SFE solutions generally provide better matches to the empirical data than previous analysis.
Similar content being viewed by others
References
Alba, J., I. Otero-Novas, C. Meseguer, and C. Batlle. 1999. “Competitor Behavior and Optimal Dispatch: Modeling Techniques for Decision-Making.” In The New Power Markets: Corporate Strategies for Risk and Reward, edited by R. Jameson. London: Risk Publications.
Andersson, B., and L. Bergman. 1995. “Market Structure and the Price of Electricity: An Ex Ante Analysis of the Deregulated Swedish Electricity Market.” The Energy Journal 16(2): 97–130.
Baldick, R., R. Grant, and E. Kahn. 2000. “Linear Supply Function Equilibrium: Generalizations, Application, and Limitation.” POWER Working paper, available from www.ucei.berkeley.edu/ucei.
Baldick, R., and W. W. Hogan. 2002. “Capacity Constrained Supply Function Equilibrium Models of Electricity Markets: Stability, Non-decreasing Constraints, and Function Space Iterations.” POWER Working paper, Revised August 2002, available from www.ucei.berkeley.edu/ucei.
Berry, C. A., B. F. Hobbs, W. A. Meroney, R. P. O'Neill, and W. R. Stewart. 1999. “Understanding How Market Power can Arise in Network Competition: A Game Theoretic Approach.” Utilities Policy 8: 139–158.
Bohn, R., A. Klevorick, and C. Stalon. 1999. “Second Report on Market Issues in the California Power Exchange Energy Markets.” Prepared for the Federal Energy Regulatory Commission by the Market Monitoring Committee of the Californai Power Exchange, March.
Borenstein, S., and J. Bushnell. 1999. “An Empirical Analysis of the Potential for Market Power in California's Electricity Industry.” Journal of Industrial Economics 47(3): 285–323.
Borenstein, S., J. Bushnell, and S. Stoft. 2000. “The Competitive Effect of Transmission Capacity in a Deregulated Electricity Market.” RAND Journal of Economics, 31: 294–325.
Bunn, D., and C. Day. 1999. “Market Structure is Fundamental.” Strategic Price Risk in Wholesale Power Markets. London: Risk Books.
Bushnell, J. 2003. “A Mixed Complementarity Model of Hydro-Thermal Electricity Competition in the Western U.S.” Operations Research 51(1): 80–93.
Day, C. J., and Bunn, D. W. 2000. “Divestiture of Generation Assets in the Electricity Pool of England and Wales: A Computational Approach to Analyzing Market Power.” Journal of Regulatory Economics 19(2): 123–141.
von der Fehr, N.-H. M., and D. Harbord. 1993. “Spot Market Competition in the U.K. Electricity Industry.” The Economic Journal 103(418)(May): 531–546.
Frame, R., and P. Joskow. 1998. Testimony in State of New Jersey Board of Public Utilities Docket No. EX94120585Y and EO97070463.
Green, R. 1996. “Increasing Competition in the British Electricity Spot Market.” Journal of Industrial Economics 44(2): 205–216.
Green, R., and D. Newbery. 1992. “Competition in the British Electricity Spot Market.” Journal of Political Economy 100(5): 929–953.
Green, R., and D. M. Newbery. 1997. “Competition in the Electricity Industry in England and Wales.” Oxford Review of Economic Policy 13: 27–46.
Hogan, W. 1997. “A Market Power Model With Strategic Interaction in Electricity Networks.” The Energy Journal 18(4): 107–142.
Klemperer, P., and M. Meyer. 1989. “Supply Function Equilibria in Oligopoly Under Uncertainty.” Econometrica 57: 1243–1277.
Laussel, D. 1992. “Strategic Commercial Policy Revisited: A Supply-Function Equilibrium Model.” American Economic Review 82(1): 84–99.
National Grid Company (NGC). Seven Year Statement, 1999.
Newbery, D. 1995. “Power Markets and Market Power.” The Energy Journal 16(3): 36–66.
Newbery, D. 1999. Privatization, Restructuring, and Regulation of Network Utilities. MIT Press.
Office of Electricity Regulation (OFFER), Report on Pool Prices Increases in Winter 1997/98, June, 1998.
Office of Electricity Regulation (OFFER), Rises in Pool Prices in July: A Decision Document, October, 1999.
Ramos, A., M. Ventosa, and M. Rivier. 1998. “Modeling Competition in Electric Energy Markets by Equilibrium Constraints.” Utilities Policy 7(4): 223–242.
Rivier, M., M. Ventosa, A. Ramos, E Martinez-Corcoles, and A. Chiarri. 1999. “A Generation Operation Planning Model in Deregulated Electricity Markets based on the Complementarity Problem.” Proceedings of the International Conference on Complementarity Problems, Madison, Wisconsin.
Rothkopf, M. 1999. “Daily Repetition: A Neglected Factor in the Analysis of Electricity Auctions.” The Electricity Journal 11: 60–70.
Rudkevich, A. 1999. “Supply Function Equilibrium in Power Markets: Learning all the Way.” TCA Technical Report Number 1299-1702, Tabors Caramanis and Associates, December.
Rudkevich, A., M. Duckworth, and R. Rosen. 1998. “Modeling Electricity Pricing in a Deregulated Generation Industry: The Potential for Oligopoly Pricing in a Poolco.” The Energy Journal 19(3): 19–48.
Scott, T. 1997. “Hydro Reservoir Management for an Electricity Market with Long Term Contracts.” Ph.D. thesis, University of Canterbury, Department of Management.
Scott, T., and G. Read. 1996. “Modeling Hydro Reservoir Operation in a Deregulated Electricity Market.” International Transactions in Operations Research 3(3): 243–253.
Turnbull, S. J. 1983. “Choosing Duopoly Solutions by Consistent Conjectures and by Uncertainty.” Economics Letters 13: 253–258.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Baldick, R., Grant, R. & Kahn, E. Theory and Application of Linear Supply Function Equilibrium in Electricity Markets. Journal of Regulatory Economics 25, 143–167 (2004). https://doi.org/10.1023/B:REGE.0000012287.80449.97
Issue Date:
DOI: https://doi.org/10.1023/B:REGE.0000012287.80449.97