Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability
Supply Function Equilibria (SFE) offer an attractive equilibrium concept for an electricity Pool in which all suppliers receive the market clearing price and are an important tool for examining market power. It is helpful to have analytical solutions available for simple models to explore market behaviour and to check computational solutions. This note derives analytic solutions for the symmetric case of linear and quadratic costs, and where each firm has an identical set of constant but different marginal cost technologies, as in most practical applications to data. Such stepped marginal cost schedules can replicate general marginal cost schedules to any desired degree of accuracy and hence symmetric SFEs can be solved analytically by piecing together recursively defined supply functions for general cost functions. The paper discusses the question of the uniqueness and stability of these symmetric solutions, but notes that finding asymmetric analytic solutions is generally difficult. It collects together and extends results scattered in earlier working papers to make them more accessible.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Holmberg, Pär, 2009.
"Numerical calculation of an asymmetric supply function equilibrium with capacity constraints,"
European Journal of Operational Research,
Elsevier, vol. 199(1), pages 285-295, November.
- Holmberg, Pär, 2005. "Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2005:12, Uppsala University, Department of Economics.
- 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.
- 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 929-53, October.
- Green, Richard & Newbery, David M G, 1991. "Competition in the British Electricity Spot Market," CEPR Discussion Papers 557, C.E.P.R. Discussion Papers.
- Natalia Fabra & Nils-Henrik von der Fehr & David Harbord, 2002.
"Designing Electricity Auctions,"
0211017, EconWPA, revised 31 Aug 2003.
- 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, 03.
- Holmberg, Pär, 2004.
"Unique Supply Function Equilibrium with Capacity Constraints,"
Working Paper Series
2004:20, Uppsala University, Department of Economics.
- Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
When requesting a correction, please mention this item's handle: RePEc:cam:camdae:0848. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Howard Cobb)
If references are entirely missing, you can add them using this form.