Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability
AbstractSupply 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.
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Bibliographic InfoPaper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0848.
Date of creation: Sep 2008
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Supply function equilibria analytic solutions; electricity markets; stability; uniqueness;
Find related papers by JEL classification:
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-11-18 (All new papers)
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- Green, Richard & Newbery, David M G, 1991.
"Competition in the British Electricity Spot Market,"
CEPR Discussion Papers
557, C.E.P.R. Discussion Papers.
- 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.
- Natalia Fabra & Nils‐Henrik Fehr & David Harbord, 2006.
"Designing electricity auctions,"
RAND Journal of Economics,
RAND Corporation, vol. 37(1), pages 23-46, 03.
- 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.
- Holmberg, Pär, 2005.
"Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints,"
Working Paper Series
2005:12, Uppsala University, Department of Economics.
- 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.
- 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, Par, 2008.
"Unique supply function equilibrium with capacity constraints,"
Elsevier, vol. 30(1), pages 148-172, January.
- Holmberg, Pär, 2004. "Unique Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2004:20, Uppsala University, Department of Economics.
- Holmberg, Pär & Newbery, David, 2009.
"The Supply Function Equilibrium and Its Policy Implications for Wholesale Electricity Auctions,"
Working Paper Series
812, Research Institute of Industrial Economics.
- 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.
- Holmberg, P. & Newbery, D., 2010. "The Supply Function Equilibrium and its Policy Implications for Wholesale Electricity Auctions," Cambridge Working Papers in Economics 1016, Faculty of Economics, University of Cambridge.
- Ayzenberg, N. & Kiseleva, N. & Zorkaltsev, V., 2013. "Models of Imperfect Competition in Analysis of Siberian Electricity Market," Journal of the New Economic Association, New Economic Association, vol. 18(2), pages 62-88.
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