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Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability

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Newbery, D

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Abstract

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.

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Paper provided by Faculty of Economics, University of Cambridge in its series Cambridge Working Papers in Economics with number 0848.

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Date of creation: Sep 2008
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Handle: RePEc:cam:camdae:0848

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Related research
Keywords: Supply function equilibria analytic solutions; electricity markets; stability; uniqueness;

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Find related papers by JEL classification:
C62 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - 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

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  1. Natalia Fabra & Nils-Henrik M. von der Fehr & David Harbord, 2006. "Designing Electricity Auctions," RAND Journal of Economics, The RAND Corporation, vol. 37(1), pages 23-46, Spring.
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  2. Holmberg, Pär, 2005. "Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2005:12, Uppsala University, Department of Economics. [Downloadable!]
  3. 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. [Downloadable!]
  4. Par Holmberg, 2007. "Supply Function Equilibrium with Asymmetric Capacities and Constant Marginal Costs," The Energy Journal, International Association for Energy Economics, vol. 28(2), pages 55-82.
  5. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January. [Downloadable!] (restricted)
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  6. 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. [Downloadable!] (restricted)
    Other versions:
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