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Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability

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  • Newbery, D
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.

Suggested Citation

  • Newbery, D, 2008. "Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability," Cambridge Working Papers in Economics 0848, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0848
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    References listed on IDEAS

    as
    1. Natalia Fabra & Nils‐Henrik Fehr & David Harbord, 2006. "Designing electricity auctions," RAND Journal of Economics, RAND Corporation, vol. 37(1), pages 23-46, March.
    2. Ross Baldick & William Hogan, 2006. "Stability of supply function equilibria implications for daily versus hourly bids in a poolco market," Journal of Regulatory Economics, Springer, vol. 30(2), pages 119-139, August.
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    4. 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 929-953, October.
    5. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2013. "Supply function equilibria: Step functions and continuous representations," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1509-1551.
    6. 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.
    7. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
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    9. 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, March.
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    Cited by:

    1. Newbery, D., 2008. "Predicting market power in wholesale electricity markets," Cambridge Working Papers in Economics 0837, Faculty of Economics, University of Cambridge.
    2. Par Holmberg, 2011. "Strategic Forward Contracting in the Wholesale Electricity Market," The Energy Journal, , vol. 32(1), pages 169-202, January.
    3. 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.
    4. 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.
    5. Pär Holmberg, 2011. "Strategic Forward Contracting in the Wholesale Electricity Market," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1), pages 169-202.
    6. Alexander Vasin & Marina Dolmatova & Gerhard-Wilhelm Weber, 2016. "Supply function equilibria for uniform price auction in oligopolistic markets," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(4), pages 819-831, December.

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    More about this item

    Keywords

    Supply function equilibria analytic solutions; electricity markets; stability; uniqueness;
    All these keywords.

    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, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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