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Supply Function Equilibrium with Asymmetric Capacities and Constant Marginal Costs


  • Par Holmberg


This paper analytically derives a Supply Function Equilibrium (SFE) of a real-time electricity market with multiple firms and asymmetric production capacities. There is a unique SFE, which is piece-wise symmetric when firms have identical constant marginal costs. It is believed that some of the properties of the derived SFE are valid for real-time markets in general. FirmsÕ capacity constraints bind at different prices (i). Still, firms with non-binding capacity constraints have smooth residual demand (ii). Approximating an asymmetric real-time market with a symmetric one, tends to overestimate mark-ups for small positive imbalances and underestimate mark-ups for large positive imbalances (iii).

Suggested Citation

  • 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.
  • Handle: RePEc:aen:journl:2007v28-02-a03

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    References listed on IDEAS

    1. Kenneth B. Medlock III & Ronald Soligo, 2001. "Economic Development and End-Use Energy Demand," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 77-105.
    2. Rossana Galli, 1998. "The Relationship Between Energy Intensity and Income Levels: Forecasting Long Term Energy Demand in Asian Emerging Countries," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 85-105.
    3. Ruth A. Judson & Richard Schmalensee & Thomas M. Stoker, 1999. "Economic Development and the Structure of the Demand for Commercial Energy," The Energy Journal, International Association for Energy Economics, vol. 0(Number 2), pages 29-57.
    4. Randall Lutter, 2000. "Developing Countries' Greenhouse Emmissions: Uncertainty and Implications for Participation in the Kyoto Protocol," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 93-120.
    5. Rothman, Dale S., 1998. "Environmental Kuznets curves--real progress or passing the buck?: A case for consumption-based approaches," Ecological Economics, Elsevier, vol. 25(2), pages 177-194, May.
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    Cited by:

    1. Albert Banal-Estañol & Augusto Rupérez Micola, 2009. "Composition of Electricity Generation Portfolios, Pivotal Dynamics, and Market Prices," Management Science, INFORMS, vol. 55(11), pages 1813-1831, November.
    2. Albert Banal-Estañol & Augusto Rupérez-Micola, 2010. "Are agent-based simulations robust? The wholesale electricity trading case," Economics Working Papers 1214, Department of Economics and Business, Universitat Pompeu Fabra.
    3. Newbery, D, 2008. "Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability," Cambridge Working Papers in Economics 0848, Faculty of Economics, University of Cambridge.
    4. 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.
    5. 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.
    6. 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.
    7. Hunt Allcott, 2012. "The Smart Grid, Entry, and Imperfect Competition in Electricity Markets," NBER Working Papers 18071, National Bureau of Economic Research, Inc.
    8. Bolle, Friedel & Grimm, Veronika & Ockenfels, Axel & del Pozo, Xavier, 2013. "An experiment on supply function competition," European Economic Review, Elsevier, vol. 63(C), pages 170-185.
    9. Genc, Talat S. & Reynolds, Stanley S., 2011. "Supply function equilibria with capacity constraints and pivotal suppliers," International Journal of Industrial Organization, Elsevier, vol. 29(4), pages 432-442, July.
    10. Knittel, Christopher R & Metaxoglou, Konstantinos, 2008. "Diagnosing Unilateral Market Power in Electricity Reserves Market," Institute of Transportation Studies, Working Paper Series qt14q6c0mk, Institute of Transportation Studies, UC Davis.

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    JEL classification:

    • F0 - International Economics - - General


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