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Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints

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Author Info
Holmberg, Pär () (Department of Economics)

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Abstract

Producers submit committed supply functions to a procurement auction, e.g. an electricity auction, before the uncertain demand has been realized. In the Supply Function Equilibrium(SFE), every firm chooses the bid maximizing his expected profit given the bids of the competitors. In case of asymmetric producers with general cost functions, previous work has shown that it is very difficult to find valid SFE. This paper presents a new numerical procedure that can solve the problem. It comprises numerical integration and an optimization algorithm that searches an end-condition. The procedure is illustrated by an example with three asymmetric firms.

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Publisher Info
Paper provided by Uppsala University, Department of Economics in its series Working Paper Series with number 2005:12.

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Length: 18 pages
Date of creation: 29 Mar 2005
Date of revision:
Handle: RePEc:hhs:uunewp:2005_012

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Postal: Department of Economics, Uppsala University, P. O. Box 513, SE-751 20 Uppsala, Sweden
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Fax: + 46 18 471 14 78
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Related research
Keywords: Supply function equilibrium; uniform-price auction; numerical integration; oligopoly; asymmetry; capacity constraint; wholesale electricity market;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
D44 - Microeconomics - - Market Structure and Pricing - - - Auctions
L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
L94 - Industrial Organization - - Industry Studies: Transportation and Utilities - - - Electric Utilities

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References listed on IDEAS
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.:
  1. Holmberg, Pär, 2004. "Unique Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2004:20, Uppsala University, Department of Economics. [Downloadable!]
    Other versions:
  2. von der Fehr, Nils-Henrik Morch & Harbord, David, 1993. "Spot Market Competition in the UK Electricity Industry," Economic Journal, Royal Economic Society, vol. 103(418), pages 531-46, May. [Downloadable!] (restricted)
    Other versions:
  3. Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics. [Downloadable!]
  4. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November. [Downloadable!] (restricted)
  5. Bolle, Friedel, 1992. "Supply function equilibria and the danger of tacit collusion : The case of spot markets for electricity," Energy Economics, Elsevier, vol. 14(2), pages 94-102, April. [Downloadable!] (restricted)
  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)
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Cited by:
(explanations, 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.)

  1. Hallberg, Daniel, 2006. "Cross-national differences in income poverty among Europe´s 50+," Working Paper Series 2006:14, Uppsala University, Department of Economics. [Downloadable!]
  2. Chen, Jie, 2006. "The Dynamics of Housing Allowance Claims in Sweden: A discrete-time hazard analysis," Working Paper Series 2006:1, Uppsala University, Department of Economics. [Downloadable!]
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  3. Berg, Lennart & Berger, Tommy, 2005. "The Q theory and the Swedish housing market –an empirical test," Working Paper Series 2005:19, Uppsala University, Department of Economics. [Downloadable!]
  4. Johansson, Fredrik & Klevmarken, Anders, 2006. "Explaining the size and nature of response in a survey on health status and economic standard," Working Paper Series 2006:2, Uppsala University, Department of Economics. [Downloadable!]
  5. Ramteen Sioshansi & Shmuel Oren, 2007. "How good are supply function equilibrium models: an empirical analysis of the ERCOT balancing market," Journal of Regulatory Economics, Springer, vol. 31(1), pages 1-35, February. [Downloadable!] (restricted)
  6. Engström, Per & Holmlund, Bertil, 2006. "Tax Evasion and Self-Employment in a High-Tax Country: Evidence from Sweden," Working Paper Series 2006:12, Uppsala University, Department of Economics. [Downloadable!]
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  7. Engström, Per & Holmlund, Bertil, 2005. "Worker Absenteeism in Search Equilibrium," Working Paper Series 2005:22, Uppsala University, Department of Economics. [Downloadable!]
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  8. Newbery, D, 2008. "Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability," Cambridge Working Papers in Economics 0848, Faculty of Economics, University of Cambridge. [Downloadable!]
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