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Numerical Calculation of an Asymmetric Supply Function Equilibrium with Capacity Constraints

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  • Holmberg, Pär

    ()
    (Department of Economics)

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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Bibliographic 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
Phone: + 46 18 471 25 00
Fax: + 46 18 471 14 78
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Web page: http://www.nek.uu.se/
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Keywords: Supply function equilibrium; uniform-price auction; numerical integration; oligopoly; asymmetry; capacity constraint; wholesale electricity market;

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References

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  1. Holmberg, Pär, 2004. "Unique Supply Function Equilibrium with Capacity Constraints," Working Paper Series 2004:20, Uppsala University, Department of Economics.
  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.
  3. Green, Richard & Newbery, David M G, 1991. "Competition in the British Electricity Spot Market," CEPR Discussion Papers 557, C.E.P.R. Discussion Papers.
  4. Holmberg, Pär, 2005. "Asymmetric Supply Function Equilibrium with Constant Marginal Costs," Working Paper Series 2005:16, Uppsala University, Department of Economics.
  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.
  6. Klemperer, Paul D & Meyer, Margaret A, 1989. "Supply Function Equilibria in Oligopoly under Uncertainty," Econometrica, Econometric Society, vol. 57(6), pages 1243-77, November.
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Citations

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Cited by:
  1. Holmberg, Pär & Newbery, David & Ralph, Daniel, 2009. "Supply Function Equilibria: Step Functions and Continuous Representations," Working Paper Series 788, Research Institute of Industrial Economics.
  2. 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.
  3. Talat S. Genc & Stanley S. Reynolds, 2010. "Supply Function Equilibria with Capacity Constraints and Pivotal Suppliers," Working Papers 1007, University of Guelph, Department of Economics and Finance.
  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. Jie Chen, 2006. "The Dynamics of Housing Allowance Claims in Sweden: A Discrete Time-Hazard Analysis," European Journal of Housing Policy, Taylor and Francis Journals, vol. 6(1), pages 1-29, April.
  6. Holmberg, Par, 2008. "Unique supply function equilibrium with capacity constraints," Energy Economics, Elsevier, vol. 30(1), pages 148-172, January.
  7. Ollikka, Kimmo & Tukiainen , Janne, 2013. "Central bank liquidity auction mechanism design and the interbank market," Research Discussion Papers 21/2013, Bank of Finland.
  8. 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.
  9. Holmberg, Pär, 2005. "Comparing Supply Function Equilibria of Pay-as-Bid and Uniform-Price Auctions," Working Paper Series 2005:17, Uppsala University, Department of Economics.
  10. 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.
  11. 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.
  12. Newbery, D, 2008. "Analytic Solutions for Supply Function Equilibria: Uniqueness and Stability," Cambridge Working Papers in Economics 0848, Faculty of Economics, University of Cambridge.
  13. Hallberg, Daniel, 2006. "Cross-national differences in income poverty among Europe´s 50+," Working Paper Series 2006:14, Uppsala University, Department of Economics.

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