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Supply Function Equilibria: Step Functions and Continuous Representations

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Author Info
Holmberg, Pär () (Research Institute of Industrial Economics (IFN))
Newbery, David (Faculty of Economics)
Ralph, Daniel (Judge Business School)

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Abstract

In most wholesale electricity markets generators must submit step-function offers of supply to a uniform price auction, and the market is cleared at the price of the most expensive offer needed to meet realised demand. Such markets can most elegantly be modelled as the pure-strategy, Nash Equilibrium of continuous supply functions, in which each supplier has a unique profit maximising choice of supply function given the choices of other suppliers. Critics argue that the discreteness and discontinuity of the required steps can rule out pure-strategy equilibria and may result in price instability. This paper argues that if prices must be selected from a finite set the resulting step function converges to the continuous supply function as the number of steps increases, reconciling the apparently very disparate approaches to modelling electricity markets.

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Publisher Info
Paper provided by Research Institute of Industrial Economics in its series Working Paper Series with number 788.

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Length: 48 pages
Date of creation: 29 Jan 2009
Date of revision:
Handle: RePEc:hhs:iuiwop:0788

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Related research
Keywords: Auctions; Supply Function Equilibria; Convergence of Step-Functions; Electricity Markets;

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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
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.:
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    Other versions:
  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. 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)
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  9. David M. Newbery, 1998. "Competition, Contracts, and Entry in the Electricity Spot Market," RAND Journal of Economics, The RAND Corporation, vol. 29(4), pages 726-749, Winter. [Downloadable!] (restricted)
    Other versions:
  10. Wilson, Robert, 1979. "Auctions of Shares," The Quarterly Journal of Economics, MIT Press, vol. 93(4), pages 675-89, November. [Downloadable!] (restricted)
  11. 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)
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    Other versions:
  13. Ilan Kremer & Kjell G. Nyborg, 2004. "Divisible-Good Auctions: The Role of Allocation Rules," RAND Journal of Economics, The RAND Corporation, vol. 35(1), pages 147-159, Spring.
  14. Frank A. Wolak, 2001. "Identification and Estimation of Cost Functions Using Observed Bid Data: An Application to Electricity Markets," NBER Working Papers 8191, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  15. Green, Richard J, 1996. "Increasing Competition in the British Electricity Spot Market," Journal of Industrial Economics, Blackwell Publishing, vol. 44(2), pages 205-16, June. [Downloadable!] (restricted)
  16. Ali Hortaçsu & Steven L. Puller, 2008. "Understanding strategic bidding in multi-unit auctions: a case study of the Texas electricity spot market," RAND Journal of Economics, RAND Corporation, vol. 39(1), pages 86-114. [Downloadable!] (restricted)
  17. Andrew Sweeting, 2007. "Market Power In The England And Wales Wholesale Electricity Market 1995-2000," Economic Journal, Royal Economic Society, vol. 117(520), pages 654-685, 04. [Downloadable!] (restricted)
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