Scandinavian Working Papers in Economics

Working Paper Series,
Research Institute of Industrial Economics

No 788: Supply Function Equilibria: Step Functions and Continuous Representations

Pär Holmberg (), David Newbery and Daniel Ralph
Additional contact information
Pär Holmberg: Research Institute of Industrial Economics (IFN), Postal: P.O. Box 55665, SE-102 15 Stockholm, Sweden
David Newbery: Faculty of Economics, Postal: University of Cambridge
Daniel Ralph: Judge Business School, Postal: University of Cambridge

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.

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

JEL-codes: C62; D43; D44; L11; L13; L94

48 pages, January 29, 2009

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