Supply Function Equilibria: Step Functions and Continuous Representations

IFN Working Paper No. 788

49 Pages Posted: 24 Sep 2010

See all articles by Par Holmberg

Par Holmberg

Research Institute of Industrial Economics (IFN)

David M. G. Newbery

University of Cambridge - Department of Applied Economics; Centre for Economic Policy Research (CEPR); CESifo (Center for Economic Studies and Ifo Institute)

Daniel Ralph

University of Cambridge - Judge Business School

Date Written: December 31, 2008

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

JEL Classification: C62, D43, D44, L11, L13, L94

Suggested Citation

Holmberg, Par and Newbery, David M. G. and Ralph, Daniel, Supply Function Equilibria: Step Functions and Continuous Representations (December 31, 2008). IFN Working Paper No. 788, Available at SSRN: https://ssrn.com/abstract=1681327 or http://dx.doi.org/10.2139/ssrn.1681327

Par Holmberg (Contact Author)

Research Institute of Industrial Economics (IFN) ( email )

Box 55665
Grevgatan 34, 2nd floor
Stockholm, SE-102 15
Sweden

David M. G. Newbery

University of Cambridge - Department of Applied Economics ( email )

Sidgwick Avenue
Cambridge, CB3 9DE
United Kingdom
+44 1223 335 246 (Phone)
+44 1223 335 299 (Fax)

Centre for Economic Policy Research (CEPR)

London
United Kingdom
+44 1223 335 246/7 (Phone)

CESifo (Center for Economic Studies and Ifo Institute)

Poschinger Str. 5
Munich, DE-81679
Germany

Daniel Ralph

University of Cambridge - Judge Business School ( email )

Trumpington Street
Cambridge, CB2 1AG
United Kingdom

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