Capacity Constrained Supply Function Equilibria: Modeling and Simulations

Abstract

This paper models the restructured wholesale electricity markets as oligopolies facing uncertain demand and “capacity constraints” where each firm chooses as its strategy a “supply function", as introduced by Klemperer and Meyer. To facilitate the computation of optimal strategies, the paper considers piecewise linear bid (or supply) functions, imposing restrictions to allow for just a few knots. It then suggests algorithms to find equilibrium strategies of firms and implements simulations consisting of various combinations of firms. The simulation results show that the firms' equilibrium supply-functions are steeper with fewer firms, with a smaller variance of demand, and with more severe asymmetry between small firms and a large firm. This paper also compares supply function equilibrium with capacity constraints to the Cournot equilibrium assuming storability and Cournot points of every demand realization. The results show that the Lerner index of the supply function equilibrium with capacity constraints is considerably smaller than that of the Cournot equilibrium assuming storability and Cournot points. The Lerner index decreases as the number of firms rises and increases as the asymmetry between firm sizes grows.