PWP-089 Capacity Constrained Supply Function Equilibrium Models of Electricity Markets: Stability, Non- decreasing constraints, and Function Space Iterations

In this paper we consider a supply function model of an electricity market where strategic firms have capacity constraints. We show that if firms have heterogeneous cost functions and capacity constraints then the differential equation approach to finding the equilibrium supply function may not be effective by itself because it produces supply functions that fail to be non-decreasing. Even when the differential equation approach yields solutions that satisfy the non-decreasing constraints, many of the equilibria are unstable, restricting the range of the equilibria that are likely to be observed in practice. We analyze the non-decreasing constraints and characterize piece-wise continuously differentiable equilibria. To find stable equilibria, we numerically solve for the equilibrium by iterating in the function space of allowable supply functions. Using a numerical example based on supply in the England and Wales market in 1999, we investigate the potential for multiple equilibria and the interaction of capacity constraints, price caps, and the length of the time horizon over which bids must remain unchanged. We empirically confirm that the range of stable supply function equilibria can be very small when there are binding price caps. Even when price caps are not binding, the range of stable equilibria is relatively small. We find that requiring supply functions to remain fixed over an extended time horizon having a large variation in demand reduces the incentive to mark up prices compared to the Cournot outcome.