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 rms have capacity constraints. We show that if rms have heterogeneous cost functions and capacity constraints then the dierential equation approach to nding the equilibrium supply function may not be elective by itself because it produces supply functions that fail to be non-decreasing. Even when the dierential 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 dierentiable equilibria. To nd 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 conrm 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 nd that requiring supply functions to remain xed over an extended time horizon having a large variation in demand reduces the incentive to mark up prices compared to the Cournot outcome.