Supply function equilibria and nonprofit-maximizing objectives

We examine the supply function equilibrium (SFE) that is often used in the analysis of multi-unit auctions, such as wholesale electricity markets, among (partially privatized) public firms. We show that in a duopoly model with linear demand and quadratic cost functions, both a partially privatized public firm and a profit-maximizing firm offers flatter supply functions as equilibrium strategies, resulting in a larger social surplus, when the public firm focuses more on social welfare. This implies that the full nationalization is optimal if firms compete in SFE, in contrast to a Cournot case, which has been used as an approximation of the wholesale electricity markets. We also confirm that the SFE converges to the (inverse) marginal cost function when the firms' social concern is improved symmetrically in the industry.