Ranking Supply Function and Cournot Equilibria in a Differentiated Product Duopoly with Demand Uncertainty

In this paper, we provide a welfare ranking for the equilibria of the supply function and quantity competitions in a differentiated product duopoly with demand uncertainty. We prove that the expected consumer surplus is always higher under the supply function competition. By numerical simulations, we also show that if the degree of product substitution is extremely low, then the supply function competition can become a superior form of competition for the duopolistic producers, as well. However, if the degree of product substitution is not extremely low, then the expected producer profits under the supply function competition can be lower than under the quantity competition in situations where the size of the demand uncertainty is below a critical level. We find that this critical level is non-decreasing in the degree of product substitution, while non-increasing both in the marginal cost of producing a unit output and in the own-price sensitivity of each inverse demand curve. Our results imply that in electricity markets with differentiated products, the regulators should not intervene to impose the quantity competition in favor of the supply function competition unless the degree of product substitution is sufficiently high and the predicted demand fluctuations are sufficiently small.