Vertically integrated firms' investments in electricity generating capacities

We compare investments in generating capacities of an integrated monopolist with the aggregate investments of two vertically integrated competing firms. The firms invest in their capacity and fix the retail price while electricity demand is uncertain. The wholesale price is determined in a unit price auction where the firms know the level of demand when they bid their capacities. Total capacities can be larger or smaller with a duopoly than with a monopoly. If the two firms select the Pareto dominant equilibrium, then the retail price is always higher and the social welfare lower in the duopoly case.