Bertrand-Edgeworth duopoly with a socially concerned firm

The government may regulate a market by obtaining partial ownership in a firm. This type of socially concerned firm behaves as a combined profit and social surplus maximizer. We investigate the presence of a socially concerned firm in the framework of a Bertrand-Edgeworth duopoly with capacity constraints. In particular, we determine the mixed-strategy equilibrium of this game and relate it to both the standard and the mixed versions of the Bertrand-Edgeworth game. In contrast to other results in the literature we find that full privatization is the socially best outcome, that is the optimal level of public ownership is equal to zero.