We analyse a mixed duopoly in which wages and salaries are determined by Nash bargaining and where the public firm's unit costs depend on its objectives. Because of constant returns to scale, welfare maximisation without restriction would eliminate or significantly weaken the private firm. Therefore, we focus on constrained welfare maximisation, in which case unit costs are normally higher in the public firm. On the other hand, the private firm may even earn more than in a monopoly if the public firm maximises profits or if the constraint offers too much protection.
Willner, J. (1999). Policy objectives and performance in a mixed market with bargaining. International Journal of Industrial Organization, 17(1), 137–145. https://doi.org/10.1016/s0167-7187(97)00036-2