Price and Quantity Competition in a Unionised Mixed Duopoly : The Cases of Substitutes and Complements

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities when unions are present. For the case of a unionised mixed duopoly, there exists a dominant strategy only for the public firm that chooses Bertrand competition irrespective of whether the goods are substitutes or complements; there is no dominant strategy for a private firm. Thus, we show that regardless of the nature of goods, social welfare under Bertrand competition is always determined in equilibrium, wherein Bertrand competition entails higher social welfare than Cournot competition. Moreover, our main results hold irrespective of the nature of goods, with the exception that when a sufficiently large parameter of complements is employed, the ranking of a private firm's profit is not reversed, which is in contrast to the standard findings