Cournot-Bertrand competition in a unionized mixed duopoly

We investigate a differentiated mixed duopoly in which private and public firms can choose to strategically set prices or quantities by facing a union bargaining process. For the case of a unionized mixed duopoly, only public firm is able to choose a type of contract based on the degree of substitutability in the equilibrium. Focusing on the case of substitute goods, we show that Bertrand (respectively, Cournot) competition entails higher social welfare than Cournot (respectively, Bertrand) competition if the degree of substitutability is relatively small (respectively, large). Thus, there are multiple Nash equilibria in the contract stage of the game. As a result, Singh and Vives' ranking of social welfare is reversed in a range of substitution values for which it is a dominant strategy for public firm to choose either quantity or price contracts.