Comparing Cournot Duopoly And Monopoly With Asymmetric Complementary Goods

This paper concerns an industry with two complementary goods. It is demonstrated that if a good is active in Cournot equilibrium, then it is active in either one of the socially optimal solution and the monopoly solution; but, the converse is not true. When demands are linear, a good is active in the monopoly solution if and only if it is socially desirable. Therefore, the monopoly would be socially better than the Cournot duopoly in selecting products. We establish that each Cournot output falls below its corresponding monopoly output regardless of whether the solutions are interior or not. However, in the monopoly solution, a good should be cross-subsidized if and only if it is a supplemental good. This result has two implications. First, a small decrease in the output level of a supplemental good raises the welfare, implying that when there exists a supplement good, lower quantities are not necessarily worse in welfare terms. Second, if each good is a base good, then the Cournot equilibrium indeed is less welfare-efficient than the monopoly solution. In order to verify whether it is possible to have a welfare reversal, we consider the case where demands are linear. We demonstrate that prices are lower in the monopoly solution, and that lower prices are better in the welfare terms. These two results imply that welfare is higher in the monopoly solution. Again, these results hold regardless of whether the solutions are interior or not.