Comparing Welfare and Profit in Quantity and Price Competition within Stackelberg Mixed Duopolies

We compare welfare and profits under price and quantity competition in mixed duopolies, wherein a state-owned public firm competes against a private firm. It has been shown that price competition yields larger profit for the private firm and greater welfare if the two firms move simultaneously, regardless of whether the private firm is domestic or foreign. We investigate welfare and profit rankings under Stackelberg competition. Under public leadership, the profit and welfare rankings have common features with the simultaneous-move game, regardless of the nationality of private firms. By contrast, under private leadership, the result depends on the nationality of the private firm. When the private firm is domestic, welfare is greater under quantity competition, while the result is reversed when the private firm is foreign. However, regardless of nationality, private firms earn more under price competition. Introducing the nonnegative profit constraint in the public firm improves welfare and increases the private firm's profit, and price competition yields a higher profit for private firms regardless of nationality and which firm is the leader. However, this constraint affects the welfare ranking. Under private leadership, quantity competition yields greater welfare regardless of the nationality of the private firm. These results indicate that profit ranking is fairly robust to the time structure in mixed Stackelberg duopolies, but welfare ranking is not.