Mixed duopoly with foreign firm and subcontracting

We consider a Hotelling model, in which a public firm competes with a foreign firm, at the mean time cooperates with it through subcontracting. We find that when there exists subcontracting, the presence of a foreign firm raises social welfare. Comparing to competing with the domestic private firm, when the public firm competes with the foreign firm, social welfare is lower, but consumer welfare is higher. And a variation in firms' costs or tariffs has no effect on either firm's location. Tariff on inputs raises domestic social welfare and government will charge an input tariff to the extent of costs difference. Tariff on final good has no effect on welfare but will raise prices and thus hurt consumers. Compared to no tariff at all, tariff on inputs alone raises retail prices, but tariffs on both inputs and final goods may reduce prices and raise consumer surplus.