We consider a Stackelberg mixed market in which a state-owned welfare-maximizing (domestic) public firm competes against a profit-maximizing (foreign) private firm. We suppose that the domestic firm is less efficient than the foreign private firm. However, the domestic firm can lower its marginal costs by conducting cost-reducing R&D investment. We examine the impacts of privatization on decisions upon cost-reducing R&D investment by the domestic firm and how these affect the domestic welfare. We show that privatization lowers productive efficiency of the domestic firm, regardless of whether the domestic firm is leader or follower. Furthermore, we also show that privatization of the domestic public firm deteriorates the domestic social welfare, regardless of whether the domestic firm is leader or follower.