This paper revisits De Fraja and Delbono (1989), which is the seminal paper on mixed oligopoly, in order to pay more attention to Stackelberg competition. First, we show that, even in Cournot competition, if the number of private firms is sufficiently small, privatization necessarily reduces social welfare. Second, we demonstrate that when a public firm is a Stackelberg leader before and after privatization, privatization necessarily reduces welfare irrespective of the number of private firms. Moreover, we show that even when a public firm remains a follower, privatization reduces welfare if the number of private firms is relatively small.