Privatization and efficiency in a differentiated industry

We consider a market in which a public firm competes against private ones, and ask what happens when the public firm is privatized. In the short run, privatization is harmful because prices rise: the disciplinary role of the public firm is lost. In the long run, privatization leads to further entry; the net effect is beneficial if consumer preference for variety is not too weak. A sufficient statistic for the social surplus to be higher in the long run is that the public firm makes a loss, This suggests that profitable firms should not necessarily be privatized