In this study, we consider a mixed downstream market wherein a vertically integrated public utility firm competes with a private firm that purchases inputs from an upstream firm under output subsidies. We construct an endogenous competition mode game and find that not only do pure Cournot and Bertrand competitions appear as equilibria, but a hybrid Bertrand-Cournot competition can also materialize depending on the subsidy rate. However, Cournot competition appears as a unique equilibrium in the private market irrespective of subsidy rate. We demonstrate that privatization, accompanied by subsidization that shifts firms’ coordination from a hybrid Bertrand-Cournot competition to a Cournot competition, could improve welfare.