Mixed duopoly, privatization and the shadow costs of public funds: exogenous and endogenous timing

The purpose of this article is to investigate how the introduction of the shadow cost of public funds in the utilitarian measure of the economywide welfare affects the behavior of a welfare maximizer public firm in a mixed duopoly. We prove that when firms play simultaneously, the mixed-Nash equilibrium can dominate any Cournot equilibria implemented after a privatization, with or without efficiency gains. This can be true both in terms of welfare and of public firm's profit. When we consider endogenous timing, we show that either mixed- Nash, private leadership or both Stackelberg equilibria can result as subgameperfect Nash equilibria (SPNE). As a consequence, the sustainability of sequential equilibria enlarges the subspace of parameters such that the market performance with an inefficient public firm is better than the one implemented after a full-efficient privatization. Absent efficiency gains, privatization always lowers welfare