Quantity competition vs. price competition under optimal subsidy in a mixed duopoly

This paper reconsiders the literature on the irrelevance of privatization in mixed markets, addressing both quantity and price competition in a duopoly with differentiated products. By allowing for partially privatizing a state-controlled firm, we explore competition under different timings of firms’ moves and derive the conditions under which an optimal subsidy allows to achieve maximum efficiency. We show that, while the ownership of the controlled firm is irrelevant when firms play simultaneously, it matters when firms compete sequentially, requiring the leader to be publicly-owned for an optimal subsidy to restore the first-best allocation, irrespective of the mode of competition. The paper also focuses on the extent to which a subsidy is needed to attain the social optimum, highlighting the equivalence between a price (quantity) game with public leadership or simultaneous moves and a quantity (price) game with private leadership.