Optimal Subsidies in the Competition Between Private and State-Owned Enterprises

Recent policy discussions have debated whether governments should treat state-owned and private enterprises equally or adopt different policies towards each type of enterprise. Such questions are pertinent for difficult economic climates in which government subsidy towards struggling state-owned enterprises seems natural, given their fundamental state-supported structure. However, should the government in turn also offer subsidies to the private sector, and how large should the subsidy be? We analyze this question in a mixed oligopoly setting, in which the government can award subsidies of different amounts to state-owned and competitive private enterprises, respectively. In a setting in which the state-owned enterprise seeks to maximize a weighted sum of social welfare and their own profits while private enterprises maximize their own profits, we find that the optimal subsidy policy is equal treatment of the different types of firms, regardless how much weight the state-owned enterprise puts on social welfare. The result suggests that equal subsidizing treatment of state-owned and private firms may be the socially efficient policy, regardless of the differences in objectives between the state-owned and private enterprises, as long as all firms share the same production technology. We show that our result is also robust to the functional form of production technology, the functional form of market demand, the composition of different types of firms in the market, and the heterogeneity of the objectives of firms. Finally, we show that heterogeneous cost structures among firms yields non-uniform optimal subsidy among the firms, and solve for the subsidy as a function of each firm's socially optimal production level