Optimal pollution control in a mixed oligopoly with research spillovers

We study optimal pollution abatement under a mixed oligopoly game when firms engage in emissions-reducing R&D that is imperfectly appropriable. The regulator uses a tax to curb emissions. Results show that in a mixed oligopoly, the public firm has positive emissions reduction in equilibrium; however, emissions reductions of the private firm could be positive or zero. Under certain conditions, the optimal pollution tax is positive; otherwise, the tax reverts to a subsidy. Comparing mixed and private duopolies, privatization leads to reductions in R&D and output, but to an increase in overall emissions, so privatization tends to make the environment worse.