Efficiency inducing taxation for polluting oligopolists

We show that there exists a time-independent tax rule that guides polluting oligopolists to achieve the socially optimum production path. The optimal tax is dependent on the current pollution stock, and it may be negative when the pollution stock is low. A surprising result is that the optimal tax rule may give firms a subsidy for an initial time interval even though under laissez-faire their output always exceeds the socially optimal output. This subsidy, however, induces firms to produce less than they would under laissez-faire.