Abatement technology innovation and pollution tax design: A dynamic analysis in monopoly

In this paper, we devise an alternative environmental policy and design a dynamic environmental tax. The two key features of this approach are: (i) environmental tax is levied on a monopoly firm's emissions intensity (emissions per unit of output) rather than on the firm's total pollution emissions; and (ii) the pollution tax rate is a state variable whose dynamic equation is operationalized with an exponential smoothing process of historical emissions intensity. We compare results from when the monopolist chooses how much effort to expend on developing clean production technology to those when it is chosen by an environmental regulator. Our main results show that: 1) whether under the firm's decision or regulator's adjustment, the saddle-point stability of steady-state equilibrium depends on the discount rate, decay rate of pollutants, and adjustment parameter; 2) the monopolist's output level is higher when the regulator chooses the firm's innovation effort than when the firm does so; 3) when a benevolent regulator chooses the firm's clean technology innovation effort, the level of effort and the resulting level of clean technology are both greater than when the firm makes this choice; 4) the pollution tax and pollution stock are higher under the firm's decision than under the regulator's adjustment.