The dynamic structure of optimal tax under environmental pollution

In this paper, we present a nonrenewable resource model including environmental pollution stock as a state variable to analyze the dynamic structure of an optimal tax. Based on the optimality conditions of our model, we showed that the optimal time path of the shadow cost of environmental pollution stock is the same as that of the costate variable of environmental pollution stock. We derived this statement by applying the Continuous Dependence on Initial Conditions Theorem (Coddington, E.A. & N. Levinston 1984, pp. 22-27) to the optimal control problem. Thus, this result provides a theoretical basis to determine the magnitude of optimal tax to be imposed over time. In addition, we observed the characteristics of two costate variables included in our model. We identified that the costate variable for resource stock is decomposed between the scarcity 3effect and the cost effect. On the other hand, the costate variable for environmental pollution stock is solely due to the disutility effect.