On the utility-function-based dynamic optimal analysis of pollution control

In this paper the utility-function-based dynamic optimal analysis concerning pollution control is studied. Firstly, based on the concrete establishment of the model and rigorous quantitive analysis, the relevant optimal solution is derived from utility function under optimization of social welfare constrained by the stock of non-renewable energy, capital and pollution. Following that, some results of our analysis are obtained: 1) that the shadow price of the stock of capital is equal to the utility loss caused by the output from the consumption or investment to control pollution; 2) that the value of optimal unit pollution is negative, which is decided by anti-pollution activities and the shadow price of non-renewable energy and pollutants; 3) that the optimal expenditure of antipollution activity exists in the point that marginal cost is equal to marginal returns; 4)and that the cost caused by the usage of the non-renewable energy, which relation to the shadow price of pollution and the proportion of flow amount of pollution from the usage of non-renewable energy. Finally some conclusions concerning the theoretical foundation for the selection of pollution control instrument are put forward and future research directions are indicated.