Optimal Production Policy Of A Firm Facing Pollution Tax Constrains

As a social planner the government want to reduce firms' pollution to the nature, so it will limit the pollution of the firms. Hartl and Kort set the upper limit as a constant value to reach the aim, then discuss how this policy instrument influences the firm's decision concerning investments and abatement efforts. After that, Wu Ansha and Li Yaqiong considered the instance that the upper limit of disposal of pollutants is the function of the production capital, and then they have carried on the research of the same problem. In this paper, we suppose the government has adopted more overall intervention, namely impose the environmental pollution tax on firms, then discuss how this policy instrument influences the firm's decision concerning investments and abatement efforts.In this paper, the method of solving this problem is to set up a rational model, and then get the optimal solution by Pontryagin Maximum Principle, also we use some conclusions of marginal condition and essential condition in Infinite Horizon. Through research of this paper, we would get some realistic and meaningful conclusion. For instance, No matter which kind of degree of pollution tax the government makes,there is an optimal route to the equilibriums; And the government can achieve the purpose that controlling the pollution or developing economy by imposing the polluting taxes; also there are multiplethe equilibriums in same case ,the government can reach the optimum equilibrium by distributing an investment grant, so it could avoid other equilibriums.We not only discuss the dynamic behavior of a firm subject to dynamic environment regulation but also offer same advices and strategies for making disposal of pollutants policy by the government.The paper has four parts. In the first chapter, the background and the necessity for the study of pollution tax and optimal control are presented. And the main work of this paper is also simply introduced. In the second chapter, some prepared knowledge would been introduced. In the third chapter, we will establish and analysis about the model of this paper. In the fourth chapter, we would analysis these questions by optimal control, and then draw the economic meaning. Also, we could offer some theoretical directions to government and Firms.