The Stochastic Model Of Endogenous Growth With Environmental Pollution

In this paper, we discuss two types of economic growth models——deterministic growth models and stochastic growth models.First, we introduce the pollution to the utility function. Through connecting the environment pollution with output, individual utility was decided by the three factors: consumption goods, population growth rate and environmental pollution. The model of endogenous population growth was established which can obtain the balance population growth level, the output and pollution growth level and the optimal strategy for controlling the environmental, and also the equilibrium analysis and dynamic analysis were made.Second,we consider a stochastic endogenous growth model with pollution. In this model we introduce pollution with disutility to the utility function in a stochastic economic growth rate and pollution level by using stochastic optimization method. It is concluded that the parameters influence on the optimal growth rate is relevant to the risk aversion and the environment preferences, and that the economic growth rate will not be able to be quick enough to control the pollution.At last,we consider a stochastic endogenous growth model with environmental spending. In this model, we introduce the disturbance of income, tax and bonus rate in this model of which the tax mainly includes the income tax and present the equilibrium analysis and dynamic analysis according to the theory of stochastic dynamics optimization. We find that the ratio of consume and capital, the ratio of capital and bonus and the economic growth rate are decided by the parameters of the model based on which we analyze the effect of production and welfare and we obtain the optimum tax rate and the optimum individual environmental investment.