Educational Investment,Government Expenditure And Stochastic Economic Growth

This paper discusses the two types of endogenous growth model ---deterministic growth model and stochastic growth model.First, we introduce the share of educational investmentεinto Uzawa-Lucas model and establish a three-dimensional dynamic system using the dynamic optimization whenεis exogenous .The system is draw to the saddle orbit. The results show that it is a positive correlation between economic growth and the share of educational investment. Furthermore we analyze thatεhas certain correlation to balanced ratio of output- capital z *and the fraction of human capital in production department v *.Butεhas ambiguous relation to consumption-capital ratioχ*.Whenεis endogenous, we obtain that economic growth has positive correlation to v and negative correlation toρ,σ.Through discussing the two conditions, we know that the share of educational investmentεhas certain relation to economic growth.Secondly, we establish a stochastic economic growth model about human capital accumulation and educational investment when educational investment and human capital are introduced into model. We supposed that human capital only influences the represents'utility and not involve in the production of outputs. Through stochastic optimization method, we obtain macroeconomic equilibrium value that is, consumption-wealth ratio, expected economic growth rate and so on. In addition, we study the output shock, the externality of private investment, the ratio of private investment and the effect of interest level to consumption-capital ratio and expected economic growth rate.Finally, we put public expenditure and private investment into education and propose a continuous-time stochastic economic growth model. The balanced consumption-capital ratio, expected economic growth rate and the optimal share of private investmentεare be determinated by using stochastic optimization method. We also obtain the consumption-capital ratio and expected economic growth rate respectively in the case the human capital enter into utility function or not. At last we explore the relation of economic growth to shock, externality and private investment ratio and conclude that if the investment ratio has less than optimal value , increasing the proportion of the investment will promote economic growth, or else will hinder development.