The Stochastic Model Of Endogenous Growth And Investment In Public Security

The effect of investment in public security on economic growth has been more and more important for economists. This paper mainly sets up two dynamic stochastic models of endogenous growth about investment in public secutrity. Using the stochastic optimization method this paper discusses the the influences of stochastic disturbance and investment in public security on the economic growth and social welfare.Firstly,we discuss a stochastic model in which the ratio of personal investment in public security is exogenous parameter.We assume that the representative has no choice on deciding tha ratio and the investment in public security is provided by government and the individual.Considering the the positive influence of good habitation to individual welfare, this paper adds the level of public security to utility function. Simultaneously, the paper thinks that the improvement of level of public security will increase economic growth, therefore the level of public security is introduced into the consumer's production function. Using stochastic dynamic optimization method, we gain consumption-wealth ratio, physical capital-wealth ratio and equilibrium economic growth rate in equilibrium.As following, we calculate optimization policy parameters in some special cases and find that in the lower lever of personal investment in public security (or tax rate),increasing the personal investment in public security (or tax rate) is in favor of welfare but not in favor economic growth. Exorbitant personal investment in public security (or tax rate) is harmful to both economic growth and welfare. At last, we discuss the influence of the revenue rate.Secondly, we discuss the case that the ratio of personal investment in public security is exogenous variable. Theoretically we get consumption-wealth ratio, optimal ratio of personal investment in public security, physical capital-wealth ratio, and equilibrium economic growth rate in equilibrium. We mostly consider the influences of parameters on the optimal ratio of personal investment in public security.