Modeling And Simulation Of Economic Growth With Age Structure

In this paper, we discuss the impact of the age structure on economic growth by using the age structure equations and economic growth equation.In Chapter1, we give a survey on the background, the main results of this paper and recent development of the economic growth model with age structure.In Chapter2, an improved discrete Solow model was set up to inquire the dynamical effects of the age structure change on economic growth. By using a comparative theorem we obtained, it is proved that the solution of the model is asymptotical stable when the age structure tends a steady state and the economic grows to a stable state after age structure change ended. By numerical simulation, we show that the economic growth is speeded up by the decline of the young dependency and slowed down by the increasing of old dependency. And there exists demographic dividend in the period of demographic transition.In Chapter3, We integral the age-structure and classical Solow model. We extend the nonlinear Gurtin-MacCamy population equation though putting the capital into mortality rate. The existence and uniqueness of the solution for the model is obtained by using the contracting mapping principle. The sufficient conditions for local asymptotic stability of equilibrium solutions of the model is given. Some special case has been studied in the final.In Chapter4, we use an extended overlapping-generations model model to inquire the individual’s optimal saving and consumption behaviour. It is proved that the individual has three types of saving behaviour which depend on the growth rate of wage. With low wage growth rate, the individual saves in part of his work period then dissaving. When the wage growth rate is high, the individual dissaving firstly in part of his work period then turns to save in rest of his work period until he retires and there exists a prime-saver age. The other type is he saves in all his work period. In the end, the effect of the wage growth rate on the individual saving behaviour is presented by the numerical simulation.In Chapter5, we use an extended Ramsey model to inquire the optimal individual saving and consumption behaviour. It is proved that the individual has two types of saving behaviour which depend on the growth rate of wage, retiring age and longevity. One type of saving and consumption behaviour is individual saving in all period he or she works. The other case is he or she dissaving firstly and then saving in the period he or she works and there exists primer-saving age. In the end, the effect of the wage, retiring age and longevity on the behaviour of individual saving and consumption is presented by the numerical simulation.