具有人口转变与人力资本的经济增长模型及仿真

An Economic Growth Model with the Demographic Transitions, Human Capital and Simulation

建立数学模型探讨了人口转变与人力资本对经济增长的影响.将描述人口转变的倒U字型人口增长率函数和人均人力资本引入Solow模型,结合人均人力资本增长方程得到二维的动力系统.证明动力系统至少存在一个非零平衡点且当非零平衡点惟一时,动力系统的解是渐近稳定的,模型描述的经济具有渐近稳定的经济增长路径.通过数值仿真展现人口转变与人力资本对经济增长的影响.

In this paper, we set up a model to inquire the affection of the demographic transition and human capital on the economic growth. Combining the function which describes the population change in the period of the demographic transition and the human growth equation with the Solow model, we obtain a two-dimension dynamical system. It is proved that the dynamical system has at least one equilibrium and the solution of the dynamical system is asymptotically stable, so the economy described by the model has stable growth path when the equilibrium is unique. In the end, the numerical simulation is given to present the affections of the demographic transition and human capital on the economic growth.