具有人口转变与人力资本的经济增长模型及仿真

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 蔡东汉 CAI Donghan 1 first-author 武汉大学数学与统计学院 武汉大学数学与统计学院 School of Mathematics and Statistics,Wuhan University School of Mathematics and Statistics,Wuhan University 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. 人口转变 人力资本 Solow模型 非零平衡点 渐近稳定性 demographic transition human capital Solow model nonzero equilibrium asymptotically stability 10.14188/j.1671-8836.2011.02.015 O242.1 国家自然科学基金资助项目（70871094）;教育部人文社会科学研究项目（09YJA790155） 2011-02-01 2021-04-01 2 57