具有内生人口转变的Ramsey模型与仿真(Ⅰ)(英文)  

THE RAMSEY MODEL WITH ENDOGENOUS DEMOGRAPHIC TRANSITION AND SIMULATION(Ⅰ)

作　　者：蔡东汉[1] 

机构地区：[1]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学杂志》2011年第2期191-196,共6页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(70871094) ;Humanities & Social Sciences Research Item of Ministry of Education of China(09YJA790155)

摘　　要：本文将内生人口转变函数引入经典的Ramsey模型.通过解家庭效用最大化问题得到一个二维的动力系统,文中证明描述模型的动力系统至少存在一个非零平衡点并着重讨论非零平衡点惟一的情形.通过数值仿真得出在最优经济增长轨道上人口转变时期的人口变化对人均消费有本质的影响,而对人均资本影响不大.In this article,the endogenous demographic transition function is integrated into the classical Ramsey model.By solving the household utility maximization problem,a two-dimensional dynamical system is obtained.It is proved that the dynamical system describing the model has at least an equilibrium and we mainly discuss the case that the dynamical system has a unique equilibrium.Using the numerical simulation,we find that the population change in the demographic transition period has substantial effect on the per capita consumption but has not notable effect on the per capita capital along the optimal growth path.

关 键 词：RAMSEY模型 非零平衡点 相图分析 数值仿真 

分 类 号：O175.1[理学—数学] O231[理学—基础数学]