数学杂志
數學雜誌
수학잡지
JOURNAL OF MATHEMATICS
2011年
2期
191-196
,共6页
Ramsey模型%非零平衡点%相图分析%数值仿真
Ramsey模型%非零平衡點%相圖分析%數值倣真
Ramsey모형%비령평형점%상도분석%수치방진
Ramsey model%nonzero equilibrium%phase portrait analysis%demographic transition%numerical simulation
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.
本文將內生人口轉變函數引入經典的Ramsey模型.通過解傢庭效用最大化問題得到一箇二維的動力繫統,文中證明描述模型的動力繫統至少存在一箇非零平衡點併著重討論非零平衡點惟一的情形.通過數值倣真得齣在最優經濟增長軌道上人口轉變時期的人口變化對人均消費有本質的影響,而對人均資本影響不大.
본문장내생인구전변함수인입경전적Ramsey모형.통과해가정효용최대화문제득도일개이유적동력계통,문중증명묘술모형적동력계통지소존재일개비령평형점병착중토론비령평형점유일적정형.통과수치방진득출재최우경제증장궤도상인구전변시기적인구변화대인균소비유본질적영향,이대인균자본영향불대.
In this article,the endogenous demographic transition function is integrated into the classical Ramsey model.By solving the household utility maximization problem.a twodimensional 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.
