Ramsey-Cass-Koopmans Model

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1、Lecture2:Infinite-Horizons&Overlapping-GenerationsModelsPart1:INFINITE-HORIZONModel8/5/20211武拉平:AdvancedMacroeconomics引言索洛模型中，储蓄率s被假定为外生参数，储蓄率的变动将影响稳态的人均消费和动态的人均消费水平。当时，与最优储蓄（相对应于最优资本存量和最优消费）相比会出现“过度储蓄”（即“过度积累”）的情况，而一个高于黄金率的储蓄率被证明是动态无效的。当时，只有在给定在当前消费与未来消费间的权衡参数条

2、件下，才能判断增加储蓄率的合理性。8/5/20212武拉平:AdvancedMacroeconomicss的变动对稳态和动态的人均消费的影响8/5/20213武拉平:AdvancedMacroeconomics储蓄率是如何决定的？必须引入消费者（家庭）行为来分析跨期预算约束条件下的消费和储蓄选择，即储蓄率的“内生化”。Ramsay&Diamendmodeldealswiththisproblem.8/5/20214武拉平:AdvancedMacroeconomicsPart1:theRamsey-Cass-Koopma

3、nsModelAssumptions:Firms--largenumberofidenticalfirms--8/5/20215武拉平:AdvancedMacroeconomicsPart1:theRamsey-Cass-KoopmansModelAssumptions:Household--largenumberofidenticalhouseholds--it8/5/20216武拉平:AdvancedMacroeconomics8/5/20217武拉平:AdvancedMacroeconomicsHousehold

4、s’UtilityFunction8/5/20218武拉平:AdvancedMacroeconomics8/5/20219武拉平:AdvancedMacroeconomicst现在一生效用函数的现值8/5/202110武拉平:AdvancedMacroeconomics把未来每个时期t的效用转化为现值的方法（1）把无限期流量转化为等点值的方法连续的复利计算和贴现计算。假设时间t连续，利息率也按复利连续计算。若利息每年按复利计算一次，最初数量到第t年将增加到(1+)t；8/5/202111武拉平:AdvancedMa

5、croeconomics若利息每年按复利计算一次，最初数量到第t年将增加到(1+)t；若利息每年按复利计算两次，则每六个月应运用年利息率的一半，而到第t年将增加到(1+/2)2t；若利息每年按复利计算n次，则到第t年将增加到(1+/n)nt8/5/202112武拉平:AdvancedMacroeconomics8/5/202113武拉平:AdvancedMacroeconomics8/5/202114武拉平:AdvancedMacroeconomics8/5/202115武拉平:AdvancedMacroecon

6、omics瞬时效用函数：CRRA8/5/202116武拉平:AdvancedMacroeconomicsCRRA的本质——边际效用对消费的弹性8/5/202117武拉平:AdvancedMacroeconomicsAboutθinutilityfunction8/5/202118武拉平:AdvancedMacroeconomicsFeaturesofutilityfunction8/5/202119武拉平:AdvancedMacroeconomicsPart1:theRamsey-Cass-KoopmansModelB

7、ehavior:Firms8/5/202120武拉平:AdvancedMacroeconomics8/5/202121武拉平:AdvancedMacroeconomicsBehavior:HouseholdBudgetConstraint8/5/202122武拉平:AdvancedMacroeconomics8/5/202123武拉平:AdvancedMacroeconomics8/5/202124武拉平:AdvancedMacroeconomics8/5/202125武拉平:AdvancedMacroeconomic

8、sBehavior:Household’sMaximization[ObjectiveFunction+constraint]8/5/202126武拉平:AdvancedMacroeconomics8/5/202127武拉平:AdvancedMacroeconomics8/5/202128武拉平:AdvancedMacroecon