给定生存函数下具有最优工作年限与闲暇的生命周期模型

The Life-cycle Model with Optimal Years of Working and Leisure under Given Survival Schedule

本文建立了具有最优工作年限与闲暇的生命周期模型,研究个人在给定的工资增长率、寿命和生存函数下如何最优地选择退休年龄的问题,其中个人从消费和退休后的闲暇得到效用.文中严格证明在给定指数生存和现实生存函数下,个体存在最优退休年龄.文中讨论了工资增长率对最优工作年限和闲暇的影响,证明在指数生存函数下退休年龄随着工资增长率的增加而增加.对于现实性生存函数,文中讨论了工资增长率和寿命对最优退休工作和闲暇的影响,得到最优退休年龄随着工资增长率和寿命的增加而增加.最后,通过数值仿真展现工资增长率及预期寿命对个人资产路径与最优退休年龄的影响.

In this paper,a life-cycle model with utility from both consumption and leisurewhich is obtained from retirement is setup to inquire how the individuals optimally chose theretirement age facing the given wage growth rate,longevity and given survival schedule.It isproved that there exists an optimal retirement age under conditions of exponential survival orrealistic survival and the retirement age increases with respect to the wage growth rate andthe longevity.In the end,the effect of wage growth rate and longevity on the retirement age ispresented by numerical simulation.