内生出生率与养老金

　　　　　　　　　　　　　　　　　　　　摘　　要



 



　　本书研究内生出生率与养老保险的问题。在动态经济模型中，如果出生率由模型中的最优化问题而决定的话，则称为内生出生率。本书设立男女家庭分工的离散时间动态模型，在这一模型中，家庭在选择自己的效用的同时也选择子女数目和子女的人力资本,使用拓扑、动态规划、最大原理和不动点定理等数学方法，证明了最佳路径的存在性，值函数的存在性，最佳路径的单调性，定常点的存在性并刻画了定常点的性质等,最后得到了在低的人力资本的定常点，女性不参加市场商品生产活动，出生率高；而在高的人力资本的定常点，女性参加市场商品生产活动，出生率低。本书使用这一模型和结果，来解释为什么随着经济的发展和技术的进步，出生率却下降的问题，也分析了我国的独生子女政策，并对我国的人口政策提出了一些建议。



　　在分析和总结了各先进国家的年金系统、年金政策和养老金改革的基础上，本书对我国的养老金政策提出一些建议。



　　本书共分六章。第一章是关于人口移转、经济增长和出生率问题的文献总结。第二章建立了静态的男女分工的生产函数，并对出生率和人力资本水平对生产函数的影响进行了分析。第三章建立了动态的家庭内男女分工模型，证明了最佳路径的存在性，最佳路径的单调性，定常点的存在性，最佳路径和刻画了定常点的性质等。第四章分析了我国的独生子女政策，用模型证实了仅从经济的最佳选择来说，独生子女并非家庭的最佳选择，然后对我国的人口政策提出一些建议。第五章总结了先进国家的养老金制度、养老金系统和养老金改革的经验和文献。第六章对我国的养老金制度、养老保险和养老金改革提出一些建议。



　　本书是从实际问题出发，建立模型，用高深的数学方法解决模型和动态系统问题，然后用得出的结论来解释和分析实际问题的一个尝试。



 



 



　　　　　　　　　　　　　　　　　　　　Abstract



 



　　This book studies the problems of endogenous fertility and
pensions.  Endogenous fertility means
that fertility is determined in the dynamic economic model. A discrete time
dynamic model of division work in a family between male and female is
established in this book.  In the model,
families determine their consumptions, the number of their children and human
capital of their children at the same time.  The existence of optimal paths, the value function and steady states,
and the monotone of the optimal path are demonstrated by using topology,
dynamic programming, maximum principle and fixed point theorems.  Finally, we obtained the result that there
are two steady states exist in the model.  The first fixed point corresponds to higher fertility, lower lever of
the human capital and the situation that there are no female in the production
of market good.  On the other hand, the
second fixed point corresponds to lower fertility, higher level of the human
capital and the situation that female takes part in the production of the
market good.  This book uses this model
and result to explain the reason why the fertility is decreasing with economic
growth and the technology progress, to analyze only one child policy of our
country and to suggest some suggestions on our population policy.



　　Based on the experience of pension systems and the reform of pension
systems in the developed countries, some suggestions on the pension system and
private pensions in our country are given in this book.



　　This book is divided in six chapters.  The overview of the literature on endogenous
fertility, demographic transition is given in Chapter1.  A static model of the division work in a
family between male and female is established and the production function in
this model is given and analyzed in Chapter 2. A dynamic model of the division
work in a family between male and female is established in Chapter 3. In this
chapter, the existence of the optimal paths, value functions and steady states,
as well as the monotone of the optimal human capital path are proved, and the
properties of the steady states are characterized.  In Chapter 4, the experience of the pension
systems and reform of the pension systems are analyzed.  Finally, in Chapter 6, some suggestions on
pension systems, private pension, and pension policy are suggested.



　　This book try to determine a model from the reality, solve the model
using topology, fixed point theorems and dynamic programming, and return back,
to analyze economic problems using the results obtained from the model.