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.