具有人力资本和科技进步的经济增长模型研究  

The study on Economic Growth Model with Human Capital and Technological Change

作　　者：王锋[1] 王珊[1] 吴聪伟[2] 

机构地区：[1]萍乡学院数学系,江西萍乡337000 [2]第二炮兵工程大学理学院,陕西西安710025

出　　处：《数学的实践与认识》2014年第5期64-71,共8页Mathematics in Practice and Theory

基　　金：江西省教育厅科技项目(GJJ11271)

摘　　要：通过引入新的变量,将二维非自治动力系统转化为二维自治的动力系统,得到包含教育,实物资本,人口和技术进步的经济增长模型.证明二维自治动力系统存在唯一的平衡点且为结点.对于给定的初始状态,模型描述的经济存在一条增长路径.通过对模型动态性质的讨论,得出维持经济长期增长的关键因素是技术进步.最后,讨论了死亡率、折旧率和对教育的投资对经济增长的影响,得出在相同的生育率的情况下,死亡率越低,经济增长越快;低折旧率对应于高经济增长,加大教育的投入也可有效地促进经济增长.In this paper the two dimentional non-autonomous dynamical system is changed into two dimentional autonomous system by introducing new variables and the economic growth model with the education, physical capital, population and technological change is obtained. It is proved that the dynamical system has a unique nonzero equilibrium which is a node. For an given initial value, the economy described by the model has an economic growth path. By analyzing the dynamical behaviors of model, it is proved that the technological change is the key factor to make the economy grow rapidly for long-term. At last, the impact of the death rate, depreciation rate of capital and the investment in education on economic growth is discussed. The lower the death rate is, the more rapidly the economy grows for the same fertility rate. Lower depreciation rate of capital leads to the higher economic growth and the higher investment into education can promote the economic growth more effectively.

关 键 词：经济增长 马尔萨斯陷阱 动力系统 人口增长 教育 科技进步 

分 类 号：O19[理学—数学]