具有内生人口生育率的Cass-Koopmans模型  

A CASS KOOPMANS MODEL WITH ENDOGENOUS FERTILITY

作　　者：蔡东汉[1] 

机构地区：[1]武汉大学

出　　处：《数学杂志》1998年第2期209-215,共7页Journal of Mathematics

摘　　要：本文在［１］的基础上合理地假设人口生育率的取值范围。通过引入强可分的效用函数和含有有效劳动时间的生产函数，得到一个具有内生生育率的Ｃａｓｓ－Ｋｏｏｐｍａｎｓ经济增长模型。证明此模型的家庭企业的人口生育率由家庭的人均资本和人均消费唯一确定。当人均消费不变，而人均资本上升时，人口生育率下降；当人均资本不变，而人均消费上升时，人口生育率上升。给出此模型至少存在一个稳态解的条件。最后讨论了可能存在的多重最优增长路径和多重稳态解及其几何性态和相互关系。In this paper, on the base of , a reasonable assumption on the fertility is given. By introducting a strongly divisible utility function and a production function with effective labor, we get an improved Cass Coopmans model with endogenous fertility. It is proved that the households fertility is determinded by the per capita capital and the per capita consumption of the household. When the per capita consumption is fixed, the fertility descreases as the per capita capital increasing; When the per capita capital is fixed, the fertility is increases as the per capita consumption increasing. Under some conditions, we prove that at least one steady state exists. At end of this paper, we discuss the posibility of exsiting multiple growth paths and multiple steady states, their relations and their geometric properties.

关 键 词：内生人口生育率 C-K模模型 经济增长模型 

分 类 号：F224.0[经济管理—国民经济]