一类CKF模型稳态解的存在唯一性及其性质

一类CKF模型稳态解的存在唯一性及其性质 The Existence and Uniqueness of a Kind of CKF Model and Its Properties 蔡东汉 CAI Dong-han 1 first-author 武汉大学数学与计算机科学学院,武汉,430072 武汉大学数学与计算机科学学院,武汉,430072 College of Mathematics and Computer Science, Wuhan University College of Mathematics and Computer Science, Wuhan University 在非强可加的Ｃｏｂｂ－Ｄｏｕｇｌａｓ型效用函数下建立了含内生生育率的Ｃ－Ｋ模型，即ＣＫＦ模型．证明模型至少存在的一个非零的稳态解，当参数满足一定条件时，稳态解是唯一的．稳态解处人口生育率与子女抚养时间成反比，与人口生育率界限成正比．讨论家庭消费、人口生育偏好和技术水平对经济发展最终状况的影响． The CKF Model under the Cobb-Douglas utility function is obtained in this paper. It is proved that at least one nonzero steady state and one growth path exist. The nonzero steady state and the growth paths is unique when the parameters satisfy a given condition. In the steady state, the fertility is high when the children rearing time is less and the fertility increases when the ability of rearing the children increases. CKF模型 Cobb-Douglas效用函数 稳态解 子女抚养时间 生育率界限 CKF model Cobb-Douglas utility function steady state children rearing time the bounded of fertility 10.14188/j.1671-8836.2000.01.002 F224 国家自然科学基金!（79970104） 2000-01-01 2021-04-01 1