一类C-K模型稳态解的存在性、唯一性和多重性

一类C-K模型稳态解的存在性、唯一性和多重性 The Equilibrium Existence, Uniqueness and Multiplicity of A Class of C-K Model 丰建文 FENG Jian-wen 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 将人口生育率作为一个内生变量结合到广泛应用的对数型效用函数和不满足Ｉｎａｄａ条件的ＣＥＳ生产函数中，得到一类含内生生育率的Ｃ－Ｋ模型，通过求解家庭效用最大化问题得出人口生育率为人均资本和人均消费的函数，进而得到一个二维动力系统．讨论此系统的非零平衡解的存在性、唯一性和多重性，并对文中的主要结论给出了经济解释． Incorporating the fertility in logarithm-type utility function and the CES production function, an improved Cass-Koopmans （C-K） model with endogenous fertility is obtained. In this model the fertility can be expressed as a function of per capita capital and per capita consumption. We have proved the equilibrium existence, uniquencess and multiplicity under some conditions. Finally we discuss the economic sense of the main results. C-K模型 内生生育率 动力系统 平衡解 C-K model endogenuous fertility dynamical system equilibrium 10.14188/j.1671-8836.2000.01.003 F224 国家自然科学基金!（79970104） 2000-01-01 2021-04-01 1