电子科技大学：《高级宏观经济学 Advanced Macroeconomics》课程教学资源（课件讲稿）Lecture 03a Ramsey Model

ADVANCED MACROECONOMICS Lecture 3a Ramsey Model 电子科大经管学院马捷

ADVANCED MACROECONOMICS Lecture 3a Ramsey Model 电子科大经管学院 马捷 1

Contents Introduction Mathematical Framework Graphical Representation ·Policy Effects 电子科大经管学院马捷 2 元元元元元

Contents  Introduction  Mathematical Framework  Graphical Representation  Policy Effects 电子科大经管学院 马捷 2

Introduction Extension to the Solow-Swan model: Agents choose consumption and investment optimally to maximize their individual utility. Endogenous labor supply 电子科大经管学院马捷 3 元元元元

Introduction  Extension to the Solow-Swan model: • Agents choose consumption and investment optimally to maximize their individual utility. • Endogenous labor supply 电子科大经管学院 马捷 3

Preferences Preferences are defined over streams of consumption and leisure: U(X)=U(x0,x1,x…),x,=(C,2) Recursive preferences:U,=W(x,,U) Additively separable preferences: U,(x)=∑U(x,) Recursive AND additively separable: U,=U(x,)+BU,+1=∑BU(x+） T=0 电子科大经管学院马捷 元元兄

Preferences  Preferences are defined over streams of consumption and leisure:  Recursive preferences:  Additively separable preferences:  Recursive AND additively separable: 电子科大经管学院 马捷 4 (x) ( , ,... ,...), ( , ) 0 1 t t t t U U x x x x  c z ( , ) t  t Ut1 U W x     0 (x) ( ) t t t U U x         0 1 ( ) ( )    t t  t  t U U x U U x

Neoclassical Preferences 1.U is continuous and twice differentiable 2.U.(c,z)>0>U(c,z) U(c,z)>0>U(c,z) Ui<UoU= 3. limU.=limU.=0, c→0 z→0 limU。=limU.=0. C-→00 2→2 电子科大经管学院马捷 5 元元元元元

Neoclassical Preferences 电子科大经管学院 马捷 5 lim lim 0. 3. lim lim , ( , ) 0 ( , ) 2. ( , ) 0 ( , ) 1. U is continuous and twice differentiable. 0 0 2                z z z c c z z c c cz cc zz z zz c cc U U U U U U U U c z U c z U c z U c z