最新巴罗宏观经济学：现代观点第4章PPT课件.ppt
巴罗宏观经济学：现代观点第巴罗宏观经济学：现代观点第4章章Key EquationsSolow Growth Modelk/k=s(y/k)s nlk is capital per workerly is real gross domestic product(real GDP)per workerly/k is the average product of capitalls is the saving ratel is the depreciation rateln is the population growth rate.2Macroeconomics Chapter 4Solow Growth ModelChange in technology level(A)In the short run,an increase in the technology level,A,raises the growth rates of capital and real GDP per worker.These growth rates remain higher during the transition to the steady state.9Macroeconomics Chapter 4Solow Growth ModelChange in technology level(A)In the long run,the growth rates of capital and real GDP per worker are the samezerofor any technology level.In this long-run or steady state situation,a higher technology level leads to higher steady-state capital and real GDP per worker,k and y,not to changes in the growth rates(which remain at zero).Af(k*)/k*=+n/s10Macroeconomics Chapter 4Solow Growth ModelChange in the labor input11Macroeconomics Chapter 4Solow Growth Model Change in the labor inputIn the short run,an increase in labor input,L(0),raises the growth rates of capital and real GDP per worker.These growth rates remain higher during the transition to the steady state.12Macroeconomics Chapter 4Solow Growth Model Change in the labor inputIn the long run,the growth rates of capital and real GDP per worker are the samezerofor any level of labor input,L(0).The steady-state capital and real GDP per worker,k and y,are the same for any L.In the long run an economy with twice as much labor input has twice as much capital and real GDP.13Macroeconomics Chapter 4Solow Growth Model Change in population growth rate14Macroeconomics Chapter 4Solow Growth Model Change in population growth rate15Macroeconomics Chapter 4Solow Growth Model Change in population growth rateIn the short run,a higher n lowers k/k and y/y.These growth rates remain lower during the transition to the steady state.16Macroeconomics Chapter 4Solow Growth Model Change in population growth rateIn the steady state,k/k and y/y are zero for any n.A higher n leads to lower steady-state capital and real GDP per worker,k and y,not to changes in the growth rates,k/k and y/y(which remain at zero).A change in n does affect the steady-state growth rates of the levels of capital and real GDP,K/K and Y/Y.17Macroeconomics Chapter 4Solow Growth ModelSum up k*=k*s,A,n,L(0)(+)(+)()()(0)18Macroeconomics Chapter 4Solow Growth Model ConvergenceOne of the most important questions about economic growth is:whether poor countries tend to converge or catch up to rich countries.19Macroeconomics Chapter 4Solow Growth Model Convergence20Macroeconomics Chapter 4Solow Growth Model ConvergenceEconomy 1 starts with lower capital per worker than economy 2k(0)1 is less than k(0)2.Economy 1 grows faster initially because the vertical distance between the s(y/k)curve and the s+n line is greater at k(0)1 than at k(0)2.21Macroeconomics Chapter 4Solow Growth Model ConvergenceThat is,the distance marked by the red arrows is greater than that marked by the blue arrows.Therefore,capital per worker in economy 1,k1,converges over time toward that in economy 2,k2.22Macroeconomics Chapter 4Solow Growth Model Convergence23Macroeconomics Chapter 4Solow Growth Model ConvergenceEconomy 1 starts at capital per worker k(0)1 and economy 2 starts at k(0)2,where k(0)1 is less than k(0)2.The two economies have the same steady-state capital per worker,k*,shown by the dashed blue line.In each economy,k rises over time toward k*.However,k grows faster in economy 1 because k(0)1 is less than k(0)2.Therefore,k1 converges over time toward k2.24Macroeconomics Chapter 4Solow Growth Model Convergencey=A f(k)and y/y=(k/k)k/k was higher initially in economy 1 than in economy 2.Therefore,y/y is also higher initially in economy 1.Hence,economy 1s real GDP per worker,y,converges over time toward economy 2s real GDP per worker.25Macroeconomics Chapter 4Solow Growth Model ConvergenceThe Solow model says that a poor economywith low capital and real GDP per workergrows faster than a rich one.The reason is the diminishing average product of capital,y/k.The Solow model predicts that poorer economies tend to converge over time toward richer ones in terms of the levels of capital and real GDP per worker.26Macroeconomics Chapter 4Solow Growth Model Convergence27Macroeconomics Chapter 4Solow Growth Model Convergence28Macroeconomics Chapter 4Solow Growth Model Convergence29Macroeconomics Chapter 4Solow Growth Model Convergence30Macroeconomics Chapter 4Solow Growth Model ConvergenceEconomy 1 starts with lower capital per worker than economy 2lk(0)1 k(0)2.Assume that economy 1 also has a lower saving rate;ls1 s2.The two economies have the same technology levels,A,and population growth rates,n.Therefore,k*1 is less than k*2.It is uncertain which economy grows faster initially.The vertical distance marked with the blue arrows may be larger or smaller than the one marked with the red arrows.31Macroeconomics Chapter 4Solow Growth Model Convergence32Macroeconomics Chapter 4Solow Growth Model ConvergenceEconomy 1 starts with lower capital per worker than economy 2lk(0)1 n2.Therefore,k*1 is less than k*2.It is again uncertain which economy grows faster initially.The vertical distance marked with the blue arrows may be larger or smaller than the one marked with the red arrows.33Macroeconomics Chapter 4Solow Growth Model Convergence34Macroeconomics Chapter 4Solow Growth Model ConvergenceEconomy 1 has a lower starting capital per workerk(0)1 k(0)2and also has a lower steady-state capital per worker k*1(the dashed brown line)is less than k*2(the dashed blue line).Each capital per worker converges over time toward its own steady-state value:k1(the red curve)toward k*1,And k2(the green curve)toward k*2.However,since k*1 is less than k*2,k1 does not converge toward k2.35Macroeconomics Chapter 4Solow Growth Model ConvergenceKey Resultslk*=k*s,A,n,L(0)(+)(+)()()(0)lk/k=k(0),k*()(+)36Macroeconomics Chapter 4Solow Growth Model ConvergenceConditional convergence:la lower k(0)predicts a higher k/k,conditional on k.Absolute convergencelthe prediction that a lower k(0)raises k/k without any conditioning is called.37Macroeconomics Chapter 4Solow Growth Model the speed of Convergence38Macroeconomics Chapter 4Solow Growth Model the speed of ConvergenceCalibration:The half-life is roughly 18 years.39Macroeconomics Chapter 4Solow Growth Model Endogenous population growthMalthus(1798)the increase of y(or k)leads to a higher growth rate of population,which reduces the level of income per capita.Modern growth theory:the higher income per capita reduces the population growth rate.40Macroeconomics Chapter 4
