巴罗宏观经济学：现代观点第4章.ppt

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1、Macroeconomics Chapter 4,1,Working with the Solow Growth Model,C h a p t e r 4,Macroeconomics Chapter 4,2,Key EquationsSolow Growth Model,k/k=s(y/k)s nk is capital per workery is real gross domestic product(real GDP)per workery/k is the average product of capitals is the saving rate is the depreciat

2、ion raten is the population growth rate.,Macroeconomics Chapter 4,3,Solow Growth ModelSteady State s(y*/k*)=s+n,We assumed that everything on the right-hand side was constant except for y/k.In the transition to the steady state,the rise in k led to a fall in y/k and,hence,to a fall in k/k.In the ste

3、ady state,k was constant and,therefore,y/k was constant.Hence,k/k was constant and equal to zero.,Macroeconomics Chapter 4,4,Solow Growth ModelChange in savings rate(s),Macroeconomics Chapter 4,5,Solow Growth ModelChange in savings rate(s),In the short run,an increase in the saving rate raises the g

4、rowth rate of capital per worker.This growth rate remains higher during the transition to the steady state.,Macroeconomics Chapter 4,6,Solow Growth ModelChange in savings rate(s),In the long run,the growth rate of capital per worker is the samezerofor any saving rate.In this long-run or steady-state

5、 situation,a higher saving rate leads to higher steady state capital per worker,k,not to a change in the growth rate(which remains at zero).Af(k*)/k*=+n/s,Macroeconomics Chapter 4,7,Solow Growth Modelthe effect of s on consumptions,In the short run,consumption decreases and k arises.c*=y*-k*-s(y*-k*

6、)=y*-k*-nk*c*=y*-(+n)k*=(MPK-n)k*In the long run,whether the consumption in the steady state increases depends on MPK.“Golden Rule”,Macroeconomics Chapter 4,8,Solow Growth ModelChange in technology level(A),Macroeconomics Chapter 4,9,Solow Growth ModelChange in technology level(A),In the short run,a

7、n 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.,Macroeconomics Chapter 4,10,Solow Growth ModelChange in technology level(A),In the long run,the growth rates of capital and real

8、 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/s,Macroeconomics Chapter 4,11,Solow

9、 Growth ModelChange in the labor input,Macroeconomics Chapter 4,12,Solow Growth Model Change in the labor input,In 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.,Macr

10、oeconomics Chapter 4,13,Solow Growth Model Change in the labor input,In 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 t

11、wice as much labor input has twice as much capital and real GDP.,Macroeconomics Chapter 4,14,Solow Growth Model Change in population growth rate,Macroeconomics Chapter 4,15,Solow Growth Model Change in population growth rate,Macroeconomics Chapter 4,16,Solow Growth Model Change in population growth

12、rate,In the short run,a higher n lowers k/k and y/y.These growth rates remain lower during the transition to the steady state.,Macroeconomics Chapter 4,17,Solow Growth Model Change in population growth rate,In the steady state,k/k and y/y are zero for any n.A higher n leads to lower steady-state cap

13、ital 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.,Macroeconomics Chapter 4,18,Solow Growth ModelSum up,k*=k*s,A,n,L(0)(+)(+)()()(0),Macro

14、economics Chapter 4,19,Solow Growth Model Convergence,One of the most important questions about economic growth is:whether poor countries tend to converge or catch up to rich countries.,Macroeconomics Chapter 4,20,Solow Growth Model Convergence,Macroeconomics Chapter 4,21,Solow Growth Model Converge

15、nce,Economy 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.,Macroeconomics Chapter 4,22,Solow Growth Model Convergence,That is,the

16、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.,Macroeconomics Chapter 4,23,Solow Growth Model Convergence,Macroeconomics Chapter 4,24,Solow Growth Model Convergence,Economy

17、 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 th

18、an k(0)2.Therefore,k1 converges over time toward k2.,Macroeconomics Chapter 4,25,Solow Growth Model Convergence,y=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

19、toward economy 2s real GDP per worker.,Macroeconomics Chapter 4,26,Solow Growth Model Convergence,The 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 po

20、orer economies tend to converge over time toward richer ones in terms of the levels of capital and real GDP per worker.,Macroeconomics Chapter 4,27,Solow Growth Model Convergence,Macroeconomics Chapter 4,28,Solow Growth Model Convergence,Macroeconomics Chapter 4,29,Solow Growth Model Convergence,Mac

21、roeconomics Chapter 4,30,Solow Growth Model Convergence,Macroeconomics Chapter 4,31,Solow Growth Model Convergence,Economy 1 starts with lower capital per worker than economy 2k(0)1 k(0)2.Assume that economy 1 also has a lower saving rate;s1 s2.The two economies have the same technology levels,A,and

22、 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.,Macroeconomics Chapter 4,32,Solow Growth Model Convergence,Macroeconomics

23、 Chapter 4,33,Solow Growth Model Convergence,Economy 1 starts with lower capital per worker than economy 2k(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

24、with the red arrows.,Macroeconomics Chapter 4,34,Solow Growth Model Convergence,Macroeconomics Chapter 4,35,Solow Growth Model Convergence,Economy 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 d

25、ashed 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.,Macroeconomics Chapter 4,36,Solow Growth Model Convergence,Key Resultsk*=k*s

26、,A,n,L(0)(+)(+)()()(0)k/k=k(0),k*()(+),Macroeconomics Chapter 4,37,Solow Growth Model Convergence,Conditional convergence:a lower k(0)predicts a higher k/k,conditional on k.Absolute convergencethe prediction that a lower k(0)raises k/k without any conditioning is called.,Macroeconomics Chapter 4,38,

27、Solow Growth Model the speed of Convergence,Macroeconomics Chapter 4,39,Solow Growth Model the speed of Convergence,Calibration:The half-life is roughly 18 years.,Macroeconomics Chapter 4,40,Solow Growth Model Endogenous population growth,Malthus(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.,