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1、 2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,2 of 42,Saving,Capital Accumulation,and Output,The effects of the saving rate-the ratio of saving to GDP on capital and output per capita are the topics of this chapter.An increase in the saving rate would lead to higher gr
2、owth for some time,and eventually to a higher standard of living in the United States.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,3 of 42,Interactions BetweenOutput and Capital,At the center of the determination of output in the long run are two relations between out
3、put and capital:The amount of capital determines the amount of output being produced.The amount of output determines the amount of saving and investment,and so the amount of capital being accumulated.,11-1,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,4 of 42,Interactio
4、ns BetweenOutput and Capital,Capital,Output,and Saving/Investment,Figure 11-1,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,5 of 42,The Effects of Capital on Output,Under constant returns to scale,we can write the relation between output and capital per worker as follow
5、s:In words:Higher capital per worker leads to higher output per worker.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,6 of 42,The Effects of Capital on Output,Since the focus here is on the role of capital accumulation,we make the following assumptions:The size of the p
6、opulation,the participation rate,and the unemployment rate are all constant.There is no technological progress.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,7 of 42,The Effects of Capital on Output,Under these assumptions,the first important relation we want to express
7、 is between output and capital per worker:,In words,higher capital per worker leads to higher output per worker.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,8 of 42,The Effects of Output onCapital Accumulation,We proceed in two steps:First,we derive the relation betwe
8、en output and investment.Then,we derive the relation between investment and capital accumulation.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,9 of 42,Output and Investment,We make three assumptions to derive the relation between output and investment:We assume the eco
9、nomy is closed.We assume public saving,T G,is equal to zero.We assume that private saving is proportional to income,soCombining these two relations gives:,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,10 of 42,Investment andCapital Accumulation,The evolution of the capi
10、tal stock is given by:,denotes the rate of depreciation.,Combining the relation from output to investment,and the relation from investment to capital accumulation,we obtain the second important relation we want to express,from output to capital accumulation:,2006 Prentice Hall Business Publishing Ma
11、croeconomics,4/e Olivier Blanchard,11 of 42,Investment andCapital Accumulation,Rearranging terms in the equation above,we can articulate the change in capital per worker over time:,In words,the change in the capital stock per worker(left side)is equal to saving per worker minus depreciation(right si
12、de).,Output and Capital per Worker:,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,12 of 42,Implications ofAlternative Saving Rates,Our two main relations are:,Combining the two relations,we can study the behavior of output and capital over time.,First relation:Capital d
13、eterminesoutput.,Second relation:Output determines capital accumulation,11-2,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,13 of 42,Dynamics of Capital and Output,From our main relations above,we express output per worker(Y/N)in terms of capital per worker to derive the
14、 equation below:,change in capital from year t to year t+1,investment during year t,depreciation during year t,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,14 of 42,Dynamics of Capital and Output,If investment per worker exceeds depreciation per worker,the change in ca
15、pital per worker is positive:Capital per worker increases.If investment per worker is less than depreciation per worker,the change in capital per worker is negative:Capital per worker decreases.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,15 of 42,Dynamics of Capital
16、and Output,Capital and Output Dynamics,When capital and output are low,investment exceeds depreciation,and capital increases.When capital and output are high,investment is less than depreciation and capital decreases.,Figure 11-2,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blan
17、chard,16 of 42,Dynamics of Capital and Output,At K0/N,capital per worker is low,investment exceeds depreciation,thus,capital per worker and output per worker tend to increase over time.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,17 of 42,Dynamics of Capital and Outpu
18、t,At K*/N,output per worker and capital per worker remain constant at their long-run equilibrium levels.,Investment per worker increases with capital per worker,but by less and less as capital per worker increases.Depreciation per worker increases in proportion to capital per worker.,2006 Prentice H
19、all Business Publishing Macroeconomics,4/e Olivier Blanchard,18 of 42,Steady-State Capital and Output,The state in which output per worker and capital per worker are no longer changing is called the steady state of the economy.In steady state,the left side of the equation above equals zero,then:,Giv
20、en the steady state of capital per worker(K*/N),the steady-state value of output per worker(Y*/N),is given by the production function:,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,19 of 42,The Saving Rate and Output,Three observations about the effects of the saving ra
21、te on the growth rate of output per worker are:The saving rate has no effect on the long run growth rate of output per worker,which is equal to zero.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,20 of 42,The Saving Rate and Output,2.Nonetheless,the saving rate determin
22、es the level of output per worker in the long run.Other things equal,countries with a higher saving rate will achieve higher output per worker in the long run.,Three observations about the effects of the saving rate on the growth rate of output per worker are:,2006 Prentice Hall Business Publishing
23、Macroeconomics,4/e Olivier Blanchard,21 of 42,The Saving Rate and Output,3.An increase in the saving rate(you can think of this increase as coming from tax change or from reductions in the budget deficit,the increase of saving rate)will lead to higher growth of output per worker for some time,but no
24、t forever.The saving rate does not affect the long-run growth rate of output per worker.After a higher saving rate,growth will end once the economy reaches its new steady state.,Three observations about the effects of the saving rate on the growth rate of output per worker are:,2006 Prentice Hall Bu
25、siness Publishing Macroeconomics,4/e Olivier Blanchard,22 of 42,The Saving Rate and Output,The Effects of Different Saving Rates,A country with a higher saving rate achieves a higher steady-state level of output per worker.,Figure 11-3,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivie
26、r Blanchard,23 of 42,Capital Accumulation and Growth in France in the Aftermath of WWII,When WWII ended in 1945,France had suffered some of the heaviest losses of all European countries.A vivid picture of the destruction of capital is provided by the numbers in Table 1.,2006 Prentice Hall Business P
27、ublishing Macroeconomics,4/e Olivier Blanchard,24 of 42,The Saving Rate and Output,The Effects of an Increase in the Saving Rate on Output per Worker,An increase in the saving rate leads to a period of higher growth until output reaches its new higher steady-state level.,Figure 11-4,2006 Prentice Ha
28、ll Business Publishing Macroeconomics,4/e Olivier Blanchard,25 of 42,The Saving Rate and Consumption,The Effects of an Increase in the Saving Rate on Output per Worker in an Economy with Technological Progress,An increase in the saving rate leads to a period of higher growth until output reaches a n
29、ew,higher path.,Figure 11-5,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,26 of 42,The Saving Rate and Consumption,Questions:When governments can use various instruments to affect the saving rate,then saving rate should governments aim for?What do people matters?output
30、or consumption?Does an increase in saving lead to an increase in consumption in the long run?,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,27 of 42,What matters to people is not how much is produced,but how much they consume.A change in the saving rate this year has no
31、 effect on capital this,and so on no effect on output and income this year.So an increase in saving comes initially with an equal decrease in consumption(ignoring the short-run effect).,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,28 of 42,An increase in saving always
32、lead to an increase in the level of out put per worker,but it not necessarily lead to an increase in consumption in the long run,conversely,consumption may decrease,not only initially,but also in the long run.Why?,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,29 of 42,C
33、onsider three situation in which saving rate are respectively 0,1,and 0r1.What an economy should aim for is to maximize the steady-state level of consumption per capita.So What an economy should choice the saving rate that can maximizes its steady-state level of consumption per capita.,2006 Prentice
34、 Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,30 of 42,The Saving Rate and Consumption,The level of capital associated with the value of the saving rate that yields the highest level of consumption in steady state is known as the golden-rule level of capital.,2006 Prentice Hall Busi
35、ness Publishing Macroeconomics,4/e Olivier Blanchard,31 of 42,The Saving Rate and Consumption,The Effects of the Saving Rate on Consumption per Worker in Steady State,An increase in the saving rate leads to an increase,then to a decrease,in consumption per worker in steady state.,Figure 11-6,2006 Pr
36、entice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,32 of 42,The Saving Rate and Consumption,For s larger than sG,increases in the saving rate still lead to higher capital and output per worker,but lower consumption per worker.For s=1,capital and output per worker are high,but all o
37、f the output is used to replace depreciation,leaving nothing for consumption.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,33 of 42,This conclusion implies that,in practice,governments face a trade-off:An increase in the saving rate implies lower consumption for some t
38、ime,higher consumption later.What should governments do?,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,34 of 42,How to set up and run a social security system?One way to run a social security system is the pay-as-you-go system,where the taxes that workers pay are the be
39、nefits that current retirees receive,which depend on demographics and the evolution of the tax rate set by the system.Another is the fully-funded system,where workers are taxed,their contributions invested in financial assets,and when workers retire,they receive the principal plus the interest payme
40、nts on their investments,which depend on the rate of return on the financial assets held by the fund.In anticipation of demographic changes,the Social Security tax rate has been increases,and contributions are now larger than benefits,leading to the accumulation of a Social Security trust fund.,Soci
41、al Security,Savings,and Capital Accumulation in the United States,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,35 of 42,From the point of view of the economy,the two systems are very different:in a pay as you go system,the contributions are redistributed,not invested;i
42、n fully funded system,they are invested,leading to a higher capital stock.In anticipation of demographic changes,the Social Security tax rate has been increases,and contributions are now larger than benefits,leading to the accumulation of a Social Security trust fund.,Social Security,Savings,and Cap
43、ital Accumulation in the United States,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,36 of 42,Getting a Senseof the Magnitudes,Assume the production function is:,Output per worker is:,Output per worker,as it relates to capital per worker is:,Given our second relation,Th
44、en,11-3,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,37 of 42,The Effects of the Saving Rate on Steady-State Output,In steady state,the left side equals zero,then:,Squaring both sides,Dividing by(K/N)and rearranging,Output per worker is given by:,In words,the steady st
45、ate capital per worker is equal to the square of the ratio of the saving rate to the depreciation rate.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,38 of 42,The Effects of the Saving Rate on Steady-State Output,Steady-state output per worker is equal to the ratio of t
46、he saving rate to the depreciation rate.A higher saving rate and a lower depreciation rate both lead to higher steady-state capital per worker and higher steady-state output per worker.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,39 of 42,The Dynamic Effects of anIncr
47、ease in the Saving Rate,Dynamic Effects of an Increase in the Saving Rate from 10 to 20%on the Level and the Growth Rate of Output per Worker,It takes a long time for output to adjust to its new higher level after an increase in the saving rate.Put another way,an increase in the saving rate leads to
48、 a long period of higher growth.,Figure 11-7,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,40 of 42,The U.S.Saving Rateand the Golden Rule,In steady state,consumption per worker is equal to output per worker minus depreciation per worker.,Knowing that:,then:,and,These e
49、quations are used to derive the Table 11-1 in the next slide.,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,41 of 42,The U.S.Saving Rateand the Golden Rule,2006 Prentice Hall Business Publishing Macroeconomics,4/e Olivier Blanchard,42 of 42,Physical VersusHuman Capital,
50、Besides physical capital,economies also have another type of capital-human capital.The set of skills of the workers in the economy is called human capital.An economy with many highly skilled workers is likely to be much more productive than an economy in which most workers cannot read or write.The c
