1、4-14-2Chapter 4Growth and Policy Item Item Item Etc.McGraw-Hill/IrwinMacroeconomics,10e 2008 The McGraw-Hill Companies,Inc.,All Rights Reserved.4-3IntroductionChapter 3 explained how GDP and GDP growth are determined by the savings rate,rate of population growth,and the rate of technological progres
2、sThe question analyzed in this chapter is“How do societys choices affect these parameters?”In many developed countries,invention and advances in technology are the key determinants of growthTechnological advances are much less important for poor countries more important to invest in human and physic
3、al capital and borrow technological advances from othersEndogenous growth theory(Romer,Lucas)explains how societys choices lead to technological progress and growth4-4Trouble With Neoclassical Growth TheoryBy the late 1980s there was great dissatisfaction with neoclassical growth theory since:1.It d
4、oes not explain the economic determinants of technological progress2.It predicts that economic growth and savings rates are uncorrelated in the steady stateEndogenous growth theory emphasizes different growth opportunities in physical and knowledge capitalDiminishing marginal returns to physical cap
5、ital,but perhaps not knowledge capitalThe idea that increased investment in human capital increases growth is key to linking higher savings rates to higher equilibrium growth rates4-5Mechanics of Endogenous GrowthNeed to modify the production function to allow for self-sustaining,endogenous growthFi
6、gure 4-1(a)shows the Solow growth diagram,with the steady state at point C where savings equals required investmentIf savings above required investment,economy is growing as more capital is added process continues until savings equals required investment(reach the steady state)Insert Figure 4-1(a)an
7、d(b)here4-6Mechanics of Endogenous GrowthNeed to modify the production function to allow for self-sustaining,endogenous growthFigure 4-1(a)shows the Solow growth diagram,with the steady state at point C where savings equals required investmentDue to the diminishing MPK,the production function and sa
8、vings function flatten out and cross the upward sloping required investment line onceInsert Figure 4-1(a)and(b)here,again4-7Mechanics of Endogenous GrowthNeed to modify the production function to allow for self-sustaining,endogenous growthEconomy illustrated in Figure 4-1(b)is described by a product
9、ion function with a constant MPK:Y=aK(1)K is the only factor,a is the MPKProduction function and savings curve become straight lines,and are always greater than required investment the higher the savings rate,the bigger the gap between savings and required investment=faster the growthInsert Figure 4
10、-1(a)and(b)here,again4-8Mechanics of Endogenous GrowthIf the savings rate,s,is constant and there is neither population growth nor depreciation of capital,then the change in the capital stock is defined as:(2)Growth rate of capital is proportional to the savings rateOutput is proportional to capital
11、,thus the growth rate of output is (3)The higher s,the higher the growth rate of output saKKORsaKsYKsaYY4-9Deeper Economics of Endogenous GrowthEliminating diminishing marginal returns to capital runs against prevailing microeconomic principlesIf there are constant returns to capital alone,there wil
12、l be increasing returns to scale to all factors taken together larger and larger firms become increasingly efficient,and should see a single firm dominate the entire economyNot realistic,so need to eliminate the possibility of increasing returns to scale to all factors,and constant returns to a sing
13、le factorAlternatively,a single firm may not capture all benefits of capital some external to the firm(Romer)When a firm increases K,firms production increases,but so does the productivity of other firmsAs long as private return has constant returns to all factors,there will be no tendency towards m
14、onopolization4-10Private vs.Social Returns to CapitalInvestment produces not only new machines,but also new ways of doing thingsFirms DO capture the production benefits of a new machine(PRIVATE RETURNS)Firms may NOT capture the benefits of new technologies and ideas,since they are easy to copy(SOCIA
15、L RETURNS)Endogenous growth theory hinges on the notion that there are substantial external returns to capitalNot realistic for physical capital,but quite for human capital:1.Contribution of new knowledge only partially captured by creator2.From one new idea springs another knowledge can grow indefi
16、nitely4-11N and the Endogenous Growth ModelAssume:1.Technology is proportional to the level of capital per worker,or 2.Technology is labor augmenting,3.Technology growth depends on capital growth,orThe GDP growth equation from Chapter 3 wasIf ,then kNKA),(ANKFY NNKKAADeriving the growth equations re
17、quires some algebra.AAkkyy)1(kkNNKKAAkkkkkkAAkkyy)1()1(Output and capital growat the same rate.4-12N and the Endogenous Growth ModelAssume:1.Technology is proportional to the level of capital per worker,or 2.Technology is labor augmenting,3.Technology growth depends on capital growth,orSince the num
18、erator and denominator of y/k grow at equal rates,y/k is constantWhat is that constant?Find by dividing the production function by K and simplifying:kNKA),(ANKFY NNKKAADeriving the growth equations requires some algebra.aFKNNKKKFKNAKKFKANKFky,1,),(4-13N and the Endogenous Growth ModelAssume:1.Techno
19、logy is proportional to the level of capital per worker,or 2.Technology is labor augmenting,3.Technology growth depends on capital growth,orThe equation for capital accumulation can be written as:Making the substitution for y/k,the growth rate of y and k becomes:kNKA),(ANKFY NNKKAADeriving the growt
20、h equations requires some algebra.)(dnkyskk)()(dnsadnkysgkkyyHigh rates of population growth and depreciation lead to a low growth rate.4-14ConvergenceDo economies with different initial levels of output eventually grow to equal standards of living or converge?Neoclassical growth theory predicts abs
21、olute convergence for economies with equal rates of saving and population growth and with access to the same technology should all reach the same steady state level of incomeConditional convergence is predicted for economies with different rates of savings and/or population growth steady state level
22、 of income will differ,but the growth rates will eventually convergeEndogenous growth theory predicts that a high savings rate leads to a high growth rate4-15ConvergenceDo economies with different initial levels of output eventually grow to equal standards of living or converge?Robert Barro tested t
23、hese competing theories,and found that:1.Countries with higher levels of investment tend to grow faster2.The impact of higher investment on growth is however transitoryCountries with higher investment will end in a steady state with higher per capita income,but not with a higher growth rateCountries
24、 do appear to converge conditionally,and thus endogenous growth theory is not very useful for explaining international differences in growth rates4-16Growth Traps and Two Sector ModelsHow do we explain a world with BOTH no growth AND high growth countries?Ghana is an example of an economy that has e
25、xperienced no growth since 1900China is an example of an economy that has experienced rapid growth in recent years Need a model in which there is a possibility of both a no growth,low income equilibrium AND a high growth,high income equilibrium elements of both neoclassical and endogenous growth the
26、ories4-17Growth Traps and Two-Sector ModelsSuppose there are two types of investment opportunities:1.Those with diminishing MPK at low income levels2.Those with with constant MPK at high income levelsFigure 4-2 illustrates such a situationThe production function has a curved segment at low levels of
27、 income and an upward sloping line at high levelsPoint A is a neoclassical steady state equilibrium,while past point B there is ongoing growth(endogenous growth theory)Insert Figure 4-2 here4-18Growth Traps and Two-Sector ModelsSuppose there are two types of investment opportunities:1.Those with dim
28、inishing MPK at low income levels2.Those with with constant MPK at high income levelsWith two outlets for investment,society must choose not only total investment,but also the division between the twoSocieties that direct I towards research and development will have ongoing growthSocieties that dire
29、ct I toward physical capital may have higher output in the short run at the expense of lower long run growthInsert Figure 4-2 here4-19Solow Model with Endogenous Population GrowthOne of the oldest ideas in economics is that population growth works against the achievement of high incomeThe Solow grow
30、th model predicts that high population growth,n,means lower steady state income as each worker will have less capital to work withOver a wide range of incomes,population growth itself depends on income,n(y)Very poor countries have high birth rates and high death rates,resulting in moderately high po
31、pulation growthAs income rises,death rates fall and population growth increasesAt very high incomes,birth rates fall,some even approaching zero population growth(ZPG)4-20Solow Model with Endogenous Population GrowthFigure 4-3 illustrates the modified investment requirement line on the Solow diagram
32、to account for n as a function of y The investment requirement line,n(y)+dk,rises slowly at low levels of income,then sharply at higher levels,and finally levels off at high levels of incomeInsert Figure 4-3 here4-21Solow Model with Endogenous Population GrowthThe investment requirement line crosses
33、 the savings curve at points A,B,and CPoint A is a poverty trap with high population growth and low incomesPoint C has low population growth at high incomesPoints A and C are stable equilibriums because the economy moves towards these pointsPoint B is an unstable equilibrium since the economy moves
34、away from itInsert Figure 4-3 here again4-22Solow Model with Endogenous Population GrowthHow can an economy escape from the low-level equilibrium?There are two possibilities.1.If a country can put on a“big push”that increases income past point B,the economy will continue unaided to the high-level at
35、 point C2.A nation can effectively eliminate the low-level trap by moving the savings curve up or the investment requirement line down so that they no longer touch at points A or B raising productivity or increasing the savings rate raises the savings line population control policies lower the inves
36、tment requirement line Insert Figure 4-3 here again4-23Truly Poor CountriesGhana,and many other countries,experienced very little growth in recent yearsIncome is so low that most of the population lives on the boarder of subsistenceCan the Solow growth model explain these countries experiences?YESSa
37、vings in Ghana is quite low(9.3%of GDP vs.34.3%and 19.4%of GDP in Japan and the US respectively)Population growth is very high in Ghana and other poor countries relative to the US and Japan The effect of low savings rates and high population growth rates are as predicted by the Solow growth model:low levels of income and capital per capita
