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Theproductionfunction生产函数),(LKAFY=LLKKAAYY−++=)1(技术进步率资本增量百分比劳动增量百分比产量的资本弹性表示资本投入每增加1%，国民收入会增加百分之几？),(LK

AFY=增长核算▪增长核算方程尽管能告诉我们经济增长的源泉及其贡献，但不能告诉我们一个国家如何选择经济增长的路径。▪所以经济学家想知道，一个国家长期的生活水平与储蓄率、人口增长率以及技术进步率之间到底是何关系？▪经济政策能

否改变一个国家经济增长的路径？▪如果能，一个贫穷的国家有没有可能赶上富裕国家的生活水平？等等。▪这些问题，利用索洛模型（新古典增长模型）便能得到一定的说明。Theproductionfunction生产函数▪生产函数的表达式:Y=F(K,L)

▪定义:y=Y/L=人均产出k=K/L=人均资本▪假设规模报酬不变，则有:zY=F(zK,zL)，对于任意z>0▪取z=1/L.那么：Y/L=F(K/L,1)y=F(k,1)y=f(k)),(LKAFY=slide4Theproductionfunction人均产出,y人均资本,kf(k)

Note:thisproductionfunctionexhibitsdiminishingMPK该生产函数表明资本的边际报酬递减.1MPK=f(k+1)–f(k)k+1kslide5两部门经济中，经济均衡条件为▪Y=C+I▪写成人均形式:y=

c+i这里c=C/L，i=I/Lslide6Theconsumptionfunction消费函数▪s=储蓄率,收入中被储蓄的比例消费函数:c=(1–s)y(人均形式)slide7Savingandinvestment储蓄与投资▪人均储蓄=y–c=y–(1–s)y=s

y▪由于经济均衡条件：y=c+i变换后得到:i=y–c=sy(investment=saving)▪使用上面的结论得到：i=sy=sf(k)slide8Output,consumption,andinvestment人均产出,y人均资本,kf(k)sf(k)k1y1i1c12

)()(LKdtdLLdtdKdtdkLKktt−==LdLkLdtdKdtdk−=2)()(LKdtdLLdtdKdtdkLKktt−==LdLkLdtdKdtdk−=knkKIdknkkKKIdknkLKKd

Kdk)(+−=−−=−=knksfkknLKKsYdk)()()(+−=+−=nkksfk−=)(slide11稳态的图示InvestmentanddepreciationCapitalperworker,ksf(k)nkk*slide12Depreci

ation折旧人均折旧,k人均资本,kk=therateofdepreciation折旧率=thefractionofthecapitalstockthatwearsouteachperiod1slide13Capitalaccumulation资本积累基本思想:投资使得资本存

量越来越大折旧使得资本存量越来越少.2)()(LKdtdLLdtdKdtdkLKktt−==LdLkLdtdKdtdk−=knkKIdknkkKKIdknkLKKdKdk)(+−=−−=−=knksfkknLKKsYdk)()()(+−=+−=slid

e15k的动态方程变为▪Withpopulationgrowthanddepreciation,theequationofmotionforkisk=sf(k)−(+n)k必需的投资实际投资其中:▪k替换已经耗费的资本▪nk为新增加的工人配备的资本slide16TheSolowMode

ldiagramInvestment,break-eveninvestmentCapitalperworker,ksf(k)(+n)kk*k=sf(k)−(+n)kslide17趋向稳态的调整过程Investmentanddepreciat

ionCapitalperworker,ksf(k)(n+)kk*k=sf(k)−(n+)kRequiredinvestmentkk1Actualinvestmentslide19趋向稳态的调整过程InvestmentanddepreciationCapitalper

worker,ksf(k)(n+)kk*k1kk2k=sf(k)−(n+)kslide20趋向稳态的调整过程InvestmentanddepreciationCapitalperworker,ksf(k)(n+)kk*k2ActualinvestmentRequ

iredinvestmentkk=sf(k)−(n+)kslide22趋向稳态的调整过程InvestmentanddepreciationCapitalperworker,ksf(k)(n+)kk*k2kk3k=sf(k)−(n+)kslide23趋向稳态的调整过程Inves

tmentanddepreciationCapitalperworker,ksf(k)(n+)kk*k3总结:只要k<k*,实际投资额将超过必需投资额,k将不断增加直到k*.k=sf(k)−(n+)kslide24KssKLow资

本存量K产出产出（y）投资sf(k)投资（i）(n+)k折旧投资大于必需的投资资本存量上升slide25投资小于必需的投资KssKHigh资本存量K产出产出（y）投资sf(k)投资（i）(n+)k折旧资本存量下

降slide26储蓄率或投资率的上升对经济的影响s2f(k)K1K2产出（y）s1f(k)投资（i）资本存量K产出(n+)k折旧y1y2Anincreaseinthesavingrateraisesinvestment……causingthecapitalstocktog

rowtowardanewsteadystate:slide27Prediction预测:▪Highershigherk*.▪Andsincey=f(k),higherk*highery*.▪Thus,theSolowmodelpred

ictsthatcountrieswithhigherratesofsavingandinvestmentwillhavehigherlevelsofcapitalandincomeperworkerin

thelongrun.slide28EgyptChadPakistanIndonesiaZimbabweKenyaIndiaCameroonUgandaMexicoIvoryCoastBrazilPeruU.K.U.S.CanadaFranc

eIsraelGermanyDenmarkItalySingaporeJapanFinland100,00010,0001,000100Incomeperpersonin1992(logarithmicscale)051015Investmentaspe

rc(average1960–1992)2025303540InternationalEvidenceonInvestmentRatesandIncomeperPersonslide29GrowthandInvestmentCopyright©2

003Southwestern/ThomsonLearning(a)GrowthRate1960–1991(b)Investment1960–1991SouthKoreaSingaporeJapanIsraelCanadaBrazilWestGermanyMexicoUnite

dKingdomNigeriaUnitedStatesIndiaBangladeshChileRwandaSouthKoreaSingaporeJapanIsraelCanadaBrazilWestGe

rmanyMexicoUnitedKingdomNigeriaUnitedStatesIndiaBangladeshChileRwandaInvestment(percentofGDP)GrowthRate(percent)0123456701020

3040投资与经济增长之间的关系是显而易见的。slide30TheimpactofpopulationgrowthInvestment,break-eveninvestmentCapitalperworker,ksf(k)(+n1)kk1*(+n2)kk2*Anincreaseinnca

usesanincreaseinbreak-eveninvestment,leadingtoalowersteady-statelevelofk.slide31Prediction:▪Highernlowerk*.▪Andsincey=f(

k),lowerk*lowery*.▪Thus,theSolowmodelpredictsthatcountrieswithhigherpopulationgrowthrateswillhavelowerlevelsofcapitalandincomeperworke

rinthelongrun.slide32ChadKenyaZimbabweCameroonPakistanUgandaIndiaIndonesiaIsraelMexicoBrazilPeruEgyptSingaporeU.S.U.K.CanadaFranceFinlan

dJapanDenmarkIvoryCoastGermanyItaly100,00010,0001,00010012340Incomeperpersonin1992(logarithmicscale)Population(average19–1992

)InternationalEvidenceonPopulationGrowthandIncomeperPerson