《高级宏观经济学(2)》课件-5.pdf

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1、IIIEconomicGrowth(Continued)BTheSolowModel1Assumptions²Closedeconomy²Household/producerY(t)=F[K(t);L(t);t]²Homogeneousgood²Constantsavingsrates(t)=s;0

2、=sF(K;L;t)¡±K3TheNeoclassicalProductionFunction²ProductionfunctionY=F(K;L)33²PropertieszPositiveanddiminishingmarginalproducts@F@F>0;>0@K@L@2F@2F<0;<0@K2@L2zConstantreturnstoscaleF(¸K;¸L)=¸F(K;L);8¸>0zInadaconditionslimFK=limFL=1K!0L!0limFK=limFL=0K!1L!1²Int

3、ensiveformofproductionfunctiony=f(k);wherey´Y=L;k´K=L;f(k)´F(k;1)zPropertiesoff(k)@Y@Y00=f(k);=f(k)¡kf(k)@K@L00limf(k)=1;limf(k)=0k!0k!1²Anexample:Cobb-Douglasproductionfunction®1¡®®Y=AKL;y=Ak344TheFundamentalDynamicEquationfortheCapitalStockK_=sf(k)¡±kLd(K=

4、L)K_k_´=¡nkdtL)k_=sf(k)¡(n+±)k5TheSteadyState²Asteadystate{allvariablesgrowatconstantrates(Figure1)k=k_=0)sf(k¤)=(n+±)k¤)k¤¤¤¤¤)y=f(k);c=(1¡s)f(k)¤¤¤)°k=°y=°c=0¤¤¤)°K=°Y=°C=n²Conclusion:Thesteadystategrowthratesofpercapitaout-put,capitalandconsumptionarealli

5、ndependentofchangesintheleveloftechnology,thesavingrate,therateofpopulationgrowth,andthedepreciationrate.356TransitionalDynamics²Theprocessofaneconomyconvergingtoitssteadystate(Figure2)k_=sf(k)¡(n+±)kk_sf(k))°k´=¡(n+±)kky_f0(k)k_kf0(k)°y´==[]°kyf(k)f(k)kf0(k

6、)0)°y=sf(k)¡(n+±)Sh(k);Sh(k)´f(k)@°f00(k)k(n+±)f0(k)y=°k¡[1¡Sh(k)]@kf(k)f(k))@°y<0if(a)kk¤.@k²Conclusion:Less-advancedeconomieshavehighergrowthrates.7PolicyExperiments²Apermanentincreaseinthesavingrate(Figure3))Temporarypositivegrowt

7、hinpercapitaoutput)Permanentlyhigherlevelsofpercapitacapitalandoutput)Nochangeinthelong-rungrowthratesofpercapitacapitalandoutput368AbsoluteandConditionalConvergence²Absoluteconvergence:@°k0=s[f(k)¡f(k)=k]=k<0@kzNote:Empiricalstudiesprovidemixedresults.²Cond

8、itionalconvergence:f(k)=k°k=(n+±)[¡1]f(k¤)=k¤zNote:Empiricalevidencesupportsthehypothesisofcon-ditionalconvergence.9TheSolowModelwithLabor-AugmentingTechnologicalProgressK_=sF[K;LA(t)]¡±K;A(t)=A