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1、WorkingwiththeSolowGrowthModelChapter41MacroeconomicsChapter4KeyEquations SolowGrowthModel∆k/k=s·(y/k)−sδ−nkiscapitalperworkeryisrealgrossdomesticproduct(realGDP)perworkery/kistheaverageproductofcapitalsisthesavingrateδisthedepreciationratenisthepopulationgrowthrate.
2、2MacroeconomicsChapter4SolowGrowthModel SteadyStates·(y*/k*)=sδ+nWeassumedthateverythingontheright-handsidewasconstantexceptfory/k.Inthetransitiontothesteadystate,theriseinkledtoafalliny/kand,hence,toafallin∆k/k.Inthesteadystate,kwasconstantand,therefore,y/kwasconsta
3、nt.Hence,∆k/kwasconstantandequaltozero.3MacroeconomicsChapter4SolowGrowthModel Changeinsavingsrate(s)4MacroeconomicsChapter4SolowGrowthModel Changeinsavingsrate(s)Intheshortrun,anincreaseinthesavingrateraisesthegrowthrateofcapitalperworker.Thisgrowthrateremainshigher
4、duringthetransitiontothesteadystate.5MacroeconomicsChapter4SolowGrowthModel Changeinsavingsrate(s)Inthelongrun,thegrowthrateofcapitalperworkeristhesame—zero—foranysavingrate.Inthislong-runorsteady-statesituation,ahighersavingrateleadstohighersteadystatecapitalperwork
5、er,k∗,nottoachangeinthegrowthrate(whichremainsatzero).A·f(k*)/k*=δ+n/s6MacroeconomicsChapter4SolowGrowthModel theeffectofsonconsumptionsIntheshortrun,consumptiondecreasesandkarises.c*=y*-δk*-s(y*-δk*)=y*-δk*-nk*maxc*=y*-(δ+n)k*k*FOC:dc*/dk*=dy*/dk*-(δ+n)=0MPK=δ+n7Mac
6、roeconomicsChapter4SolowGrowthModel theeffectofsonconsumptions⊿c*=⊿y*-(δ+n)⊿k*=(MPK-δ-n)⊿k*Inthelongrun,whethertheconsumptioninthesteadystateincreasesdependsonMPK.Dynamicinefficient“GoldenRule”8MacroeconomicsChapter4SolowGrowthModel Changeintechnologylevel(A)9Macroec
7、onomicsChapter4SolowGrowthModel Changeintechnologylevel(A)Intheshortrun,anincreaseinthetechnologylevel,A,raisesthegrowthratesofcapitalandrealGDPperworker.Thesegrowthratesremainhigherduringthetransitiontothesteadystate.10MacroeconomicsChapter4SolowGrowthModel Changein
8、technologylevel(A)Inthelongrun,thegrowthratesofcapitalandrealGDPperworkerarethesame—zero—foranytechnologylevel.Inthislong-runorstea
