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1、WorkingwiththeSolowGrowthModelChapter41MacroeconomicsChapter4KeyEquations SolowGrowthModel∆k/k=s·(y/k)−sδ−nkiscapitalperworkeryisrealgrossdomesticproduct(realGDP)perworkery/kistheaverageproductofcapitalsisthesavingrateδisthedepreciationratenisthepopulatio
2、ngrowthrate.2MacroeconomicsChapter4SolowGrowthModel SteadyStates·(y*/k*)=sδ+nWeassumedthateverythingontheright-handsidewasconstantexceptfory/k.Inthetransitiontothesteadystate,theriseinkledtoafalliny/kand,hence,toafallin∆k/k.Inthesteadystate,kwasconstantan
3、d,therefore,y/kwasconstant.Hence,∆k/kwasconstantandequaltozero.3MacroeconomicsChapter4SolowGrowthModel Changeinsavingsrate(s)4MacroeconomicsChapter4SolowGrowthModel Changeinsavingsrate(s)Intheshortrun,anincreaseinthesavingrateraisesthegrowthrateofcapitalp
4、erworker.Thisgrowthrateremainshigherduringthetransitiontothesteadystate.5MacroeconomicsChapter4SolowGrowthModel Changeinsavingsrate(s)Inthelongrun,thegrowthrateofcapitalperworkeristhesame—zero—foranysavingrate.Inthislong-runorsteady-statesituation,ahigher
5、savingrateleadstohighersteadystatecapitalperworker,k∗,nottoachangeinthegrowthrate(whichremainsatzero).A·f(k*)/k*=δ+n/s6MacroeconomicsChapter4SolowGrowthModel theeffectofsonconsumptionsIntheshortrun,consumptiondecreasesandkarises.c*=y*-δk*-s(y*-δk*)=y*-δk*
6、-nk*∆c*=∆y*-(δ+n)∆k*=(MPK-δ-n)∆k*Inthelongrun,whethertheconsumptioninthesteadystateincreasesdependsonMPK.“GoldenRule”7MacroeconomicsChapter4SolowGrowthModel Changeintechnologylevel(A)8MacroeconomicsChapter4SolowGrowthModel Changeintechnologylevel(A)Inthes
7、hortrun,anincreaseinthetechnologylevel,A,raisesthegrowthratesofcapitalandrealGDPperworker.Thesegrowthratesremainhigherduringthetransitiontothesteadystate.9MacroeconomicsChapter4SolowGrowthModel Changeintechnologylevel(A)Inthelongrun,thegrowthratesofcapita
8、landrealGDPperworkerarethesame—zero—foranytechnologylevel.Inthislong-runorsteadystatesituation,ahighertechnologylevelleadstohighersteady-statecapitalandrealGDPperworker,k∗andy∗,nottochangesinthegrowthrates(whichrema
