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1、SolutionstoExercisesinIntroductiontoEconomicGrowth(SecondEdition)CharlesI.Jones(withChaoWeiandJesseCzelusta)DepartmentofEconomicsU.C.BerkeleyBerkeley,CA94720-3880September18,200111IntroductionNoproblems.2TheSolowModelExercise1.Adecreaseintheinvestmentrate.Adecreaseintheinvestment
2、ratecausesthesy~curvetoshiftdown:atanygivenlevelofk~,theinvestment-technologyratioisloweratthenewrateofsav-ing/investment.Assumingtheeconomybeganinsteadystate,thecapital-technologyratioisnowhigherthanisconsistentwiththereducedsavingrate,soitdeclinesgradually,asshowninFigure1.Figu
3、re1:ADecreaseintheInvestmentRate~(n+g+d)k~s'y~s''y~~k**k*ThelogofoutputperworkeryevolvesasinFigure2,andthedynamicsof~_thegrowthrateareshowninFigure3.Recallthatlogy~=logk~andk=k~=s00k~ 1 (n+g+d).Thepolicypermanentlyreducesthelevelofoutputperworker,butthegrowthrateperworkerisonlyte
4、mporarilyreducedandwillreturntoginthelongrun.2Figure2:y(t)LOGyTIMEFigure3:GrowthRateofOutputperWorker.y/ygt*TIME3Exercise2.Anincreaseinthelaborforce.Thekeytothisquestionistorecognizethattheinitialeffectofasuddenin-creaseinthelaborforceistoreducethecapital-laborratiosincekK=LandK
5、isfixedatamomentintime.Assumingtheeconomywasinsteadystatepriortotheincreaseinlaborforce,kfallsfromktosomenewlevelk1.Noticethatthisisamovementalongthesyand(n+d)kcurvesratherthanashiftofeitherschedule:bothcurvesareplottedasfunctionsofk,sothatachangeinkisamovementalongthecurves.(For
6、thisreason,itissomewhattrickytoputthisquestionfirst!)Atk1,sy>(n+d)k1,sothatk_>0,andtheeconomyevolvesaccordingtotheusualSolowdynamics,asshowninFigure4.Figure4:AnIncreaseintheLaborForce(n+d)ksyk1k*kIntheshortrun,percapitaoutputandcapitaldropinresponsetoainlargeflowofworkers.Thenthese
7、twovariablesstarttogrow(atadecreasingrate),untilinthelongrunpercapitacapitalreturnstotheoriginallevel,k.Inthelongrun,nothinghaschanged!Exercise3.Anincometax.Assumethatthegovernmentthrowsawaytheresourcesitreceivesintaxes.Thenanincometaxreducesthetotalamountavailableforinvestingan
8、dshiftstheinvestmentcurvedownasshowninFi
