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【上海交通大学-安泰】中级宏观经济学作业

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【上海交通大学-安泰】中级宏观经济学作业【上海交通大学-安泰】中级宏观经济学作业Assignment#21.IntheUnitedStates,thecapitalshareofGDPisabout50%,theaveragegrowthintotaloutputis3%peryear,thedepreciaterateis5%peryear,thecapital-outputratiois4.SupposethattheproductionfunctionisCobb-Douglas,sothatthecapitalshareofoutputiscon...

【上海交通大学-安泰】中级宏观经济学作业
【上海交通大学-安泰】中级宏观经济学作业Assignment#21.IntheUnitedStates,thecapitalshareofGDPisabout50%,theaveragegrowthintotaloutputis3%peryear,thedepreciaterateis5%peryear,thecapital-outputratiois4.SupposethattheproductionfunctionisCobb-Douglas,sothatthecapitalshareofoutputisconstant,andtheUnitedStateshasbeeninasteadystate.(10points)a)Whatmustthesavingratebeintheinitialsteadystate?b)Whatisthemarginalproductofcapitalintheinitialsteadystate?c)Whatwillthecapital-outputratiobeattheGoldenRulesteadystate?d)WhatmustthesavingratebetoreachtheGoldenRatesteadystate?2.ProveeachofthefollowingstatementsaboutthesteadystateoftheSolowmodelwithpopulationgrowthandtechnologicalprogress.(10points)a)Thecapital-outputratioisconstantb)Capitalandlaboreachearnaconstantshareofaneconomy’sincome.c)Totalcapitalincomeandtotallaborincomebothgrowattherateofpopulationgrowthplustherateoftechnologicalprogress,n+g.d)Therealrentalpriceofcapitalisconstant,andtherealwagegrowsattherateoftechnologicalprogressg.3.ThecountryofLeverettisasmallopeneconomy.Suddenly,achangeinworldfashionsmakestheexportsofLeverettunpopular.(10points)a)WhathappensinLeveretttosaving,investment,netexports,theinterestrate,andtheexchangerate?b)ThecitizensofLeverettliketotravelabroad.Howwillthischangeintheexchangerateaffectthem?c)ThefiscalpolicymakersofLeverettwanttoadjusttaxestomaintaintheexchangerateatitspreviouslevel.Whatshouldtheydo?Iftheydothis,whataretheoveralleffectsonsaving,investment,netexports,andtheinterestrate?4.ConsideraneconomywiththefollowingCobb-Douglasproductionfunction:Y=K1/3L2/3Theeconomyhas1000unitsofcapitalandalaborforceof1000workers.(10points)a)Derivetheequationdescribinglabordemandinthiseconomyasafunctionoftherealwageandthecapitalstockb)Iftherealwagecanadjusttoequilibratelaborsupplyandlabordemand,whatistherealwage?Inthisequilibrium,whatareemployment,output,andthetotalamountearnedbyworkers?c)NowsupposethatCongress,concernedaboutthewelfareoftheworkingclass,passesalawrequiringfirmstopayworkerarealwageof1unitofoutput.Howdoesthiswagecomparetotheequilibriumwage?d)Congresscannotdictatehowmanyworkersfirmshireatthemandatedwage.Giventhisfact,whataretheeffectsofthislaw?Specifically,whathappenstoemployment,output,andthetotalamountearnedbyworkers?e)WillCongresssucceedinitsgoalofhelpingtheworkingclass?Explain.5.Supposeweknowthatworkerstendtoreceive70%ofalltheincomeearnedinGermany,thattheGermandepreciationrateis10%,andthatthereisnopopulationgrowthortechnologicalprogress.SupposeweCANNOTassumetheproductionfunctioninGermanytakestheconvenientCobb-Douglasform,butwecanassumethatwhatevertheproductionfunctionis,ithasconstantreturnstoscale,thattheonlytwofactorsofproductionarecapitalandlabor,thatmarketsarecompetitive,andthatfirmsmaximizeprofits.Usingjustthisinformation,computewhatsavingrateGermanyshouldtrytohave,ifitwantstoenjoythemaximumamountofconsumptionperpersoninsteadystate(thatis,toachievethegoldenrule).(10points)
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