曼昆宏观经济经济学第九版英文原版答案3资料.docx
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曼昆宏观经济经济学第九版英文原版答案3资料.docx
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曼昆宏观经济经济学第九版英文原版答案3资料
AnswerstoTextbookQuestionsandProblems
CHAPTER3 NationalIncome:
WhereItComesFromandWhereItGoes
QuestionsforReview
1.Thefactorsofproductionandtheproductiontechnologydeterminetheamountofoutputaneconomycanproduce.Thefactorsofproductionaretheinputsusedtoproducegoodsandservices:
themostimportantfactorsarecapitalandlabor.Theproductiontechnologydetermineshowmuchoutputcanbeproducedfromanygivenamountsoftheseinputs.Anincreaseinoneofthefactorsofproductionoranimprovementintechnologyleadstoanincreaseintheeconomy’soutput.
2.Whenafirmdecideshowmuchofafactorofproductiontohireordemand,itconsidershowthisdecisionaffectsprofits.Forexample,hiringanextraunitoflaborincreasesoutputandthereforeincreasesrevenue;thefirmcomparesthisadditionalrevenuetotheadditionalcostfromthehigherwagebill.Theadditionalrevenuethefirmreceivesdependsonthemarginalproductoflabor(MPL)andthepriceofthegoodproduced(P).AnadditionalunitoflaborproducesMPLunitsofadditionaloutput,whichsellsforPdollarsperunit.Therefore,theadditionalrevenuetothefirmisPMPL.ThecostofhiringtheadditionalunitoflaboristhewageW.Thus,thishiringdecisionhasthefollowingeffectonprofits:
ΔProfit=ΔRevenue–ΔCost
=(PMPL)–W.
Iftheadditionalrevenue,PMPL,exceedsthecost(W)ofhiringtheadditionalunitoflabor,thenprofitincreases.Thefirmwillhirelaboruntilitisnolongerprofitabletodoso—thatis,untiltheMPLfallstothepointwherethechangeinprofitiszero.Intheequationabove,thefirmhireslaboruntilΔProfit=0,whichiswhen(PMPL)=W.
Thisconditioncanberewrittenas:
MPL=W/P.
Therefore,acompetitiveprofit-maximizingfirmhireslaboruntilthemarginalproductoflaborequalstherealwage.Thesamelogicappliestothefirm’sdecisionregardinghowmuchcapitaltohire:
thefirmwillhirecapitaluntilthemarginalproductofcapitalequalstherealrentalprice.
3.Aproductionfunctionhasconstantreturnstoscaleifanequalpercentageincreaseinallfactorsofproductioncausesanincreaseinoutputofthesamepercentage.Forexample,ifafirmincreasesitsuseofcapitalandlaborby50percent,andoutputincreasesby50percent,thentheproductionfunctionhasconstantreturnstoscale.
Iftheproductionfunctionhasconstantreturnstoscale,thentotalincome(orequivalently,totaloutput)inaneconomyofcompetitiveprofit-maximizingfirmsisdividedbetweenthereturntolabor,MPLL,andthereturntocapital,MPKK.Thatis,underconstantreturnstoscale,economicprofitiszero.
4.ACobb–DouglasproductionfunctionhastheformF(K,L)=AKαL1–α.Thetextshowedthattheparameterαgivescapital’sshareofincome.Soifcapitalearnsone-fourthoftotalincome,thenα=0.25.Hence,F(K,L)=AK0.25L0.75.
5.Consumptiondependspositivelyondisposableincome—i.e.theamountofincomeafteralltaxeshavebeenpaid.Higherdisposableincomemeanshigherconsumption.
Thequantityofinvestmentgoodsdemandeddependsnegativelyontherealinterestrate.Foraninvestmenttobeprofitable,itsreturnmustbegreaterthanitscost.Becausetherealinterestratemeasuresthecostoffunds,ahigherrealinterestratemakesitmorecostlytoinvest,sothedemandforinvestmentgoodsfalls.
6.Governmentpurchasesareameasureofthevalueofgoodsandservicespurchaseddirectlybythegovernment.Forexample,thegovernmentbuysmissilesandtanks,buildsroads,andprovidesservicessuchasairtrafficcontrol.AlloftheseactivitiesarepartofGDP.Transferpaymentsaregovernmentpaymentstoindividualsthatarenotinexchangeforgoodsorservices.Theyaretheoppositeoftaxes:
taxesreducehouseholddisposableincome,whereastransferpaymentsincreaseit.ExamplesoftransferpaymentsincludeSocialSecuritypaymentstotheelderly,unemploymentinsurance,andveterans’benefits.
7.Consumption,investment,andgovernmentpurchasesdeterminedemandfortheeconomy’soutput,whereasthefactorsofproductionandtheproductionfunctiondeterminethesupplyofoutput.Therealinterestrateadjuststoensurethatthedemandfortheeconomy’sgoodsequalsthesupply.Attheequilibriuminterestrate,thedemandforgoodsandservicesequalsthesupply.
8.Whenthegovernmentincreasestaxes,disposableincomefalls,andthereforeconsumptionfallsaswell.Thedecreaseinconsumptionequalstheamountthattaxesincreasemultipliedbythemarginalpropensitytoconsume(MPC).ThehighertheMPCis,thegreateristhenegativeeffectofthetaxincreaseonconsumption.Becauseoutputisfixedbythefactorsofproductionandtheproductiontechnology,andgovernmentpurchaseshavenotchanged,thedecreaseinconsumptionmustbeoffsetbyanincreaseininvestment.Forinvestmenttorise,therealinterestratemustfall.Therefore,ataxincreaseleadstoadecreaseinconsumption,anincreaseininvestment,andafallintherealinterestrate.
ProblemsandApplications
1.a.Accordingtotheneoclassicaltheoryofdistribution,therealwageequalsthemarginalproductoflabor.Becauseofdiminishingreturnstolabor,anincreaseinthelaborforcecausesthemarginalproductoflabortofall.Hence,therealwagefalls.
GivenaCobb–Douglasproductionfunction,theincreaseinthelaborforcewillincreasethemarginalproductofcapitalandwillincreasetherealrentalpriceofcapital.Withmoreworkers,thecapitalwillbeusedmoreintensivelyandwillbemoreproductive.
b.Therealrentalpriceequalsthemarginalproductofcapital.Ifanearthquakedestroyssomeofthecapitalstock(yetmiraculouslydoesnotkillanyoneandlowerthelaborforce),themarginalproductofcapitalrisesand,hence,therealrentalpricerises.
GivenaCobb–Douglasproductionfunction,thedecreaseinthecapitalstockwilldecreasethemarginalproductoflaborandwilldecreasetherealwage.Withlesscapital,eachworkerbecomeslessproductive.
c.Ifatechnologicaladvanceimprovestheproductionfunction,thisislikelytoincreasethemarginalproductsofbothcapitalandlabor.Hence,therealwageandtherealrentalpricebothincrease.
d.Highinflationthatdoublesthenominalwageandthepricelevelwillhavenoimpactontherealwage.Similarly,highinflationthatdoublesthenominalrentalpriceofcapitalandthepricelevelwillhavenoimpactontherealrentalpriceofcapital.
2.a.Tofindtheamountofoutputproduced,substitutethegivenvaluesforlaborandlandintotheproductionfunction:
Y=1000.51000.5=100.
b.Accordingtothetext,theformulasforthemarginalproductoflaborandthemarginalproductofcapital(land)are:
MPL=(1–α)AKαL–α.
MPK=αAKα–1L1–α.
Inthisproblem,αis0.5andAis1.Substituteinthegivenvaluesforlaborandlandtofindthemarginalproductoflaboris0.5andmarginalproductofcapital(land)is0.5.Weknowthattherealwageequalsthemarginalproductoflaborandtherealrentalpriceoflandequalsthemarginalproductofcapital(land).
c.Labor’sshareoftheoutputisgivenbythemarginalproductoflabortimesthequantityoflabor,or50.
d.Thenewlevelofoutputis70.71.
e.Thenewwageis0.71.Thenewrentalpriceoflandis0.35.
f.Labornowreceives35.36.
3.Aproductionfunctionhasdecreasingreturnstoscaleifanequalpercentageincreaseinallfactorsofproductionleadstoasmallerpercentageincreaseinoutput.Forexample,ifwedoubletheamountsofcapitalandlaboroutputincreasesbylessthandouble,thentheproductionfunctionhasdecreasingreturnstoscale.Thismayhappenifthereisafixedfactorsuchaslandintheproductionfunction,andthisfixedfactorbecomesscarceastheeconomygrowslarger.
Aproductionfunctionhasincreasingreturnstoscaleifanequalpercentageincreaseinallfactorsofproductionleadstoalargerpercentageincreaseinoutput.Forexample,ifdoublingtheamountofcapitalandlaborincreasestheoutputbymorethandouble,thentheproductionfunctionhasincreasingreturnstoscale.Thismayhappenifspecializationoflaborbecomesgreaterasthepopulationgrows.Forexample,ifonlyoneworkerbuildsacar,thenittakeshimalongtimebecausehehastolearnmanydifferentskills,andhemustconstantlychangetasksandtools.Butifmanyworkersbuildacar,theneachonecanspecializeinaparticulartaskandbecomemoreproductive.
4.a.ACobb–DouglasproductionfunctionhastheformY=AKαL1–α.ThetextshowedthatthemarginalproductsfortheCobb–Douglasproductionfunctionare:
MPL=(1–α)Y/L.
MPK=αY/K.
Competitiveprofit-maximizingfirmshirelaboruntilitsmarginalproductequalstherealwage,andhirecapitaluntilitsmarginalproductequalstherealrentalrate.UsingthesefactsandtheabovemarginalproductsfortheCobb–Douglasproductionfunction,wefind:
W/P=MPL=(1–α)Y/L.
R/P=MPK=αY/K.
Rewritingthis:
(W/P)L=MPLL=(1–α)Y.
(R/P)K=MPKK=αY.
Notethattheterms(W/P)Land(R/P)Karethewagebillandtotalreturntocapital,respectively.Giventhatthevalueofα=0.3,thentheaboveformulasindicatethatlaborreceives70percentoftotaloutput(orincome)andcapitalreceives30percentoftotaloutput(orincome).
b.Todeterminewhathappenstototaloutputwhenthelaborforceincreasesby10percent,considertheformulafortheCobb–Douglasproductionfunction:
Y=AKαL1–α.
LetY1equaltheinitialvalueofoutputandY2equalfinaloutput.Weknowthatα=0.3.WealsoknowthatlaborLincreasesby10percent:
Y1=AK0.3L0.7.
Y2=AK0.3(1.1L)0.7.
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