多恩布什宏观经济学第十版课后习题答案09.docx
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多恩布什宏观经济学第十版课后习题答案09
CHAPTER9
INCOMEANDSPENDING
SolutionstotheProblemsintheTextbook:
ConceptualProblems:
1.IntheKeynesianmodel,thepricelevelisassumedtobefixed,thatis,theAS-curveishorizontalandthelevelofoutputisdeterminedsolelybyaggregatedemand.Theclassicalmodel,ontheotherhand,assumesthatpricesalwaysfullyadjusttomaintainafull-employmentlevelofoutput,thatis,theAS-curveisvertical.Sincethemodelofincomedeterminationinthischapterassumesthatthepricelevelisfixed,itisaKeynesianmodel.
2.Anautonomousvariable’svalueisdeterminedoutsideofagivenmodel.Inthischapterthefollowingcomponentsofaggregatedemandhavebeenspecifiedasbeingautonomous:
autonomousconsumption(C*)autonomousinvestment(Io),governmentpurchases(Go),lumpsumtaxes(TAo),transferpayments(TRo),andnetexports(NXo).
3.Sinceitoftentakesalongtimeforpolicymakerstoagreeonaspecificfiscalpolicymeasure,itisquitepossiblethateconomicconditionsmaydrasticallychangebeforeafiscalpolicymeasureisimplemented.Inthesecircumstancesapolicymeasurecanactuallybedestabilizing.Maybetheeconomyhasalreadybeguntomoveoutofarecessionbeforepolicymakershaveagreedtoimplementataxcut.Ifthetaxcutisenactedatatimewhentheeconomyisalreadybeginningtoexperiencestronggrowth,inflationarypressurecanbecreated.
Whilesuchinternallagsareabsentwithautomaticstabilizers(incometaxes,unemploymentbenefits,welfare),theseautomaticstabilizersarenotsufficienttoreplaceactivefiscalpolicywhentheeconomyentersadeeprecession.
4.Incometaxes,unemploymentbenefits,andthewelfaresystemareoftencalledautomaticstabilizerssincetheyautomaticallyreducetheamountbywhichoutputchangesasaresultofachangeinaggregatedemand.Thesestabilizersareapartoftheeconomicmechanismandthereforeworkwithoutanycase-by-casegovernmentintervention.Forexample,whenoutputdeclinesandunemploymentincreases,theremaybeanincreaseinthenumberofpeoplewhofallbelowthepovertyline.Ifwehadnowelfaresystemorunemploymentbenefits,thenconsumptionwoulddropsignificantly.Butsinceunemployedworkersgetunemploymentcompensationandpeoplelivinginpovertyareeligibleforwelfarepayments,consumptionwillnotdecreaseasmuch.Therefore,aggregatedemandmaynotbereducedbyasmuchasitwouldhavewithouttheseautomaticstabilizers.
5.Thefull-employmentbudgetsurplusisthebudgetsurplusthatwouldexistiftheeconomywereatthefull-employmentlevelofoutput,giventhecurrentspendingortaxstructure.Sincethesizeofthefull-employmentbudgetsurplusdoesnotdependonthepositioninthebusinesscycleandonlychangeswhenthegovernmentimplementsafiscalpolicychange,thefull-employmentbudgetsurpluscanbeusedasameasureoffiscalpolicy.Othernamesforthefull-employmentbudgetsurplusarethestructuralbudgetsurplus,thecyclicallyadjustedsurplus,thehigh-employmentsurplus,andthestandardizedemploymentsurplus.Thesenamesmaybepreferable,sincetheydonotsuggestthatthereisaspecificfull-employmentlevelofoutputthatwewereunabletomaintain.
TechnicalProblems:
1.a.AD=C+I=100+(0.8)Y+50=150+(0.8)Y
TheequilibriumconditionisY=AD==>
Y=150+(0.8)Y==>(0.2)Y=150==>Y=5*150=750.
1.b.SinceTA=TR=0,itfollowsthatS=YD-C=Y-C.Therefore
S=Y-[100+(0.8)Y]=-100+(0.2)Y==>S=-100+(0.2)750=-100+150=50.
1.c.IfthelevelofoutputisY=800,thenAD=150+(0.8)800=150+640=790.
ThereforetheamountofinvoluntaryinventoryaccumulationisUI=Y-AD=800-790=10.
1.d.AD'=C+I'=100+(0.8)Y+100=200+(0.8)Y
FromY=AD'==>Y=200+(0.8)Y==>(0.2)Y=200==>Y=5*200=1,000
Note:
Thisresultcanalsobeachievedbyusingthemultiplierformula:
∆Y=(multiplier)(∆Sp)=(multiplier)(∆I)==>∆Y=5*50=250,
thatis,outputincreasesfromYo=750toY1=1,000.
1.e.From1.a.and1.d.wecanseethatthemultiplieris5.
1.f.SpY=Sp
AD1=200=(0.8)Y
ADo=150+(0.8)Y
200
150
0
7501,000Y
2.a.Sincethempchasincreasedfrom0.8to0.9,thesizeofthemultiplierisnowlargerandweshouldthereforeexpectahigherequilibriumincomelevelthanin1.a.
AD=C+I=100+(0.9)Y+50=150+(0.9)Y==>
Y=AD==>Y=150+(0.9)Y==>(0.1)Y=150==>Y=10*150=1,500.
2.b.From∆Y=(multiplier)(∆I)=10*50=500==>Y1=Yo+∆Y=1,500+500=2,000.
2.c.Sincethesizeofthemultiplierhasdoubledfrom5to10,thechangeinoutput(Y)thatresultsfromachangeininvestment(I)nowhasalsodoubledfrom250to500.
2.d.SpY=Sp
AD1=200=(0.9)Y
ADo=150+(0.9)Y
200
150
01,5002,000Y
3.a.AD=C+I+G+NX=50+(0.8)YD+70+200=320+(0.8)[Y-(0.2)Y+100]
=400+(0.8)(0.8)Y=400+(0.64)Y
FromY=AD==>Y=400+(0.64)Y==>(0.36)Y=400
==>Y=(1/0.36)400=(2.78)400=1,111.11
Thesizeofthemultiplieris(1/0.36)=2.78.
3.b.BS=tY-TR-G=(0.2)(1,111.11)-100-200=222.22-300=-77.78
3.c.AD'=320+(0.8)[Y-(0.25)Y+100]=400+(0.8)(0.75)Y=400+(0.6)Y
FromY=AD'==>Y=400+(0.6)Y==>(0.4)Y=400==>Y=(2.5)400=1,000
Thesizeofthemultiplierisnowreducedto2.5.
3.d.BS'=(0.25)(1,000)-100-200=-50
BS'-BS=-50-(-77.78)=+27.78
Thesizeofthemultiplierandequilibriumoutputwillbothincreasewithanincreaseinthemarginalpropensitytoconsume.Thereforeincometaxrevenuewillalsogoupandthebudgetsurplusshouldincrease.
3.e.Iftheincometaxrateist=1,thenallincomeistaxed.Thereisnoinducedspendingandequilibriumincomeonlyincreasesbythechangeinautonomousspending,thatis,thesizeofthemultiplieris1.
FromY=C+I+G==>Y=Co+c(Y-1Y+TRo)+Io+Go
==>Y=Co+cTRo+Io+Go=Ao
4.InProblem3.d.wehadasituationwherethefollowingwasgiven:
Y=1,000,t=0.25,G=200andBS=-50.
Assumenowthatt=0.3andG=250==>
AD'=50+(0.8)[Y-(0.3)Y+100]+70+250=370+(0.8)(0.7)Y+80=450+(0.56)Y.
FromY=AD'==>Y=450+(0.56)Y==>(0.44)Y=450
==>Y=(1/0.44)450=1,022.73
BS'=(0.3)(1,022.73)-100-250=306.82-350=-43.18
BS'-BS=-43.18-(-50)=+6.82
Thebudgetsurplushasincreased,sincetheincreaseintaxrevenueislargerthantheincreaseingovernmentpurchases.
5.a.Whileanincreaseingovernmentpurchasesby∆G=10willchangeintendedspendingby∆Sp=10,adecreaseingovernmenttransfersby∆TR=-10willchangeintendedspendingbyasmalleramount,thatis,byonly∆Sp=c(∆TR)=c(-10).Thechangeinintendedspendingequals∆Sp=(1-c)(10)andequilibriumincomeshouldthereforeincreaseby
∆Y=(multiplier)(1-c)10.
5.b.Ifc=0.8andt=0.25,thenthesizeofthemultiplieris
α=1/[1-c(1-t)]=1/[1-(0.8)(1-0.25)]=1/[1-(0.6)]=1/(0.4)=2.5.
Thechangeinequilibriumincomeis
∆Y=α(∆Ao)=α[∆G+c(∆TR)]=(2.5)[10+(0.8)(-10)]=(2.5)2=5
5.c.∆BS=t(∆Y)-∆TR-∆G=(0.25)(5)-(-10)-10=1.25
AdditionalProblems:
1."Anincreaseinthemarginalpropensitytosaveincreasestheimpactofoneadditionaldollarinincomeonconsumption."Commentonthisstatement.Inyouranswerdiscusstheeffectofsuchachangeinthempsonthesizeoftheexpendituremultiplier.
Thefactthatthemarginalpropensitytosave(1-c)hasrisenimpliesthatthemarginalpropensitytoconsume(c)hasfallen.Thismeansthatnowoneextradollarinincomeearnedwillaffectconsumptionbylessthanbeforethereductioninthempc.Whenthempcishigh,oneextradollarinincomeraisesconsumptionbymorethanwhenthempcislow.Ifthempsislarger,thentheexpendituremultiplierwillbelarger,sincetheexpendituremultiplierisdefinedas1/(1-c).
2.Usingasimplemodeloftheexpendituresectorwithoutanygovernmentinvolvement,explaintheparadoxofthriftthatassertsthatadesiretosavemaynotleadtoanincreaseinactualsaving.
Theparadoxofthriftoccursbecausethedesiretoincreasesavingleadstoalowerconsumptionlevel.Butalowerlevelofspendingsendstheeconomyintoarecessionandwegetanewequilibriumatalowerlevelofoutput.Intheend,theincreaseinautonomoussavingisexactlyoffsetbythedecreaseininducedsavingduetothelowerincomelevel.Inotherwords,theeconomyisinequilibriumwhenS=Io.Sincethelevelofautonomousinvestment(Io)hasnotchanged,thelevelofsavingatthenewequilibriumincomelevelmustalsoequalIo.
Thiscanalsobederivedmathematically.Sinceanincreaseindesiredsavingisequivalenttoadecreaseindesiredconsumption,thatis,∆Co=-∆So,theeffectonequilibriumincomeis
∆Y=[1/(1-c)](∆Co)=[1/(1-c)](-∆So).
Thereforetheoveralleffectontotalsavingis
∆S=s(∆Y)+∆So=[s/(1-c)](-∆So)+∆So=0,sinces=1-c.
3."Whenaggregatedemandfallsbelowthecurrentoutputlevel,anunintendedinventoryaccumulationoccursandtheeconomyisnolongerinanequilibrium."Commentonthisstatement.
Ifaggregatedemandfallsbelowtheequilibriumoutputlevel,productionexceedsdesiredspending.Whenfirmsseeanunwantedaccumulationintheirinventories,theyrespondbyreducingproduction.Thelevelofoutputfallsandeventuallyreachesalevelatwhichtotaloutputequalsdesiredspending.Inotherwords,theeconomyeventuallyreachesanewequilibriumatalowervalueofoutput.
4.Forasimplemodeloftheexpendituresectorwithoutanygovernmentinvolvement,derivethemultiplierintermsofthemarginalprope
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