多恩布什宏觀經(jīng)濟(jì)學(xué)第十版課后習(xí)題答案09

多恩布什宏觀經(jīng)濟(jì)學(xué)第十版課后習(xí)題答案09CHAPTER9INCOMEANDSPENDINGSolutionstotheProblemsintheTextbook: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)YTheequilibriumconditionisY=AD==>12Y=150+(0.8)Y==>(0.2)Y=150==>Y=5*150=750.1.b.SinceTA=TR=0,itfollowsthatS=YD-C=Y-C.ThereforeS=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)YFromY=AD'==>Y=200+(0.8)Y==>(0.2)Y=200==>Y=5*200=1,000Note:Thisresultcanalsobeachievedbyusingthemultiplierformula:Y=(multiplier)(?Sp)=(multiplier)(?I)==>?Y=5*50=250,thatis,outputincreasesfromYo=750toY1=1,000.1.e.From1.a.and1.d.wecanseethatthemultiplieris5.1.f.Sp20015007501,000Y2.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)nowhasalsodoubledfrom250to500.2001503.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)YFromY=AD==>Y=400+(0.64)Y==>(0.36)Y=400==>Y=(1/0.36)400=(2.78)400=1,111.11Thesizeofthemultiplieris(1/0.36)=2.78.3.b.BS=tY-TR-G=(0.2)(1,111.11)-100-200=222.22-300=-77.783.c.AD'=320+(0.8)[Y-(0.25)Y+100]=400+(0.8)(0.75)Y=400+(0.6)YFromY=AD'==>Y=400+(0.6)Y==>(0.4)Y=400==>Y=(2.5)400=1,000Thesizeofthemultiplierisnowreducedto2.5.3.d.BS'=(0.25)(1,000)-100-200=-50BS'-BS=-50-(-77.78)=+27.78Thesizeofthemultiplierandequilibriumoutputwillbothincreasewithanincreaseinthemarginalpropensitytoconsume.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=Ao4.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=1,022.73BS'=(0.3)(1,022.73)-100-250=306.82-350=-43.18BS'-BS=-43.18-(-50)=+6.82Thebudgetsurplushasincreased,sincetheincreaseintaxrevenueislargerthantheincreaseingovernmentpurchases.5.a.Whileanincreaseingovernmentpurchasesby?G=10willchangeintendedspendingby?Sp=10,adecreaseingovernmenttransfersby?TR=-10willchangeintendedspendingbyasmalleramount,thatis,byonly?Sp=c(?TR)=c(-10).Thechangeinintendedspendingequals?Sp=(1-c)(10)andequilibriumincomeshouldthereforeincreasebyY=(multiplier)(1-c)10.5.b.Ifc=0.8andt=0.25,thenthesizeofthemultiplierisα=1/[1-c(1-t)]=1/[1-(0.8)(1-0.25)]=1/[1-(0.6)]=1/(0.4)=2.5.ThechangeinequilibriumincomeisY=α(?Ao)=α[?G+c(?TR)]=(2.5)[10+(0.8)(-10)]=(2.5)2=55.c.?BS=t(?Y)-?TR-?G=(0.25)(5)-(-10)-10=1.25AdditionalProblems:1."Anincreaseinthemarginalpropensitytosaveincreasestheimpactofoneadditionaldollarinincomeonconsumption."Commentonthisstatement.Inyouranswerdiscusstheeffectofsuchachangeinthempsonthesizeoftheexpendituremultiplier.Thefactthatthemarginalpropensitytosave(1-c)hasrisenimpliesthatthemarginalpropensitytoconsume(c)hasfallen.Thismeansthatnowoneextradollarinincomeearnedwillaffectconsumptionby3lessthanbeforethereductioninthempc.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).ThereforetheoveralleffectontotalsavingisS=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,derivethemultiplierintermsofthemarginalpropensitytosave(s)ratherthanthemarginalpropensitytoconsume(c).Doesthisformulastillholdwhenthegovernmententersthepictureandleviesanincometax?Inthetext,theexpendituremultiplierforamodelwithoutanygovernmentinvolvementwasderivedasα=1/(1-c).Butsincethemarginalpropensitytosaveiss=1-c,themultipliernowbecomesα=1/s=1/(1-c).Inthetext,wehavealsoseenthatifthegovernmententersthepictureandleviesanincometax,thenthesimpleexpendituremultiplierchangestoα=1/[1-c(1-t)]=1/(1-c').Bysubstitutings=1-c,thisequationcanbeeasilymanipulated,togetα’=1/[1-c+ct]=1/[s+(1-s)t]=1/s'.Justass=1–c,wecansaythats'=1-c',sinces'=1-c'=1-c(1-t)=1-c+ct=s+(1-s)t.Thiscanalsobederivedinanotherway:S=YD-C=YD-(C*+cYD)=-C*+(1-c)YD=-C*+sYDIfweassumeforsimplicitythatTR=0andNX=0,thenS+TA=I+G==>-C*+sYD+TA=I*+G*==>s(Y-tY-TA*)+tY+TA*=C*+I*+G*==>4[s+(1-s)t]Y=C*+I*+G*-(1-s)TA*=A*==>Y=(1/[s+(1-s)t])A*=(1/s')A*.5.Thebalancedbudgettheoremstatesthatthegovernmentcanstimulatetheeconomywithoutincreasingthebudgetdeficitifanincreaseingovernmentpurchases(G)isfinancedbyanequivalentincreaseintaxes(TA).Showthatthisistrueforasimplemodeloftheexpendituresectorwithoutanyincometaxes.Iftaxesandgovernmentpurchasesareincreasedbythesameamount,thenthechangeinthebudgetsurpluscanbecalculatedasBS=?TAo-?G=0,since?TAo=?G.TheresultingchangeinnationalincomeisY=?C+?G=c(?YD)+?G=c(?Y-?TAo)+?G=c(?Y)-c(?TAo)+?G=c(?Y)+(1-c)(?G)since?TAo=?G.==>(1-c)(?Y)=(1-c)(?G)==>?Y=?GInthiscase,theincreaseinoutput(Y)isexactlyofthesamemagnitudeastheincreaseingovernmentpurchases(G).Thisoccurssincethedecreaseinthelevelofconsumptionduetothehigherlumpsumtaxhasexactlybeenoffsetbytheincreaseinthelevelofconsumptioncausedbytheincreaseinincome.6.Assumeamodelwithoutincometaxesandinwhichtheonlytwocomponentsofaggregatedemandareconsumptionandinvestment.Showthat,inthiscase,thetwoequilibriumconditionsY=C+IandS=Iareequivalent.Wecanderivetheequilibriumvalueofoutputbysettingactualincomeequaltointendedspending,thatis,Y=C+I==>Y=C*+cY+I*==>(1-c)Y=C*+I*==>Y=[1/(1-c)](C*+I*)=[1/(1-c)]A*.ButsinceS=YD-C=Y-[C*+cY]=-C*+(1-c)Y,wecanderivethesameresultfromS=I*==>S=-C*+(1-c)Y=I*==>(1-c)Y=C*+I*==>Y=[1/(1-c)](C*+I*)=[1/(1-c)]A*.7.Inanefforttostimulatetheeconomyin1976,PresidentFordaskedCongressfora$20billiontaxcutincombinationwitha$20billioncutingovernmentpurchases.Doyouconsiderthisagoodpolicyproposal?Whyorwhynot?Thisisnotagoodpolicyproposal.Accordingtothebalancedbudgettheorem,equaldecreasesingovernmentpurchasesandtaxeswilldecreaseratherthanincreaseincome.Thereforetheintendedresultwouldnotbeachieved.8.Assumethefollowingmodeloftheexpendituresector:Sp=C+I+G+NXC=420+(4/5)YDYD=Y-TA+TRTA=(1/6)YTRo=180Io=160Go=100NXo=-40(a)Assumethegovernmentwouldliketoincreasetheequilibriumlevelofincome(Y)tothefull-employmentlevelY*=2,700.Byhowmuchshouldgovernmentpurchases(G)bechanged?(b)AssumewewanttoreachY*=2,700bychanginggovernmenttransferpayments(TR)instead.ByhowmuchshouldTRbechanged?(c)Assumeyouincreasebothgovernmentpurchases(G)andtaxes(TA)bythesamelumpsumof?G=?TAo=+300.Wouldthischangeinfiscalpolicybesufficienttoreachthefull-employmentlevelofoutputatY*=2,700?Whyorwhynot?(d)Brieflyexplainhowadecreaseinthemarginalpropensitytosavewouldaffectthesizeoftheexpendituremultiplier.5a.Sp=C+I+G+NX=420+(4/5)[Y-(1/6)Y+100]+160+180-40=720+(4/5)(5/6)Y+80=800+(2/3)YFromY=Sp==>Y=800+(2/3)Y==>(1/3)Y=800==>Y=3*800=2,400==>theexpendituremultiplierisα=3From?Y=α(?Ao)==>300=3(?Ao)==>(?Ao)=100Thusgovernmentpurchasesshouldbechangedby?G=?Ao=100.b.Since?Ao=100and?Ao=c(?TRo)==>100=(4/5)(?TRo)==>?TRo=125.c.Thisisamodelwithincometaxes,sothebalancedbudgettheoremdoesnotapplyinitsstrictestform,whichstatesthatanincreaseingovernmentpurchasesandtaxesbyacertainamountincreasesnationalincomebythatsameamount,leavingthebudgetsurplusunchanged.Heretotaltaxrevenueactuallyincreasesbymorethan100,sincetaxesareinitiallyincreasedbyalumpsumof100,butthenincometaxesalsochangeduetothechangeinincome.Thusincomedoesnotincreaseby?Y=300,aswecanseebelow.Y=α(?G)+α[(-c)(αTAo)=3*300+3*[-(4/5)300]=900-720=180Thischangeinfiscalpolicywillincreaseincomebyonly?Y=180,fromY0=2,400toY1=2,580,andwewillbeunabletoreachY*=2,700.d.Ifthemarginalpropensitytosavedecreases,peoplespendalargerportionoftheiradditionaldisposableincome,thatis,thempcandtheslopeofthe[C+I+G+NX]-lineincrease.Thiswillleadtoanincreaseintheexpendituremultiplierandequilibriumincome.9.AssumeamodelwithincometaxessimilartothemodelinProblem9above.Thistime,however,youhaveonlylimitedinformationaboutthemodel,thatis,youonlyknowthatthemarginalpropensitytoconsumeoutofdisposableincomeisc=0.75,andthattotalautonomousspendingisAo=900,suchthatSp=Ao+c'Y=900+c'Y.Youalsoknowthatyoucanreachthefull-employmentlevelofoutputatY*=3,150byincreasinggovernmenttransfersbyalumpsumof?TR=200.(a)Whatisyourcurrentequilibriumlevel?(b)Isitpossibletodeterminethesizeoftheexpendituremultiplierwiththeinformationyouhave?(c)Assumeyouwanttochangetheincometaxrate(t)inordertoreachthefull-employmentlevelofincomeY*=3,150.Howwouldthischangeintheincometaxrateaffectthesizeoftheexpendituremultiplier?a.Since?A=c(?TR)=(0.75)200=150,thenew[C+I+G+NX]-lineisoftheformSp1=1,050+c1Y.Foreachmodeloftheexpendituresectorwecanderivetheequilibriumlevelofincomebyusingthefollowingequation:Y*=αAo=1/(1-c’)==>3,150=α1,050==>theexpendituremultiplierisα=3.Ifwenowchangeautonomousspendingby?A=150,thenincomewillhavetochangeby?Y=α(?A)==>?Y=3*150=450.ThereforetheoldequilibriumlevelofincomemusthavebeenY=3,150-450=2,700.b.Fromourworkabovewecanseethatthesizeofthemultiplierisα=3.c.Thenew[C+I+G+NX]-lineisoftheformSp2=900+c2Y.Thisnewintendedspendinglineintersectsthe45-degreelineatY=3,150.Thustheslopeofthenewintendedspendinglinecanbederivedasc2=(3,150-900)/(3,150)=5/7.FromY=Sp2==>Y=900+(5/7)Y==>(2/7)Y=900==>Y=(7/2)900=(3.5)900=3,150.6Thenewvalueofthemultiplieris3.5Sp3,1509002,7003,150Y10.Assumeyouhavethefollowingmodeloftheexpendituresector:Sp=C+I+G+NXC=400+(0.8)YDIo=200Go=300+(0.1)(Y*-Y)YD=Y-TA+TRNXo=-40TA=(0.25)YTRo=50(a)WhatisthesizeoftheoutputgapifpotentialoutputisatY*=3,000?(b)Byhowmuchwouldinvestment(I)havetochangetoreachequilibriumatY*=3,000,andhowdoesthischangeaffectthebudgetsurplus?(c)Fromthemodelaboveyoucanseethatgovernmentpurchases(G)arecounter-cyclical,thatistheyareincreasedasnationalincomedecreases.IfyoucomparethisspecificationofGwithaconstantlevelofG,howisthevalueoftheexpendituremultiplieraffected?(d)AssumetheequationfornetexportsischangessuchthatNXo=-40isnowNX1=-40-mY,with0<m<1.Howwouldthisaffectexpendituremultiplier?a.Sp=400+(0.8)YD+200+300+(0.1)(3,000-Y)-40=1,160+(0.8)(Y-(0.25)Y+50)-(0.1)Y=1,200+[(0.8)(0.75)-(0.1)]Y=1,200+(0.5)YY=Sp==>Y=1,200+(0.5)Y==>(0.5)Y=1,200==>Y=2*1,200=2,400TheoutputgapisY*-Y=3,000-2,400=600.b.From?Y=(mult.)(?A)==>600=2(?I)==>?I=300BuS=TA-TR-G=(0.25)(2,400)-50-[300+(0.1)(600)]=600-50-300-60=190BuS*=(0.25)(3,000)-50-300=400,sothebudgetsurplusincreasesby?BuS=210.c.Ifgovernmentpurchasesareusedasastabilizationtool,thesizeofthemultipliershouldbelowerthanifthelevelofgovernmentspendingisfixed.Inthemodeloftheexpendituresectorabove,theslopeofthe[C+I+G+NX]-lineisc'=0.5comparedtoc"=0.6,whengovernmentpurchasesweredefinedasG=300.d.Withthischange,netexportsdecreaseasnationalincomeincreases.Thisadditionalleakageimpliesthatthesizeofthemultiplierwilldecrease.Inthemodelabove,theslopeofthe[C+I+G+NX]-linedecreasesfromc'=(0.5)toc"=(0.5)-m.Thereforetheexpendituremultiplierwilldecreasefrom1/[1-(0.5)]to1/[1-(0.5)+m].711.Assumeyouhavethefollowingmodeloftheexpendituresector:Sp=C+I+G+NXC=Co+cYDYD=Y-TA+TRTA=TAoTR=TRoI=IoG=GoNX=NXo(a)Ifadecreaseinincome(Y)by800leadstoadecreaseinsavings(S)by160,whatisthesizeoftheexpendituremultiplier?(b)Ifadecreaseintaxes(TA)by400leadstoanincreaseinincome(Y)by1,200,howlargeisthemarginalpropensitytosave?(c)Ifanincreaseinimportsby200(?NX=-200)leadstoadecreaseinconsumption(C)by800,whatisthesizeoftheexpendituremultiplier?Recallthattheexpendituremultiplierforsuchasimplemodelcanbecalculatedas:α=1/(1-c)a.(?S)/(?Y)=1-c=(-160)/(-800)=.2==>1/(1-c)=1/(.2)=5==>themultiplierisα=5.b.From(?Y)=α[-c(?TAo)]==>(?Y)/(?TAo)=(-c)α=(-c)/(1-c)==>(1,200)/(-400)=-3=(-c)/(1-c)==>-3(1-c)=-c==>c=3/4==>mps=1-c=1/4=0.25.c.?Y=?C+?NX=-800+(-200)=-1,000==>c=(?C)/(?Y)=(-800)/(-1,000)=.8==>multiplier=α=1/(1-c)=1/(.2)=512.Explainwhyincometaxation,theSocialSecuritysystem,andunemploymentinsuranceareconsideredautomaticstabilizers.Incometaxes,unemploymentbenefits,andtheSocialSecuritysystemareoftencalledautomaticstabilizersbecausetheyreducetheamountbywhichoutputchangesasaresultofachangeinaggregatedemand.Thesestabilizersareapartofthestructureoftheeconomyandthereforeworkwithoutanyactualgovernmentintervention.Forexample,whenoutputdeclinesandunemploymentincreases.Ifwehadnounemploymentinsurance,peopleoutofworkwouldnotreceiveanydisposableincomeandthenconsumptionwoulddropsignificantly.Butsinceunemployedworkersgetunemploymentcompensation,consumptionwillnotdecreaseasmuch.Therefore,aggregatedemandmaynotbereducedbyasmuchasitwouldhavewithouttheseautomaticstabilizers.13.Assumeasimplemodeloftheexpendituresectorwithapositiveincometaxrate(t).Showmathematicallyhowanincreaseinlumpsumtaxes(TAo)wouldaffectthebudgetsurplus.FromBS=TA-G-TR=tY+TAo-G–TR==>?BS=t(?Y)+?TAo=t(mult.)(-c)(?TAo)+?TAo=t[1/(1-c+ct)](-c)(?TAo)+?TAo=([-(ct)+1-c+(ct)]/[1-c+(ct)])(?TAo)=(1-c)/[1-c+(ct)])(?TAo)>0,sincec<1Inotherwords,alumpsumtaxincreasewouldincreasethebudgetsurplus.14.Trueorfalse?Why?"Ataxcutwillincreasenationalincomeandwillthereforealwaysincreasethebudgetsurplus."False.Althoughataxcutraisesnationalincome,notalloftheincreaseinincomeisspent,norisitcompletelytaxedaway.Incometaxrevenuesfallandthebudgetdeficitrises.Assumethefollowingmodeloftheexpendituresector:Sp=C+I+G+NXI=IoC=Co+cYDG=GoYD=Y-TA+TRNX=NXoTA=TAo+tYBS=TA-G-TRTR=TRo8FromY=Sp==>Y=Co+c(Y-TAo-tY+TRo)+Io+Go+NXo==>Y=Co-cTAo+cTRo+Io+Go+NXo+c(1-t)Y=Ao+c'Y==>Y=[1/(1-c')]Aowithc'=c(1-t)Thus?Y=[1/(1-c')][(-c)(?TAo)]and?BS=t(?Y)+(?TAo)={[t(-c)]/(1-c')+1}(?TAo)==>={[-(ct)+1-c+(ct)]/[1-c+(ct)]}(?TAo)={(1-c)/[1-c+(ct)]}(?TAo)>0if?TA>0.Therefore,iftaxesfall,thatis,if?TA<0,thebudgetsurplusdecreases.15.Assumeasimplemodeloftheexpendituresectorwithapositiveincometaxrate(t).Showmathematicallyhowadecreaseinautonomousinvestment(Io)wouldaffectthebudgetsurplus.Adecreaseinautonomousinvestment(Io)willhaveamultipliereffectandwillthereforedecreasenationalincomeandtaxrevenue.Thebudgetsurpluswilldecreaseasshownbelow:?BS=t(?Y)=tα(?Io)<016."Anincreaseingovernmentpurchaseswillalwayspayforitself,asitraisesnationalincomeandhencethegovernment'staxrevenues."Commentonthisstatement.Anincreaseingovernmentpurchaseswillincreasethebudgetdeficit.Ifweassumeamodeloftheexpendituresectorwithincometaxes,thenthemultiplierequals[1/(1-c')]withc'=c(1-t).Thechangeinthebudgetsurplusthatarisesfromachangeingovernmentpurchasescanbecalculatedas?BS=t(?Y)-?G=t[1/(1-c')](?G)-?G={[t-1+c-(ct)]/[1-c+(ct)]}(?G)=-{[(1-c)(1-t)]/(1-c+(ct)]}(?G)<0,sine?G>0.Therefore,ifgovernmentpurchasesareincreased,thebudgetsurpluswilldecrease.17.Isthesizeoftheactualbudgetsurplusalwaysagoodmeasurefordeterminingfiscalpolicy?Whataboutthesizeofthefull-employmentbudgetsurplus?Theactualbudgetsurplushasacyclicalandastructuralcomponent.Thecyclicalcomponentofthebudgetsurpluschangeswithchangesinthelevelofincomewhetherornotanyfiscalpolicymeasurehasbeenimplemented.Thisimpliesthattheactualbudgetsurplusalsochangeswithchangesinincomeandisthereforenotaverygoodmeasureforassessingfiscalpolicy.Thestructur