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CHAPTER3GROWTHANDACCUMULATIONSolutionstotheProblemsintheTextbookConceptualProblems:
1.Theproductionfunctionprovidesaquantitativelinkbetweeninputsandoutput.ForexampletheCobb-Douglasproductionfunctionmentionedinthetextisoftheform:Y=FNK=AN1-KwhereYrepresentsthelevelofoutput.1-andareweightsequaltothesharesoflaborNandcapitalKinproductionwhileAisoftenusedasameasurefortheleveloftechnology.Itcanbeeasilyshownthatlaborandcapitaleachcontributetoeconomicgrowthbyanamountthatisequaltotheirindividualgrowthratesmultipliedbytheirrespectiveshareinincome.
2.TheSolowmodelpredictsconvergencethatiscountrieswiththesameproductionfunctionsavingsrateandpopulationgrowthwilleventuallyreachthesamelevelofincomepercapita.Inotherwordsapoorcountrymayeventuallycatchuptoaricheronebysavingatthesamerateandmakingtechnologicalinnovations.Howeverifthesecountrieshavedifferentsavingsratestheywillreachdifferentlevelsofincomepercapitaeventhoughtheirlong-termgrowthrateswillbethesame.
3.Aproductionfunctionthatomitsthestockofnaturalresourcescannotadequatelypredicttheimpactofasignificantchangeintheexistingstockofnaturalresourcesontheeconomicperformanceofacountry.Forexamplethediscoveryofnewoilreservesoranentirelynewresourcewouldhaveasignificanteffectonthelevelofoutputthatcouldnotbepredictedbysuchaproductionfunction.
4.InterpretingtheSolowresidualpurelyastechnologicalprogresswouldignoreforexampletheimpactthathumancapitalhasonthelevelofoutput.InotherwordsthisresidualnotonlycapturestheeffectoftechnologicalprogressbutalsotheeffectofchangesinhumancapitalHonthegrowthrateofoutput.ToeliminatethisproblemwecanexplicitlyincludehumancapitalintheproductionfunctionsuchthatY=FKNH=ANaKbHcwitha+b+c=
1.ThenthegrowthrateofoutputcanbecalculatedasY/Y=A/A+aN/N+bK/K+cH/H.
5.Thesavingsfunctionsy=sfkassumesthataconstantfractionofoutputissaved.Theinvestmentrequirementthatisthen+dk-linerepresentstheamountofinvestmentneededtomaintainaconstantcapital-laborratiok.Asteady-stateequilibriumisreachedwhensavingisequaltotheinvestmentrequirementthatiswhensy=n+dk.Atthispointthecapital-laborratiok=K/NisnotchangingsocapitalKlaborNandoutputYallmustbegrowingatthesameratethatistherateofpopulationgrowthn=N/N.
6.Inthelongruntherateofpopulationgrowthn=N/Ndeterminesthegrowthrateofthesteady-stateoutputpercapita.Intheshortrunhoweverthesavingsratetechnologicalprogressandtherateofdepreciationcanallaffectthegrowthrate.
7.LaborproductivityisdefinedasY/NthatistheratioofoutputYtolaborinputN.Asurgeinlaborproductivitythereforeoccursifoutputgrowsatafasterratethanlaborinput.IntheU.S.wehaveexperiencedsuchasurgeinlaborproductivitysincethemid-1990sduetotheenormousgrowthinGDP.Thissurgecanbeexplainedfromtheintroductionofnewtechnologiesandmoreefficientuseofexistingtechnologies.Manyclaimthattheincreasedinvestmentinanduseofcomputertechnologyhasstimulatedeconomicgrowth.Furthermoreincreasedglobalcompetitionhasforcedmanyfirmstocutcostsbyreorganizingproductionandeliminatingsomejobs.Thuswithlargeincreasesinoutputandaslowerrateofjobcreationweshouldexpectlaborproductivitytoincrease.Oneshouldalsonotethatahigher-skilledlaborforcealsocancontributetoanincreaseinlaborproductivitysincethesamenumberofworkerscanproducemoreoutputifworkersaremorehighlyskilled.TechnicalProblems:
1.a.AccordingtoEquation2thegrowthofoutputisequaltothegrowthinlabortimesthelaborshareplusthegrowthofcapitaltimesthecapitalshareplustherateoftechnicalprogressthatisY/Y=1-N/N+K/K+A/Awhere1-istheshareoflaborNandistheshareofcapitalK.ThusifweassumethattherateoftechnologicalprogressA/Aiszerothenoutputgrowsatanannualrateof
3.6percentsinceY/Y=
0.62%+
0.46%+0%=
1.2%+
2.4%=+
3.6%
1.b.Theso-calledRuleof70suggeststhatthelengthoftimeittakesforoutputtodoublecanbecalculatedbydividing70bythegrowthrateofoutput.Since70/
3.6=
19.44itwilltakejustunder20yearsforoutputtodoubleatanannualgrowthrateof
3.6%
1.c.NowthatA/A=2%wecancalculateeconomicgrowthasY/Y=
0.62%+
0.46%+2%=
1.2%+
2.4%+2%=+
5.6%.Thusitwilltake70/
5.6=
12.5yearsforoutputtodoubleatthisnewgrowthrateof
5.6%.
2.a.AccordingtoEquation2thegrowthofoutputisequaltothegrowthinlabortimesthelaborshareplusthegrowthofcapitaltimesthecapitalshareplusthegrowthrateoftotalfactorproductivityTFPthatisY/Y=1-N/N+K/K+A/Awhere1-istheshareoflaborNandistheshareofcapitalK.Inthisexample=
0.3;thereforeifoutputgrowsat3%andlaborandcapitalgrowat1%eachthenwecancalculatethechangeinTFPinthefollowingway3%=
0.31%+
0.71%+A/A==A/A=3%-1%=2%thatisthegrowthrateoftotalfactorproductivityis2%.
2.b.Ifbothlaborandthecapitalstockarefixedandoutputgrowsat3%thenallthisgrowthhastobecontributedtothegrowthinfactorproductivitythatisA/A=3%.
3.a.IfthecapitalstockgrowsbyK/K=10%theeffectonoutputwouldbeanadditionalgrowthrateofY/Y=.310%=3%.
3.b.IflaborgrowsbyN/N=10%theeffectonoutputwouldbeanadditionalgrowthrateofY/Y=.710%=7%.
3.c.IfoutputgrowsatY/Y=7%duetoanincreaseinlaborbyN/N=10%andthisincreaseinlaborisentirelyduetopopulationgrowththenpercapitaincomewoulddecreaseandpeople’swelfarewoulddecreasesincey/y=Y/Y-N/N=7%-10%=-3%.
3.d.Ifthisincreaseinlaborisduetoaninfluxofwomenintothelaborforcetheoverallpopulationdoesnotincreaseandincomepercapitawouldincreasebyy/y=7%.Thereforepeopleswelfarewouldincrease.
4.Figure3-4showsoutputperheadasafunctionofthecapital-laborratiothatisy=fk.Thesavingsfunctionissy=sfkanditintersectsthestraightn+dk-linerepresentingtheinvestmentrequirement.Atthisintersectiontheeconomyisinasteady-stateequilibrium.Nowletusassumethattheeconomyisinasteady-stateequilibriumbeforetheearthquakehitsthatisthesteady-statecapital-laborratioiscurrentlyk*.Assumefurtherforsimplicitythattheearthquakedoesnotaffectpeoplessavingsbehavior.Iftheearthquakedestroysonequarterofthecapitalstockbutlessthanonequarterofthelaborforcethenthecapital-laborratiofallsfromk*tok1andper-capitaoutputfallsfromy*toy
1.Nowsavingisgreaterthantheinvestmentrequirementthatissy1d+nk1andthecapitalstockandthelevelofoutputpercapitawillgrowuntilthesteadystateatk*isreachedagain.Howeveriftheearthquakedestroysonequarterofthecapitalstockbutmorethanonequarterofthelaborforcethenthecapital-laborratioincreasesfromk*tok
2.Savingnowwillbelessthantheinvestmentrequirementandthusthecapital-laborratioandthelevelofoutputpercapitawillfalluntilthesteadystateatk*isreachedagain.Ifexactlyonequarterofboththecapitalstockandthelaborstockaredestroyedthenthesteadystateismaintainedthatisthecapital-laborratioandtheoutputpercapitadonotchange.Iftheseverityoftheearthquakehasaneffectonpeoples’savingsbehaviorthenthesavingsfunctionsy=sfkwillmoveeitherupordowndependingonwhetherthesavingsratesincreasesifpeoplesavemoresomorecanbeinvestedinanefforttorebuildordecreasesifpeoplesavelesssincetheydecidethatlifeistooshortnottoliveitup.yy=fky2y*n+dky1sy0k1k*k2k
5.a.Anincreaseinthepopulationgrowthratenaffectstheinvestmentrequirementandthen+dk-linegetssteeper.Asthepopulationgrowsmoresavingmustbeusedtoequipnewworkerswiththesameamountofcapitalthattheexistingworkersalreadyhave.Thereforeoutputpercapitaywilldecreaseaswillthenewoptimalcapital-laborratiowhichisdeterminedbytheintersectionofthesy-curveandthen1+dk-line.Sinceper-capitaoutputwillfallwewillhaveanegativegrowthrateintheshortrun.Howeverthesteady-stategrowthrateofoutputwillincreaseinthelongrunsinceitwillbedeterminedbythenewandhigherrateofpopulationgrowth.yn1+dky=fkyono+dky1sy0k1kok
5.b.Startingfromaninitialsteady-stateequilibriumatalevelofper-capitaoutputy*theincreaseinthepopulationgrowthratenwillcausethecapital-laborratiotodeclinefromk*tok
1.Outputpercapitawillalsodeclineaprocessthatwillcontinueatadiminishingrateuntilanewsteady-statelevelisreachedaty
1.Thegrowthrateofoutputwillgraduallyadjusttothenewandhigherleveln
1.yy*y1tot1tkk*k1tot1t
6.a.AssumetheproductionfunctionisoftheformY=FKNZ=AKaNbZc==Y/Y=A/A+aK/K+bN/N+cZ/Zwitha+b+c=
1.NowassumethatthereisnotechnologicalprogressthatisA/A=0andthatcapitalandlaborgrowatthesameratethatisK/K=N/N=n.IfwealsoassumethatallnaturalresourcesavailablearefixedsuchthatZ/Z=0thentherateofoutputgrowthwillbeY/Y=an+bn=a+bn.Inotherwordsoutputwillgrowataratelessthannsincea+b
1.Thereforeoutputperworkerwillfall.
6.b.IfthereistechnologicalprogressthatisA/A0thenoutputwillgrowfasterthanbeforenamelyY/Y=A/A+a+bn.IfA/Acthenoutputwillgrowataratelargerthanninwhichcaseoutputperworkerwillincrease.
6.c.Ifthesupplyofnaturalresourcesisfixedthenoutputcanonlygrowataratethatissmallerthantherateofpopulationgrowthandweshouldexpectlimitstogrowthaswerunoutofnaturalresources.Howeveriftherateoftechnologicalprogressissufficientlylargethenoutputcangrowataratefasterthanpopulationevenifwehaveafixedsupplyofnaturalresources.
7.a.IftheproductionfunctionisoftheformY=K1/2AN1/2andAisnormalizedto1thenwehaveY=K1/2N1/
2.Inthiscasecapitalsandlaborssharesofincomeareboth50%.
7.b.ThisisaCobb-Douglasproductionfunction.
7.c.Asteady-stateequilibriumisreachedwhensy=n+dk.FromY=K1/2N1/2==Y/N=K1/2N-1/2==y=k1/2==sk1/2=n+dk==k-1/2=n+d/s=
0.07+
0.03/.2=1/2==k1/2=2=y==k=
4.
8.a.Iftechnologicalprogressoccursthenthelevelofoutputpercapitaforanygivencapital-laborratioincreases.Thefunctiony=fkincreasestoy=gkandthusthesavingsfunctionincreasesfromsfktosgk.ygky2fkn+dksgky1sfk0k1k2k
8.b.Sincegkfkitfollowsthatsgksfkforeachlevelofk.Thereforetheintersectionofthesgk-curvewiththen+dk-lineisatahigherlevelofk.Thenewsteady-stateequilibriumwillnowbeatahigherlevelofsavingandoutputpercapitaandatahighercapital-laborratio.
8.c.Afterthetechnologicalprogressoccursthelevelofsavingandinvestmentwillincreaseuntilanewandhigheroptimalcapital-laborratioisreached.Theratioofinvestmenttocapitalwillalsoincreaseinthetransitionperiodsincemorehastobeinvestedtoreachthehigheroptimalcapital-laborratio.kk2k10t1t2t
9.TheCobb-DouglasproductionfunctionisdefinedasY=FNK=AN1-K.ThemarginalproductoflaborcanthenbederivedasMPN=Y/N=1-AN-K=1-AN1-K/N==1-Y/N==laborsshareofincome=[MPN*N]/Y=1-Y/N*[N/Y]=1-AdditionalProblems
1.Assumelaborsshareofincomeis80%capitalsshareofincomeis20%andtheleveloftechnologyisfixed.GiveaCobb-DouglasaggregateproductionfunctionwithonlytwoinputslaborNandcapitalKthatwillrepresentsuchaneconomy.Iflaborgrowsby
2.4%andcapitalgrowsby
1.2%byhowmuchwilloutputinthiseconomygrowTheCobb-Douglasproductionfunctionisofthegeneralform:Y=FNK=AN1-KwhereYrepresentsthelevelofoutput.1-andareweightsequaltothesharesoflaborNandcapitalKinproductionwhileAisoftenusedasameasurefortheleveloftechnology.Inthiscasethisproductionfunctionhasthefollowingform:Y=N
0.8K
0.2ThegrowthofoutputcanbecalculatedbyusingthefollowingformulaY/Y=1-N/N+K/K+A/A=
0.
82.4%+
0.
21.2%+0%=
1.92%+
0.24%=+
2.16%
2.AssumeaCobb-Douglasaggregateproductionfunctioninwhichlaborsshareofincomeis80%andcapitalsshareofincomeis20%.ByhowmuchwouldrealGDPinthiseconomygrowiflaborgrowsat3%thecapitalstockgrowsat2%andtotalfactorproductivityincreasesby
2.4%ThegrowthofoutputcanbecalculatedasthesumofthegrowthinlabortimesthelaborshareplusthegrowthofcapitaltimesthecapitalshareplusthechangeintotalfactorproductivitythatisY/Y=1-N/N+K/K+A/Awhere1-istheshareoflaborNistheshareofcapitalKandA/Aisthechangeintotalfactorproductivity.ThereforewecancalculatetotaloutputgrowthasY/Y=
0.83%+
0.22%+
2.4%=
2.4%+
0.4%+
2.4%=
5.2%.
3.AssumeaCobb-Douglasaggregateproductionfunctioninwhichlaborsshareofincomeis80%andcapitalsshareofincomeis20%.ByhowmuchwillrealGDPinthiseconomygrowiflaborgrowsat
2.5%thecapitalstockgrowsat
1.5%andtotalfactorproductivityincreasesby
2.1%ThegrowthofoutputcanbecalculatedasthesumofthegrowthinlabortimesthelaborshareplusthegrowthofcapitaltimesthecapitalshareplusthechangeintotalfactorproductivitythatisY/Y=1-N/N+K/K+A/Awhere1-istheshareoflaborNandistheshareofcapitalKandA/Aisthechangeintotalfactorproductivity.ThereforewecancalculatetotaloutputgrowthasY/Y=
0.
82.5%+
0.
21.5%+
2.1%=
2.0%+
0.3%+
2.1%=
4.4%.
4.Assumethatlaborsshareofincomeisthreetimesaslargeascapitalsshareandthatcapitallaborandoutputallgrowatthesameraten.UseaCobb-Douglasaggregateproductionfunctionthathasconstantreturnstoscaletoshowthatlaborwillbealargersourceofgrowththancapitalifthereisnotechnologicalprogress.Withtheshareoflaborbeing1-=
0.75andtheshareofcapitalbeing=
0.25wegetthefollowingaggregateproductionfunction:Y=AN1-K=AN3/4K1/4WecangetthegrowthaccountingequationbytakingthetotalderivativeofthisequationandthendividingbothsidesoftheequationbyYthatisY/Y=A/A+1-N/N+K/K=0+
0.75n+
0.25n=n.ThereforeweseethatlaborcontributesthreetimesasmuchtogrowthascapitalintheabsenceoftechnologicalprogressthatisifA/A=
0.
5.Assumeaneconomyinwhichtheleveloftechnologyandthestockofcapitalarefixed.IfthereisasuddenincreaseinthelaborforceduetoimmigrationhowwouldthestandardoflivingbeaffectedWoulditmakeadifferenceiftheincreaseinthelaborforcewereinsteadcausedbyahigherlaborforceparticipationrateofwomenIftheincreaseinthelaborforcewereentirelyduetoaninfluxofforeignersthenthepopulationwouldincreaseandlivingstandardswoulddecreasesinceper-capitaincomewoulddecrease.Howeveriftheincreaseinthelaborforcewereduetoanincreaseinthelaborforceparticipationofwomenthenincomepercapitawouldincreasesincetheoverallpopulationwouldnotincrease.Thereforetherewouldbeanincreaseinlivingstandards.
6.Brieflydistinguishbetweenthesetwoconcepts:decreasingreturnstoscaleandthelawofdiminishingmarginalreturns.Decreasingreturnstoscaleoccurwhenaproportionalincreaseinallinputsleadstoaless-than-proportionalincreaseinoutput.Thelawofdiminishingmarginalreturnsstatesthatthemarginalproductofeachunitofinputwilldeclineastheamountofthatinputisincreasedwhileallotherinputsconstantareheldconstant.Inotherwordsifweonlyincreaseoneofseveralinputsoutputwillincreasebutatadecreasingrate.
7.Commentonthefollowingstatement:Technologicaladvancesincreaseoutputintheshortrunbuthavenoimpactonlong-rungrowthinoutputpercapitasincethisisdeterminedentirelybytherateofpopulationgrowth.Whentechnologicaladvancesoccurtheneachinputbecomesmoreproductiveandthetotalfactorproductivityandgrowthofoutputrise.Thisimpliesthattechnologicaladvancescanhaveveryprofoundimplicationsforoutputgrowth.Totaloutputgrowsatarateequaltothesumofthegrowthrateofthepopulationandtherateoftechnologicalprogress.
8.TheSolowgrowthmodelpredictsthatacountrywithalowsavingsratecaneventuallyachievethesamelivingstandardasacountrywithahighsavingsrateaslongasbothcountrieshavethesamerateofpopulationgrowthandaccesstothesametechnology.Commentonthisstatement.TheSolowmodelpredictsthattwocountriesthathavethesameproductionfunctionsavingsrateandpopulationgrowthwilleventuallyreachthesamelevelofincomepercapita.Inotherwordsapoorcountrymayeventuallycatchuptoaricheronebysavingatanequivalentratetothatoftherichercountryandbyimplementingtechnologicalinnovations.Howeverifthetwocountrieshavedifferentsavingsratesthentheywillreachdifferentlevelsofincomepercapitaeventhoughtheirgrowthratesultimatelywillbethesame.Thereforethecountrywiththelowersavingsratewillhavealowerstandardofliving.
9.Theneoclassicalgrowthmodelpredictsthatanationsper-capitaGDPcanonlygrowiftechnologicalprogressoccurs.Commentonthisstatement.Theneoclassicalgrowthmodelgenerallyassumesaproductionfunctionwithconstantreturnstoscale.Intheabsenceoftechnologicalprogressthismodelreachesasteady-stateequilibriumatanoptimalcapital-outputratiok*.Atthispointoutputgrowsatthesamerateasthepopulation.Thisimpliesthatoutputpercapitaremainsconstant.Intheshort-runhoweverthecapital-outputratiokmaybebelowtheoptimallevelk*.Ifsothelevelofsavingwillexceedthelevelofinvestmentneededtokeepthecapital-laborratioconstant.Inthiscasethecapital-laborratiowillincreasewhichimpliesthatoutputperheadwillincreaseuntiltheoptimallevelk*isreached.Atk*thecapital-laborratioandoutputperheadarebothconstantagain.
10.Ahigherpopulationgrowthisalwaysdesirablesinceitwillleadtohigherlivingstandards.Commentonthisstatementwiththehelpofadiagramderivedfromtheneoclassicalgrowthmodel.Iftherateofpopulationgrowthnincreasesthecapitalstockwillgrowatalowerratethanpopulation.Sincethecountryhastofeeditspeoplenotenoughwillbesavedandinvestedtokeepthecapital-laborratiokatitsoriginallevel.Thereforethecapital-laborratiokdecreasesuntilanewsteadystateisreached.Inotherwordstheinvestmentrequirementthatisthen+dk-linegetssteeperaspopulationgrowthnincreases.Then+dk-linewillnowintersectthesy-curveatalowersteady-statecapital-laborratiok.Thisimpliesalowerlevelofoutputpercapitayandthereforealowerlivingstandard.Thusthestatementiswrong.k2k1k
11.IftheU.S.canincreaseitsnationalsavingsrateitcanachieveahigherlong-termgrowthrate.Commentonthisstatementwiththehelpofadiagramderivedfromtheneoclassicalgrowthmodel.Ifthesavingsrateincreasesthenthesy-curveshiftsupandwegetanewintersectionwiththen+dklineatahighersteadystatecapital-laborratioandahigherlevelofoutputpercapita.Inotherwordsasthelevelofsavingsandinvestmentincreasesthelaborforcewillbesuppliedwithmorecapitaluntilanewandhigheroptimalcapital-laborratiokandoutputpercapitalevelyisreached.Thusthegrowthrateofrealoutputwillincreaseonlytemporarily.Butinthelongrunwhilethelevelofoutputpercapitaishigherthegrowthrateofrealoutputwillagainbeequaltothepopulationgrowthn.
12.Anincreaseinthedepreciationratereducesthelevelofoutputpercapitaandthecapital-laborratio.CommentonthisstatementAnincreasingdepreciationratedindicatesthatthecapitalstockiswearingoutatafasterratethanpreviously.Thisleadstoareductionintheoptimalcapital-laborratioandinthelevelofoutput.Inotherwordsthen+dk-linebecomessteeperasthedepreciationrateincreases.Thesavingsfunctionsy=sfknowintersectsthenewn+dk-lineatalowercapital-laborratiokwhichimpliesalowerlevelofoutputpercapitay.
13.TrueorfalseWhyTheneoclassicalgrowthmodelpredictsthatadecreaseinthesavingsratepermanentlyaffectsthegrowthrateofrealoutput.False.Asthesavingsratedecreasesasmallerproportionofoutputissavedateachlevelofthecapital-laborratiok.Thesavingscurveshiftsfromsy=sfktos1y=s1fk.Nowsavingsislessthantheinvestmentrequirementn+dkattheoriginalcapital-laborratiok*sothecapitalstockbeginstogrowmoreslowly.Duringthetransitiontothenewequilibriumatalowersteady-statecapital-laborratioandaloweroutputpercapitathereisatemporarydeclineinthegrowthofoutputandthelevelofoutputpercapitadecreases.Howeverinthelongrunthegrowthrateofrealoutputwillnotbeaffected.yyoy=fkn+dky1sys1y0kok1k
14.Commentonthefollowingstatement:Anationwithadecliningpopulationgrowthwillexperienceafallinlivingstandards;thereforegovernmentsshoulddesignpoliciestoincreasepopulationgrowth.Ifanationspopulationgrowthdeclinesthenthecurrentlevelofsavingwillbehigherthanthelevelofinvestmentrequiredtomaintainaconstantcapital-laborratio.Thereforethecapital-laborratiowillincreaseuntilanewsteady-stateequilibriumisreached.Thenewoptimalcapital-laborratioisdeterminedbytheintersectionofthesaving-curvesywiththenewn1+dk-linethatisthenewinvestmentrequirementline.Thenewandlargeroptimalcapital-laborratiok*impliesalargerlevelofincomepercapitay*andthereforeahigherstandardoflivingforthecountryspopulation.Thereforethereisnoneedtodesignpoliciestoincreasepopulationgrowth.Asamatteroffactastheprecedinganalysissuggestsanincreaseinpopulationgrowthwoulddecreaselivingstandards.yy=fky1no+dkyon1+dksy0kok1k
15.Ahighlevelofpublicspendingcrowdsoutinvestmentspending.Thereforethegovernmentneedstocutitsexpenditurestofreeresourcesforinvestment.Commentonthisstatement.Bydecreasingthelevelofpublicspendingandreducingthebudgetdeficitthegovernmentcanincreasethelevelofnationalsaving.Thereforemorefundswillbeavailableforinvestment.Iftherateofcapitalaccumulationincreasesthenthegrowthrateofoutputcanincreaseatleasttemporarilyandthiswillincreasethelevelofoutputpercapita.Howevertheneoclassicalgrowthmodelpredictsthatthelong-termgrowthratewillnotbeaffectedsincethisrateissolelydeterminedbypopulationgrowthandtechnologicalprogress.Inadditionadecreaseingovernmentspendingmayintheshortrunleadtoarecessionnegativelyaffectingthelevelofinvestmentspending.。