曼昆宏观经济学第九版-课后习题答案

AnswerstoTextbookQuestionsandProblems

CHAPTER1TheScienceofMacroeconomics

QuestionsforReview

1.Microeconomicsisthestudyofhowindividualfirmsandhouseholdsmakedecisions,and

howtheyinteractwithoneanother.Microeconomicmodelsoffirmsandhouseholdsare

basedonprinciplesofoptimization-firmsandhouseholdsdothebesttheycangiven

theconstraintstheyface.Forexample,householdschoosewhichgoodstopurchasein

ordertomaximizetheirutility,whereasfirmsdecidehowmuchtoproduceinorderto

maximizeprofits.Incontrast,macroeconomicsisthestudyoftheeconomyasawhole;it

focusesonissuessuchashowtotaloutput,totalemployment,andtheoverallpricelevel

aredetermined.Theseeconomy-widevariablesarebasedontheinteractionofmany

householdsandmanyfirms;therefore,microeconomicsformsthebasisfor

macroeconomics.

2.Economistsbuildmodelsasameansofsummarizingtherelationshipsamongeconomic

variables.Modelsareusefulbecausetheyabstractfromthemanydetailsintheeconomy

andallowonetofocusonthemostimportanteconomicconnections.

3.Amarket-clearingmodelisoneinwhichpricesadjusttoequilibratesupplyanddemand.

Market-clearingmodelsareusefulinsituationswherepricesareflexible.Yetinmany

situations,flexiblepricesmaynotbearealisticassumption.Forexample,laborcontracts

oftensetwagesforuptothreeyears.Or,firmssuchasmagazinepublisherschangetheir

pricesonlyeverythreetofouryears.Mostmacroeconomistsbelievethatpriceflexibility

isareasonableassumptionforstudyinglong-runissues.Overthelongrun,prices

respondtochangesindemandorsupply,eventhoughintheshortruntheymaybeslow

toadjust.

ProblemsandApplications

1.MonetarypolicyintheUnitedStatesandtheEuropeanUnionhasbeenabigtopicof

conversationinearly2015.TheEUembarkeduponaquantitativeeasingpolicyinMarch

2015inanattempttostimulategrowthandpreventdeflation.Therehasbeensome

concernthattheinflationrateinEuropewillturnnegative.IntheUnitedStates,thereis

continueddiscussionandspeculationconcerningwhentheFederalReservemightchoose

toincreasethetargetfederalfundsrate.AlsointheUnitedStates,theunemployment

ratehasdeclinedtoabout5.5percentandthissuggeststhatwagesmaybegintoincrease.

TheFederalReservewillbewatchingforwageandpriceincreasesastheydecidewhen

toincreaseinterestrates.

2.Manyphilosophersofsciencebelievethatthedefiningcharacteristicofascienceisthe

useofthescientificmethodofinquirytoestablishstablerelationships.Scientistsexamine

data,oftenprovidedbycontrolledexperiments,tosupportordisproveahypothesis.

Economistsaremorelimitedintheiruseofexperiments.Theycannotconductcontrolled

experimentsontheeconomy;theymustrelyonthenaturalcourseofdevelopmentsin

theeconomytocollectdata.Totheextentthateconomistsusethescientificmethodof

inquiry,thatis,developinghypothesesandtestingthem,economicshasthe

characteristicsofascience.

3.Wecanuseasimplevariantofthesupply-and-demandmodelforpizzatoanswerthis

question.Assumethatthequantityoficecreamdemandeddependsnotonlyontheprice

oficecreamandincome,butalsoonthepriceoffrozenyogurt:

0=久P\c,P”,Y).

Weexpectthatdemandforicecreamriseswhenthepriceoffrozenyogurtrises,because

icecreamandfrozenyogurtaresubstitutes.Thatis,whenthepriceoffrozenyogurtgoes

up,Iconsumelessofitand,instead,fulfillmoreofmyfrozendesserturgesthroughthe

consumptionoficecream.

Thenextpartofthemodelisthesupplyfunctionforicecream,0=5(Re).Finally,in

equilibrium,supplymustequaldemand,sothat0二。.Yand用aretheexogenous

variables,andQandAcaretheendogenousvariables.Figure1-1usesthismodeltoshow

thatafallinthepriceoffrozenyogurtresultsinaninwardshiftofthedemandcurvefor

icecream.Thenewequilibriumhasalowerpriceandquantityoficecream.

Figure1-1

Pic

\S

Q

Quantityoficecream

4.Thepriceofhaircutschangesratherinfrequently.Fromcasualobservation,hairstylists

tendtochargethesamepriceoveraone-ortwo-yearperiodirrespectiveofthedemand

forhaircutsorthesupplyofcutters.Amarket-clearingmodelforanalyzingthemarket

forhaircutshastheunrealisticassumptionofflexibleprices.Suchanassumptionis

unrealisticintheshortrunwhenweobservethatpricesareinflexible.Overthelongrun,

however,thepriceofhaircutsdoestendtoadjust;amarket-clearingmodelistherefore

appropriate.

AnswerstoTextbookQuestionsandProblems

CHAPTER2TheDataofMacroeconomics

QuestionsforReview

1.GDPmeasuresthetotalincomeearnedfromtheproductionofthenewfinalgoodsand

servicesinthe

economy,anditmeasuresthetotalexpendituresonthenewfinalgoodsandservices

producedintheeconomy.GDPcanmeasuretwothingsatoncebecausethetotal

expendituresonthenewfinalgoodsandservicesbythebuyersmustbeequaltothe

incomeearnedbythesellersofthenewfinalgoodsandservices.Asthecircularflow

diagraminthetextillustrates,thesearealternative,equivalentwaysofmeasuringtheflow

ofdollarsintheeconomy.

2.ThefourcomponentsofGDPareconsumption,investment,governmentpurchases,and

netexports.

TheconsumptioncategoryofGDPconsistsofhouseholdexpendituresonnewfinalgoods

andservices,suchasthepurchaseofanewtelevision.TheinvestmentcategoryofGDP

consistsofbusinessfixedinvestment,residentialfixedinvestment,andinventory

investment.Whenabusinessbuysnewequipmentthiscountsasinvestment.Government

purchasesconsistsofpurchasesofnewfinalgoodsandservicesbyfederal,state,and

localgovernments,suchaspaymentsfornewmilitaryequipment.Netexportsmeasures

thevalueofgoodsandservicessoldtoothercountriesminusthevalueofgoodsand

servicesforeignerssellus.WhentheU.S.sellscorntoforeigncountries,itcountsinthe

netexportcategoryofGDP.

3.Theconsumerpriceindex(CPI)measurestheoveralllevelofpricesintheeconomy.It

tellsusthepriceofafixedbasketofgoodsrelativetothepriceofthesamebasketinthe

baseyear.TheGDPdeflatoristheratioofnominalGDPtorealGDPinagivenyear.The

GDPdeflatormeasuresthepricesofallgoodsandservicesproduced,whereastheCPI

onlymeasurespricesofgoodsandservicesboughtbyconsumers.TheGDPdeflator

includesonlydomesticallyproducedgoods,whereastheCPIincludesdomesticand

foreigngoodsboughtbyconsumers.Finally,theCPIisaLaspeyresindexthatassigns

fixedweightstothepricesofdifferentgoods,whereastheGDPdeflatorisaPaascheindex

thatassignschangingweightstothepricesofdifferentgoods.Inpractice,thetwoprice

indicestendtomovetogetheranddonotoftendiverge.

4.TheCPImeasuresthepriceofafixedbasketofgoodsrelativetothepriceofthesame

basketinthebaseyear.ThePCEdeflatoristheratioofnominalconsumerspendingto

realconsumerspending.TheCPIandthePCEdeflatoraresimilarinthattheybothonly

includethepricesofgoodspurchasedbyconsumers,andtheybothincludethepriceof

importedgoodsaswellasdomesticallyproducedgoods.Thetwomeasuresdiffer

becausetheCPImeasuresthechangeinthepriceofafixedbasketwhereasthegoods

measuredbythePCEdeflatorchangefromyeartoyeardependingonwhatconsumers

arepurchasinginthatparticularyear.

5.TheBureauofLaborStatistics(BLS)classifieseachpersonintooneofthefollowingthree

categories:employed,unemployed,ornotinthelaborforce.Theunemploymentrate,

whichisthepercentageofthelaborforcethatisunemployed,iscomputedasfollows:

,-NumberofUnemployed

UnemploymentRate=—xlOO.

LaborForce

Notethatthelaborforceisthenumberofpeopleemployedplusthenumberofpeople

unemployed.

6.Everymonth,theBureauofLaborStatisticsundertakestwosurveystomeasure

employment.First,theBLSsurveysabout60,000householdsandtherebyobtainsan

estimateoftheshareofpeoplewhosaytheyareworking.TheBLSmultipliesthisshare

byanestimateofthepopulationtoestimatethenumberofpeopleworking.Second,the

BLSsurveysabout160,000businessestablishmentsandaskshowmanypeoplethey

employ.Eachsurveyisimperfect;sothetwomeasuresofemploymentarenotidentical.

ProblemsandApplications

1.FromthemainWebpageclickontheinteractivedatatabatthetop,selectGDP,

beginusingthedata,section1,andthentable1.1.1.RealGDPgrewatarateof2.2

percentinquarter4of2014.Whencomparedtogrowthratesof-2.1percent,4.6

percent,and5percentforthefirstthreequartersof2014,therateof2.2percentwas

slightlybelowaverage.Fromthemainb/Webpageselectthedatatoolstab,then

toppicks.Checktheboxfortheunemploymentrateandretrievethedata.The

unemploymentrateinMarch2015was5.5percent,whichwasaboutequaltothenatural

rateofunemployment,orthelongrunaveragerate.Fromthemainpage,select

theeconomicreleasestab,theninflationandprices.AccessthereportfortheCPI.In

February2015,theinflationrateforallitemswas0percent,andiffoodandenergywere

excludedtheratewas1.7percent.Theinflationratewasbelowaverageandbelowthe

FederalReserve'stargetof2percent.

2.Valueaddedbyeachpersonisequaltothevalueofthegoodproducedminusthe

amountthepersonpaidforthematerialsneededtomakethegood.Therefore,thevalue

addedbythefarmeris$1.00($1-0=$1).Thevalueaddedbythemilleris$2:shesells

theflourtothebakerfor$3butpaid$1fortheflour.Thevalueaddedbythebakeris$3:

shesellsthebreadtotheengineerfor$6butpaidthemiller$3fortheflour.GDPisthe

totalvalueadded,or$1+$2+$3=$6.NotethatGDPequalsthevalueofthefinalgood

(thebread).

3.Whenawomanmarriesherbutler,GDPfallsbytheamountofthebutler1ssalary.This

happensbecauseGDPmeasurestotalincome,andthereforeGDP,fallsbytheamountof

thebutler1slossinsalary.IfGDPtrulymeasuresthevalueofallgoodsandservices,then

themarriagewouldnotaffectGDPsincethetotalamountofeconomicactivityis

unchanged.ActualGDP,however,isanimperfectmeasureofeconomicactivitybecause

thevalueofsomegoodsandservicesisleftout.Oncethebutler'sworkbecomespart

ofhishouseholdchores,hisservicesarenolongercountedinGDP.Asthisexample

illustrates,GDPdoesnotincludethevalueofanyoutputproducedinthehome.

4.a.TheairplanesoldtotheU.S.AirForcecountsasgovernmentpurchasesbecausethe

AirForceispartofthegovernment.

b.TheairplanesoldtoAmericanAirlinescountsasinvestmentbecauseitisacapital

goodsoldtoaprivatefirm.

c.TheairplanesoldtoAirFrancecountsasanexportbecauseitissoldtoaforeigner.

d.TheairplanesoldtoAmeliaEarhartcountsasconsumptionbecauseitissoldtoa

privateindividual.

e.Theairplanebuilttobesoldnextyearcountsasinvestment.Inparticular,theairplane

iscountedasinventoryinvestment,whichiswheregoodsthatareproducedinone

yearandsoldinanotheryeararecounted.

5.Dataonparts(a)to(f)canbedownloadedfromtheBureauofEconomicAnalysis.Goto

theWebsite,clickontheinteractivedatatabatthetop,selectGDP,beginusing

thedata,section1,andthentable1.1.5.Choosethe"modifythedata"optiontoselect

theyearsyouinwhichyouareinterested.Bydividingeachcomponent(a)to(f)by

nominalGDPandmultiplyingby100,weobtainthefollowingpercentages:

195019802014

a.Personalconsumptionexpenditures64.0%61.3%68.5%

b.Grossprivatedomesticinvestment18.8%18.5%16.4%

c.Governmentconsumptionpurchases16.9%20.6%18.2%

d.Netexports0.2%-0.5%3.1%

e.Nationaldefensepurchases7.6%6.3%4.4%

f.Imports3.9%10.3%16.5%

(Note:TheabovedatawasdownloadedApril3,2015,fromtheBEAWebsite.)

Amongotherthings,weobservethefollowingtrendsintheeconomyovertheperiod

1950-2015:

a.Personalconsumptionexpenditureshavebeenaroundtwo-thirdsofGDPbetween

1980and2015.

b.TheshareofGDPgoingtogrossprivatedomesticinvestmentremainedfairlysteady.

c.Thesharegoingtogovernmentconsumptionpurchasesrosesharplyfrom1950to

1980.

d.Netexports,whichwerepositivein1950,havebeennegativesincethattime.

e.Thesharegoingtonationaldefensepurchaseshasfallen.

f.ImportshavegrownrapidlyrelativetoGDP.

6.a.GDPmeasuresthevalueofthefinalgoodsandservicesproduced,or$1,000,000.

b.NNPisequaltoGNPminusdepreciation.Inthisexample,GDPisequaltoGNP

becausethereare

noforeigntransactions.Therefore,NNPisequalto$875,000.

c.NationalincomeisequaltoNNP,or$875,000.

d.Employeecompensationisequalto$600,000.

e.Proprietors'incomemeasurestheincomeoftheowner,andisequalto150,000.

f.Corporateprofitisequaltocorporatetaxesplusdividendsplusretainedearnings,

or$275,000.

Retainedearningsiscalculatedassalesminuswagesminusdividendsminus

depreciationminuscorporatetax,or$75,000.

g.Personalincomeisequaltoemployeecompensationplusdividends,or$750,000.

h.Disposablepersonalincomeispersonalincomeminustaxes,or$550,000.

7.a.i.NominalGDPisthetotalvalueofgoodsandservicesmeasuredatcurrentprices.

Therefore,

=(P20；0Xft201；)+(P^10X0

NominalGDP2010\hotdogs^hotdogsf\burgers-没burgers),

二($2x200)+($3x200)

=$400+$600

=$1,000.

=(堂xQ；*)+(8”52O15\

NominalGDP2015X0

\houlogs^hotdogs)\burgers—burgers)

=($4x250)+($4x500)

二$1,000+$2,000

二$3,000.

ii.RealGDPisthetotalvalueofgoodsandservicesmeasuredatconstantprices.

Therefore,tocalculaterealGDPin2015(withbaseyear2010),multiplythe

quantitiespurchasedintheyear2015bythe2010prices:

RealGDP2015=(P；吗xQ”；xQ^i5)

\hotdogs。hotdogs)\burgers=burgers/

=($2x250)+($3x500)

二$500+$1,500

=$2,000.

RealGDPfor2010iscalculatedbymultiplyingthequantitiesin2010bytheprices

in2010.Sincethebaseyearis2010,realGDP2010equalsnominalGDP2010,whichis

$10,00.Hence,realGDPincreasedbetween2010and2015.

iii.TheimplicitpricedeflatorforGDPcomparesthecurrentpricesofallgoodsand

servicesproducedtothepricesofthesamegoodsandservicesinabaseyear.It

iscalculatedasfollows:

NominalGDP

ImplicitPriceDeflator^=2(11()=1

RealGDP2010

UsingthevaluesforNominalGDP2015andrealGDP2015calculatedabove:

_$3,000

ImplicitPriceDeflatoroi5

2一$2,000

=1.50.

Thiscalculationrevealsthatpricesofthegoodsproducedintheyear2015

increasedby50percentcomparedtothepricesthatthegoodsintheeconomy

soldforin2010.(Because2010isthebaseyear,thevaluefortheimplicitprice

deflatorfortheyear2010is1.0becausenominalandrealGDParethesamefor

thebaseyear.)

iv.Theconsumerpriceindex(CPI)measuresthelevelofpricesintheeconomy.The

CPIiscalledafixed-weightindexbecauseitusesafixedbasketofgoodsover

timetoweightprices.Ifthebaseyearis2010,theCPIin2015ismeasuringthe

costofthebasketin2015relativetothecostin2010.TheCPI2015iscalculatedas

follows:

(P竺吗)+(PyxQ”。)

\hotdogs=hotdogs/'burgers口buyers7

CPI2015

(P*xQ力)+(P产)

'holdogshotaogsz'burgersQburgers'

=$16,000,000

$10,00(),000

二1.6.

Thiscalculationshowsthatthepriceofgoodspurchasedin2015increasedby60

percentcomparedtothepricesthesegoodswouldhavesoldforin2010.TheCPI

for2010,thebaseyear,equals1.0.

b.TheimplicitpricedeflatorisaPaascheindexbecauseitiscomputedwithachanging

basketofgoods;theCPIisaLaspeyresindexbecauseitiscomputedwithafixed

basketofgoods.From(7.a.iii),theimplicitpricedeflatorfortheyear2015is1.50,

whichindicatesthatpricesroseby50percentfromwhattheywereintheyear2010.

From(7.a.iv.),theCPIfortheyear2015is1.6,whichindicatesthatpricesroseby60

percentfromwhattheywereintheyear2010.

Ifpricesofallgoodsroseby,forexample,50percent,thenonecouldsay

unambiguouslythatthepricelevelroseby50percent.Yet,inourexample,relative

priceshavechanged.Thepriceofhotdogsroseby1020percent;thepriceof

hamburgersroseby33.33percent,makinghamburgersrelativelylessexpensive.

AsthediscrepancybetweentheCPIandtheimplicitpricedeflatorillustrates,the

changeinthepriceleveldependsonhowthegoods'pricesareweighted.TheCPI

weightsthepriceofgoodsbythequantitiespurchasedintheyear2010.Theimplicit

pricedeflatorweightsthepriceofgoodsbythequantitiespurchasedintheyear2015.

Sincethequantityofthetwogoodswasthesamein2010,theCPIisplacingequal

weightonthetwopricechanges.In2015,thequantityofhamburgerswastwiceas

largeashotdogs,sothereistwiceasmuchweightplacedonthehamburgerprice

relativetothehotdogprice.Forthisreason,theCPIshowsalargerinflationrate一

moreweightisplacedonthegoodwiththelargerpriceincrease.

8.a.Theconsumerpriceindexusestheconsumptionbundleinyear1tofigureouthow

muchweighttoputonthepriceofagivengood:

CPIJ($2xl0)+($lxq

($lxl0)+($2x0)

=(%*。力+(尸二x。；)

=2.

AccordingtotheCPI,priceshavedoubled.

b.Nominalspendingisthetotalvalueofoutputproducedineachyear.Inyear1and

year2,Abbybuys10applesfor$1each,sohernominalspendingremainsconstant

at$10,Forexample,

(222

NominalSpending2=P,xgxQ)

二($2x0)+($1x10)

=$10.

c.Realspendingisthetotalvalueofoutputproducedineachyearvaluedattheprices

prevailinginyear1.Inyear1,thebaseyear,herrealspendingequalshernominal

spendingof$10.Inyear2,sheconsumes10greenapplesthatareeachvaluedat

theiryear1priceof$2,soherrealspendingis$20.Thatis,

RealSpending=仍4。方)+(尸二乂0二)

=($1xO)+($2x10)

=$20.

Hence,Abby'srealspendingrisesfrom$10to$20.

d.TheimplicitpricedeflatoriscalculatedbydividingAbby'snominalspendinginyear

2byherrealspendingthatyear:

,14cc,…NominalSpending,

二-

ImplicitPriceDeflator22

RealSpending2

$10

~$20

=0.5.

Thus,theimplicitpricedeflatorsuggeststhatpriceshavefallenbyhalf.Thereason

forthisisthatthedeflatorestimateshowmuchAbbyvaluesherapplesusingprices

prevailinginyear1.Fromthisperspectivegreenapplesappearveryvaluable.Inyear

2,whenAbbyconsumes10greenapples,itappearsthatherconsumptionhas

increasedbecausethedeflatorvaluesgreenapplesmorehighlythanredapples.The

onlywayshecouldstillbespending$10onahigherconsumptionbundleisifthe

priceofthegoodshewasconsumingfell.

e.IfAbbythinksofredapplesandgreenapplesasperfectsubstitutes,thenthecostof

livinginthiseconomyhasnotchanged—ineitheryearitcosts$10toconsume10

apples.AccordingtotheCPI,however,thecostoflivinghasdoubled.Thisisbecause

theCPIonlytakesintoaccountthefactthattheredapplepricehasdoubled;theCPI

ignoresthefallinthepriceofgreenapplesbecausetheywerenotintheconsumption

bundleinyear1.IncontrasttotheCPI,theimplicitpricedeflatorestimatesthecost

oflivinghasbeencutinhalf.Thus,theCPI,aLaspeyresindex,overstatestheincrease

inthecostoflivingandthedeflator,aPaascheindex,understatesit.

9.a.Thelaborforceincludesfulltimeworkers,parttimeworkers,thosewhoruntheirown

business,

andthosewhodonothaveajobbutarelookingforajob.Thelaborforceconsists

of70people.Theworkingagepopulationconsistsofthelaborforceplusthosenot

inthelaborforce.The10discouragedworkersandthe10retiredpeoplearenotin

thelaborforce,butassumingtheyarecapableofworking,theyarepartoftheadult

population.Theadultpopulationconsistsof90people,sothelaborforce

participationrateisequalto70/90or77.8percent.

b.Thenumberofunemployedworkersisequalto10,sotheunemploymentrateis

10/70or14.3percent.

c.Thehouseholdsurveyestimatestotalemploymentbyaskingasampleofhouseholds

abouttheiremploymentstatus.Thehouseholdsurveywouldreport60people

employed.Theestablishmentsurveyestimatestotalemploymentbyaskingasample

ofbusinessestoreporthowmanyworkerstheyareemploying.Inthiscasethe

establishmentsurveywouldreport55peopleemployed.The5peoplewith2jobs

wouldbecountedtwice,andthe10peoplewhoruntheirownbusinesswouldnot

becounted.

10.AsSenatorRobertKennedypointedout,GDPisanimperfectmeasureofeconomic

performanceorwell-being.Inadditiontotheleft-outitemsthatKennedycited,GDPalso

ignorestheimputedrentondurablegoodssuchascars,refrigerators,andlawnmowers;

manyservicesandproductsproducedaspartofhouseholdactivity,suchascookingand

cleaning;andthevalueofgoodsproducedandsoldinillegalactivities,suchasthedrug

trade.TheseimperfectionsinthemeasurementofGDPdonotnecessarilyreduceits

usefulness.Aslongasthesemeasurementproblemsstayconstantovertime,thenGDPis

usefulincomparingeconomicactivityfromyeartoyear.Moreover,alargeGDPallows

ustoaffordbettermedicalcareforourchildren,newerbooksfortheireducation,and

moretoysfortheirplay.Finally,countrieswithhigherlevelsofGDPtendtohavehigher

levelsoflifeexpectancy,betteraccesstocleanwaterandsanitation,andhigherlevelsof

education.GDPisthereforeausefulmeasureforcomparingthelevelofgrowthand

developmentacrosscountries.

11.a.RealGDPfallsbecauseDisneyWorlddoesnotproduceanyserviceswhileitisclosed.

Thiscorrespondstoadecreaseineconomicwell-beingbecausetheincomeof

workersandshareholdersofDisneyWorldfalls(theincomesideofthenational

accounts),andpeople'sconsumptionofDisneyWorldfalls(theexpendituresideof

thenationalaccounts).

b.RealGDPrisesbecausetheoriginalcapitalandlaborinfarmproductionnowproduce

morewheat.Thiscorrespondstoanincreaseintheeconomicwell-beingofsociety,

sincepeoplecannowconsumemorewheat.(Ifpeopledonotwanttoconsumemore

wheat,thenfarmersandfarmlandcanbeshiftedtoproducingothergoodsthat

societyvalues.)

c.RealGDPfallsbecausewithfewerworkersonthejob,firmsproduceless.This

accuratelyreflectsafallineconomicwell-being.

d.RealGDPfallsbecausethefirmsthatlayoffworkersproduceless.Thisdecreases

economicwell-beingbecauseworkers*incomesfall(theincomeside),andthere

arefewergoodsforpeopletobuy(theexpenditureside).

e.RealGDPislikelytofall,asfirmsshifttowardproductionmethodsthatproducefewer

goodsbutemitlesspollution.Economicwell-being,however,mayrise.Theeconomy

nowproduceslessmeasuredoutputbut