曼昆宏观经济学第九版-课后习题答案

AnswerstoTextbookQuestionsandProblems

CHAPTER1 TheScienceofMacroeconomics

QuestionsforReview

1. Microeconomicsisthestudyofhowindividualfirmsandhouseholdsmakedecisions,andhowtheyinteractwithoneanother.Microeconomicmodelsoffirmsandhouseholdsarebasedonprinciplesofoptimization—firmsandhouseholdsdothebesttheycangiventheconstraintstheyface.Forexample,householdschoosewhichgoodstopurchaseinordertomaximizetheirutility,whereasfirmsdecidehowmuchtoproduceinordertomaximizeprofits.Incontrast,macroeconomicsisthestudyoftheeconomyasawhole;itfocusesonissuessuchashowtotaloutput,totalemployment,andtheoverallpricelevelaredetermined.Theseeconomy-widevariablesarebasedontheinteractionofmanyhouseholdsandmanyfirms;therefore,microeconomicsformsthebasisformacroeconomics.

2. Economistsbuildmodelsasameansofsummarizingtherelationshipsamongeconomicvariables.Modelsareusefulbecausetheyabstractfromthemanydetailsintheeconomyandallowonetofocusonthemostimportanteconomicconnections.

3. Amarket-clearingmodelisoneinwhichpricesadjusttoequilibratesupplyanddemand.Market-clearingmodelsareusefulinsituationswherepricesareflexible.Yetinmanysituations,flexiblepricesmaynotbearealisticassumption.Forexample,laborcontractsoftensetwagesforuptothreeyears.Or,firmssuchasmagazinepublisherschangetheirpricesonlyeverythreetofouryears.Mostmacroeconomistsbelievethatpriceflexibilityisareasonableassumptionforstudyinglong-runissues.Overthelongrun,pricesrespondtochangesindemandorsupply,eventhoughintheshortruntheymaybeslowtoadjust.

ProblemsandApplications

1. MonetarypolicyintheUnitedStatesandtheEuropeanUnionhasbeenabigtopicofconversationinearly2015.TheEUembarkeduponaquantitativeeasingpolicyinMarch2015inanattempttostimulategrowthandpreventdeflation.TherehasbeensomeconcernthattheinflationrateinEuropewillturnnegative.IntheUnitedStates,thereiscontinueddiscussionandspeculationconcerningwhentheFederalReservemightchoosetoincreasethetargetfederalfundsrate.AlsointheUnitedStates,theunemploymentratehasdeclinedtoabout5.5percentandthissuggeststhatwagesmaybegintoincrease.TheFederalReservewillbewatchingforwageandpriceincreasesastheydecidewhentoincreaseinterestrates.

2. Manyphilosophersofsciencebelievethatthedefiningcharacteristicofascienceistheuseofthescientificmethodofinquirytoestablishstablerelationships.Scientistsexaminedata,oftenprovidedbycontrolledexperiments,tosupportordisproveahypothesis.Economistsaremorelimitedintheiruseofexperiments.Theycannotconductcontrolledexperimentsontheeconomy;theymustrelyonthenaturalcourseofdevelopmentsintheeconomytocollectdata.Totheextentthateconomistsusethescientificmethodofinquiry,thatis,developinghypothesesandtestingthem,economicshasthecharacteristicsofascience.

3. Wecanuseasimplevariantofthesupply-and-demandmodelforpizzatoanswerthisquestion.Assumethatthequantityoficecreamdemandeddependsnotonlyonthepriceoficecreamandincome,butalsoonthepriceoffrozenyogurt:

Qd=D(PIC,PFY,Y).

Weexpectthatdemandforicecreamriseswhenthepriceoffrozenyogurtrises,becauseicecreamandfrozenyogurtaresubstitutes.Thatis,whenthepriceoffrozenyogurtgoesup,Iconsumelessofitand,instead,fulfillmoreofmyfrozendesserturgesthroughtheconsumptionoficecream.

Thenextpartofthemodelisthesupplyfunctionforicecream,Qs=S(PIC).Finally,inequilibrium,supplymustequaldemand,sothatQs=Qd.YandPFYaretheexogenousvariables,andQandPICaretheendogenousvariables.Figure1-1usesthismodeltoshowthatafallinthepriceoffrozenyogurtresultsinaninwardshiftofthedemandcurveforicecream.Thenewequilibriumhasalowerpriceandquantityoficecream.

4. Thepriceofhaircutschangesratherinfrequently.Fromcasualobservation,hairstyliststendtochargethesamepriceoveraone-ortwo-yearperiodirrespectiveofthedemandforhaircutsorthesupplyofcutters.Amarket-clearingmodelforanalyzingthemarketforhaircutshastheunrealisticassumptionofflexibleprices.Suchanassumptionisunrealisticintheshortrunwhenweobservethatpricesareinflexible.Overthelongrun,however,thepriceofhaircutsdoestendtoadjust;amarket-clearingmodelisthereforeappropriate.

AnswerstoTextbookQuestionsandProblems

CHAPTER2 TheDataofMacroeconomics

QuestionsforReview

1. GDPmeasuresthetotalincomeearnedfromtheproductionofthenewfinalgoodsandservicesinthe

economy,anditmeasuresthetotalexpendituresonthenewfinalgoodsandservicesproducedintheeconomy.GDPcanmeasuretwothingsatoncebecausethetotalexpendituresonthenewfinalgoodsandservicesbythebuyersmustbeequaltotheincomeearnedbythesellersofthenewfinalgoodsandservices.Asthecircularflowdiagraminthetextillustrates,thesearealternative,equivalentwaysofmeasuringtheflowofdollarsintheeconomy.

2. ThefourcomponentsofGDPareconsumption,investment,governmentpurchases,andnetexports.

TheconsumptioncategoryofGDPconsistsofhouseholdexpendituresonnewfinalgoodsandservices,suchasthepurchaseofanewtelevision.TheinvestmentcategoryofGDPconsistsofbusinessfixedinvestment,residentialfixedinvestment,andinventoryinvestment.Whenabusinessbuysnewequipmentthiscountsasinvestment.Governmentpurchasesconsistsofpurchasesofnewfinalgoodsandservicesbyfederal,state,andlocalgovernments,suchaspaymentsfornewmilitaryequipment.Netexportsmeasuresthevalueofgoodsandservicessoldtoothercountriesminusthevalueofgoodsandservicesforeignerssellus.WhentheU.S.sellscorntoforeigncountries,itcountsinthenetexportcategoryofGDP.

3. Theconsumerpriceindex(CPI)measurestheoveralllevelofpricesintheeconomy.Ittellsusthepriceofafixedbasketofgoodsrelativetothepriceofthesamebasketinthebaseyear.TheGDPdeflatoristheratioofnominalGDPtorealGDPinagivenyear.TheGDPdeflatormeasuresthepricesofallgoodsandservicesproduced,whereastheCPIonlymeasurespricesofgoodsandservicesboughtbyconsumers.TheGDPdeflatorincludesonlydomesticallyproducedgoods,whereastheCPIincludesdomesticandforeigngoodsboughtbyconsumers.Finally,theCPIisaLaspeyresindexthatassignsfixedweightstothepricesofdifferentgoods,whereastheGDPdeflatorisaPaascheindexthatassignschangingweightstothepricesofdifferentgoods.Inpractice,thetwopriceindicestendtomovetogetheranddonotoftendiverge.

4.TheCPImeasuresthepriceofafixedbasketofgoodsrelativetothepriceofthesamebasketinthebaseyear.ThePCEdeflatoristheratioofnominalconsumerspendingtorealconsumerspending.TheCPIandthePCEdeflatoraresimilarinthattheybothonlyincludethepricesofgoodspurchasedbyconsumers,andtheybothincludethepriceofimportedgoodsaswellasdomesticallyproducedgoods.ThetwomeasuresdifferbecausetheCPImeasuresthechangeinthepriceofafixedbasketwhereasthegoodsmeasuredbythePCEdeflatorchangefromyeartoyeardependingonwhatconsumersarepurchasinginthatparticularyear.

5. TheBureauofLaborStatistics(BLS)classifieseachpersonintooneofthefollowingthreecategories:employed,unemployed,ornotinthelaborforce.Theunemploymentrate,whichisthepercentageofthelaborforcethatisunemployed,iscomputedasfollows:

UnemploymentRate=.

Notethatthelaborforceisthenumberofpeopleemployedplusthenumberofpeopleunemployed.

6. Everymonth,theBureauofLaborStatisticsundertakestwosurveystomeasureemployment.First,theBLSsurveysabout60,000householdsandtherebyobtainsanestimateoftheshareofpeoplewhosaytheyareworking.TheBLSmultipliesthissharebyanestimateofthepopulationtoestimatethenumberofpeopleworking.Second,theBLSsurveysabout160,000businessestablishmentsandaskshowmanypeopletheyemploy.Eachsurveyisimperfect;sothetwomeasuresofemploymentarenotidentical.

ProblemsandApplications

1. FromthemainWebpageclickontheinteractivedatatabatthetop,selectGDP,beginusingthedata,section1,andthentable1.1.1.RealGDPgrewatarateof2.2percentinquarter4of2014.Whencomparedtogrowthratesof−2.1percent,4.6percent,and5percentforthefirstthreequartersof2014,therateof2.2percentwasslightlybelowaverage.FromthemainWebpageselectthedatatoolstab,thentoppicks.Checktheboxfortheunemploymentrateandretrievethedata.TheunemploymentrateinMarch2015was5.5percent,whichwasaboutequaltothenaturalrateofunemployment,orthelongrunaveragerate.Fromthemainpage,selecttheeconomicreleasestab,theninflationandprices.AccessthereportfortheCPI.InFebruary2015,theinflationrateforallitemswas0percent,andiffoodandenergywereexcludedtheratewas1.7percent.TheinflationratewasbelowaverageandbelowtheFederalReserve’stargetof2percent.

2. Valueaddedbyeachpersonisequaltothevalueofthegoodproducedminustheamountthepersonpaidforthematerialsneededtomakethegood.Therefore,thevalueaddedbythefarmeris$1.00($1–0=$1).Thevalueaddedbythemilleris$2:shesellstheflourtothebakerfor$3butpaid$1fortheflour.Thevalueaddedbythebakeris$3:shesellsthebreadtotheengineerfor$6butpaidthemiller$3fortheflour.GDPisthetotalvalueadded,or$1+$2+$3=$6.NotethatGDPequalsthevalueofthefinalgood(thebread).

3. Whenawomanmarriesherbutler,GDPfallsbytheamountofthebutler’ssalary.ThishappensbecauseGDPmeasurestotalincome,andthereforeGDP,fallsbytheamountofthebutler’slossinsalary.IfGDPtrulymeasuresthevalueofallgoodsandservices,thenthemarriagewouldnotaffectGDPsincethetotalamountofeconomicactivityisunchanged.ActualGDP,however,isanimperfectmeasureofeconomicactivitybecausethevalueofsomegoodsandservicesisleftout.Oncethebutler’sworkbecomespartofhishouseholdchores,hisservicesarenolongercountedinGDP.Asthisexampleillustrates,GDPdoesnotincludethevalueofanyoutputproducedinthehome.

4. a. TheairplanesoldtotheU.S.AirForcecountsasgovernmentpurchasesbecausetheAirForceispartofthegovernment.

b. TheairplanesoldtoAmericanAirlinescountsasinvestmentbecauseitisacapitalgoodsoldtoaprivatefirm.

c. TheairplanesoldtoAirFrancecountsasanexportbecauseitissoldtoaforeigner.

d. TheairplanesoldtoAmeliaEarhartcountsasconsumptionbecauseitissoldtoaprivateindividual.

e. Theairplanebuilttobesoldnextyearcountsasinvestment.Inparticular,theairplaneiscountedasinventoryinvestment,whichiswheregoodsthatareproducedinoneyearandsoldinanotheryeararecounted.

5. Dataonparts(a)to(f)canbedownloadedfromtheBureauofEconomicAnalysis.GototheWebsite,clickontheinteractivedatatabatthetop,selectGDP,beginusingthedata,section1,andthentable1.1.5.Choosethe“modifythedata”optiontoselecttheyearsyouinwhichyouareinterested.Bydividingeachcomponent(a)to(f)bynominalGDPandmultiplyingby100,weobtainthefollowingpercentages:

1950 1980 2014

a.Personalconsumptionexpenditures 64.0% 61.3% 68.5%

b.Grossprivatedomesticinvestment 18.8% 18.5% 16.4%

c.Governmentconsumptionpurchases 16.9% 20.6% 18.2%

d.Netexports 0.2% –0.5% 3.1%

e.Nationaldefensepurchases 7.6% 6.3% 4.4%

f.Imports 3.9% 10.3% 16.5%

(Note:TheabovedatawasdownloadedApril3,2015,fromtheBEAWebsite.)

Amongotherthings,weobservethefollowingtrendsintheeconomyovertheperiod1950–2015:

a. Personalconsumptionexpenditureshavebeenaroundtwo-thirdsofGDPbetween1980and2015.

b. TheshareofGDPgoingtogrossprivatedomesticinvestmentremainedfairlysteady.

c. Thesharegoingtogovernmentconsumptionpurchasesrosesharplyfrom1950to1980.

d. Netexports,whichwerepositivein1950,havebeennegativesincethattime.

e. Thesharegoingtonationaldefensepurchaseshasfallen.

f. ImportshavegrownrapidlyrelativetoGDP.

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

b. NNPisequaltoGNPminusdepreciation.Inthisexample,GDPisequaltoGNPbecausethereare

noforeigntransactions.Therefore,NNPisequalto$875,000.

c. NationalincomeisequaltoNNP,or$875,000.

d. Employeecompensationisequalto$600,000.

e. Proprietors’incomemeasurestheincomeoftheowner,andisequalto150,000.

f. Corporateprofitisequaltocorporatetaxesplusdividendsplusretainedearnings,or$275,000.

Retainedearningsiscalculatedassalesminuswagesminusdividendsminusdepreciationminuscorporatetax,or$75,000.

g. Personalincomeisequaltoemployeecompensationplusdividends,or$750,000.

h. Disposablepersonalincomeispersonalincomeminustaxes,or$550,000.

7. a. i. NominalGDPisthetotalvalueofgoodsandservicesmeasuredatcurrentprices.Therefore,

NominalGDP2010 =

=($2200)+($3200)

=$400+$600

=$1,000.

NominalGDP2015 =

=($4250)+($4500)

=$1,000+$2,000

=$3,000.

ii. RealGDPisthetotalvalueofgoodsandservicesmeasuredatconstantprices.Therefore,tocalculaterealGDPin2015(withbaseyear2010),multiplythequantitiespurchasedintheyear2015bythe2010prices:

RealGDP2015 =

=($2250)+($3500)

=$500+$1,500

=$2,000.

RealGDPfor2010iscalculatedbymultiplyingthequantitiesin2010bythepricesin2010.Sincethebaseyearis2010,realGDP2010equalsnominalGDP2010,whichis$10,00.Hence,realGDPincreasedbetween2010and2015.

iii. TheimplicitpricedeflatorforGDPcomparesthecurrentpricesofallgoodsandservicesproducedtothepricesofthesamegoodsandservicesinabaseyear.Itiscalculatedasfollows:

ImplicitPriceDeflator2015 ==1

UsingthevaluesforNominalGDP2015andrealGDP2015calculatedabove:

ImplicitPriceDeflator2015=$3,000$2,000

=1.50.

Thiscalculationrevealsthatpricesofthegoodsproducedintheyear2015increasedby50percentcomparedtothepricesthatthegoodsintheeconomysoldforin2010.(Because2010isthebaseyear,thevaluefortheimplicitpricedeflatorfortheyear2010is1.0becausenominalandrealGDParethesameforthebaseyear.)

iv. Theconsumerpriceindex(CPI)measuresthelevelofpricesintheeconomy.TheCPIiscalledafixed-weightindexbecauseitusesafixedbasketofgoodsovertimetoweightprices.Ifthebaseyearis2010,theCPIin2015ismeasuringthecostofthebasketin2015relativetothecostin2010.TheCPI2015iscalculatedasfollows:

CPI2015 =

=

=1.6.

Thiscalculationshowsthatthepriceofgoodspurchasedin2015increasedby60percentcomparedtothepricesthesegoodswouldhavesoldforin2010.TheCPIfor2010,thebaseyear,equals1.0.

b. TheimplicitpricedeflatorisaPaascheindexbecauseitiscomputedwithachangingbasketofgoods;theCPIisaLaspeyresindexbecauseitiscomputedwithafixedbasketofgoods.From(7.a.iii),theimplicitpricedeflatorfortheyear2015is1.50,whichindicatesthatpricesroseby50percentfromwhattheywereintheyear2010.From(7.a.iv.),theCPIfortheyear2015is1.6,whichindicatesthatpricesroseby60percentfromwhattheywereintheyear2010.

Ifpricesofallgoodsroseby,forexample,50percent,thenonecouldsayunambiguouslythatthepricelevelroseby50percent.Yet,inourexample,relativepriceshavechanged.Thepriceofhotdogsroseby1020percent;thepriceofhamburgersroseby33.33percent,makinghamburgersrelativelylessexpensive.

AsthediscrepancybetweentheCPIandtheimplicitpricedeflatorillustrates,thechangeinthepriceleveldependsonhowthegoods’pricesareweighted.TheCPIweightsthepriceofgoodsbythequantitiespurchasedintheyear2010.Theimplicitpricedeflatorweightsthepriceofgoodsbythequantitiespurchasedintheyear2015.Sincethequantityofthetwogoodswasthesamein2010,theCPIisplacingequalweightonthetwopricechanges.In2015,thequantityofhamburgerswastwiceaslargeashotdogs,sothereistwiceasmuchweightplacedonthehamburgerpricerelativetothehotdogprice.Forthisreason,theCPIshowsalargerinflationrate–moreweightisplacedonthegoodwiththelargerpriceincrease.

8. a. Theconsumerpriceindexusestheconsumptionbundleinyear1tofigureouthowmuchweighttoputonthepriceofagivengood:

CPI2 =

=

=2.

AccordingtotheCPI,priceshavedoubled.

b. Nominalspendingisthetotalvalueofoutputproducedineachyear.Inyear1andyear2,Abbybuys10applesfor$1each,sohernominalspendingremainsconstantat$10.Forexample,

NominalSpending2 =

=($20)+($110)

=$10.

c. Realspendingisthetotalvalueofoutputproducedineachyearvaluedatthepricesprevailinginyear1.Inyear1,thebaseyear,herrealspendingequalshernominalspendingof$10.Inyear2,sheconsumes10greenapplesthatareeachvaluedattheiryear1priceof$2,soherrealspendingis$20.Thatis,

RealSpending2 =

=($10)+($210)

=$20.

Hence,Abby’srealspendingrisesfrom$10to$20.

d. TheimplicitpricedeflatoriscalculatedbydividingAbby’snominalspendinginyear2byherrealspendingthatyear:

ImplicitPriceDeflator2 =

=

=0.5.

Thus,theimplicitpricedeflatorsuggeststhatpriceshavefallenbyhalf.ThereasonforthisisthatthedeflatorestimateshowmuchAbbyvaluesherapplesusingpricesprevailinginyear1.Fromthisperspectivegreenapplesappearveryvaluable.Inyear2,whenAbbyconsumes10greenapples,itappearsthatherconsumptionhasincreasedbecausethedeflatorvaluesgreenapplesmorehighlythanredapples.Theonlywayshecouldstillbespending$10onahigherconsumptionbundleisifthepriceofthegoodshewasconsumingfell.

e. IfAbbythinksofredapplesandgreenapplesasperfectsubstitutes,thenthecostoflivinginthiseconomyhasnotchanged—ineitheryearitcosts$10toconsume10apples.AccordingtotheCPI,however,thecostoflivinghasdoubled.ThisisbecausetheCPIonlytakesintoaccountthefactthattheredapplepricehasdoubled;theCPIignoresthefallinthepriceofgreenapplesbecausetheywerenotintheconsumptionbundleinyear1.IncontrasttotheCPI,theimplicitpricedeflatorestimatesthecostoflivinghasbeencutinhalf.Thus,theCPI,aLaspeyresindex,overstatestheincreaseinthecostoflivingandthedeflator,aPaascheindex,understatesit.

9. a. Thelaborforceincludesfulltimeworkers,parttimeworkers,thosewhoruntheirownbusiness,

andthosewhodonothaveajobbutarelookingforajob.Thelaborforceconsistsof70people.Theworkingagepopulationconsistsofthelaborforceplusthosenotinthelaborforce.The10discouragedworkersandthe10retiredpeoplearenotinthelaborforce,butassumingtheyarecapableofworking,theyarepartoftheadultpopulation.Theadultpopulationconsistsof90people,sothelaborforceparticipationrateisequalto70/90or77.8percent.

b. Thenumberofunemployedworkersisequalto10,sotheunemploymentrateis10/70or14.3percent.

c. Thehouseholdsurveyestimatestotalemploymentbyaskingasampleofhouseholdsabouttheiremploymentstatus.Thehouseholdsurveywouldreport60peopleemployed.Theestablishmentsurveyestimatestotalemploymentbyaskingasampleofbusinessestoreporthowmanyworkerstheyareemploying.Inthiscasetheestablishmentsurveywouldreport55peopleemployed.The5peoplewith2jobswouldbecountedtwice,andthe10peoplewhoruntheirownbusinesswouldnotbecounted.

10. AsSenatorRobertKennedypointedout,GDPisanimperfectmeasureofeconomicperformanceorwell-being.Inadditiontotheleft-outitemsthatKennedycited,GDPalsoignorestheimputedrentondurablegoodssuchascars,refrigerators,andlawnmowers;manyservicesandproductsproducedaspartofhouseholdactivity,suchascookingandcleaning;andthevalueofgoodsproducedandsoldinillegalactivities,suchasthedrugtrade.TheseimperfectionsinthemeasurementofGDPdonotnecessarilyreduceitsusefulness.Aslongasthesemeasurementproblemsstayconstantovertime,thenGDPisusefulincomparingeconomicactivityfromyeartoyear.Moreover,alargeGDPallowsustoaffordbettermedicalcareforourchildren,newerbooksfortheireducation,andmoretoysfortheirplay.Finally,countrieswithhigherlevelsofGDPtendtohavehigherlevelsoflifeexpectancy,betteraccesstocleanwaterandsanitation,andhigherlevelsofeducation.GDPisthereforeausefulmeasureforcomparingthelevelofgrowthanddevelopmentacrosscountries.

11. a. RealGDPfallsbecauseDisneyWorlddoesnotproduceanyserviceswhileitisclosed.Thiscorrespondstoadecreaseineconomicwell-beingbecausetheincomeofworkersandshareholdersofDisneyWorldfalls(theincomesideofthenationalaccounts),andpeople’sconsumptionofDisneyWorldfalls(theexpendituresideofthenationalaccounts).

b. RealGDPrisesbecausetheoriginalcapitalandlaborinfarmproductionnowproducemorewheat.Thiscorrespondstoanincreaseintheeconomicwell-beingofsociety,sincepeoplecannowconsumemorewheat.(Ifpeopledonotwanttoconsumemorewheat,thenfarmersandfarmlandcanbeshiftedtoproducingothergoodsthatsocietyvalues.)

c. RealGDPfallsbecausewithfewerworkersonthejob,firmsproduceless.Thisaccuratelyreflectsafallineconomicwell-being.

d. RealGDPfallsbecausethefirmsthatlayoffworkersproduceless.Thisdecreaseseconomicwell-beingbecauseworkers’incomesfall(theincomeside),andtherearefewergoodsforpeopletobuy(theexpenditureside).

e. RealGDPislikelytofall,asfirmsshifttowardproductionmethodsthatproducefewergoodsbutemitlesspollution.Economicwell-being,however,mayrise.Theeconomynowproduceslessmeasuredoutputbutmorecleanair.Cleanairisnottradedinmarketsand,thus,doesnotshowupinmeasuredGDP,butisneverthelessagoodthatpeoplevalue.

f. RealGDPrisesbecausethehighschoolstudentsgofromanactivityinwhichtheyarenotproducingmarketgoodsandservicestooneinwhichtheyare.Economicwell-being,however,maydecrease.Inidealnationalaccounts,attendingschoolwouldshowupasinvestmentbecauseitpresumablyincreasesthefutureproductivityoftheworker.Actualnationalaccountsdonotmeasurethistypeofinvestment.NotealsothatfutureGDPmaybelowerthanitwouldbeifthestudentsstayedinschool,sincethefutureworkforcewillbelesseducated.

g. MeasuredrealGDPfallsbecausefathersspendlesstimeproducingmarketgoodsandservices.Theactualproductionofgoodsandservicesneednothavefallenbecausebutunmeasuredproductionofchild-rearingservicesrises.Thewell-beingoftheaveragepersonmayverywellriseifweassumethefathersandthechildrenenjoytheextratimetheyarespendingtogether.

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.Thetextshowedthatthep