从国外网站档下来的英文版宏经习题Word格式.docx
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C.Atechnologicaladvanceimprovestheproductionfunction.
Problem2:
Ifa10-percentincreaseinbothcapitalandlaborcausesoutputtoincreasebylessthan10percent,theproductionfunctionissaidtoexhibitdecreasingreturnstoscale.Ifitcausesoutputtoincreasebymorethan10percent,theproductionfunctionissaidtoexhibitincreasingreturnstoscale.Whymightaproductionfunctionexhibitincreasingordecreasingreturnstoscale?
Problem3:
Supposethataneconomy’sproductionfunctionisCobb-Douglaswithparameteralpha=0.3.
3.3A.Whatfractionsofincomedocapitalandlaborreceive?
3.3B.Supposethatimmigrationraisesthelaborforceby10percent.Whathappenstototaloutput(inpercent)?
Therentalpriceofcapital?
Therealwage?
3.3C.Supposethatagiftofcapitalfromabroadraisesthecapitalstockby10percent.Whathappenstototaloutput(inpercent)?
3.3D.SupposethatatechnologicaladvanceraisesthevalueoftheparameterAby10percent.Whathappenstototaloutput(inpercent)?
Problem4.:
Empiricallythetrendintherealwagecloselytracksthetrendinlaborproductivity.Explainwhy?
Problem5.A.Overthepastcentury,theproductivityoffarmershasrisensubstantiallybecauseoftechnologicalprogress.Accordingtotheneoclassicaltheory,whatshouldhavehappenedtotheirrealwage?
B.Overthesameperiod,theproductivityofbarbershasremainedconstant.Supposeworkerscanmovefreelybetweenfarmersandbeingbarbers.Whatdoesthismobilityimplyforthewagesoffarmersandbarbers?
C.Whatdoyourpreviousanswersimplyforthepriceofhaircutsrelativetothepriceoffood?
D.Whobenefitsfromtechnologicalprogressinfarming–farmersorbarbers?
Problem6.:
(Harder)ConsideraCobb-Douglasproductionfunctionwiththreeinputs.Kiscapital(thenumberofmachines),Lislabor(thenumberofworkers),andHishumancapital(thenumberofcollegedegreesamongtheworkers).Theproductionfunctionis:
Problem6A.Deriveanexpressionforthemarginalproductoflabor.Howdoesanincreaseintheamountofhumancapitalaffectthemarginalproductoflabor?
Problem6B.Deriveanexpressionforthemarginalproductofhumancapital.Howdoesanincreaseintheamountofhumancapitalaffectthemarginalproductofhumancapital?
Problem6C.Whatistheincomesharepaidtolabor?
Whatistheincomesharepaidtohumancapital?
Inthenationalincomeaccountsofthiseconomy,whatshareoftotalincomedoyouthinkworkerswouldappeartoreceive?
(Hint:
Considerwherethereturntohumancapitalshowsup.)
Problem6D.Anunskilledworkersearnsthemarginalproductoflabor,whereasaskilledworkerearnsthemarginalproductoflaborplusthemarginalproductofhumancapital.Usingyouranswersto(a)and(b),findtheratiooftheskilledwagetotheunskilledwage.Howdoesanincreaseintheamountofhumancapitalaffectthisratio?
Explain.
Problem6E.Somepeopleadvocategovernmentfundingofcollegescholarshipsasawayofcreatingamoreegalitariansociety.Othersarguethatscholarshipshelponlythosewhoareabletogotocollege.Doyouranswerstotheprecedingquestionsshedlightonthisdebate?
THELABORMARKET
ConsideraneconomywiththefollowingCobb-Douglasproductionfunction:
.Theeconomyhas1000unitsofcapitalandalaborforceof1000workers.
A.Derivetheequationdescribingthelabordemandinthiseconomyasafunctionoftherealwageandthecapitalstock.B.Iftherealwagecanadjusttoequilibratelaborsupplyandlabordemand,whatistherealwage?
Inthisequilibrium,whatisemployment,output,andthetotalamountearnedbyworkers?
C.Assumethataminimumwageof1dollarisimposedbyCongress.Whathappenstoemployment,output,andthetotalamountearnedbyworkers.D.Didtheminimumwagehelptheworkingclassinthisexample?
Supposethatacountryexperiencesareductioninproductivity(A);
A.Whathappenstothelabordemandcurve?
B.Whatistheeffectonemployment,unemploymentandtherealwageifweassumeperfectcompetition?
Assumethatthelaborsupplycurveisvertical.
C.Howwouldthischangeinproductivityaffectemploymentifunionspreventtherealwagefromfalling?
TOPICS1and3:
GROWTHACCOUNTING(“TILLVÄ
XTBOKFÖ
RING”)ANDGROWTHRATES
Inaneconomywhichischaracterizedbyperfectcompetitioninthegoodsandlabormarket,theownersofcapitalgettwo-thirdsofnationalincome,andtheworkersreceiveone-third.AssumeaCobb-Douglasaggregateproductionfunction.
Problem1A:
Themenstayathomeinthiseconomy,whilethewomenworkinfactories.Ifsomeofthemenstartedworkingoutsidethehomesothatthelaborforceincreasedby5percent,whatwouldhappentothemeasuredoutputoftheeconomy?
Doeslaborproductivity(outputperworker)increase,decreaseorstaythesame?
Doestotalfactorproductivity(A)increase,decrease,orstaythesame?
Problem1B:
Inyear1,thecapitalstockwas6,thelaborinputwas3,andoutputwas12.Inyear2,thecapitalstockwas7,thelaborinputwas4,andoutputwas14.Whathappenedtototalfactorproductivitybetweentheyears?
Assumeaneconomywhichischaracterizedbyperfectcompetitioninthegoodsandlabormarket,inwhichtheownersofcapitalgetone-thirdofnationalincome,andtheworkersreceivetwo-thirds.AssumeaCobb-Douglasaggregateproductionfunction.
Assumethattotaloutputandtotalcapitalstockgrowat3.6percentperyear,andthatlaborinputgrowsbyonepercentperyear.Usethegrowth-accountingequationtodivideoutputgrowthintothreesources–capital,labor,andtotalfactorproductivity–howmuchofoutputgrowthwouldyouattributetoeachsource?
Problem4.IfGDPpercapitainSweden(in1995prices)in1995and2000were194and222thousandsofkronor,whatwastheaverageannualrateofeconomicgrowthduringthis5-yearperiod?
Problem5.Ifavariableduringa30-yearperiodincreasesby54percent,whataverageannualgrowthratedoesthiscorrespondto?
Problem6.IfthegrowthrateofGDPpercapitawas2percentbetween1960and1990,andthepopulationgrowthratewas3percentduringthesameperiod,whatwasthegrowthrateofGDPduringthisperiod?
Problem7:
AssumethatGDPpercapitainSwedenandZambiain2002were16000and800USD,respectively,andthatthegrowthrateofGDPpercapitainSwedenandZambiais1and7percent,respectively.
a)Howdoestheabsolutedifferencebetweenthe2countriesdevelopovertime?
Thatis,GDPpercapitainSweden–GDPpercapitainZambia.
b)Howdoestherelativedifferencedevelopovertime?
Thatis,GDPpercapitainSweden/GDPpercapitainZambia.
YoumaywanttouseEXCELtoanswerthesequestions.
Problem8:
Ifyourwageis100kronorandthegrowthrateis5percent,howmanyyearsdoesittakeforyourwagetodouble?
TOPIC4:
ECONOMICGROWTHTHEORY:
THESOLOWMODEL
Problem00:
ShowintheSolow-diagramandexplaininwords:
A.Theeffectofanincreasedsavingrateonthesteady-statelevelsofproductionperworker(Y/L),capitalperworker(K/L),andtherealwage(W/P).
B.Theeffectofalowerpopulationgrowthrateonthesteady-statelevelsofproductionperworker(Y/L),capitalperworker(K/L),andtherealwage(W/P).
C.Theeffectofabettertechnologyonthesteady-statelevelsofproductionperworker(Y/L),capitalperworker(K/L),andtherealwage(W/P).
Problem01A.Inthelong-runequilibrium,assumethatthelong-runpopulationgrowthrateis2percent(thatis,n=0.02),andthelong-rungrowthrateofAis0percent(thatis,g=0),calculatethelong-runequilibriumgrowthrateofY,(Y/L),K,(K/L),andtherealwage(W/P).
Problem01B.Inthelong-runequilibrium,assumethatthelong-runpopulationgrowthrateis2percent(thatis,n=0.02),andthelong-rungrowthrateofAis2percent(thatis,g=0.02),calculatethelong-runequilibriumgrowthrateofY,(Y/L),K,(K/L),andtherealwage(W/P).
QuantitativequestionsontheSolowModel:
CountryAandBhastheproductionfunction:
A.Doesthisproductionfunctionhaveconstantreturnstoscale?
B.Whatistheper-workerproductionfunction,Y/L=f(K/L)
C.Assumethatneithercountryexperiencespopulationgrowthortechnologicalprogressandthat5percentofcapitaldepreciateseachyear.AssumefurtherthatcountryAsaves10percentofoutputeachyear,andcountryBsaves20percentofoutputeachyear.Findthesteadystatelevelofcapitalperworker,thesteady-statelevelofincomeperworkerandconsumptionperworker.
D.Supposethatbothcountriesstartoffwithacapitalstockperworkerof2.Whatarethelevelsofincomeperworkerandconsumptionperworker?
Rememberingthatthechangeinthecapitalstockisgrossinvestmentminusdepreciation,calculatecapitalstockperworker,incomeperworker,andconsumptionperworkerovertime.HowmanyyearswillitbebeforeconsumptionperworkerinCountryBishigherthanthelevelofconsumptionperworkerincountryA.
InthediscussionofGermanandJapanesepostwargrowth,thetextdescribeswhathappenswhenpartofthecapitalstockisdestroyedinawar.Bycontrast,supposethatawardoesnotaffectthecapitals