英文版宏观经济典型例题附带答案15页

Macroeconomics1、2、3、4、Abbyconsumesonlyapples.Inyear1,redapplescost1dollareach,greenapplescost2dollareach,andAbbybuys10redapples.Inyear2,redapplescost2dollar,greenapplescost1dollar,andAbbybuys10greenapples.a.Computeaconsumerpriceindexforapplesforeachyear.Assumethatyear1isthebaseyearinwhichtheconsumerbasketisfixed.Howdoesyourindexchangefromyear1toyear2?b.ComputeAbby’snominalspendingonapplesineachyear.Howdoesitchangefromyear1toyear2?c.Usingyear1asthebaseyear,computeAbby’srealspendingonapplesineachyear.Howdoesitchangefromyear1toyear2?d.Definingtheimplicitpricedeflatorasnominalspendingdividedbyrealspending,computethedeflatorforeachyear.Howdoesthedeflatorchangefromyear1toyear2?SupposethatAbbyisequallyhappyeatingredorgreenapples.HowmuchhasthetruecostoflivingincreasedforAbby?Comparethisanswertoyouranswerstoparts(a)and(d).WhatdoesthisexampletellyouaboutLaspeyresandPaaschepriceindexes?a.AccordingtotheCPI(消費物價指數),priceshavedoubled.b.N-spendingisthetotalvalueofoutputproducedineachyear.InY1andY2,Abbybuys10applesfor$1each,soherN-spendingremainsconstantat$10.c.R-spendingisthetotalvalueofoutputproducedineachyearvaluedatthepricesprevailinginY1.InY1,thebaseyear,herR-spendingequalsherN-spendingof$10.Inyear2,sheconsumes10greenapplesthatareeachvaluedattheirY1priceof$2,soherrealspendingis$20.Hence,Abby’srealspendingrisesfrom$10to$20.d.Thus,theimplicitpricedeflatorsuggeststhatpriceshavefallenbyhalf.e.IfAbbythinksofredapplesandgreenapplesasperfectsubstitutes,thenthecostoflivinginthiseconomyhasnotchanged.AccordingtotheCPI,however,thecostoflivinghasdoubled.IncontrasttotheCPI,theimplicitpricedeflatorestimatesthecostoflivinghashalved.Thus,theCPI,aLaspeyresindex,overstatestheincreaseinthecostoflivingandthedeflator,aPaascheindex,understatesit.ThischapterofthetextdiscussesthedifferencebetweenLaspeyresandPaascheindicesinmoredetail.5、6、Supposethataneconomy’sproductionfunctionisCobb-Douglaswithparameter0.3.a.Whatfractionsofincomedocapitalandlaborreceive?b.Supposethatimmigrationincreasesthelaborforceby10percent.Whathappentototaloutput?Therentalpriceofcapital?Therealwage?c.Supposethatagiftofcapitaformabroadraisesthecapitalstockby10percent.Whathappenstototaloutput(inpercent).Therentalpriceofcapital?Therealwage?d.SupposethatatechnologicaladvanceraisesthevalueoftheparameterAby10percent.Whathappenstototaloutput?Therentalpriceofcapital?Therealwage?7、Supposethatthemoneydemandfunctiontakestheform(/)(,)/(5)dMPLiYYia.Ifoutputgrowsatrateg,atwhatratewillthedemandforrealbalancesgrow(assumingconstantnominalinterestrates)?b.Whatisthevelocityofmoneyinthiseconomy?c.Ifinflationandnominalinterestratesareconstant,atwhatrate,ifany,willvelocitygrow?d.Howwillapermanentincreaseinthelevelofinterestratesaffectthelevelofvelocity?Howwillitaffectthesubsequentgrowthrateofvelocity?8、ConsideraneconomywiththefollowingCobb-Douglasproductionfunction:1323YKLTheeconomyhas1000unitsofcapitalandalaborforceof1000workers.a.Derivetheequationdescribinglabordemandinthiseconomyasafunctionoftherealwageandthecapitalstock.b.Iftherealwagecanadjusttoequilibratelaborsupplyandlabordemand,whatistherealwage?Inthisequilibrium,whatareemployment,output,andthetotalamountearnedbyworkers?c.NowsupposethatCongress,concernedaboutthewelfareoftheworkingclass,passesalawrequiringfirmstopayworkersarealwageof1unitofoutput.Howdoesthiswagecomparetotheequilibriumwage?d.Congresscannotdictatehowmanyworkersfirmhireatthemandatedwage.Giventhisfact,whataretheeffectsofthislaw?Specifically,whathappenstoemployment,outputandthetotalamountearnedbyworkers?e.WillCongresssucceedinitsgoalofhelpingtheworkingclass?Explain.f.Doyouthinkthatthisanalysisprovidesagoodwayofthinkingaboutaminimum-wagelaw?Whyorwhynot?9、Onecountry,A,thecapitalshareofGDPis30percent,theaveragegrowthinoutputis3percentperyear,thedepreciationrateisabout4percentperyear,andthecapital-outputrateisabout2.5.SupposethattheproductionfunctionisCobb-Douglas,sothecapitalshareisconstant,andthatcountryAhasbeeninasteadystate;.a.Whatmustthesavingratebeintheinitial?b.Comparethecapital-outputratioattheGoldenRulesteadystatetothecapital-outputratiointheinitialstate.c.WhatmustthesavingratebetoreachtheGoldenRulesteadystate?Dosesitneedtobeincreasedordecreased?WhatpoliciesmightcountryApurse?10、Twocountries,RichlandandPoorland,aredescribedbytheSolowgrowthmodel.TheyhavethesameCobb-Douglasproductionfunction,1(,)FKLAKL,butwithdifferentquantitiesofcapitalandlabor,.Richlandsave32percentofitsincome,whilePoorlandsaves10percent.Richlandhaspopulationgrowthof1percentperyear,whilePoorlandhaspopulationgrowthof3percent.(Thenumbersinthisproblemarechosentobeapproximatelyrealisticdescriptionsofrichandpoornations.)Bothnationshavetechnologicalprogressatrateof2percentperyearanddepreciationatarateof5percentperyear.a.Whatistheper-workerproductionfunctionf(k)?b.SolvefortheratioofRichland’ssteady-stateincomeperworkertoPoorland’s.(Hint:Theparameterwillplayaroleinyouranswer.)c.IftheCobb-Douglasparametertakestheconventionalvalueofabout1/3,howmuchhighershouldincomeperworkerinRichlandcomparedtoPoorla