史蒂芬威廉森宏觀經濟學第四版課后題答案最新Solution-CH4

1、2011PearsonEducation,Inc.PublishingasAddisonWesley2011PearsonEducation,Inc.PublishingasAddisonWesleyChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximizationTextbookQuestionSolutionsQuestionsforReviewConsumersconsumeanaggregateconsumptiongoodandleisure.Consumerspreferencesaresumma

2、rizedinautilityfunction.Thefirstpropertyisthatmoreisalwayspreferredtoless.Thispropertyassuresusthataconsumptionbundlewithmoreofonegoodandnolessoftheothergoodthananysecondbundlewillalwaysbepreferredtothesecondbundle.Thesecondpropertyisthataconsumerlikesdiversityinhisorherconsumptionbundle.Thispropert

3、yassuresusthatalinearcombinationoftwoconsumptionbundleswillalwaysbepreferredtothetwooriginalbundles.Thethirdpropertyisthatbothconsumptionandleisurearenormalgoods.Thispropertyassuresusthatanincreaseinaconsumersincomewillalwaysinducetheindividualtoconsumemoreofbothconsumptionandleisure.Thefirstpropert

4、yofindifferencecurvesisthattheyaredownwardsloping.Thispropertyisadirectconsequenceofthepropertythatmoreisalwayspreferredtoless.Thesecondpropertyofindifferencecurvesisthattheyarebowedtowardtheorigin.Thispropertyisadirectconsequenceofconsumerspreferencefordiversity.Consumersmaximizetheamountofutilityt

5、heycanderivefromtheirgivenamountofavailableresources.Theoptimalbundlehasthepropertythatitrepresentsapointoftangencyofthebudgetlinewithanindifferencecurve.Anequivalentpropertyisthatthemarginalrateofsubstitutionofleisureforconsumptionandleisureisequaltotherealwage.Inresponsetoanincreaseindividendincom

6、e,theconsumerwillconsumemoregoodsandmoreleisure.Inresponsetoanincreaseintherealvalueofalump-sumtax,theconsumerwillconsumelessgoodsandlessleisure. WilliamsonMacroeconomics,FourthEditionChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization 2011PearsonEducation,Inc.PublishingasAd

7、disonWesley2011PearsonEducation,Inc.PublishingasAddisonWesleyAnincreaseintherealwagemakestheconsumermorewelloff.Asaresultofthispureincomeeffect,theconsumerwantsmoreleisure.Alternatively,theincreaseintherealwageinducesasubstitutioneffectinwhichtheconsumeriswillingtoconsumelessleisureinexchangeforwork

8、ingmorehours(consuminglessleisure).Theneteffectofthesetwocompetingforcesistheoreticallyambiguous.Therepresentativefirmseekstomaximizeprofits.Astheamountoflaborisincreased,holdingtheamountofcapitalconstant,eachworkergetsasmallershareofthefixedamountofcapital,andthereisareductionineachworkersmarginalp

9、roductivity.Anincreaseintotalfactorproductivityshiftstheproductionfunctionupward.Therepresentativefirmsprofitisequaltoitsproduction(revenuemeasuredinunitsofgoods)minusitsvariablelaborcosts(therealwagetimestheamountoflaborinput).Aunitincreaseinlaborinputaddsthemarginalproductoflabortorevenueandaddsth

10、erealwagetolaborcosts.Theamountoflabordemandisthatamountoflaborinputthatequatesmarginalrevenuewithmarginallaborcosts.Thisquantityoflabor,labordemand,cansimplybereadoffthemarginalproductoflaborschedule.Problems1.Considerthetwohypotheticalindifferencecurvesinthefigurebelow.PointAisonbothindifferencecu

11、rves,I1andI2.Byconstruction,theconsumerisindifferentbetweenAandB,asbothpointsareonI2.Inlikefashion,theconsumerisindifferentbetweenAandC,asbothpointsareonI1.ButatpointC,theconsumerhasmoreconsumptionandmoreleisurethanatpointB.Aslongastheconsumerprefersmoretoless,heorshemuststrictlypreferCtoA.Wetherefo

12、recontradictthehypothesisthattwoindifferencecurvescancross.Nextrearrangeintheform:Indifferencecurvesarethereforelinearwithslope,-a/b,whichrepresentsthemarginalrateofsubstitution.Therearetwomaincases,accordingtowhethera/bwora/bw.Thetoppaneloftheleftfigurebelowshowsthecaseofa/bw.Inthiscasetheindiffere

13、ncecurvesaresteeperthanthebudgetline,andtheconsumerpickspointB,atwhichl=handC=n-T.Inthecoincidentalcaseinwhicha/b=w,thehighestattainableindifferencecurvecoincideswiththeindifferencecurve,andtheconsumerisindifferentamongallpossibleamountsofleisureandhoursworked.(c)Thisutilityfunctiondoeshavetheproper

14、tythatmoreispreferredtoless.However,themarginalrateofsubstitutionisconstant,andthereforethisutilityfunctiondoesnotsatisfythepropertyofdiminishingmarginalrateofsubstitution.3.(a)Usingtheformulasintheexamplefromthetextbook,oneobtains:l=C=(0.75x160.86)/(1+0.75)=3.89UQ匸dEnsuQo-3perfectcomplements,theent

15、iremovefrompointBtopointFisduetotheincomeeffect.4.Whenthegovernmentimposesaproportionaltaxonwageincome,theconsumersbudgetconstraintisnowgivenby:C=w(lt)(h-1)+n-T,wheretisthetaxrateonwageincome.Inthefigurebelow,thebudgetconstraintfort=0,isFGH.Whent0,thebudgetconstraintisEGH.Theslopeoftheoriginalbudget

16、lineis-w,whiletheslopeofthenewbudgetlineis-(l-t)w.InitiallytheconsumerpicksthepointAontheoriginalbudgetline.Afterthetaxhasbeenimposed,theconsumerpickspointB.ThesubstitutioneffectoftheimpositionofthetaxistomovetheconsumerfrompointAtopointDontheoriginalindifferencecurve.ThepointDisatthetangentpointofi

17、ndifferencecurve,Il,withalinesegmentthatisparalleltoEG.Thepuresubstitutioneffectinducestheconsumertoreduceconsumptionandincreaseleisure(workless).Thetaxalsomakestheconsumerworseoff,inthatheorshecannolongerbeonindifferencecurve,Il,butmustmovetothelesspreferredindifferencecurve,I2.Thispureincomeeffect

18、movestheconsumertopointB,whichhaslessconsumptionandlessleisurethanpointD,becausebothconsumptionandleisurearenormalgoods.Theneteffectofthetaxistoreduceconsumption,butthedirectionoftheneteffectonleisureisambiguous.Thefigureshowsthecaseinwhichthesubstitutioneffectonleisuredominatestheincomeeffect.Inthi

19、scase,leisureincreasesandhoursworkedfall.Althoughconsumptionmustfall,hoursworkedmayrise,fall,orremainthesame.Chapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization #Chapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization isnochange.IfitisbetweenBandE,sayatH

20、,thenthehouseholdwillreoptimizewiththenewtaxdeduction.ThenewbundleistheneithersomewherebetweenEandF,andtheMRSequalsw(1-t).OrweobtainacornersolutionatE,andtheMRSissomewherebetweenwandw(1-t).ThemovefromHtoEisduetotheincomeeffect,andifthereisanoptimalstrictlybetweenEandF,themovefromEtothatpointisduetot

21、hesubstitutioneffect. WilliamsonMacroeconomics,FourthEditionChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization 2011PearsonEducation,Inc.PublishingasAddisonWesley2011PearsonEducation,Inc.PublishingasAddisonWesleyForaconsumerwhopaystaxes,hiswage,andthusisMRSdoesnotchange.Thus

22、themovefromHtoJisapurenegativeincomeeffect.Theincreaseindividendincomeshiftsthebudgetlineupward.Thereductioninthewagerateflattensthebudgetline.Onepossibilityisdepictedinthefiguresbelow.TheoriginalbudgetconstraintHGLshiftstoHFE.Therearetwoincomeeffectsinthiscase.Theincreaseindividendincomeisapositive

23、incomeeffect.Thereductioninthewagerateisanegativeincomeeffect.Thedrawinginthetopfigureshowsthecasewherethesetwoincomeeffectsexactlycancelout.InthiscaseweareleftwithapuresubstitutioneffectthatmovestheconsumerfrompointAtopointB.Therefore,consumptionfallsandleisureincreases.Asleisureincreases,hoursofwo

24、rkmustfall.Themiddlefigureshowsacaseinwhichtheincreaseindividendincome,thedistanceGF,islargerandsotheincomeeffectispositive.Theconsumerwindsuponahigherindifferencecurve,leisureunambiguouslyincreases,andconsumptionmayeitherincreaseordecrease.Thebottomfigureshowsacaseinwhichtheincreaseindividendincome

25、,thedistanceGF,issmallerandsotheincomeeffectisnegative.Theconsumerwindsuponalowerindifferencecurve,consumptionunambiguouslydecreases,andleisuremayeitherincreaseordecrease._HhThisproblemintroducesahigher,overtimewageforhoursworkedaboveathreshold,q.Thisproblemalsoabstractsfromanydividendincomeandtaxes

26、.(a)ThebudgetconstraintisnowEJGinthefigurebelow.Thebudgetconstraintissteeperforlevelsofleisurelessthanh-q,becauseofthehigherovertimewage.Thefiguredepictspossiblechoicesfortwodifferentconsumers.Consumer#1pickspointAonherindifferencecurve,I1.Consumer#2pickspointBonhisindifferencecurve,I2.Consumer#1cho

27、osestoworkovertime;consumer#2doesnot.anindifferencecurvetangenttoEJGclosetopointJ.Inorderforthistohappen,anindifferencecurvewouldneedtobeclosetorightangledasinthecaseofpurecomplement.Itisunlikelythatconsumerswishtoconsumegoodsandleisureinfixedproportions,andsopointslikeAandBaremoretypical.Foranyothe

28、rallowableshapefortheindifferencecurve,itisimpossibleforpointJtobechosen.(c)AnincreaseintheovertimewagesteepenssegmentEJofthebudgetconstraint,buthasnoeffectonthesegmentJG.Foranindividuallikeconsumer#2,theincreaseintheovertimewagehasnoeffectupuntilthepointatwhichtheincreaseislargeenoughtoshifttheindi

29、vidualtoapointlikepointA.Consumer#2receivesnoincomeeffectbecausetheincomeeffectarisesoutofahigherwagerateoninframarginalunitsofwork.Anindividuallikeconsumer#1hasthetraditionalincomeandsubstitutioneffectsofawageincrease.Consumer#1increasesherconsumption,butmayeitherincreaseorreducehoursofworkaccordin

30、gtowhethertheincomeeffectoutweighsthesubstitutioneffect.Lump-sumTaxvs.ProportionalTax.Supposethatwestartwithaproportionaltax.UndertheproportionaltaxtheconsumersbudgetlineisEFHinthefigurebelow.Theconsumerchoosesconsumption,C*,andleisure,l*,atpointAonindifferencecurveI1.Ashifttoalump-sumtaxsteepensthe

31、budgetline.Theabsolutevalueoftheslopeofthebudgetlineis(1-t)w,andthasfallentozero.Theimpositionofthelump-sumtaxshiftsthebudgetlinedownwardinaparallelfashion.Byconstruction,thelump-sumtaxmustraisethesameamountofrevenueastheproportionaltax.TheconsumermustthereforebeabletocontinuetoconsumeC*oftheconsump

32、tiongoodandl*ofleisureafterthechangeintaxcollection.Therefore,thenewbudgetlinemustalsopassthroughpointA.ThenewbudgetlineislabeledLGHinthefigurebelow.Withthelump-sumtax,theconsumercan #WilliamsonMacroeconomics,FourthEditionChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization 2

33、011PearsonEducation,Inc.PublishingasAddisonWesley2011PearsonEducation,Inc.PublishingasAddisonWesley #WilliamsonMacroeconomics,FourthEditionChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization #2011PearsonEducation,Inc.PublishingasAddisonWesley2011PearsonEducation,Inc.Publishi

34、ngasAddisonWesleydobetterbychoosingpointB,onthehigherindifferencecurve,I2.Therefore,theconsumerisclearlybetteroff.WearealsoassuredthatconsumptionwillbegreateratpointBthanatpointA,andthatleisurewillbesmalleratpointBthanatpointA.Isurerepresentsalltimeusedfornonmar書activities.Ifthegovernmentisnowprovid

35、ingfor甲9.Leisomeofththerebyallowingmoretimeforotheractivities,includingmarketwork.Concretely,thistranslatesinachangeofpreferencesforhouseholds.Forthesameamountofconsumption,theyarenowwillingtoworkmore,orinotherwords,theyarewillingtoforegosomeadditionalleisure.Onthefigurebelow,thenewindifferencecurve

36、islabeledI2.ItcancrossindifferencecurveI1becausepreferences,aswemeasurethemhere,havechanged.TheequilibriumbasketofgoodsforthehouseholdnowshiftsfromAtoB.Thisleadstoreducedleisure(froml*1tol*2),andthusincreasedhoursworked,andincreasedconsumption(fromC*1toC*2)thankstohigherlaborincomeatthefixedwage.ose

37、,likeprovidingfreechildcaithhouseholdswilltakeadvantageofsuchaprogram, WilliamsonMacroeconomics,FourthEditionChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization #2011PearsonEducation,Inc.PublishingasAddisonWesley2011PearsonEducation,Inc.PublishingasAddisonWesley WilliamsonMa

38、croeconomics,FourthEditionChapter4ConsumerandFirmBehavior:TheWork-LeisureDecisionandProfitMaximization 2011PearsonEducation,Inc.PublishingasAddisonWesley2011PearsonEducation,Inc.PublishingasAddisonWesleyThefirmchoosesitslaborinput,Nd,soastomaximizeprofits.Whenthereisnotax,profitsforthefirmaregivenby

39、n=zF(K,Nd)一wNd.Thatis,profitsarethedifferencebetweenrevenueandcosts.Inthetopfigureonthefollowingpage,therevenuefunctioniszF(K,Nd)andthecostfunctionisthestraightline,wNd.Thefirmmaximizesprofitsbychoosingthequantityoflaborwheretheslopeoftherevenuefunctionequalstheslopeofthecostfunction:MP=w.NThefirmsd

40、emandforlaborcurveisthemarginalproductoflaborscheduleinthebottomfigureonthefollowingpage.Withataxthatisproportionaltothefirmsoutput,thefirmsprofitsaregivenby:n=zF(K,Nd)wNdtzF(K,Nd)=(1t)zF(K,Nd),wheretheterm(1t)zF(K,Nd)istheafter-taxrevenuefunction,andasbefore,wNdisthecostfunction.Inthetopfigurebelow

41、,thetaxactstoshiftdowntherevenuefunctionforthefirmandreducestheslopeoftherevenuefunction.Asbefore,thefirmwillmaximizeprofitsbychoosingthequantityoflaborinputwheretheslopeoftherevenuefunctionisequaltotheslopeofthecostfunction,buttheslopeoftherevenuefunctionis(1t)MP,sothefirmchoosesthequantityofNlabor

42、where(1t)MP=w.NInthebottomfigurebelow,thelabordemandcurveisnow(1t)MP,andthelabordemandcurveNhasshifteddown.Thetaxactstoreducetheafter-taxmarginalproductoflabor,andthefirmwillhirelesslaboratanygivenrealwage.ThefirmchoosesitslaborinputNdsoastomaximizeprofits.Whenthereisnosubsidy,profitsforthefirmaregi

43、venbyn=zF(K,Nd)一wNd.Thatis,profitsarethedifferencebetweenrevenueandcosts.InthetopfigureonthefollowingpagetherevenuefunctioniszF(K,Nd)andthecostfunctionisthestraightline,wNd.Thefirmmaximizesprofitsbychoosingthequantityoflaborwheretheslopeoftherevenuefunctionequalstheslopeofthecostfunction:MP=w.NThefi

44、rmsdemandforlaborcurveisthemarginalproductoflaborscheduleinthebottomfigurebelow.Withanemploymentsubsidy,thefirmsprofitsaregivenby:n=zF(K,Nd)-(ws)NdwherethetermzF(K,Nd)istheunchangedrevenuefunction,and(w一s)Ndisthecostfunction.Thesubsidyactstoreducethecostofeachunitoflaborbytheamountofthesubsidy,s.Inthetopfigurebelow,thesubsidyactstosh