范里安微观作业(钟鸿钧8次)

Problemset#1(PreferencesandUtility)ECON3113Multiplechoice1.Theassumptionthatpreferencesarecompleterequirestheconsumer(a)torankanytwobaskets.(b)tosaythatbasketCispreferredtobasketAifbasketBispreferredtobasketAandbasketCispreferredtobasketB.(c)torankabasketwithmoreunitsofallgoodshigherthanabasketwithfewerunitsofallgoods.(d)tohaveadiminishingmarginalrateofsubstitution.2.AssumethataconsumerpreferswatchingtheWorldSeriestowatchingtheSuperBowlandthatthissameconsumerpreferswatchingtheSuperBowltowatchingtheStanleyCupchampionshipgame.Furtherassumethatthissameconsumerstates,“IwouldprefertowatchtheStanleyCupchampionshipgametotheWorldSeries.”Thisconsumer’spreferencesviolatewhichofthefollowingkeyassumptions?(a)Completeness.(b)Transitivity.(c)Moreisbetter.(d)Bothcompletenessandtransitivity.3.Identifythetruthfulnessofthefollowingstatements.I.Ordinalutilitygivesusinformationaboutwhichbaskettheconsumerprefersandthemagnitudeofthepreference.II.Cardinalutilitygivesusinformationaboutwhichbaskettheconsumerprefersbutnotabouttheintensityofthosepreferences.(a)BothIandIIaretrue.(b)BothIandIIarefalse.(c)Iistrue;IIisfalse.1(d)Iisfalse;IIistrue.4.Marginalutility(a)istheratiooftotalutilitytototalconsumption.(b)istherateatwhichtotalutilitychangesasthelevelofconsumptionrises.(c)willalwaysbeequaltotheproduct’sprice.(d)tellsusnothing;we’reonlyconcernedwithtotalutility.5.Supposethataconsumerhastheutilityfunctionu(A,B)=3A+4B.TheMRSis(a)0.75(b)1.25(c)1.00sinceAandBareperfectsubstitutes(d)cannotbedeterminedsincethevaluesofAandBareunknown6.Supposethataconsumerhastheutilityfunctionu(A,B)=3A+4B.IfAismeasuredonthehorizontalaxis,(a)Theindifferencecurveswillbevertical.(b)Theindifferencecurveswillbehorizontal.(c)Theindifferencecurveswillbestraightlineswithslope-0.75.(d)Theindifferencecurveswillbestraightlineswithslope-1.25.7.Considerthefollowingthreemarketbaskets.BasketGoodxGoodyA26B64C45IfBasketAandBasketBareonthesameindifferencecurve,preferencessatisfytheusualassumptions,andtheindifferencecurveshaveadiminishingmarginalrateofsubstitution,(a)BasketCispreferredtoBasketA(b)BasketAispreferredtoBasketC(c)TheconsumerisindifferentbetweenBasketAandBasketC2(d)ThereisnotenoughinformationtodeterminehowtheconsumerwouldrankBasketArelativetoBasketC.8.Considertheutilityfunctionu=min{2x,y}.Ifxisonthehorizontalaxis,theindifferencecurvesforthisutilityfunctionwillbe(a)vertical(b)horizontal(c)upwardsloping(d)L-shapedProblems1.CoachSteroidlikeshisplayerstobebig,fast,andobedient.IfplayerAisbetterthanplayerBintwoofthesethreecharacteristics,SteroidwillpreferAtoB.Threeplayerstryoutforquarterback.WilburWestinghouse(W)weighs320pounds,runsveryslowly,andisquiteobedient.HaroldHotpoint(H)weighs240pounds,runsextremelyfast,andisextremelydisobedient.JerryJacuzzi(J)weighs150pounds,runsataveragespeed,andisextremelyobedient.DoesCoachSteroidhavetransitivepreferences?Explainyouranswer.2.Ike’sutilityfunctionisU(x,y)=25xy.Hehas12unitsofgoodxand8unitsofgoody.Ben’sutilityfunctionforthesametwogoodsisU(x,y)=4x+4y.Benhas9unitsofxand13unitsofy.DoesIkepreferhisownbasketorBen’s?HowaboutBen?3.Considerthefollowingutilityfunction:u(x1,x2)=2x1+3x2.a)Isthepreferencerepresentedbythisutilityfunctionmonotonic,i.e.,moreisbetter?b)Drawatypicalindifferencecurveandlabelaweaklypreferredset.c)CalculatetheMRS.DoesthispreferenceexhibitdiminishingMRS?4.Considerthefollowingutilityfunction:u(x1,x2)=x21x32.a)Isthepreferencerepresentedbythisutilityfunctionmonotonic?b)Drawatypicalindifferencecurveandlabeltheweaklypreferredset.3c)CalculatethemarginalutilitiesandtheMRS.DoesthispreferenceexhibitdiminishingMRS?5.Considerthefollowingutilityfunction:u(x1,x2)=min{2x1,3x2}.a)Isthepreferencerepresentedbythisutilityfunctionmonotonic?b)Drawatypicalindifferencecurveandlabelaweaklypreferredset.c)calculatetheMRS.DoesthispreferenceexhibitdiminishingMRS?4SolutiontoProblemSet#1(PreferencesandUtility)ECON3113Multiplechoice1.(a).2.(b).3.(b).4.(b).5.(a).Theutilityfunctionu(A,B)=3A+4B.MUA=3,MUB=4,⇒MRS=MUAMUB=34=0.75.6.(c)7.(a).NotethatCisexactlyhalfofA+B.Therefore,ifwedrawaline,thesethreebasketswillbeonthesameline.NowweknowthatthepreferenceexhibitsdiminishingMRS,whichimpliesthattheindifferencecurveisconvex.DrawinganindifferencecurvethatgoesthroughAandB(theyareonthesameindifferencecurve),thenCmustbeoutsidethiscurvesincethecurveisconvex.8.(d).Problems1.SteroidprefersWtoH(WH)becauseWisheavierandmoreobedient.HeprefersHtoJ(HJ)becauseHisheavierandfaster.ButheprefersJtoW(JW)becauseJismoreobedientandfasterthanW.Sincehispreferenceshaveacycle,theycannotbetransitive.2.Ike’sbasketis(x,y)=(12,8)andBen’sbasketis(9,13).IkewouldpreferBen’sbasketsince9×1312×8⇒U(9,13)U(12,8).However,Benprefershisownbasketsince,4×9+4×134×12+4×8⇒U(9,13)U(12,8).13.a)Yes,thepreferenceismonotonic,sincetheutilitygoesupwheneitherx1orx2goesup.Alternatively,wecansaythatthepreferenceismonotonicsinceMU1=∂u∂x1=20andMU2=∂u∂x2=30.b)Theequationfortheindifferencecurvewithutilitylevelkis2x1+3x2=k.Weplotthegraphfork=6inFigure1.Figure1:Indifferencecurve:2x1+3x2=6.Pickanybasketonthisindifferencecurve,sa