范里安微观作业(姚澜6次集合版)

ProblemSetⅠPartⅠ(TrueorFalse)1.Thereare3goods.Thepriceofgood1is-1,thepriceofgood2is+1,andthepriceofgood3is+2.Itisphysicallypossibleforaconsumertoconsumeanycommoditybundlewithnonnegativeamountsofeachgood.Aconsumerwhohasanincomeof10couldaffordtoconsumesomecommoditybundlesthatinclude5unitsofgood1and6unitsofgood2.2.Ifallpricesaredoubledandmoneyincomeisleftthesame,thebudgetsetdoesnotchangebecauserelativepricesdonotchange.3.Iftherearetwogoodsandthepricesofbothgoodsrise,thenthebudgetlinemustbecomesteeper.4.IfsomeonehastheutilityfunctionU=1,000+2min{x,y},thenxandyareperfectcomplementsforthatperson.5.Iftherearetwogoods,ifaconsumerprefersmoreofeachgoodtoless,andifshehasadiminishingmarginalrateofsubstitution,thenherpreferencesareconvex.6.Ifpreferencesareconvex,thenforanycommoditybundlex,thesetofcommoditybundlesthatareworsethanxisaconvexset.7.BillKatzprefersmoreofgood1tolessandhepreferslessofgood2tomore.Billhasconvexpreferences.Ifwedrawhisindifferencecurveswithgood1onthehorizontalaxisandgood2ontheverticalaxis,thenhisindifferencecurveshavepositiveslopebutgetsteeperastheyrise.8.Aconsumerwhoisunabletodetectsmalldifferencesintheamountofwaterinherbeercouldhaveatransitivestrictpreferencerelationbutisunlikelytohaveatransitiveindifferencerelation.9.IfMelodyhasmoreclassicalrecordsthanrockandrollrecords,sheiswillingtoexchangeexactly1classicalrecordfor2rockandrollrecords,butifshehasmorerockandrollrecordsthanclassicalrecords,thensheiswillingtoexchangeexactly1rockandrollrecordfor2classicalrecords.Melodyhasconvexpreferences.10.Withquasilinearpreferences,theslopeofindifferencecurvesisconstantalongallraysthroughtheorigin.11.WandaLotthastheutilityfunctionU(x,y)=max{x,y}.Wanda’spreferencesareconvex.12.Mr.Surlyconsumesonlytwogoodsandhatesthemboth.HisutilityfunctionisU(x,y)=-max{x,y}.Mr.Surlyhas(weakly)convexpreferences.13.Alice’sutilityfunctionisU(x,y)=x2y.Steve’sutilityfunctionisU(x,y)=x2y+2x.AliceandStevehavethesamepreferencessinceSteve’sutilityfunctionisamonotonictransformationofAlice’s.14.AconsumerhaspreferencesrepresentedbytheutilityfunctionU(x1,x2)=10(x21+2x1x2+x22)-50.Forthisconsumer,goods1and2areperfectsubstitutes.15.ApersonwiththeutilityfunctionU(x1,x2)=min{x1+2x2,2x1+x2}hasconvexbutnotstrictlyconvexpreferences.16.MaxGrosshastheutilityfunctionU(x,y)=max{x,y}.Ifthepriceofxisthesameasthepriceofy,Maxwillbuyequalamountsofxandy.17.Ifaconsumerdoesnothaveconvexpreferences,thenapointoftangencybetweenherindifferencecurveandherbudgetlinemustbeanoptimalconsumptionpoint.18.Ambrose’sutilityfunctionisU(x,y)=x+4y1/2.Thepriceofxis$1andthepriceofyis$2.Ifhisincomerisesfrom$100to$150,hisconsumptionofyincreasesbymorethan10%butlessthan50%.19.MaryGranola’sutilityfunctionisU(x,y)=min{x+2y,y+2x}.Marymaximizesherutilitysubjecttoabudgetconstraint.Ifshechoosesthebundle(5,6),thenthepriceofxmustbeexactlytwicethepriceofy.PartⅡ(Singlechoice)1.BillyBobwantstogainsomeweightsothathecanplayfootball.Billyconsumesonlymilkshakesandspinach.Milkshakescosthim$1eachandspinachcosts$2perserving.Amilkshakehas850caloriesandaservingofspinachhas200calories.BillyBobneverspendsmorethan$20adayonfoodandhealwaysconsumesatleast8,000caloriesperday.Whichofthefollowingisnecessarilytrue?a.BillyBobconsumesatleast9milkshakesaday.b.BillyBobneverconsumesmorethan6servingsofspinachaday.c.BillyBobneverconsumespositiveamountsofbothgoods.d.BillyBobconsumesonlymilkshakes.e.Noneoftheabove.2.Ifyouhaveanincomeof$40tospend,commodity1costs$4perunit,andcommodity2costs$8perunit,thentheequationforyourbudgetlinecanbewrittena.x1/4+x2/8=40.b.(x1+x2)/12=40.c.x1+2x2=10.d.5x1+9x2=41.e.12(x1+x2)=40.3.Ifyoucouldexactlyaffordeither5unitsofxand21unitsofy,or9unitsofxand5unitsofy,thenifyouspentallofyourincomeony,howmanyunitsofycouldyoubuy?a.57b.14c.25d.41e.Noneoftheabove.4.Murphyusedtoconsume100unitsofXand50unitsofYwhenthepriceofXwas$2andthepriceofYwas$4.IfthepriceofXroseto$4andthepriceofYroseto$9,howmuchwouldMurphy’sincomehavetorisesothathecouldstillaffordhisoriginalbundle?a.$700b.$450c.$350d.$1,050e.Noneoftheabove.5.Supposetherearetwogoods,thepricesofbothgoodsarepositive,andaconsumer’sincomeisalsopositive.Iftheconsumer’sincomedoublesandthepriceofbothgoodstriple,a.theconsumer’sbudgetlinegetssteeperandshiftsinward.b.theslopeoftheconsumer’sbudgetlinedoesnotchangebutthebudgetlineshiftsoutwardawayfromtheorigin.c.theconsumer’sbudgetlinegetssteeperandshiftsoutward.d.theslopeoftheconsumer’sbudgetlinedoesnotchangebutthebudgetlineshiftsinwardtowardtheorigin.e.theconsumer’sbudgetlinegetsflatterandshiftsinward.6.Ifthereareonlytwogoods,ifmoreofgood1isalwayspreferredtoless,andiflessofgood2isalwayspreferredtomore,thenindifferencecurvesa.slopedownward.b.slopeupward.c.maycross.d.couldtaketheformofellipses.e.Noneoftheabove.7.Charlie’sindifferencecurveshavetheequationxB=constant/xA,wherelargerconstantsdenotebetterindifferencecurves.Charliestrictlyprefersthebundle(10,17)toa.thebundle(11,16).b.thebundle(17,10).c.thebundle(12,15).d.morethanoneofthesebundles.e.noneofthesebundles.8.RecallthatTommyTwit’smothermeasuresthedepartureofanybun