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Mid-termB6-1IntermediateMicroeconomicsMid-termTest2005(B)Name:StudentNo.:Class:No.12345678910AnswerNo.11121314151617181920AnswerNo.21222324252627282930AnswerSection1Trueorfalse.（20points,2pointseach）1.Alice'sutilityfunctionisU(x,y)=x2y.Steve'sutilityfunctionisU(x,y)=x2y+2x.AliceandStevehavethesamepreferencessinceSteve'sutilityfunctionisamonotonictransformationofAlice's.2.Aconsumerwhocanborrowandlendatthesameinterestrateshouldpreferanendowmentwithahigherpresentvaluetoanendowmentwithalowerpresentvalue,nomatterhowheplanstoallocateconsumptionoverthecourseofhislife.3.Iftwoassetshavethesameexpectedrateofreturnbutdifferentvariances,arisk-averseinvestorshouldalwayschoosetheonewiththesmallervariance,nomatterwhatotherassetssheholds.4.FredhasaCobb-Douglasutilityfunctionwithexponentsthatsumto1.Sallyconsumesthesametwogoods,butthetwogoodsareperfectsubstitutesforher.Despitethesedifferences,FredandSallyhavethesamepriceoffercurves.5.Ifallpricesdoubleandincometriples,thenthebudgetlinewillbecomesteeper.6.IfsomeonehasaCobb-Douglasutilityfunctionandnoincomefromanysourceotherthanlaborearnings,thenanincreaseinwageswillnotchangetheamountthatpersonchoosestowork.7.Susanisanetborrowerwhentheinterestrateis10%andanetsaverwhentheinterestrateis20%.Adecreaseintheinterestratefrom20%to10%maymakeSusanworseoff.8.Withquasi-linearpreferences,theequivalentvariationandthecompensatingvariationinincomeduetoapriceincreaseofonegoodarethesame.9.Foraconsumerwhohasanallowancetospendandnoendowmentofgoods,adecreaseinthepriceofaGiffengoodconsumedmakeshimbetteroff.10.Themarginalrateofsubstitutionmeasuresthedistancebetweenoneindifferencecurveandthenextone.Mid-termB6-2Section2SingleChoice.(80points,4pointseach)11.Janetconsumestwocommoditiesxandy.Herutilityfunctionismin{x+2y,y+2x}.Shechoosestobuy10unitsofgoodxand20unitsofgoody.Thepriceofgoodxis$1.Janet'sincomeisA.$40.B.$50.C.$30.D.$20.E.Thereisnotenoughinformationintheproblemtodetermineherincomebecausewearenottoldthepriceofgoody.12.Hollyconsumesxandy.Thepriceofxis4andthepriceofyis4.Holly'sonlysourceofincomeisherendowmentof6unitsofxand6unitsofywhichshecanbuyorsellatthegoingprices.Sheplanstoconsume7unitsofxand5unitsofy.Ifthepriceschangeto$7forxand$7fory,A.sheisbetteroff.B.sheisworseoff.C.sheisneitherbetteroffnorworseoff.D.sheisbetteroffifshehasnonconvexpreferences.E.Wecan'ttellwhethersheisbetterofforworseoffunlessweknowherutilityfunction.13.Clarissa'sutilityfunctionisU(r,z)=z+120r-r2,whereristhenumberofroseplantsshehasinhergardenandzisthenumberofzinnias.Shehas250squarefeettoallocatetorosesandzinnias.Roseseachtakeup4squarefeetandzinniaseachtakeup1squarefoot.Shegetstheplantsforfreefromagenerousfriend.Ifsheacquiresanother100squarefeetoflandforhergardenandherutilityfunctionremainsunchanged,shewillplantA.99morezinniasandsomemoreroses.B.20morerosesand20morezinnias.C.25morerosesandnomorezinnias.D.100morezinniasandnomoreroses.E.Noneoftheabove.Mid-termB6-314.Willispaid$10anhourforthefirst40hoursperweekthatheworks.Hecanalsoworkasmanyhoursovertimeashewishesto.Heispaid$15anhourforeveryhourthatheworksbeyond40hoursaweek.LeisureisanormalgoodforWillandheiscurrentlyworkingsomeovertime.Ifhishourlywageforthefirst40hoursperweekthatheworksrisesto$12andhiswagesforovertimeremainat$15perhour,hewillchoosetoworkA.fewerhoursperweek.B.morehoursperweek.C.thesamenumberofhoursperweek.D.morehoursperweekifandonlyifhisincomeexceedshislaborincome.E.morehoursperdayifandonlyifheworkslessthan20hoursovertimeperweek.15.Albinhasquasi-linearpreferencesandhelovespretzels.Hisinversedemandfunctionforpretzelsisp(x)=49-6x,wherexisthenumberofpretzelsthatheconsumes.Heiscurrentlyconsuming8pretzelsatapriceof$1perpretzel.Ifthepriceofpretzelsrisesto$7perpretzel,thechangeinAlbin'sconsumersurplusisA.-$90.B.-$56.C.-$42.D.-$45.E.-$42.16.Jane'sutilityfunctionisU(x,y)=x+2y,wherexisherconsumptionofgoodXandyisherconsumptionofgoodY.Herincomeis$2.ThepriceofYis$2.ThecostperunitofXdependsonhowmanyunitsshebuys.ThetotalcostofxunitsofXisthesquarerootofx.A.Thebundle(1/4,3/4)isJane'sutilitymaximizingchoice,givenherbudget.B.Thebundle(1,1/2)isJane'sutilitymaximizingchoice,givenherbudget.C.Givenherbudget,JanewouldmaximizeherutilitybyspendingallofherincomeongoodX.D.Givenherbudget,JanewouldmaximizeherutilitybyspendingallofherincomeongoodY.E.Noneoftheabove.17.Whenthepriceswere($5,$1),Vanessachosethebundle(x,y)=(6,3).Nowatthenewprices,(px,py),shechoosesthebundle(x,y)=(5,7).ForVanessa'sbehaviortobeconsistentwiththeweakaxiomofrevealedpreference,itmustbethatA.4pypx.B.px4py.C.5pypx.D.py=5px.E.Noneoftheabove.Mid-termB6-418.Inanisolatedmountainvillage,theonlycropiscorn.Villagersplanfortwotimeperiods.Inthefirsttimeperiodeachvillagerwillharvest100bushels.Inthesecondtimeperiod,nocornwillbeharvested.Thereisnotradewiththerestoftheworldandnostocksofcornremainfrombeforethefirstperiod.Corncanbestoredfromonetimeperiodtothenext,butratseat25%ofwhatisstored.ThevillagersallhaveCobb-DouglasutilityfunctionsU(C1,C2)=C1C2andcanallocatetheirowncornbetweenconsumptionandstorageastheywish.Iftheintroductionofcat