半期考試答案詳解

1、Mid-termcheckingproblemsofIntermediateEconomicsAnswerSheet1.MultipleChoices(20 x2=40)(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)ACBBCDBAAD(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)BABADABCBC2.TrueorFalse(15X1=15)(1)(2)(3)(4)(5)(6)(7)(8)(9)(10)FTFTFFTTFT(11)(12)(13)(14)(15)TTFFT1.MultipleChoices(20 x2=40)Ifshespen

2、dsallofherincomeonlemonsandtangerines,Isabellacanjustafford30lemonsand8tangerinesperday.Shecouldalsouseherentirebudgettobuy6lemonsand14tangerinesperday.Thepriceoflemonsis6guineaseach.HowmuchisIsabellasincomeperday?(a)372guineas(b)377guineas(c)371guineas(d)363guineasInyear1,thepriceofgoodxwas1,thepri

3、ceofgoodywas1,andincomewas30.Inyear2,thepriceofxwas6,thepriceofgoodywas5,andincomewas30.Onagraphwithxonthehorizontalaxisandyonthevertical,thenewbudgetlineis:flatterthantheoldoneandliesbelowit.flatterthantheoldoneandliesaboveit.steeperthantheoldoneandliesbelowit.steeperthantheoldoneandliesaboveit.Fan

4、nyconsumesgoodsxandy.Herindifferencecurvesaredescribedbytheformulay=k/(x+7).Highervaluesofkcorrespondtobetterindifferencecurves.Whichofthefollowingistrue?Fannylikesgoodyandhatesgoodx.Fannyprefersbundle(8,9)tobundle(9,8).Fannyprefersbundle(9,5)tobundle(5,9).Fannylikesgoodxandhatesgoody.Manuelconsumes

5、onlyapplesandbananas.Heprefersmoreapplestoless,buthegetstiredofbananas.Ifheconsumesfewerthan17bananasperweek,hethinksthatonebananaisaperfectsubstituteforoneapple.Butyouwouldhavetopayhimoneappleforeachbananabeyond17thatheconsumes.Theindifferencecurvethatpassesthroughtheconsumptionbundlewith25applesan

6、d26bananasalsopassesthroughthebundlewithAapplesand11bananas,whereAequals:(a)21(b)22(c)24(d)26Chenhaspreferencesrepresentedbytheutilityfunction:U(x,y)=min4xy,y6x.Ifxisonthehorizontalaxisandyisontheverticalaxis,whatistheslopeofhisindifferencecurveatthepoint(9,4)?Theslopeis-4.(b)Theslopeis-6/4.(c)Thesl

7、opeis-1/6(d)Theslopeis-1/4.RaymondspreferencesarerepresentedbytheutilityfunctionU(x;y)=x=yify0andU(x;y)=0ify=0.Raymondhasindifferencecurvesthatarerectangularhyperbolas.Raymondprefersmoreofeachgoodtoless.Raymondhasquasi-linearpreferences.Raymondhasindifferencecurvesthatareupwardslopingstraightlinesif

8、y0.Hanshas27dollars,whichhedecidestospendonxandy.Commodityxcosts$16perunitandcommodityycosts$10perunit.HehastheutilityfunctionU(x;y)=5x2+2y2andhecanpurchasefractionalunitsofxandy.Hanswillchooseonlyx.Hanswillchooseonlyy.Hanswillchoosesomeofeachcommodity,butmoreythanx.Hanswillchoosesomeofeachcommodity

9、,butmorexthany.Paulsutilityfunctionisminx3y,3xy.Simonsutilityfunctionismin3x9y,9x3y.PaulandSimonhavethesameincomeandfacethesameprices.Whichofthefollowingistrue?PaulandSimonwilldemandthesameamountofgoodx.PaulwilldemandmoreythanSimon.SimonwilldemandmoreythanPaul.Eachwillprefertheothersconsumptionbundl

10、etohisown.Daisyreceivedataperecorderasabirthdaygiftandisnotabletoreturnit.HerutilityfunctionisU(x,y,z)=x+z1/2f(y)wherezisthenumberoftapesshebuys,yisthenumberoftaperecordersshehasandxistheamountofmoneyshehaslefttospend.f(y)=0ify1andf(y)=32ifyis1orgreater.Thepriceoftapesis4andshecaneasilyaffordtobuydo

11、zensoftapes.Howmanytapeswillshebuy?(a)16(b)18(c)14(d)20Waltconsumesstrawberriesandcreambutonlyinthefixedratioofthreeboxesofstrawberriestotwocartonsofcream.Atanyotherratio,theexcessgoodsaretotallyuselesstohim.Thecostofaboxofstrawberriesis10andthecostofacartonofcreamis10.Waltsincomeis200.Whichofthefol

12、lowingistrue?Waltdemands10cartonsofcream.Waltdemands10boxesofstrawberries.Waltconsidersstrawberriesandcartonsofcreamtobeperfectsubstitutes.Waltdemands12boxesofstrawberriesRememberthattheLaspeyrespriceindexusestheoldquantitiesfortheweights.In1971,goodxcost3andgoodycost1.Thecurrentpriceofgoodxis3andth

13、ecurrentpriceofgoodyis5.In1971theconsumptionbundlewas(x,y)=(3,5).Thecurrentconsumptionbundleis(x,y)=(9,4).TheLaspeyresindexofcurrentpricesrelativeto1971pricesisclosesttowhichofthefollowingnumbers?(a)3.36(b)2.43(c)0.30(d)1.52Atprices(4,12);Harrychoosesthebundle(9,4).Attheprices(8,4);Harrychoosesthebu

14、ndle(2,9).Isthisbehaviorconsistentwiththeweakaxiomofrevealedpreference?(a)Yes(b)No(c)Itdependsonhisincome.(d)Wewouldhavetoobserveathirdchoicetobeabletosay.Cindyconsumesgoodsxandy.Herdemandforxisgivenbyx(px,m)=0.05m-5.15px.Nowherincomeis419,thepriceofxis3,andthepriceofyis1.Ifthepriceofxrisesto4andifw

15、edenotetheincomeeffectonherdemandforxbyDIandthesubstitutioneffectonherdemandforxbyDS,then:(a)DI=-0.28andDS=-0.52.(b)DI=-0.28andDS=-4.88.(c)DI=-0.52andDS=-0.52.(d)DI=0andDS=-2.00.Waldoconsumesonlyapplesandbananasandbananasareaninferiorgoodforhim.Thepriceofapplesincreases,butthereisanincreaseinhisinco

16、methatkeepshimonthesameindifferencecurveasbefore.(Waldohasconvexpreferences;andheprefersmoretolessofeithergood.)(a)Afterthechange,Waldowillbuymorebananasandlessapples.Afterthechange,Waldowillbuylessbananasandmoreapples.Afterthechange,Waldowillbuymoreofbothgoods.Afterthechange,Waldowillbuylessofbothg

17、oods.Reginaldisfondofcigars.HisutilityfunctionisU(x,c)=x+10c-5c2wherecisthenumberofcigarshesmokesperweekandxisthemoneythathespendsonconsumptionofothergoods.Reginaldhas$200aweektospend.Cigarsusedtocosthim$1each,buttheirpricewentupto$2each.Thispriceincreasewasasbadforhimaslosingthefollowingamountofinc

18、ome:(a)$5(b)$7.25(c)$9(d)$8.50HollyconsumesonlygoodsXandY.Herincomeis600andherutilityfunctionisU(x,y)=maxx,ywherexisthenumberofunitsofXsheconsumesandyisthenumberofunitsofYsheconsumes.ThepriceofgoodYis1.ThepriceofgoodXusedtobe1/2;butisnow2.TheequivalentvariationofthispricechangeforHollyis:(a)300.(b)6

19、00.(c)150.(d)800.Thedemandfunctionisdescribedbytheequationq(p)=190-p/5.Theinversedemandfunctionisdescribedby:(a)q(p)=190-5p.(b)p(q)=950-5q.(c)q(p)=1/(190-p/5).(d)p(q)=1/190-q/5.Ifthedemandfunctionforticketstoaplayisq=3600-45p;atwhatpricewilltotalrevenuebemaximized?(a)160(b)80(c)40(d)20Thedemandfunct

20、ionforfreshstrawberriesisq=200-5pandthesupplyfunctionisq=60+2p.Whatistheequilibriumprice?(a)10(b)20(c)40(d)50Theinversedemandfunctionforcasesofwhiskeyisdefinedbyp=241-11qandtheinversesupplyfunctionisdefinedbyp=17+5q.Originallytherewasnotaxonwhiskey.Thenthegovernmentbegantotaxsuppliersofwhiskey$112fo

21、reverycasetheysold.Howmuchdidthepricepaidbyconsumersrisewhenthenewequilibriumwasreached.(a)Itroseby112dollars.(b)Itroseby114dollars.(c)Itroseby77dollars.(d)Itroseby75dollarsTrueorFalse(15X1=15)Iftherearetwogoodswithpositivepricesandthepriceofonegoodisreduced,whileincomeandotherpricesremainconstant,t

22、henthesizeofthebudgetsetisreduced.Aconsumerprefersmoretolessofeverygood.Herincomerises,andthepriceofoneofthegoodsfallswhileotherpricesstayconstant.Thesechangesmusthavemadeherbetteroff.Ifpreferencesaretransitive,moreisalwayspreferredtoless.Aconsumerwithconvexpreferenceswhoisindifferentbetweenthebundl

23、es(1,2)and(9,6)willlikethebundle(5,4)atleastaswellaseitherofthefirsttwobundles.Withquasilinearpreferences,theslopeofindifferencecurvesisconstantalongallraysthroughtheorigin.ApersonwiththeutilityfunctionU(x,y)=y+x2hasconvexpreferences.Sharonspendsallofherincomeonpeachesandstrawberries.Peachesareanorm

24、algoodforher.Herincomeincreasedby20percentandpricesdidnotchange.Herconsumptionofstrawberriescouldnothaveincreasedbymorethan20percent.Agoodisaluxurygoodiftheincomeelasticityofdemandforitisgreaterthan1.Ifincomeisdoubledandallpricesaredoubled,thenthedemandsforluxurygoodswillmorethandouble.Thestrongaxio

25、mofrevealedpreferencerequiresthatifaconsumerchoosesxwhenhecanaffordy;andchoosesywhenhecanaffordz;thenhewillnotchoosezwhenhecanaffordx.Itispossibleforaconsumertosatisfytheweakaxiomofrevealedpreference,butviolatethestrongaxiomofrevealedpreference.AGiffengoodmustbeaninferiorgood.Thecompensateddemandfun

26、ctionreferstothedemandfunctionofsomeonewhoisadequatelypaidforwhatheorshesells.Consumerssurplusisanothernameforexcessdemand.TheinversedemandcurveP(x)foragoodxmeasuresthepriceperunitatwhichthequantityxwouldbedemanded.Essay(45points)1(5points).Useanexampletoexplainwhytakingamonotonictransformationofaut

27、ilityfunctiondoesnotchangethemarginalrateofsubstitution.U,MUx111U1MU x211MU U22U-1MU U222(x1, x2).Answer1:ConsiderutilityfunctionsU1x1x2andU22(x1x2)wherex10andx20.Atany(x1,x2),bythedefinitionofthemarginalrateofsubstitution(MRS),forU1,theMRSisMRS；%andforU2,theMRSisMRsU2 ,2 (10 points). Assume that Sm

28、ith s utility functiorUs X Y (unit: dollar), the price of good X and Y are Px $2and FY $3 . His income is $500 per month. Answer the following questions:(a) How many good X and good Y does Smith buy per month?(b) If Smith has the membership of good X sspecial customer and the membership costs $100,

29、he can buy good X at a price of $1. Please help Smith to decide whether to buy the membership.Answer 2: (a) Smiths choice with respect to X and Y can written asx,x1，x2U1U2ThenMRSx1,x21MRSx1,x2forany(Further,theconclusionholdsforanymonotonictransformationf.LetU2(x1,x2)f(U1(x1,x2)whereU1isanygivenfuti

30、lityfunction.Atany(xx2),wehaveMRSU2x2f MUU；f MU U21MUMUU1x1U1x2MRSU11x2 . Thus the conclusion follows.) TOC o 1-5 h z maxUmaxX2Y2X,YX,Ys.t.PxXPYY2X3Y500Theutility-maximizingconditionsareMUxMUy2XY22X2YPx232X3Y500ThenwehaveX*125andY*250383.33.(b)Bybuyingthemembershipthatcosts$100,theproblemofSmithscho

31、iceis22maxUmaxXYx,yx,ySt.PXXPYYX3Y400Followingtheproblem-solvingprocedurein(a),weconcludethatifhebuysthemembership,hewillpurchaseXm*200andYm*200366.67.NowwecalculatetheSmithsutilities,UandUm,gainedinthesetwocaserespectively.*2*22222*2*2U(X)(Y)125(250/3)200(200/3)(Xm)(Ym)UmThus,hewillbuythemembership

32、.3(20points).Consideramarketwith2consumers.Consumer1sutilityfunctionandincomeareU1(Xi,x2)x；4x34_and$100.Consumer2sutilityfunctionandincomeare.2.1.3-U(Xi,X2)lnXiX2and$200.Pleaseanswer44x1cWhatareConsumer1sand2sindividualdemandfunctionsfor1?Whatisthemarketdemandfunctionforx1?Assumefurtherthatoriginalp

33、riceofx1is$5andgoesupto$10.Calculate(Slutsky)substitutioneffectandincomeeffectforConsumer2sdemand.Answer3:(a)Letp1andp2beGood1and2sprices.ThenConsumer1sutilitymaximizationisdescribedas11434maxU(x1,x2)maxx1x2X1,x2x1,x2s.t.p1x1p2x2m1wherem1100.Thentheoptimizationconditionsare1MU X113 4 3 4X1 X24p1X2p1

34、1MU x231 41 4一 X1 X2p23x1p24p1 x1p2X2MRSx1,x2m1pMm14p1X1p2X2m1ThusConsumer1sinversedemandfunctionisp1m141X125X1where the superscription 1 indexes Consumer 1.Similarly, Consumer 2 s utility maximization is described.2 .1 .maxU (X1, X2) max - ln x1X1,x2X1,x2 4ass.t.pX1p2X2m2wherem2200.Thentheoptimizat

35、ionconditionsareMU xiMRS”？2-MU X214XiT4PiP23x1PlXiPiP23P1X1 P2P2X2m2P1X1P2X2m2ThusConsumer2sinversedemandfunctionisP2Pi3xicurveswherethesuperscription2indexesConsumer2.P23p75 P23pNotethatthemarketdemandcurveistheoutcomeofaddingindividualsdemandhorizontally.AtanygivenpriceofGood1,thequantitydemandedi

36、nthemarketis TOC o 1-5 h z M1225X1X1X1PiP2Thatis,themarketinversedemandfunctionis75p1-M3x1.2P2FromConsumer2sdemandfunctionX1,his/herquantitydemandedat653P122P2withm2200isx1(p1,m2)x(5,200)15Tokeephis/herpurchasingpowerconstant,his/herincomeneedstoraise HYPERLINK l bookmark7 o Current Document ,一P2P2b

37、ym2(105).Thentheincomenecessarytokeeppurchasingpowerconstantis153m220050250.Sothequantitydemandedatp110withm2200-p2is3 HYPERLINK l bookmark15 o Current Document 一(口凡)x2(10,2009)卷330Thenbythedefinitionof(Slutsky)substitutioneffect,wehave HYPERLINK l bookmark17 o Current Document X12sx2(p1,m2)xlpf)x2(10,200號)xf(5,200)黑330Nowturntotheincomeeffect.Clearly,his/herquantitydemandedatp110withisirrelevanttotheincome,sotheincomeeffectis0,andthesubstitutioneffectise