中级微观经济学习题.docx

中级微观经济学习题.docx

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中级微观经济学习题

1BUDGETCONSTRAINT

1.Apoorpersonwhohasanincomeof$1000receives$100worthoffoodstamps.Drawthebudgetconstraintifthefoodstamprecipientcansellthesecouponsontheblackmarketforlessthantheirfacevalue.

2.Since1979,recipientshavebeengivenfoodstamps.Before1979,however,peopleboughtfoodstampsatasubsidizedrate.Forexample,toget$1worthoffoodstamps,ahouseholdpaidabout15￠（theexactamountvariedbyhouseholdcharacteristicsandotherfactors）.Whatisthebudgetconstraintfacinganindividualifthatindividualmaybuyupto$100permonthinfoodstampsat15￠pereach$1coupon.

3.Duringhisfirstyearatschool,Ximingbuyseightnewcollegetextbooksatacostof$50each.Usedbookscost$30each.Whenthebookstoreannouncesa20%increaseinnewtextsanda10%increaseinusedtextsnextyear,Ximing’sfatheroffershim$80extra.IsXimingbetteroff,thesame,orworseoffafterthepricechange?

Why?

2PREFERENCES

1.Juliaconsumescansofanchovies,A,andboxesofbiscuits,B.Eachofherindifferencecurvesreflectsstrictlydiminishingmarginalratesofsubstitution.WhereA=2andB=2,hermarginalrateofsubstitutionbetweencansofanchoviesandboxesofbiscuitsequals-1.Willshepreferabundlewiththreecansofanchoviesandaboxofbiscuitstoabundlewithtwoofeach?

Why?

2.Whatassumptionorassumptionsruleoutthefollowingphenomenon:

Geoffreyhasabundleconsistingof6applesand8raspberries.Hestatesthatifheisgiven1moreapple,hewillaskfor3moreraspberriestokeephimindifferentbetweenhisoldbundleandthenewbundlethathewillhaveafterhereceivesthe1additionalapple.

3.Drawindifferencecurvesforthefollowingpeople:

a）Johnsays:

“Igetnosatisfactionfrom1ounceofvermouthor3ouncesofgin,but1ounceofvermouthand3ouncesofgin（amartini）reallyturnmeon.”

b）Stevesays:

“Iwillnotcutmyhairtopleasemybossunlessshepaysme.Mypriceis$300plus$1forevery1/8inchofhairthatiscut.Inotherwords,forevery$1above$300thatthebosspaysme,Iwillcut1/8inchoffmyhair.”

c）InPartbofthisproblem,whatisthemarginalrateofsubstitutionbetweendollarsandhairintheregionbelowandabove$300?

d）Annsays:

“Ienjoybeerandpretzels,butafter12beers,anyadditionalbeermakesmesick.”

4.Jeffreyisfiveyearsold.Helikescandyandhatesspinach.Heisallowed2candybarsaday,buthismotheroffershim1additionalcandybarforevery2ounceofspinachheeats.

a）Ontheseterms,Jeffreyeats3ouncesofspinachand3.5candybarseachday.Usingindifferencecurves,illustratehisoptionalchoice.

b）SupposethatJeffrey’smotherdoesnotgivehim2“free”candybarseachdaybutstillgiveshim1candybarforevery2ounceofspinachheeats.WouldhisspinachconsumptionbegreaterorsmallerthaninParta?

Explainyouranswer.

4CHOICE

1.TarahasautilityfunctionU（B,Z）=ABZβ,WhereA,,andβareconstraints,Bisburritos,andZispizzas.Ifthepriceofburritos,pBis$2andthepriceofpizzas,pZis$1,whatisTara’soptimalbundle?

2.Assumethattherearetwogoodsintheworld:

applesandraspberries.SaythatGeoffreyhasautilityfunctionforthesegoodsofthefollowingtype,whererdenotesthequantityofraspberriesandathequantityifapples:

U=r·a.

a）Drawanindifferencecurvethatisdefinedbythisutilityfunctionandhasautilitylevelof2500.

b）WhatisthemarginalrateofsubstitutionbetweentheraspberriesandtheappleswhenGeoffreyconsumes50raspberriesand50apples?

WhatisthemarginalrateofsubstitutionbetweenthesetwogoodswhenGeoffreyconsumes100raspberriesand50apples?

c）Ifthepriceofraspberriesis$1perunitandthepriceofapplesis$1perunitandGeoffreyhas$100tospend,whatbundleofraspberriesandappleswillhebuy?

Isthemarginalrateofsubstitutionequaltotheratioofthepricesofthesegoodsintheoptimalbundle?

Ifnot,whynot?

d）Iftheunitpricesoftheraspberriesandtheapplesare$4and$3,respectively,whatbundleofraspberriesandappleswillGeoffreybuywithhisincomeof$100?

3.Steve’sutilityfunctionisU=BC,whereB=veggieburgersperweekandC=packsofcigarettesperweek.Whatishismarginalrateofsubstitutionifveggieburgersareontheverticalaxisandcigarettesareonthehorizontalaxis?

Steve’sincomeis$120,thepriceofaveggieburgeris$2,andthatofapackofcigarettesis$1.HowmanyburgersandhowmanypacksofcigarettesdoesSteveconsumetomaximizehisutility?

Whenanewtaxraisesthepriceofaburgerto$3,whatishisnewoptimalbundle?

Illustrateyouranswersinagraph.

5DEMAND

1.Roger’sutilityfunctionisU=B1/4Z3/4,hisincomeisY,thepriceofBispB,andthepriceofZispZ.Derivehisdemandcurves.

2.DeriveRoger’sEngelcurveforBfortheutilitygiveninproblem2.

7CONSUMER’SSUPPLUS

1.Iftheinversedemandfunctionisp=a–bQ,whatistheconsumersurplusifpriceisa/2?

2.IfthesupplyfunctionisQ=Apη,whatistheproducersurplusifpriceisp*?

9EQUILIBRIUM

1.In1998,aviruskilledmorethanhalftheoystersusedtoproducepearlsintheworld’sbusiestunderseafactory.Useadiagramtoindicatewhythepriceofpearlsrose18%.Howdidtheequilibriumquantitychange?

2.Increasingly,insteadofadvertisinginnewspapers,individualsandfirmsuseWebsitesthatofferfreeclassifiedads,suchasR,J,M,andportalslikeYahooandAmericaOnline.Usingasupply-and-demandmodel,explainwhatwillhappentotheequilibriumlevelsofnewspaperadvertisingastheuseoftheInternetgrows.WillthegrowthoftheInternetaffectthesupplycurve,thedemandcurveorboth?

Why?

3.TheU.S.supplyoffrozenorangejuicecomesfromFloridaandBrazil.WhatistheeffectofafreezethatdamagesorangesinFloridaonthepriceoffrozenorangejuiceintheU.S.andonthequantitiesoforangejuicesoldbyFloridianandBrazilianfirms?

4.ThesupplyofcornbytheU.S.isQa=a+bp,andthesupplybytherestoftheworldisQr=c+ep.Whatistheworldsupply?

5.Arentcontrollawlimitsthepriceofanapartment.Whatisthelikelyeffectofsuchalawintheshortrun?

Whatisthelikelyeffectofthelawinthelongrun?

Besuretodiscussthequantityandqualityofapartmentsavailableforrent.

6.Thegovernmentwantstodrivethepriceofsoybeansabovetheequilibriumprice,p1top2.ItoffersgrowersapaymentofxtoreducetheiroutputfromQ1（theequilibriumlevel）toQ2,whichisthequantitydemandedbyconsumersatp2.Howlargemustxbeforgrowerstoreduceoutputtothislevel?

Whataretheeffectsofthisprogramonconsumers,farmers,andtotalwelfare?

Comparethisapproachto（a）offeringapricesupportofp2,（b）offeringapricesupportandaquotasetatQ1,and（c）offeringapricesupportandaquotasetatQ2.

10TECHNOLOGY

1.Michelle’sbusinessproducesceramiccupsusinglabor,clay,andakiln.Shecanmanufacture25cupsadaywithoneworkerand35withtwoworkers.Doesherproductionprocessillustratediminishingreturnstoscaleordiminishingmarginalreturnstoscale?

Whatisthelikelyexplanationforwhyoutputdoesn’tincreaseproportionatelywiththenumberofworkers?

2.Supposethattheproductionfunctionisq=L3/4K1/4.

a.Whatistheaverageproductoflabor，holdingcapitalfixedat

?

b.Whatisthemarginalproductoflabor?

c.Doesthisproductionfunctionhaveincreasing,constant,ordecreasingreturnstoscale?

3.AgoodrecipeforaFrenchdishcalledcevicherequires16ouncesoffilletofredsnapper,3ouncesoflimejuice,1ounceofcoriander,and8ouncesofBermudaonion.Thiscombinationofinputsisexpressedinthefollowingproductionfunction:

Inthisproductionfunction,z1isfilletofredsnapper,z2islimejuice,z3iscoriander,andz4isBermudaonion.Theunitofmeasureforeachinputistheounce,andtheunitofmeasureforceviche（theoutput）isthequantityproducedbytherecipe.Ifarestauranthasonhand32ouncesofsnapper,9ouncesoflimejuice,5ouncesofcoriander,and48ouncesofonion,howmany“units”ofcevichecanitproduce?

4.Constructatotalproductcurveforafunctionthatexhibitsdiminishingmarginalproductthroughout.Thenconstructanothertotalproductcurveforafunctionthatexhibitsinitiallyconstantandsubsequentlydiminishingmarginalproduct.Belowthegraphsofthesetwototalproductscurve,derivethecorrespondingaverageandmarginalfunctions.Checktoseethatthecurvesyouhavedrawnareconsistentwithwhatyouknowabouttherelationshipbetweentheaverageandmarginalproductcurves.

11PROFITMAXIMIZATION

1.Youhave60minutestotakeanexamwithtwoquestions.Youwanttomaximizeyourscore.Towardtheendoftheexam,themoretimeyouspendoneitherquestion,thefewerextrapointsperminutesyougetforthatquestion.Howshouldyouallocatetimebetweenthetwoquestions?

（Hint:

Thinkaboutproducinganoutputofascoreontheexamusinginputsoftimespentoneachoftheproblem）

2.Acompetitivefirm’sproductionfunctionisy=L+2LK+K.Whatisitsmarginalrevenueproductoflabor?

3.Afirm’sproductionfunctionisy=ALαKβ.Whatisthefirm’smarginalrevenueproductoflabor?

4.AcompetitivefirmhastheproductionoffunctionQ=20L–

L2,whereQisthenumberofunitsofoutputproducedandListhenumberofunitsoflabor（theonlyinput）used.Theoutputpriceis$2,thewagerateis$1,andthefirmfacesafixedcostof$100.

a）Whatistheprofit-maximizingquantityoflabordemandedbythefirm?

b）Whatisthefirm’sprofitintheshortrun?

c）If,inthelongrun,the