中级微观经济学习题及答案

1ANSWERS1TheMarket1.Supposethattherewere25peoplewhohadareservationpriceof$500,andthe26thpersonhadareservationpriceof$200.Whatwouldthedemandcurvelooklike?1.1.Itwouldbeconstantat$500for25apartmentsandthendropto$200.2.Intheaboveexample,whatwouldtheequilibriumpricebeiftherewere24apartmentstorent?Whatiftherewere26apartmentstorent?Whatiftherewere25apartmentstorent?1.2.Inthefirstcase,$500,andinthesecondcase,$200.Inthethirdcase,theequilibriumpricewouldbeanypricebetween$200and$500.3.Ifpeoplehavedifferentreservationprices,whydoesthemarketdemandcurveslopedown?1.3.Becauseifwewanttorentonemoreapartment,wehavetoofferalowerprice.Thenumberofpeoplewhohavereservationpricesgreaterthanpmustalwaysincreaseaspdecreases.4.Inthetextweassumedthatthecondominiumpurchaserscamefromtheinner-ringpeople—peoplewhowerealreadyrentingapartments.2Whatwouldhappentothepriceofinner-ringapartmentsifallofthecondominiumpurchaserswereouter-ringpeople—thepeoplewhowerenotcurrentlyrentingapartmentsintheinnerring?1.4.Thepriceofapartmentsintheinnerringwouldgoupsincedemandforapartmentswouldnotchangebutsupplywoulddecrease.5.Supposenowthatthecondominiumpurchaserswereallinner-ringpeople,butthateachcondominiumwasconstructedfromtwoapartments.Whatwouldhappentothepriceofapartments?1.5.Thepriceofapartmentsintheinnerringwouldrise.6.Whatdoyousupposetheeffectofataxwouldbeonthenumberofapartmentsthatwouldbebuiltinthelongrun?1.6.Ataxwouldundoubtedlyreducethenumberofapartmentssuppliedinthelongrun.7.SupposethedemandcurveisD(p)=100−2p.Whatpricewouldthemonopolistsetifhehad60apartments?Howmanywouldherent?Whatpricewouldhesetifhehad40apartments?Howmanywouldherent?1.7.Hewouldsetapriceof25andrent50apartments.Inthesecondcasehewouldrentall40apartmentsatthemaximumpricethemarket3wouldbear.ThiswouldbegivenbythesolutiontoD(p)=100−2p=40,whichisp∗=30.8.Ifourmodelofrentcontrolallowedforunrestrictedsubletting,whowouldendupgettingapartmentsintheinnercircle?WouldtheoutcomebeParetoefficient?1.8.Everyonewhohadareservationpricehigherthantheequilibriumpriceinthecompetitivemarket,sothatthefinaloutcomewouldbeParetoefficient.(Ofcourseinthelongruntherewouldprobablybefewernewapartmentsbuilt,whichwouldleadtoanotherkindofinefficiency.)2BudgetConstraint1.Originallytheconsumerfacesthebudgetlinep1x1+p2x2=m.Thenthepriceofgood1doubles,thepriceofgood2becomes8timeslarger,andincomebecomes4timeslarger.Writedownanequationforthenewbudgetlineintermsoftheoriginalpricesandincome.2.1.Thenewbudgetlineisgivenby2p1x1+8p2x2=4m.2.Whathappenstothebudgetlineifthepriceofgood2increases,butthepriceofgood1andincomeremainconstant?2.2.Theverticalintercept(𝐱𝟐axis)decreasesandthehorizontalintercept(𝐱𝟏axis)staysthesame.Thusthebudgetlinebecomesflatter.43.Ifthepriceofgood1doublesandthepriceofgood2triples,doesthebudgetlinebecomeflatterorsteeper?2.3.Flatter.Theslopeis−2𝐩𝟏/3𝐩𝟐.4.Whatisthedefinitionofanumerairegood?2.4.Agoodwhosepricehasbeensetto1;allothergoods’pricesaremeasuredrelativetothenumerairegood’sprice.5.Supposethatthegovernmentputsataxof15centsagallonongasolineandthenlaterdecidestoputasubsidyongasolineatarateof7centsagallon.Whatnettaxisthiscombinationequivalentto?2.5.Ataxof8centsagallon.6.Supposethatabudgetequationisgivenby𝐩𝟏𝐱𝟏+𝐩𝟐𝐱𝟐=m.Thegovernmentdecidestoimposealump-sumtaxofu,aquantitytaxongood1oft,andaquantitysubsidyongood2ofs.Whatistheformulaforthenewbudgetline?2.6.(𝐩𝟏+t)𝐱𝟏+(𝐩𝟐−s)𝐱𝟐=m−u.7.Iftheincomeoftheconsumerincreasesandoneofthepricesdecreasesatthesametime,willtheconsumernecessarilybeatleast5aswell-off?2.7.Yes,sinceallofthebundlestheconsumercouldaffordbeforeareaffordableatthenewpricesandincome.3Preferences1.Ifweobserveaconsumerchoosing(𝐱𝟏,𝐱𝟐)when(𝐲𝟏,𝐲𝟐)isavailableonetime,arewejustifiedinconcludingthat(𝐱𝟏,𝐱𝟐)(𝐲𝟏,𝐲𝟐)?3.1.No.Itmightbethattheconsumerwasindifferentbetweenthetwobundles.Allwearejustifiedinconcludingisthat(𝐱𝟏,𝐱𝟐)(𝐲𝟏,𝐲𝟐).2.ConsideragroupofpeopleA,B,Candtherelation“atleastastallas,”asin“AisatleastastallasB.”Isthisrelationtransitive?Isitcomplete?3.2.Yestoboth.3.Takethesamegroupofpeopleandconsidertherelation“strictlytallerthan.”Isthisrelationtransitive?Isitreflexive?Isitcomplete?3.3.Itistransitive,butitisnotcomplete—twopeoplemightbethesameheight.Itisnotreflexivesinceitisfalsethatapersonisstrictlytallerthanhimself.4.AcollegefootballcoachsaysthatgivenanytwolinemenAandB,healwayspreferstheonewhoisbiggerandfaster.Isthispreferencerelationtransitive?Isitcomplete?63.4.Itistransitive,butnotcomplete.WhatifAwerebiggerbutslowerthanB?Whichonewouldheprefer?5.Cananindifferencecurvecrossitself?Forexample,couldFigure3.2depictasingleindifferencecurve?3.5.Yes.Anindifferencecurvecancrossitself,itjustcan’tcrossanotherdistinctindifferencecurve.6.CouldFigure3.2beasingleindifferencecurveifpreferencesaremonotonic?3.6.No,becausetherearebundlesontheindifferencecurvethathavestrictlymoreofbothgoodsthanotherbundlesonthe(alleged)indifferencecurve.7.Ifbothpepperoniandanchoviesarebads,willtheindifferencecurvehaveapositiveoranegativeslope?3.7.Anegativeslope.Ifyougivetheconsumermoreanchovies,you’vemadehimworseoff,soyouhavetotakeawa