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Chapter1NAMETheMarketIntroduction.Theproblemsinthischapterexaminesomevariationsontheapartmentmarketdescribedinthetext.Inmostoftheproblemsweworkwiththetruedemandcurveconstructedfromthereservationpricesoftheconsumersratherthanthe\smootheddemandcurvethatweusedinthetext.Rememberthatthereservationpriceofaconsumeristhatpricewhereheisjustindi erentbetweenrentingornotrentingtheapartment.Atanypricebelowthereservationpricetheconsumerwilldemandoneapartment,atanypriceabovethereservationpricetheconsumerwillde-mandzeroapartments,andexactlyatthereservationpricetheconsumerwillbeindi erentbetweenhavingzerooroneapartment.Youshouldalsoobservethatwhendemandcurveshavethe\stair-caseshapeusedhere,therewilltypicallybearangeofpriceswheresupplyequalsdemand.Thuswewillaskforthethehighestandlowestpriceintherange.1.1(3)Supposethatwehave8peoplewhowanttorentanapartment.Theirreservationpricesaregivenbelow.(Tokeepthenumberssmall,thinkofthesenumbersasbeingdailyrentpayments.)Person=ABCDEFGHPrice=402530351018155(a)Plotthemarketdemandcurveinthefollowinggraph.(Hint:Whenthemarketpriceisequaltosomeconsumeri'sreservationprice,therewillbetwodi erentquantitiesofapartmentsdemanded,sinceconsumeriwillbeindi erentbetweenhavingornothavinganapartment.)2THEMARKET(Ch.1)012345678102030406050PriceApartments(b)Supposethesupplyofapartmentsis xedat5units.Inthiscasethereisawholerangeofpricesthatwillbeequilibriumprices.Whatisthehighestpricethatwouldmakethedemandforapartmentsequalto5units?$18.(c)Whatisthelowestpricethatwouldmakethemarketdemandequalto5units?$15.(d)Withasupplyof4apartments,whichofthepeopleA{Hendupgettingapartments?A,B,C,D.(e)Whatifthesupplyofapartmentsincreasesto6units.Whatistherangeofequilibriumprices?$10to$15.1.2(3)Supposethatthereareoriginally5unitsinthemarketandthat1ofthemisturnedintoacondominium.(a)SupposethatpersonAdecidestobuythecondominium.Whatwillbethehighestpriceatwhichthedemandforapartmentswillequalthesupplyofapartments?Whatwillbethelowestprice?Enteryouran-swersincolumnA,inthetable.ThencalculatetheequilibriumpricesofapartmentsifB,C,:::,decidetobuythecondominium.NAME3PersonABCDEFGHHighprice1818181825252525Lowprice1515151518151818(b)Supposethatthereweretwopeopleateachreservationpriceand10apartments.Whatisthehighestpriceatwhichdemandequalssupply?18.Supposethatoneoftheapartmentswasturnedintoacondo-minium.Isthatpricestillanequilibriumprice?Yes.1.3(2)Supposenowthatamonopolistownsalltheapartmentsandthatheistryingtodeterminewhichpriceandquantitymaximizehisrevenues.(a)Fillintheboxwiththemaximumpriceandrevenuethatthemonop-olistcanmakeifherents1,2,:::,8apartments.(Assumethathemustchargeonepriceforallapartments.)Number12345678Price403530251815105Revenue40709010090907040(b)WhichofthepeopleA{Fwouldgetapartments?A,B,C,D.(c)Ifthemonopolistwererequiredbylawtorentexactly5apartments,whatpricewouldhechargetomaximizehisrevenue?$18.(d)Whowouldgetapartments?A,B,C,D,F.(e)Ifthislandlordcouldchargeeachindividualadi erentprice,andheknewthereservationpricesofalltheindividuals,whatisthemaximumrevenuehecouldmakeifherentedall5apartments?$148.(f)If5apartmentswererented,whichindividualswouldgettheapart-ments?A,B,C,D,F.1.4(2)Supposethatthereare5apartmentstoberentedandthatthecityrent-controlboardsetsamaximumrentof$9.FurthersupposethatpeopleA,B,C,D,andEmanagetogetanapartment,whileF,G,andHarefrozenout.4THEMARKET(Ch.1)(a)Ifsublettingislegal|or,atleast,practiced|whowillsublettowhominequilibrium?(Assumethatpeoplewhosubletcanevadethecityrent-controlrestrictions.)E,whoiswillingtopayonly$10foranapartmentwouldsublettoF,whoiswillingtopay$18.(b)Whatwillbethemaximumamountthatcanbechargedforthesubletpayment?$18.(c)Ifyouhaverentcontrolwithunlimitedsublettingallowed,whichoftheconsumersdescribedabovewillendupinthe5apartments?A,B,C,D,F.(d)Howdoesthiscomparetothemarketoutcome?It'sthesame.1.5(2)Inthetextwearguedthatataxonlandlordswouldnotgetpassedalongtotherenters.Whatwouldhappenifinsteadthetaxwasimposedonrenters?(a)Toanswerthisquestion,considerthegroupofpeopleinProblem1.1.Whatisthemaximumthattheywouldbewillingtopaytothelandlordiftheyeachhadtopaya$5taxonapartmentstothecity?Fillintheboxbelowwiththesereservationprices.PersonABCDEFGHReservationPrice35202530513100(b)Usingthisinformationdeterminethemaximumequilibriumpriceifthereare5apartmentstoberented.$13.(c)Ofcourse,thetotalpricearenterpaysconsistsofhisorherrentplusthetax.Thisamountis$18.(d)Howdoesthiscomparetowhathappensifthetaxisleviedonthelandlords?It'sthesame.Chapter2NAMEBudgetConstraintIntroduction.Theseworkoutsaredesignedtobuildyourskillsinde-scribingeconomicsituationswithgraphsandalgebra.Budgetsetsareagoodplacetostart,becauseboththealgebraandthegraphingareveryeasy.Wheretherearejusttwogoods,aconsumerwhoconsumesx1unitsofgood1andx2unitsofgood2issaidtoconsumetheconsumptionbun-dle,(x1;x2).Anyconsumptionbundlecanberepresentedbyapointonatwo-dimensionalgraphwithquantitiesofgood1onthehorizontalaxisandquantitiesofgood2ontheverticalaxis.Ifthepricesarep1forgood1andp2forgood2,andiftheconsumerhasincomem,thenshecana ordanyconsumptionbundle,(x1;x2),suchth