微观经济学 平狄克《微观经济学》课后答案 11-12

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CHAPTER11

PRICINGWITHMARKETPOWER

TEACHINGNOTES

Thechapterbeginswithamoretraditionaldiscussionofpricediscriminationandthenappliestheanalysisofthird-degreepricediscriminationtointertemporalpricediscriminationandpeak-loadpricing.Thechaptercontinueswithdiscussionsoftwo-parttariffs,bundling,andthedistinctionbetweenbundlingandtying.Althoughtwo-parttariffsandbundlingareusuallynotcoveredatthislevel,thistextstressesanintuitiveunderstandingofhowconsumersurplusisconvertedtoproducersurplus.Thechapterconcludeswithanintroductiontooptimaladvertising.

Sincethischapterisuniqueinitscoverage,thereisanextensivesetofexercises.Exercises(1),(3)-(6),(8),and(9)focusonpricediscrimination.Exercises(2),(7),(10),and(13)applythetwo-parttariffmodel.Allothers,exceptforExercise(17),requireanunderstandingofbundling;Exercise(17)isamathematicaltreatmentofadvertising.Manyexercisesrequiresomealgebraicornumericmanipulation.TheAppendixtothechaptercanbedifficultformoststudentsandshouldnotbecoveredinclassunlessyouareteachingamathematicalorbusiness-orientedcourse.ShouldyouchoosetoincludetheAppendix,makesurestudentshaveanintuitivefeelforthemodelbeforepresentingthealgebraorgeometry.

Whenintroducingthischapter,highlighttherequirementsforprofitablepricediscrimination:(1)supply-sidemarketpower,(2)theabilitytoseparatecustomers,and(3)differingdemandelasticitiesfordifferentclassesofcustomers.Thediscussionoffirst-degreepricediscriminationbeginswiththeconceptofareservationprice.Thetextusesreservationpricesthroughoutthechapter.SincethediscussionofFigure11.2maybeconfusingtostudents,analternativepresentationcouldbeginwithadiagramsimilartoFigure9.1,withtheadditionofinformationfromFigure10.9.Showthatwithfirst-degreepricediscriminationthemonopolistcapturesdeadweightlossandallconsumersurplus.Also,stressthatwithperfectdiscriminationthemarginalrevenuecurvecoincideswiththedemandcurve.

First-degreepricediscriminationisbestfollowedbythediscussiononthird-degree,ratherthansecond-degree,pricediscrimination.Whenyoudocoversecond-degreepricediscrimination,notethatmanyutilitiesnowchargehigherpricesforlargerblocks.(Useyourownelectricitybillasanexample.)Thegeometryofthird-degreepricediscriminationistoodifficultformoststudents;therefore,theyneedacarefulexplanationoftheintuitionbehindthemodel.Slowlyintroducethealgebrasothatstudentscanseethattheprofit-maximizingquantitiesineachmarketarethosewheremarginalrevenueequalsmarginalcost.Ifstudentsunderstandthisbasicconcept,theywillbeabletodoExercise(8).ThissectionconcludeswithExamples11.1and11.2.Becauseoftheprevalenceofcoupons,rebates,andairlinetravel,allstudentswillbeabletorelatetotheseexamples.

Whenpresentingintertemporalpricediscriminationandpeak-loadpricing,beginbycomparingthesimilaritiesintheanalysiswiththird-degreepricediscrimination.Discussthedifferencebetweentheseformsofexploitingmonopolypowerandthird-degreepricediscrimination.Here,marginalrevenueandcostareequalwithincustomerclassbutneednotbeequalacrossclasses.

Studentseasilygraspthecaseofatwo-parttariffwithasinglecustomer.Fewerwillunderstandthecasefortwocustomers.Fewerstillwillunderstandthecaseofmanydifferentcustomers.Insteadofmovingdirectlyintoadiscussionofmorethanonecustomer,youcouldintroduceExample11.4togiveconcretemeaningtoentryandusagefees.Thenreturntothecasesdealingwithmorethanonecustomer.

Whendiscussingbundling,pointoutthatinFigure11.12pricesareonbothaxes.Tointroducebundling,considerstartingwithExample11.5andamenufromalocalrestaurant.Makesurestudentsunderstandwhenbundlingisprofitable(whendemandsarenegativelycorrelated)andthatmixedbundlingcanbemoreprofitablethaneithersellingseparatelyorpurebundling(demandsareonlysomewhatnegativelycorrelatedand/orwhenmarginalproductioncostsaresignificant).Todistinguishtying,frombundling,pointoutthatwithtyingthefirstproductisuselesswithoutthesecondproduct.

REVIEWQUESTIONS

1.Supposeafirmcanpracticeperfect,first-degreepricediscrimination.Whatisthelowestpriceitwillcharge,andwhatwillitstotaloutputbe?

Whenthefirmisabletopracticeperfectfirst-degreepricediscrimination,eachunitissoldatthereservationpriceofeachconsumer,assumingeachconsumerpurchasesoneunit.Becauseeachunitissoldattheconsumer’sreservationprice,marginalrevenueissimplythepriceofthelastunit.Weknowthatfirmsmaximizeprofitsbyproducinganoutputsuchthatmarginalrevenueisequaltomarginalcost.Fortheperfectpricediscriminator,thatpointiswherethemarginalcostcurveintersectsthedemandcurve.IncreasingoutputbeyondthatpointwouldimplythatMR<MC,andthefirmwouldlosemoneyoneachunitsold.Forlowerquantities,MR>MC,andthefirmshouldincreaseitsoutput.

2.Howdoesacarsalespersonpracticepricediscrimination?Howdoestheabilitytodiscriminatecorrectlyaffecthisorherearnings?

Therelevantrangeofthedemandcurvefacingthecarsalespersonisboundedabovebythemanufacturer’ssuggestedretailpriceplusthedealer’smarkupandboundedbelowbythedealer’spriceplusadministrativeandinventoryoverhead.Bysizingupthecustomer,thesalespersondeterminesthecustomer’sreservationprice.Throughaprocessofbargaining,asalespriceisdetermined.Ifthesalespersonhasmisjudgedthereservationpriceofthecustomer,eitherthesaleislostbecausethecustomer’sreservationpriceislowerthanthesalesperson’sguessorprofitislostbecausethecustomer’sreservationpriceishigherthanthesalesperson’sguess.Thus,thesalesperson’scommissionispositivelycorrelatedtohisorherabilitytodeterminethereservationpriceofeachcustomer.

3.Electricutilitiesoftenpracticesecond-degreepricediscrimination.Whymightthisimproveconsumerwelfare?

Consumersurplusishigherunderblockpricingthanundermonopolypricingbecausemoreoutputisproduced.Forexample,assumetherearetwopricesP1andP2,withP1greaterthanP2.CustomerswithreservationpricesaboveP1payP1,capturingsurplusequaltotheareaboundedbythedemandcurveandP1.Thisalsowouldoccurwithmonopolypricing.Underblockpricing,customerswithreservationpricesbetweenP1andP2capturesurplusequaltotheareaboundedbythedemandcurve,thedifferencebetweenP1andP2,andthedifferencebetweenQ1andQ2.Thisquantityisgreaterthanthesurpluscapturedundermonopoly,henceblockpricing,undertheseassumptions,improvesconsumerwelfare.

Figure11.3

4.Givesomeexamplesofthird-degreepricediscrimination.Canthird-degreepricediscriminationbeeffectiveifthedifferentgroupsofconsumershavedifferentlevelsofdemandbutthesamepriceelasticities?

Toengageinthird-degreepricediscrimination,theproducermustseparatecustomersintodistinctmarkets(sorting)andpreventtheresellingoftheproductfromcustomersinonemarkettocustomersinanothermarket(arbitrage).Whileexamplesinthischapterstressthetechniquesforseparatingcustomers,therearealsotechniquesforpreventingresale.Forexample,airlinesrestricttheuseoftheirticketsbyprintingthenameofthepassengerontheticket.Otherexamplesincludedividingmarketsbyageandgender,e.g.,chargingdifferentpricesformovieticketstodifferentagegroups.Ifcustomersintheseparatemarketshavethesamepriceelasticities,thenfromequation11.2weknowthatthepricesarethesameinallmarkets.Whiletheproducercaneffectivelyseparatethemarkets,thereislittleprofitincentivetodoso.

5.Showwhyoptimal,third-degreepricediscriminationrequiresthatmarginalrevenueforeachgroupofconsumersequalsmarginalcost.Usethisconditiontoexplainhowafirmshouldchangeitspricesandtotaloutputifthedemandcurveforonegroupofconsumersshiftedoutward,sothatmarginalrevenueforthatgroupincreased.

Weknowthatfirmsmaximizeprofitsbychoosingoutputsomarginalrevenueisequaltomarginalcost.IfMRforonemarketisgreaterthanMC,thenthefirmshouldincreasesalestomaximizeprofit,thusloweringthepriceonthelastunitandraisingthecostofproducingthelastunit.Similarly,ifMRforonemarketislessthanMC,thefirmshoulddecreasesalestomaximizeprofit,therebyraisingthepriceonthelastunitandloweringthecostofproducingthelastunit.ByequatingMRandMCineachmarket,marginalrevenueisequalinallmarkets.

Ifthequantitydemandedincreased,themarginalrevenueateachpricewouldalsoincrease.IfMR=MCbeforethedemandshift,MRwouldbegreaterthanMCafterthedemandshift.TolowerMRandraiseMC,theproducershouldincreasesalestothismarketbyloweringprice,thusincreasingoutput.ThisincreaseinoutputwouldincreaseMCofthelastunitsold.Tomaximizeprofit,theproducermustincreasetheMRonunitssoldinothermarkets,i.e.,increasepriceintheseothermarkets.Thefirmshiftssalestothemarketexperiencingtheincreaseindemandandawayfromothermarkets.

6.Whenpricingautomobiles,Americancarcompaniestypicallychargeamuchhigherpercentagemarkupovercostfor“luxuryoption”items(suchasleathertrim,etc.)thanforthecaritselforformore“basic”optionssuchaspowersteeringandautomatictransmission.Explainwhy.

Thiscanbeexplainedasaninstanceofthird-degreepricediscrimination.Inordertousethemodelofthird-degreepricediscriminationpresentedinthetext,weneedtoassumethatthecostsofproducingcaroptionsisafunctionofthetotalnumberofoptionsproducedandtheproductionofeachtypeofoptionsaffectscostsinthesameway.Forsimplicity,wecanassumethattherearetwotypesofoptionpackages,“luxury”and“basic,”andthatthesetwotypesofpackagesarepurchasedbytwodifferenttypesofconsumers.Inthiscase,therelationshipacrossproducttypesMR1=MR2musthold,whichimpliesthat:

P1/P2=(1+1/E2)/(1+1/E1)

where1and2denotetheluxuryandbasicproductstypes.

Thismeansthatthehigherpriceischargedforthepackagewiththelowerelasticityofdemand.Thusthepricingofautomobilescanbeexplainedifthe“luxury”optionsarepurchasedbyconsumerswithlowelasticitiesofdemandrelativetoconsumersofmore“basic”packages.

7.Howispeak-loadpricingaformofpricediscrimination?Canitmakeconsumersbetteroff?Giveanexample.

Pricediscriminationinvolvesseparatingcustomersintodistinctmarkets.Thereareseveralwaysofsegmentingmarkets:bycustomercharacteristics,bygeography,andbytime.Inpeak-loadpricing,sellerschargedifferentpricestocustomersatdifferenttimes.Whenthereisahigherquantitydemandedateachprice,ahigherpriceischarged.Peak-loadpricingcanincreasetotalconsumersurplusbychargingalowerpricetocustomerswithelasticitiesgreaterthantheaverageelasticityofthemarketasawhole.Mosttelephonecompanieschargeadifferentpriceduringnormalbusinesshours,eveninghours,andnightandweekendhours.Callerswithmoreelasticdemandwaituntiltheperiodwhenthechargeisclosesttotheirreservationprice.

8.Howcanafirmdetermineanoptimaltwo-parttariffifithastwocustomerswithdifferentdemandcurves?(Assumethatitknowsthedemandcurves.)

Ifallcustomershadthesamedemandcurve,thefirmwouldsetapriceequaltomarginalcostandafeeequaltoeachconsumer’sconsumersurplus.Withconsumerswithdifferentdemandcurvesand,therefore,differentlevelsofconsumersurplus,thefirmisfacedwiththefollowingproblem.Ifitsetstheuserfeeequaltothelargerconsumersurplus,thefirmwillearnprofitsonlyfromtheconsumerswiththelargerconsumersurplusbecausethesecondgroupofconsumerswillnotpurchaseanyofthegood.Ontheotherhand,ifthefirmsetsthefeeequaltothesmallersurplusofthesecondconsumer,thefirmwillearnrevenuesfrombothtypesofconsumers.

9.WhyisthepricingofaGillettesafetyrazoraformofatwo-parttariff?MustGillettebeamonopolyproducerofitsbladesaswellasitsrazors?SupposeyouwereadvisingGilletteonhowtodeterminethetwopartsofthetariff.Whatprocedurewouldyousuggest?

Bysellingtherazorandthebladesseparately,thepricingofaGillettesafetyrazorcaninvolveatwo-parttariff.IfGillettehasnomonopolypowerintheblademarket,thepriceofbladesisdriventomarginalcost;thepriceofthebladecouldnotbeusedtocaptureconsumersurplus.IfGillettehasmonopolypowerintheblademarket,itshoulddeterminetheoptimalpriceoftherazorandresultingprofitforeachpriceforblades.Itshouldchoosethebladepricethatmaximizesprofit,astrategythatwouldinvolveestimatingthedemandfunctionforshaving.

10.WhydidLoewsbundleGonewiththeWindandGettingGertie’sGarter?Whatcharacteristicofdemandsisneededforbundlingtoincreaseprofits?

LoewsbundleditsfilmGonewiththeWindandGettingGertie’sGartertomaximizerevenues.BecauseLoewscouldnotpricediscriminatebychargingadifferentpricetoeachcustomeraccordingtothecustomer’spriceelasticity,itchosetobundlethetwofilmsandchargetheatersforshowingbothfilms.ThepricewouldhavebeenthecombinedreservationpricesofthelasttheaterthatLoewswantedtoattract.Ofcourse,thistacticwouldonlymaximizerevenuesifdemandsforthetwofilmswerenegativelycorrelated.

11.Howdoesmixedbundlingdifferfrompurebundling?Underwhatconditionsismixedbundlingpreferredtopurebundling?Whydomanyrestaurantspracticemixedbundling(byofferingacompletedinneraswellasanàlacartemenu)insteadofpurebundling?

Purebundlinginvolvessellingproductsonlyasapackage.Mixedbundlingallowstheconsumertopurchasetheproductseitherseparatelyortogether.Mixedbundlingyieldshigherprofitsthanpurebundlingwheneitherdemandsfortheindividualproductsdonothaveastrongnegativecorrelation,ormarginalcostsarehigh,orboth.Restaurantscanmaximizeprofitswithmixedbundlingbyofferingbothàlacarteandfulldinnersbycharginghigherpricesforindividualitemstocapturetheconsumers’willingnesstopayandlowerpricesforfulldinnerstoinducecustomerswithlowerreservationpricestopurchasemoredinners.

12.Howdoestyingdifferfrombundling?Whymightafirmwanttopracticetying?

Tyinginvolvesthesaleoftwoormoregoodsorservicesthatmustbeusedascomplements.Bundlingcaninvolvecomplementsorsubstitutes.Tyingallowsthefirmtomonitorcustomerdemandandmoreeffectivelydetermineprofit-maximizingpricesforthetiedproducts.Forexample,amicrocomputerfirmmightsellitscomputer,thetyingproduct,withminimummemoryandauniquearchitecture,thensellextramemory,thetiedproduct,abovemarginalcost.

13.Whyisitincorrecttoadvertiseuptothepointthatthelastdollarofadvertisingexpendituresgeneratesanotherdollarofsales?Whatisthecorrectruleforthemarginaladvertisingdollar?

Ifthefirmincreasesadvertisingexpenditurestothepointthatthelastdollarofadvertisinggeneratesanotherdollarofsales,itwillnotbemaximizingprofits,becausethefirmisignoringadditionaladvertisingcosts.Thecorrectruleistoadvertisesothatthemarginalrevenueofanadditionaldollarofadvertisingequalstheadditionaldollarsspentonadvertisingplusthemarginalproductioncostoftheincreasedsales.

14.Howcanafirmcheckthatitsadvertising-to-salesratioisnottoohighortoolow?Whatinformationwoulditneed?

Thefirmcancheckwhetheritsadvertising-to-salesratioisprofitmaximizingbycomparingitwiththenegativeoftheratiooftheadvertisingelasticityofdemandtothepriceelasticityofdemand.Thefirmmustknowboththeadvertisingelasticityofdemandandthepriceelasticityofdemand.

EXERCISES

1.Pricediscriminationrequirestheabilitytosortcustomersandtheabilitytopreventarbitrage.Explainhowthefollowingcanfunctionaspricediscriminationschemesanddiscussbothsortingandarbitrage:

a. requiringairlinetravelerstospendatleastoneSaturdaynightawayfromhometoqualifyforalowfare.

TherequirementofstayingoverSaturdaynightseparatesbusinesstravelers,whoprefertoreturnfortheweekend,fromtourists,whotravelontheweekend.Arbitrageisnotpossiblewhentheticketspecifiesthenameofthetraveler.

b. insistingondeliveringcementtobuyers,andbasingpricesonbuyers’locations.

Bybasingpricesonthebuyer’slocation,customersaresortedbygeography.Pricesmaythenincludetransportationcharges.Thesecostsvaryfromcustomertocustomer.Thecustomerpaysforthesetransportationchargeswhetherdeliveryisreceivedatthebuyer’slocationoratthecementplant.Sincecementisheavyandbulky,transportationchargesmaybelarge.Thispricingstrategyleadsto“based-point-pricesystems,”whereallcementproducersusethesamebasepointandcalculatetransportationchargesfromthisbasepoint.Individualcustomersarethenquotedthesameprice.Forexample,inFTCv.CementInstitute,333U.S.683[1948],theCourtfoundthatsealedbidsbyelevencompaniesfora6,000-barrelgovernmentorderin1936allquoted$3.286854perbarrel.

c. sellingfoodprocessorsalongwithcouponsthatcanbesenttothemanufacturertoobtaina$10rebate.

Rebatecouponswithfoodprocessorsseparateconsumersintotwogroups:(1)customerswhoarelesspricesensitive,i.e.,thosewhohavealowerelasticityofdemandanddonotrequesttherebate;and(2)customerswhoaremorepricesensitive,i.e.,thosewhohaveahigherdemandelasticityanddorequesttherebate.Thelattergroupcouldbuythefoodprocessors,sendintherebatecoupons,andreselltheprocessorsatapricejustbelowtheretailpricewithouttherebate.Topreventthistypeofarbitrage,sellerscouldlimitthenumberofrebatesperhousehold.

d. offeringtemporarypricecutsonbathroomtissue.

Atemporarypricecutonbathroomtissueisaformofintertemporalpricediscrimination.Duringthepricecut,price-sensitiveconsumersbuygreaterquantitiesoftissuethantheywouldotherwise.Non-price-sensitiveconsumersbuythesameamountoftissuethattheywouldbuywithoutthepricecut.Arbitrageispossible,buttheprofitsonresellingbathroomtissueprobablycannotcompensateforthecostofstorage,transportation,andresale.

e. charginghigh-incomepatientsmorethanlow-incomepatientsforplasticsurgery.

Theplasticsurgeonmightnotbeabletoseparatehigh-incomepatientsfromlow-incomepatients,butheorshecanguess.Onestrategyistoquoteahighpriceinitially,observethepatient’sreaction,andthennegotiatethefinalprice.Manymedicalinsurancepoliciesdonotcoverelectiveplasticsurgery.Sinceplasticsurgerycannotbetransferredfromlow-incomepatientstohigh-incomepatients,arbitragedoesnotpresentaproblem.

2.Ifthedemandfordrive-inmoviesismoreelasticforcouplesthanforsingleindividuals,itwillbeoptimalfortheaterstochargeoneadmissionfeeforthedriverofthecarandanextrafeeforpassengers.TrueorFalse?Explain.

True.Approachthisquestionasatwo-parttariffproblemwheretheentryfeeisachargeforthecarplusthedriverandtheusagefeeisachargeforeachadditionalpassengerotherthanthedriver.Assumethatthemarginalcostofshowingthemovieiszero,i.e.,allcostsarefixedanddonotvarywiththenumberofcars.Thetheatershouldsetitsentryfeetocapturetheconsumersurplusofthedriver,asingleviewer,andshouldchargeapositivepriceforeachpassenger.

3.InExample11.1wesawhowproducersofprocessedfoodsandrelatedconsumergoodsusecouponsasameansofpricediscrimination.AlthoughcouponsarewidelyusedintheUnitedStates,thatisnotthecaseinothercountries.InGermany,theuseofcouponsisprohibitedbylaw.

a.DoesprohibitingtheuseofcouponsinGermanymakeGermanconsumersbetterofforworseoff?

Ingeneral,wecannottellwhetherconsumerswillbebetterofforworseoff.Totalconsumersurpluscanincreaseordecreasewithpricediscrimination,dependingonthenumberofdifferentpriceschargedandthedistributionofconsumerdemand.Note,forexample,thattheuseofcouponscanincreasethemarketsizeandthereforeincreasethetotalsurplusofthemarket.Dependingontherelativedemandcurvesoftheconsumergroupsandtheproducer’smarginalcostcurve,theincreaseintotalsurpluscanbebigenoughtoincreasebothproducersurplusandconsumersurplus.ConsiderthesimpleexampledepictedinFigure11.3.a:

Figure11.3.a

Inthiscasetherearetwoconsumergroupswithtwodifferentdemandcurves.Assumingmarginalcostiszero,withoutpricediscrimination,consumergroup2isleftoutofthemarketandthushasnoconsumersurplus.Withpricediscrimination,consumer2isincludedinthemarketandcollectssomeconsumersurplus.Atthesametime,consumer1paysthesamepriceunderdiscriminationinthisexample,andthereforeenjoysthesameconsumersurplus.Theuseofcoupons(pricediscrimination)thusincreasestotalconsumersurplusinthisexample.

Furthermore,althoughthenetchangeinconsumersurplusisambiguousingeneral,thereisatransferofconsumersurplusfromprice-insensitivetoprice-sensitiveconsumers.Thus,price-sensitiveconsumerswillbenefitfromcoupons,eventhoughonnetconsumersasawholecanbeworseoff.

b.DoesprohibitingtheuseofcouponsmakeGermanproducersbetterofforworseoff?

ProhibitingtheuseofcouponswillmaketheGermanproducersworseoff,oratleastnotbetteroff.Iffirmscansuccessfullypricediscriminate(i.e.theycanpreventresale,therearebarrierstoentry,etc.),pricediscriminationcannevermakeafirmworseoff.

4.SupposethatBMWcanproduceanyquantityofcarsataconstantmarginalcostequalto$15,000andafixedcostof$20million.YouareaskedtoadvisetheCEOastowhatpricesandquantitiesBMWshouldsetforsalesinEuropeandintheU.S.ThedemandforBMWsineachmarketisgivenby:

QE=18,000-400PEandQU=5500-100PU

wherethesubscriptEdenotesEurope,thesubscriptUdenotestheUnitedStates,andallpricesandcostsareinthousandsofdollars.AssumethatBMWcanrestrictU.S.salestoauthorizedBMWdealersonly.

a. WhatquantityofBMWsshouldthefirmsellineachmarketandwhatwillthepricebeineachmarket?Whatisthetotalprofit?

Withseparatemarkets,BMWchoosestheappropriatelevelsofQEandQUtomaximizeprofits,whereprofitsare:

.

SolveforPEandPUusingthedemandequations,andsubstitutetheexpressionsintotheprofitequation:

.

Differentiatingandsettingeachderivativetozerotodeterminetheprofit-maximizingquantities:

and

SubstitutingQEandQUintotheirrespectivedemandequations,wemaydeterminethepriceofcarsineachmarket:

6,000=18,000-400PE,orPE=$30,000and

2,000=5,500-100PU,orPU=$35,000.

SubstitutingthevaluesforQE,QU,PE,andPUintotheprofitequation,wehave

={(6,000)(30)+(2,000)(35)}-{(8,000)(15))+20,000},or

=$110,000,000.

b. IfBMWwereforcedtochargethesamepriceineachmarket,whatwouldbethequantitysoldineachmarket,theequilibriumprice,andthecompany’sprofit?

IfBMWchargedthesamepriceinbothmarkets,wesubstituteQ=QE+QUintothedemandequationandwritethenewdemandcurveas

Q=23,500-500P,orininverseforas.

Sincethemarginalrevenuecurvehastwicetheslopeofthedemandcurve:

.

Tofindtheprofit-maximizingquantity,setmarginalrevenueequaltomarginalcost:

,orQ*=8,000.

SubstitutingQ*intothedemandequationtodetermineprice:

SubstitutingintothedemandequationsfortheEuropeanandAmericanmarketstofindthequantitysold

QE=18,000-(400)(31),orQE=5,600and

QU=5,500-(100)(31),orQU=2,400.

SubstitutingthevaluesforQE,QU,andPintotheprofitequation,wefind

={(5,600)(31)+(2,400)(31)}-{(8,000)(15))+20,000},or

=$108,000,000.

5.Amonopolistisdecidinghowtoallocateoutputbetweentwomarkets.Thetwomarketsareseparatedgeographically(EastCoastandMidwest).Demandandmarginalrevenueforthetwomarketsare:

P1=15-Q1 MR1=15-2Q1

P2=25-2Q2 MR2=25-4Q2.

Themonopolist’stotalcostisC=5+3(Q1+Q2).Whatareprice,output,profits,marginalrevenues,anddeadweightloss(i)ifthemonopolistcanpricediscriminate?(ii)ifthelawprohibitschargingdifferentpricesinthetworegions?

Withpricediscrimination,themonopolistchoosesquantitiesineachmarketsuchthatthemarginalrevenueineachmarketisequaltomarginalcost.Themarginalcostisequalto3(theslopeofthetotalcostcurve).

Inthefirstmarket

15-2Q1=3,orQ1=6.

Inthesecondmarket

25-4Q2=3,orQ2=5.5.

Substitutingintotherespectivedemandequations,wefindthefollowingpricesforthetwomarkets:

P1=15-6=$9and

P2=25-2(5.5)=$14.

Notingthatthetotalquantityproducedis11.5,then

=((6)(9)+(5.5)(14))-(5+(3)(11.5))=$91.5.

Themonopolydeadweightlossingeneralisequalto

DWL=(0.5)(QM-QC)(PC-PM).

Here,

DWL1=(0.5)(12-6)(9-3)=$18and

DWL2=(0.5)(11-5.5)(14-3)=$30.25.

Therefore,thetotaldeadweightlossis$48.25.

Withoutpricediscrimination,themonopolistmustchargeasinglepricefortheentiremarket.Tomaximizeprofit,wefindquantitysuchthatmarginalrevenueisequaltomarginalcost.Addingdemandequations,wefindthatthetotaldemandcurvehasakinkatQ=5:

Thisimpliesmarginalrevenueequationsof

Withmarginalcostequalto3,MR=18.33-1.33Qisrelevantherebecausethemarginalrevenuecurve“kinks”whenP=$15.Todeterminetheprofit-maximizingquantity,equatemarginalrevenueandmarginalcost:

18.33-1.3