产业组织理论课后习题答案

Instructor’sManualforIndustrialOrganizationTheoryandApplicationsbyOzShyTheMITPressCambridge,MassachusettsLondon,EnglandCopyrightc�1995–2004OzShy.Allrightsreserved.ThemanualwastypesetbytheauthorusingtheLATEX2εdocumentpreparationsoftwarebyLeslieLamport(aspecialversionofDonaldKnuth’sTEXprogram)duringthemonthsfromSeptember1995toNovember1995whileIwasvisitingtheEconomicsDepartmentoftheUniversityofMichigan.Allthe�guresarealsodrawninLATEXusingsoftwarecalledTEXcaddevelopedbyGeorgHorn,whichcanbedownloadedfromvariousmainframes.Version1.0[Draft20],(1995):Preparedforthe�rstprintingofthe�rsteditionbkman21.tex�rstdrafttobepostedontheWeb(2000/07/07)(paralleltothe5thPrintingofthebook)v.24(2004/04/14):6.1.d,6.1.eThisversion:bkman24.tex2004/04/1417:36ContentsTotheInstructorv2BasicConceptsinNoncooperativeGameTheory13Technology,ProductionCost,andDemand74PerfectCompetition95TheMonopoly116MarketsforHomogeneousProducts177MarketsforDi�erentiatedProducts258Concentration,Mergers,andEntryBarriers299ResearchandDevelopment3310TheEconomicsofCompatibilityandStandards3511Advertising3712Quality,Durability,andWarranties3913PricingTactics:Two-PartTari�andPeak-LoadPricing4314MarketingTactics:Bundling,Upgrading,andDealerships4515Management,Compensation,andRegulation4916PriceDispersionandSearchTheory5117MiscellaneousIndustries53TotheInstructorBeforeplanningthecourse,IurgetheinstructortoreadcarefullythePrefaceofthebookthatsuggestsdi�erentwaysoforganizingcoursesfordi�erentlevelsofstudentsandalsoprovidesalistofcalculus-freetopics.Thegoalsofthismanualare:•Toprovidetheinstructorwithmysolutionsforalltheproblemslistedattheendofeachchapter;•toconveytotheinstructormyviewsofwhattheimportantconceptsineachtopicare;•tosuggestwhichtopicstochoosefordi�erenttypesofclassesandlevelsofstudents.Finally,pleasealertmetoanyerrorsorincorrectpresentationsthatyoudetectinthebookandinthismanual.(e-mailaddressesaregivenbelow).Notethattheerrata�les(accordingtotheprintingsequence)arepostedontheWebinPDFformat.Beforereportingerrorsandtypos,pleaseviewtheerrata�lestoseewhethertheerroryoufoundwasalreadyidenti�edandcorrected.Haifa,Israel,(April14,2004)E-mail:ozshy@ozshy.comBackup:OzBackup@yahoo.comWeb-page:www.ozshy.comCatalog-page:http://mitpress.mit.edu/book-home.tcl?isbn=0262691795Thisdraft:bkman24.tex2004/04/1417:36Chapter2BasicConceptsinNoncooperativeGameTheoryAninstructorofashortcourseshouldlimitthediscussionofgametheorytothefourmostimportantconceptsinthischapterthatareessentialfortheunderstandingmostoftheanalysespresentedinthisbook:1.Thede�nitionofagame(De�nition2.1):Itisimportantthatthestudentwillunderstandthatagameisnotproperlyde�nedunlessthelistofplayers,theactionsetofeachplayer,andthepayo�functionsareclearlystated.Itisimportantthatthestudentwillunderstandthemeaningofthetermoutcomeasalistofthespeci�cactionschosenbyeachplayer(andnotalistofpayo�sascommonlyassumedbystudents).2.Nashequilibrium(De�nition2.4).3.Welfarecomparisonsamongoutcomes(De�nition2.6).4.Extensiveformgames,strategies(comparewithactions),subgames,andtheSPE(De�-nition2.10).Iurgetheinstructortodiscusstheissuesofexistence,uniqueness,andmultipleequilibriainclass.Moreprecisely,itisimportantthatthestudentwillknowthatinordertoproveexistence,itissu�cientto�ndonlyoneNEoutcome;however,toprovenonexistence,thestudentmustgooveralloutcomesandshowthatatleastoneplayerbene�tsfromunilateraldeviation.Ibelievethattheabovecanbecoveredin2lectures,orinthreehoursofinstruction.Ifyouwishtodevotemoretimetogametheory,youcanintroducetheequilibriumindominantactions(De�nition2.3)beforeteachingtheNEequilibriumconcept.Ifyouwishtoemphasismoregametheory,Iadvisecoveringrepeatedgames(section2.3).AnswerstoExercises1.(a)ItisstraightforwardtoconcludethatR1(a2)=�WARifa2=WARWARifa2=PEACEandR2(a1)=�WARifa1=WARWARifa2=PEACE.Thatis,WARiseachplayer’sbestresponsetoeachactiontakenbytheotherplayer(hence,WARisadominantactionforeachplayer).Now,(ˆa1,ˆa2)=(WAR,WAR)isa(unique)NEsincethisoutcomeisonthebest-responsefunctionofeachplayer.(b)RJ(aR)=�ωifaR=ωφifaR=φandRR(aJ)=�φifaJ=ωωifaJ=φ.TheredoesnotexistaNEforthisgamesincetheredoesnotexistanoutcometheisonbothbest-responsefunctions.Thatis,RJ(ω)=ω,butRR(ω)=φ,butRJ(φ)=φ,butRR(φ)=ω,soRJ(ω)=ω,andsoon.2BasicConceptsinNoncooperativeGameTheory(c)Rα(aβ)=�Bifaβ=LTifaβ=RandRβ(aα)=�Lifaα=TRifaα=B.ANEdoesnotexistforthisgamesinceRα(L)=B,butRβ(B)=R,butRα(R)=T,soRβ(T)=L,andsoon.2.(a)If(T,L)isaNE,thenπα(T,L)=a≥e=πα(B,L),andπβ(T,L)=b≥d=πβ(T,R).(b)If(T,L)isanequilibriumindominantactions,thenThastobeadominantactionforplayerα,thatisπα(T,L)=a≥e=πα(B,L)andπα(T,R)=c≥g=πα(B,R);andLisadominantactionforplayerβ,thatisπβ(T,L)=b≥d=πβ(T,R),andπβ(B,L)=f≥h=πβ(T,R).Letusobservethattheparameterrestrictionsgiveninpart(a)arealsoincludedinpart(b)con�rmingProposition2.1whichstatesthatanequilibriumindominantactionsisalsoaNE.(c)i.(T,L)Paretodominates(T,R)if(a≥candb>d)or(a>candb≥d);ii.(T,L)Paretodominates(B,R)if(a≥gandb>h)or(a>gandb≥h);iii.(T,L)Paretodominates(B,L)if(a≥eandb>f)or(a>eandb≥f).(d)Looselyspeaking,theoutcomesareParetononcomparableifoneplayerprefers(T,L)over(B,R),whereastheotherplayerprefers(B,R)overtheoutcome(T,L).For-mally,eitherπα(T,L)=a>g=πα(B,R)butπβ(T,L)=b<h=πβ(B,R),orπα(T,L)=a<g=πα(B,R)butπβ(T,L)=b>h=πβ(B,R).3.(a)TherearethreeParetooptimaloutcomes:i.(n1,n2)=(100,100),whereπ1(100,100)=π2(100,100)=100;ii.(n1,n2)=(100,99),whereπ1(100,99)=98andπ2(100,99)=101;iii.(n1,n2)=(99,100),whereπ1(99,100)=101andπ2(99,100)=98;(b)ThereisnoNEforthisgame.1Toprovethis,wehavetoshowthatforeveryoutcome(n1,n2),oneoftheplayerswillbene�tfromchanginghisorherdeclaredvalue.Letuslookatthefollowingoutcomes:1Atypointhequestion(�rstprinting)leadstothisundesirableresult(seeBasu,K.1994.“TheTraveler’sDilemma:ParadoxesofRationalityinGameTheory.”AmericanEconomicReview84:391–395;foramechanismthatgenerates(2,2)asauniqueNEoutcome).BasicConceptsinNoncooperativeGameTheory3i.If(n1,n2)=(100,100),thenplayer1canincreasehisorherpayo�toπ1=101bydeclaringn1=99.ii.If(n1,n2)=(99,100),thenplayer2canincreasehisorherpayo�fromπ2=98toπ2=99bydeclaringn2=99.Hence,playersalwaysbene�tfromdeclaringavalueofonedollarlowerthantheotherplayer,andsoon.iii.If(n1,n2)=(2,2),thenplayer1canincreasehisorherpayo�fromπ1=2toπ1=98bydeclaringn1=100.4.(a)ThereareseveralNEoutcomesforthisgame.Forexample,(LG,SM,SM)isaNEoutcomesinceπC(LG,SM,SM)=α≥γ=πC(SM,SM,SM)πF(LG,SM,SM)=β=β=πF(LG,LG,SM)πG(LG,SM,SM)=β=β=πG(LG,SM,LG).Hence,no�rm�ndsitpro�tabletounilaterallychangethetypeofcarsitproduces.(b)Again,thereareseveralNE.Theoutcome(LG,SM,SM)isalsoaNEforthisgame,andtheproofisidenticaltotheonegiveninpart(a).5.(a)Therearethreesubgames:thegameitself,andtwopropersubgameslabeledJL(forJacobleft)andJR(forJacobright).ThethreesubgamesareillustratedinSolution-Figure2.1.•◦•φωωφφωRachelJacobπR=2πJ=1πR=0πJ=0πR=0πJ=0πR=1πJ=2•ωφπR=0πJ=0πR=1πJ=2•φωπR=2πJ=1πR=0πJ=0JLJRSolution-Figure2.1:ThreesubgamesofthedynamicBattleoftheSexes(b)Oneeasywayto�ndNEoutcomesforanextensiveformgameistoconstructanormal-formrepresentation.2However,thenormal-formrepresentationisalreadygiveninTable2.2.Also,equation(2.1)provesthattheNEoutcomesinvolvethetwoplayersgoingtogethereithertofootballortotheopera.Formally,itiseasytoverifythatthefollowingthreeoutcomesconstituteNE:sJ=�φifsR=ωφifsR=φandsR=φ,2Thissubquestionmayconfusestudentswhoarealreadythinkingintermsofbackwardinduction.SinceouranalysisisbasedonSPEyoumaywanttoavoidassigningthissubquestion(only).Also,aninstructorteachingfromthe�rstprintingisurgedtochangethissubquestionto�ndingtheNEfortheentiregameonly;hence,topostpone�ndingtheNEforthesubgamestothenextsubquestion,wheretheNEofthesubgamesareusedto�ndtheSPE.4BasicConceptsinNoncooperativeGameTheorysJ=�ωifsR=ωωifsR=φandsR=ω,sJ=�ωifsR=ωφifsR=φandsR=φ.(2.1)(c)Usingbackwardinduction,we�rstconstructJacob’sstrategy(whichconstitutestheNashequilibriaforthetwopropersubgames).LookingatthepropersubgamesinSolution-Figure2.1,weconcludethatRJ(aR)=�ωifaR=ω(subgameJR)φifaR=φ(subgameJL).Now,welookforRachel’sstrategy(givenJacob’sbestresponse).IfRachelplaysaR=ω,thenherutilityisgivenbyπR(ω,RJ(ω))=1.Incontrast,ifRachelplaysaR=φ,thenherutilityisgivenbyπR(φ,RJ(φ))=2>1.Altogether,thestrategiessR=aR=φandRJ(aR)=�ωifaR=ωφifaR=φconstituteauniqueSPE.(d)No!Jacob’sbestresponseistoplayφwheneverRachelplaysφ.Thus,Jacob’sannouncementconstitutesanincrediblethreat.3Clearly,Rachel,whoknowsJacob’sbest-responsefunctioninthesecondstage,shouldignoreJacob’sannouncement,sinceJacob,himself,wouldignoreitifRachelplaysφinthe�rststage.6.(a)Jacob’sexpectedpayo�isgivenby:EπJ(θ,ρ)=θρ×2+θ(1−ρ)×0+(1−θ)ρ×0+(1−θ)(1−ρ)×1=2+3θρ−ρ−θ.Rachel’sexpectedpayo�isgivenby:EπR(θ,ρ)=θρ×1+θ(1−ρ)×0+(1−θ)ρ×0+(1−θ)(1−ρ)×2=2+3θρ−2ρ−2θ.(b)Theplayers’best-responsefunctionsaregivenbyRJ(ρ)=�����0ifρ<1/3[0,1]ifρ=1/31ifλ>1/3andRR(θ)=�����0ifθ<2/3[0,1]ifθ=2/31ifθ>2/3.Theplayers’best-responsefunctionsaredrawninSolution-Figure2.2.(c)Solution-Figure2.2demonstratesthat(θ,ρ)=(2/3,1/3)isaNEinmixedactions.Also,notethattheoutcomes(0,0)and(1,1)arealsoNEoutcomesinmixedactionsandarethesameasthepureNEoutcomes.3Instructors:Hereisagoodopportunitytodiscusstheconceptsofcredibleandincrediblethreats.BasicConceptsinNoncooperativeGameTheory5✻✲ρθ✻✲θρ✻✲ρθ11111113RR(θ)RJ(ρ)RR(θ)RJ(ρ)•232313••Solution-Figure2.2:Best-responsefunctionsfortheBattleoftheSexesinmixedactions(d)Substituting(θ,ρ)=(2/3,1/3)intotheplayers’payo�functions(de�nedabove)yieldEπJ(2/3,1/3)=EπR(2/3,1/3)=23.(e)Thebest-responsefunctionsinSolution-Figure2.2intersectthreetimes,meaningthatinthemixedextensiongame,therearetwoequilibria:thetwopureNEoutcomesandoneNEinmixedactions.Incontrast,Figure2.3hasonlyoneintersectionsinceinthatgameNEinpurestrategiesdoesnotexist,andthereforethebest-responsefunctionsintersectonlyonce,attheNEinmixedactions.Chapter3Technology,ProductionCost,andDemandThischaptersummarizesthebasicmicroeconomictoolsthestudentsneedtoknowpriortotakingthisclass.Myadvicefortheinstructorisnottospendtimeonthischapterbutsimplyassignthischapter(withorwithouttheexercises)asreadinginthe�rstclass.However,myadviceistoreturn(orrefer)tothischapterwheneverde�nitionsareneeded.Forexample,whenyou�rstencounteradiscussionofreturnstoscale,Iurgeyoutomakeaformalde�nitionandreferthestudentstoDe�nition3.2.Similarly,whenaddressingelasticityissues,studentsshouldbereferredtoDe�nition3.3.AnswerstoExercises1.(a)Letλ>1.Then,byDe�nition3.2,thetechnologyexhibitsIRSif(λl)α(λk)β=λα+βlαkβ>λlαkβ,whichholdswhenα+β>1.UsingthesameprocedureandDe�nition3.2,thistechnologyexhibitCRSifα+β=1,andDRSifα+β<1.(b)Inthistechnology,thefactorsaresupportingsinceMPL(l,k)≡∂Q∂l=αlα−1kβ,hence,∂MPL(l,k)∂k=αβlα−1kβ−1,whichisgreaterthanzeroundertheassumptionthatα,β>0.2.(a)Letλ>1.Then,byDe�nition3.2,thetechnologyexhibitsIRSif(λl)α+(λk)α=λα(lα+kα)>λ(lα+kα),whichholdsifα>1.Similarly,thetechnologyexhibitsDRSifα<1,andCRSifα=1.(b)MPL(l,k)=αlα−1.Hence,∂MPL(l,k)/∂k=0.Therefore,thefactorsareneithersubstitutesnorcomplements.3.Letλ>1.This(quasi-linear)technologyexhibitsDRSsinceλl+√λk<λl+λ√k=λ(l+√k).4.(a)AC(Q)=TC(Q)Q=FQ+c,andMC(Q)=∂TC(Q)∂Q=c.ThesefunctionsaredrawninFigure4.2inthebook.8Technology,ProductionCost,andDemand(b)Clearly,AC(Q)declineswithQ.Hence,AC(Q)isminimizedwhenQ=+∞.(c)Decliningaveragecostfunctionre�ectsanincreasingreturnstoscaletechnology.5.(a)UsingDe�nition3.3,ηp(Q)≡∂Q(p)∂QpQ=(−1)pQ=−99−QQ.Hence,ηp(Q)=−2whenQ=33.(b)Fromtheabove,ηp(Q)=−1whenQ=99/2=49.5.(c)Theinversedemandfunctionisgivenbyp(Q)=99−Q.Therefore,TR(Q)=p(Q)Q=(99−Q)Q.Hence,MR(Q)≡dTR(Q)/dQ=99−2Q,whichisaspecialcaseofFigure3.3.(d)MR(Q)=0whenQ=49.5.Thatis,themarginalrevenueiszeroattheoutputlevelwherethedemandelasticityis−1(unitelasticity).(e)UsingFigure3.5,CS(33)=(99−33)662=2178,andCS(66)=(99−66)332=544.56.(a)p�=AQ.Hence,p=A1�Q−1�.(b)ηp=∂Q(p)∂QpQ=A(−�)p−�−1pQ=A(−�)p−�Ap−�=−�.Thus,theelasticityisconstantinthesensethatitdoesnotvarywiththequantityconsumed.(c)Thedemandiselasticifηp<−1,henceif�>1.Thedemandisinelasticif−1<ηp≤0,henceif0≤�<1.(d)ByProposition3.3,MR=p[1+1/(−�)].Hence,pMR=1�1+1−�=��−1whichisindependentofQ.Chapter4PerfectCompetitionAperfectlycompetitivemarketischaracterizedbynonstrategic�rms,where�rmstakethemarketpriceasgivenanddecidehowmuchtoproduce(and,whethertoenter,iffreeentryisallowed).Moststudentsprobablyhadsomediscussionofperfectlycompetitivemarketsintheirintermediatemicroeconomicsclass.However,giventheimportanceofthismarketstructure,Iurgetheinstructortodevotesometimeinordertomakesurethatthestudentsunderstandwhatprice-takingbehaviormeans.Itisnowtherighttimetoemphasizethat,ineconomics,thetermcompetitivereferstopricetakingbehaviorofagents.Forexample,wegenerallyassumethatourconsumersarecompetitive,whichmeansthattheydonotbargainoverpricesandtakeallpricesandtheirincomeasgiven.Inacompetitivemarketstructure,wemakeasimilarassumptionaboutthe�rms.Youmaywanttoemphasizeanddiscussthefollowingpoints:1.Theassumptionofpricetakingbehaviorhasnothingtodowiththenumberof�rmsintheindustry.Forexample,onecouldsolveforacompetitiveequilibriumeveninthepresenceofone�rm(seeanexerciseattheendofthischapter).Notethatthisconfusionoftenarisessincecertainmarketstructuresyieldmarketallocationssimilartothecompetitiveallocationwhenthenumberof�rmsincreases(seeforexamplesubsection6.1.2whichshowsthattheCournotallocationmayconvergetothecompetitiveallocationwhenthenumberof�rmsincreasestoin�nity).2.Amajorreasonforstudyingandusingalternative(noncompetitive)marketstructuresstemsfromthefactthatthecompetitivemarketstructureveryoften“fails”toexplainwhyconcentratedindustriesareobserved.3.Anothermajorreasonforstudyingalternativemarketstructuresstemsfromthenonexis-tenceofacompetitiveequilibriumwhen�rms’technologiesexhibitIRS.Finally,notethatthischapterdoesnotsolveforacompetitiveequilibriumunderdecreasingreturnstoscaletechnologiesfortworeasons:(i)othermarketstructuresanalyzedinthisbookarealsodevelopedmainlyforCRS(unitcost)technologies,and(ii)moststudentsarefamiliarwiththeDRSfromtheirintermediatemicroeconomicsclass.However,theexerciseattheendofthischapterdealswithaDRStechnology.AnswerstoExercises1.Firm1takespasgivenandchoosesq1tomaxq1π1=pq1−wL1=p�L1−wL1.10PerfectCompetitionThe�rstandsecondorderconditionsaregivenby0=dπ1dL1=p2√L1−w,d2π1d(L1)2=−p4L3/21<0.Hence,q1=√L1=p/(2w).2.Giventhatthereisonlyone�rm,thesupplyequalsdemandequilibriumconditionyieldsthat120−pe=pe/2.Therefore,pe=80;hence,qe1=Qe=pe/2=40.3.Fromtheproductionfunction,wecan�ndtheequilibriumemploymentleveltobeLe1=(qe1)2=1600.Hence,π1=peqe1−wLe1=80×40−1600=1600.4.Giventhatthe�rmshavethesametechnologies,theyhavethesamesupplyfunctions.Therefore,thesupplyequalsdemandconditionbecomes120−pe=pe/2+pe/2,whichyieldspe=60,Qe=120−60=60,hence,qe1=qe2=30.5.Clearly,thecompetitivepriceislowerandtheaggregateproductionishigherwhentheindustryconsistsoftwo�rms.6.✲✻pp=2q1q1✲✻pp=2q2q2✲✻pp=q1+q2Q=q1+q230306060•••120120p=120−QSolution-Figure4.1:Competitiveequilibriumwithtwo�rmsChapter5TheMonopolyMoststudentsencounterthemonopolyproblemintheirintermediatemicroeconomicsclass.However,theinstructorwouldprobablywanttomakesurethatallstudentsfullyunderstandthemonopoly’schoiceproblemandthee�ectofpriceelasticityonthemonopoly’sprice,aswellastheargumentsagainstmonopoly(section5.2).Ialsourgetheinstructornottoskipdiscussingdiscriminatingmonopoly(section5.3).Theremainingsections,thecartel(section5.4),andthedurablegoodsmonopolies(sec-tion5.5)aremoreoptionaldependingontheinstructor’stastesandstudents’ability.AnswerstoExercises1.(a)ηp≡dQdppQ=a�p−�−1pap−�=−�.Hence,theexponentialdemandfunctionhasaconstantpriceelasticity.ByPropo-sition3.3,MR(Q)=p�1+1−��=p��−1��.(b)Equatingmarginalrevenuetomarginalcostyields1MR=pM��−1��=c=MC;hence,pM=�c�−1.(c)As�increases,thedemandbecomesmoreelastic,hence,themonopolypricemustfall.Formally,dpMd�=c(�−1)−�c(�−1)2<0.(d)The�rstedition(�rstprinting)containsatypo.Thequestionaskswhathappenstothemonopoly’spricewhen�→+1.Clearly,pM→+∞.Thereasonis,thatwhen�=1,the(entire)demandhasaunitelasticity,implyingthatrevenuedoesnotvarywithprice(orquantityproduced).Hence,giventhattherevenueisconstant(infactTR=awhen�=1),thenthepro�tmaximizationproblemisreducedtocostminimizationwhichyieldsthatthemonopolywould“attempt”toproduceaslittleaspossible(butstillastrictlypositiveamount).1Theinstructormaywanttoemphasizetothestudentsthatinthecaseofconstant-elasticitydemandfunctions(exponentialdemandfunctions)itiseasiertosolveforthemonopoly’sprice�rst(usingProposition3.3)andthensolveforthequantityproducedbysubstitutingthepriceintothedemandfunction.Thisprocedurebecomesveryhandywhensolvingmonopolisticcompetitionequilibriaanalyzedinsection7.2.12TheMonopoly(e)Invertingthedemandfunctionyieldsp(Q)=a1/�Q−1/�.Thus,TR(Q)≡p(Q)Q=a1�Q1−1�.Hence,MR(Q)≡dTR(Q)dQ=a1�Q−1��1−1��.(f)Equatingmarginalrevenuetomarginalcostyieldsa1�Q−1��1−1��=c,yieldingthatthemonopoly’spro�tmaximizingoutputisQM=a��−1�c��.NotethatthesameresultisachievedbysubstitutingpM(calculatedbefore)intothedemandfunction.2.(a)Solution-Figure5.1illustratesanaggregatedemandcomposedofthetwogroupsofconsumers,whereeachgroupsharesacommonvaluationfortheproduct.✲QpVHVLnHnH+nL✻Solution-Figure5.1:Aggregatedemandcomposedoftwoconsumergroups(b)Themonopolyhastwooptions2:settingahighprice,p=VH,oralowprice,p=VL.Solution-Figure5.1revealsthatthepro�tlevels(revenuesinceproductioniscostless3)aregivenbyπ|p=VH=nHVH,andπ|p=VL=(nH+nL)VL.Comparingthetwopro�tlevelsyieldsthemonopoly’spro�tmaximizingprice.Hence,pM=�VHifVH>(nH+nL)VL/nHVLotherwise.2Instructorsareurgedtoassignordiscussthisexercise,sinceitprovidesagoodopportunitytointroducethestudenttoadiscrete(logicbased)analysiswhichisusedlaterinawidevarietyoftopics(seeforexamplethesectionontying[section14.1]).3The�rstprintingofthe�rsteditionneglectstoassumethatproductionofG-Jeansiscostless.TheMonopoly13Thus,themonopolysetsahighpriceifeithertherearemanyhighvaluationcon-sumers(nHislarge)and/ortheseconsumersarewillingtopayaveryhighprice(VHishigh).3.(a)Inmarket1,p1=2−q1.Hence,byProp