EXTERNALITIESANDPUBLICGOODS
TEACHINGNOTES
Thischapterdiscussestheremainingtypesofmarketfailurewhichwereintroducedatthe CHAPTER18 endofChapter16,andwhichwerenotcoveredinChapter17. Section18.1definestheconceptof externalities,bothpositiveandnegative.Section18.2discussesmethodsofcorrectingforthemarket failure that arisesinthepresence ofexternalities. Thesetwosections giveagood selfcontained overviewofexternalitiesasatypeofmarketfailure.Thenexttwosections,18.3and18.4,explorethe relationshipbetweentheexistenceofexternalitiesandpropertyrights.Section18.5discussespublic goodsandsection18.6offersabriefdiscussionofdeterminingtheoptimallevelofthepublicgoodto provide.Overallthechapterprovidesagoodsolidoverviewofsomeveryinterestingproblems.Any instructorwhohadthetimeanddesiretoexpanduponthepresentationinthechaptercouldfinda wealthofinformationbyconsultinganenvironmentalorresourceeconomicstextbook.Therearean abundanceofexamplesrelatedtopollutionornaturalresourceissuesthatyoucouldchoosetotalk about.Checkyourlocalnewspaperforideas. Theconsumptionofmanygoodsinvolvesthecreationofexternalities.Stressthedivergence between social and private costs, and the difference between the private (industry competitive) equilibriumandthesociallyoptimal(efficient)equilibrium.Youcanusethestudentsknowledgeof consumerandproducersurplustoexplorethewelfaregainofmovingtotheefficientequilibrium. Exercise(5)presentstheclassicbeekeeper/appleorchardproblem,originallypopularizedinMeade, ExternalEconomiesandDiseconomiesinaCompetitiveSituation,EconomicJournal(March1952). Empiricalresearchonthisexamplehasshownthatbeekeepersandorchardownershavesolvedmany oftheirproblems:seeCheung,TheFableoftheBees:AnEconomicInvestigation, JournalofLaw andEconomics(April1973). Oneofthemainthemesofthelawandeconomicsliteraturesince1969istheapplicationof Coases insight on the assignment of property rights. The original article is clear and can be understoodbystudents. Stresstheproblemsposedbytransactionscosts. Foralivelydebate,ask students whether nonsmokers should begranted the right to smokeless air inpublic places (see Exercise (4)). For an extended discussion of the Coase Theorem at the undergraduate level, see Polinsky,Chapters36,AnIntroductiontoLaw&Economics(Little,Brown&Co.,1983). Thelasttwosectionsfocusonpublicgoodsandprivatechoice.Pointoutthesimilaritiesand differences between public goods and other activities with externalities. Since students confuse nonrivalandnonexclusivegoods,createatablesimilartothefollowingandgiveexamplestofillinthe cells: Exclusive Rival Nonrival MostGoods Congestion Nonexclusive AirandWater PublicGoods
Chapter18:ExternalitiesandPublicGoods
Thenextstumblingblockforstudentsisachievinganunderstandingofwhyweaddindividual demand curves vertically rather than horizontally. Stress that by summing horizontally you are asking the total quantity supplied/demanded at any given price. By summing vertically you are askingthetotalwillingnesstopayforagivenquantity. Thepresentationofpublicchoiceisalimitedintroductiontothesubject,butyoucaneasily expandonthismaterial.Alogicalextensionofthischapterisanintroductiontocostbenefitanalysis. For applications of this analysis, see Part III, Empirical Analysis of Policies and Programs, in HavemanandMargolis(eds.),PublicExpenditureandPolicyAnalysis(HoughtonMifflin,1983).
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Chapter18:ExternalitiesandPublicGoods
QUESTIONSFORREVIEW
1. Which of the following describes an externality and which does not? Explain the difference. a. ApolicyofrestrictedcoffeeexportsinBrazilcausestheU.S.priceofcoffeetorise, whichinturnalsocausesthepriceofteatorise. Externalitiescausemarketinefficienciesbecausethepriceofthegooddoesnotreflect thetruesocialvalueofthegood.ApolicyofrestrictingcoffeeexportsinBrazilcauses theU.S.priceofcoffeetorise,becausesupplyisreduced.Asthepriceofcoffeerises, consumersswitchtotea,therebyincreasingthedemandfortea,andhence,increasing thepriceoftea.Thesearemarketeffects,notexternalities. b. Anadvertisingblimpdistractsamotoristwhothenhitsatelephonepole. Anadvertisingblimpisproducinginformationbyannouncingtheavailabilityofsome goodorservice.However,itsmethodofsupplyingthisinformationcanbedistracting for some consumers, especially those consumers who happen to be driving near telephone poles. The blimp is creating a negative externality that influences the driverssafety. Sincethepricechargedbytheadvertisingfirmdoesnotincorporate theexternalityofdistractingdrivers,toomuchofthistypeofadvertisingisproduced fromthepointofviewofsocietyasawhole. 2. Compare and contrast the following three mechanisms for treating pollution externalitieswhenthecostsandbenefitsofabatementareuncertain:(a)anemissionsfee, (b)anemissionsstandard,and(c)asystemoftransferableemissionspermits. Sincepollutioncreatesanexternalcostthatisnotreflectedinthemarginalcostof production, its emission creates an externality. Three policy tools can be used to reduce pollution: an emissions fee, an emissions standard, and a system of transferablepermits. Thechoicebetweenafeeandastandardwilldependonthe marginal cost and marginal benefit of reducing pollution. If small changes in abatement yield large benefits while adding little tocost, the cost of not reducing emissionsishigh. Thus,standardsshouldbeused. However,ifsmallchangesin abatement yield little benefit while adding greatly to cost, the cost of reducing emissionsishigh.Thus,feesshouldbeused. A system of transferable emissions permits combines the features of fees and standardstoreducepollution.Underthissystem,astandardissetandfeesareused to transfer permits to the firm that values them the most (i.e., a firm with high abatementcosts). However,thetotalnumberofpermitscanbeincorrectlychosen. Toofewpermitswillcreateexcessdemand,increasingpriceandinefficientlydiverting resourcestoownersofthepermits. Typically,pollutioncontrolagenciesimplement oneofthreemechanisms,measuretheresults,reassessthesuccessoftheirchoice, thenresetnewlevelsoffeesorstandardsorselectanewpolicytool. 3. When doexternalitiesrequiregovernment intervention? When issuchintervention unlikelytobenecessary? Economic efficiency can be achieved without government intervention when the externality affects a small number of people and when property rights are well specified.Whenthenumberofpartiesissmall,thecostofnegotiatinganagreement among thepartiesissmall. Further, theamountofrequiredinformation(i.e.,the costs of and benefits to each party) is small. When property rights are not well specified, uncertainty regarding costs and benefits increases and efficient choices might not be made. The costs of coming to an agreement, including the cost of delaying such an agreement, could be greater than the cost of government intervention,includingtheexpectedcostofchoosingthewrongpolicyinstrument.
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Chapter18:ExternalitiesandPublicGoods 4.Consideramarketinwhichafirmhasmonopolypower.Supposeinadditionthatthe firmproducesunderthepresenceof(i)apositiveor(ii)anegativeexternality.Doesthe externalitynecessarilyleadtoagreatermisallocationofresources? Inthepresenceofanegativeexternalitythemarketwillproducetoomuchoutput, ascomparedtothesociallyoptimalsolution.Themonopolistwillhoweverproduce toolittleoutput.Itispossiblethereforethatthemonopolistbyhimselfwillproduce closertothesociallyoptimalsolutionthanthecompetitivefirmswould.Forthecase ofthepositiveexternalitythecompetitivefirmswillproducetoolittleoutput,the monopolist will produce even less, and the monopolist is therefore leading to a greatermisallocationofresources. 5. Externalities arise solely because individuals are unaware of the consequences of theiractions.Agreeordisagree?Explain. Thisisnotatruestatement.Itisnotthatpeopleareunawarebutthattheyarenot forcedtoconsiderandaccountforalloftheconsequencesoftheiractions.Ifafirm dumpswasteintoariverthataffectsaswimmingareadownstreamitisgenerating anexternalitygivenitisnotforcedtoconsiderthecostitisimposingonusersofthe swimmingarea.Thisistruewhetherthefirmisawareofthesecostsornot. 6. To encourage an industry to produce at the socially optimal level the government shouldimposeaunittaxonoutputthatisequaltothemarginalcostofproduction.True orfalse?Explain. Thisstatementisfalse.Whileataxcanencouragefirmstoproduceatthesocially optimallevel,thetaxshouldbesetequaltothemarginalexternalcostandnotthe marginalprivatecost.Firmswillmaximizeprofitbyproducingatthepointwhere priceisequaltomarginalcost.Whenthereareexternalcostsinvolvedthemarginal cost ofthefirm istoolow from societys point ofview, andasaresult toomuch outputisproduced.Bysettingataxequaltotheadditionalcostnotbeingrealized bythefirm(themarginalexternalcost)thefirmwillbeencouragedtoconsiderall costsandwillreduceoutputbecausethetaxwillincreasetheoverallmarginalcost. 7. GeorgeandStanlivenextdoortoeachother. Georgelikestoplantflowersinhis garden, but every time he does, Stans dog comes over and digs them up. Since it is Stans dog that is causing the damage, if economic efficiency is to be achieved, it is necessarythatStanpaytoputupafencearoundhisyardtokeepthedogin.Agreeor disagree?Explain. Ifthereareleashlawsthenthiswouldbetrue.Stanwouldeitherneedtokeephis dogonaleashorputupafence. Ingeneral,itispossibleforthetwopartiesto bargainandcomeupwithasolutionthatwillbenefitbothofthem.Theycouldfor examplesplitthecostofthefence. EconomicefficiencydoesnotrequirethatStan payforthefence.ItmerelyrequiresthatStanandGeorgenegotiateoverhowbest toaddresstheproblemandcomeupwithasolutionthatwillworkforbothofthem. 8. Anemissionsfeeispaidtothegovernment,whereasaninjurerwhoissuedandheld liablepaysdamagesdirectlytothepartyharmedbyanexternality. Whatdifferencesin thebehaviorofvictimsmightyouexpecttoariseunderthesetwoarrangements? Whenvictimscanreceivethedamagesdirectly,theyaremorelikelytofileaclaim, initiate a suit, and try tooverstate their damages. When victims are not ableto receivethedamagesdirectly,theyarelesslikelytoreportviolationsandarelesslikely tooverstatetheirdamages.Intheory,emissionsfeespaidtothegovernmentrequire thepollutingfirmtopaycompensationforanydamageinflictedandhencetomove towardsthesociallyoptimallevelofproduction. Anindividualwhoisinjuredbya firmspollutingbehaviorisagainlesslikelytofileacomplaintiftheydonotfeelthey candirectlyreceivethecompensation.
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Chapter18:ExternalitiesandPublicGoods 9.Whydoesfreeaccesstoacommonpropertyresourcegenerateaninefficientoutcome? Freeaccesstoaresourcemeansthatthemarginalcosttotheuserislessthanthe socialcostbecauseeachuserhasnoincentivetoconsiderhowhisuseoftheresource willaffect theuseoftheresource byother users. Theuse ofacommonproperty resourcebyapersonorfirmexcludesothersfromusingit. Forexample,theuseof waterbyoneconsumerrestrictsitsusebyanother. Sinceprivatemarginalcostis belowsocialmarginalcost,toomuchoftheresourceisconsumedbytheindividual user, creating aninefficient outcome. Eachindividualusing thecommonproperty resourceconsidersonlyhisownactionsanddoesnotconsiderhowalloftheusers collectivelyareimpactingtheresource. 10. Publicgoodsarebothnonrivalandnonexclusive. Explaineachofthesetermsand showclearlyhowtheydifferfromeachother. Agoodis nonrival if,foranylevelofproduction,themarginalcostofprovidingthe goodtoanadditionalconsumeriszero(althoughtheproductioncostofanadditional unit couldbegreaterthanzero). Agoodis nonexclusive ifitisimpossibleorvery expensivetoexcludeindividualsfromconsumingit. Publicgoodsare nonrival and nonexclusive.Commoditiescanbe(1)exclusiveandrival,(2)exclusiveandnonrival, (3)nonexclusiveandrival,or(4)nonexclusiveandnonrival.Mostofthecommodities discussedinthetexttothispointhavebeenofthefirsttype.Inthischapter,wefocus oncommoditiesofthelasttype. Nonrival refers to the production of a good or service for one more customer. It usuallyinvolvesaproductionprocesswithhighfixedcosts,suchasthecostofbuilding ahighway orlighthouse. (Rememberthatfixedcost depends ontheperiodunder consideration:thecostoflightingthelampatthelighthousecanvaryovertime,but doesnotvarywiththenumberofconsumers.)Nonexclusiverefersto exchange,where the cost of charging consumers is prohibitive. Incurring the cost of identifying consumersandcollectingfromthemwouldresultinlosses.Someeconomistsfocuson thenonexclusionpropertyofpublicgoodsbecauseitisthischaracteristicthatposes themostsignificantproblemsforefficientprovision. 11. Avillageislocatednextto1000acresofprimegrazingland. Thevillagepresently ownsthelandandallowsallresidentstograzecowsfreely.Somemembersofthevillage councilhavesuggestedthatthelandisbeingovergrazed.Isthislikelytobetrue?These same members have also suggested that the village should either require grazers to purchaseanannualpermit,orselloffthelandtothegrazers.Wouldeitherofthesebea goodidea? Itistruethatthecommonlandislikelytobeovergrazedsinceeachindividualwill consider onlytheirownprivatecost and notthetruesocialcost ofgrazing. The social cost ofgrazing islikely tobehigherthananyoneindividualsprivatecost because no one individual has an incentive to take into account how his grazing affectstheopportunitiesofothers.Forexample,oneindividualcoulddecidetograze onlyincertainareasduringcertaintimesoftheyear,whilepreservingotherareas forothertimesoftheyear.However,theindividualwillnotdothisiftheresourceis common property as any other grazer can come along and freely disrupt the preservation system that the individual has set up. Selling annual permits or sellingthelandoutright wouldbeviableoptionstotheovergrazingproblem. By requiringthegrazerstobuyapermit,theirmarginalcostswillgoupandgrazing should go down. If an individual purchases the land they will then have an incentivetoconsiderallofthecostsassociatedwithusingtheland,andasaresult willuseitinsuchawaythattheresourceispreservedsincetheyalonecaptureallof thebenefitsofpreservingtheresource.
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Chapter18:ExternalitiesandPublicGoods
12. Publictelevisionisfundedinpartbyprivatedonations,eventhoughanyonewitha televisionsetcanwatchforfree. Canyouexplainthisphenomenoninlightofthefree riderproblem? Thefreeriderproblemreferstothedifficultyofexcludingpersonsfromconsuminga nonexclusive commodity. Nonpaying consumers can freeride on commodities providedbypayingcustomers. Publictelevisionisfundedinpartbycontributions. Someviewerscontribute,butmostwatchwithoutpaying,hopingthatsomeoneelse willpaysotheywillnot.Tocombatthisproblemthesestations(1)askconsumersto assesstheirtruewillingnesstopay,then(2)askconsumerstocontributeuptothis amount,and(3)attempttomakeeveryoneelsefeelguiltyforfreeriding. 13.Explainwhythemedianvoteroutcomeneednotbeefficientwhenmajorityrulevoting determinesthelevelofpublicspending. Themedianvoteristhecitizenwiththemiddlepreference:halfthevotingpopulation ismorestronglyinfavoroftheissueandhalfismorestronglyopposedtotheissue. Under majorityrule voting, where each citizens vote is weighted equally, the preferred spending levelonpublicgoodsprovisionofthe medianvoter willwinan election against any other alternative. However, majority rule is not necessarily efficient,becauseitgiveseachcitizenspreferencesequalweight. Foranefficient outcome,wewouldneedasystemthatmeasuresandaggregatesthewillingnessto payofthosecitizensconsumingthepublicgood. Majority ruleisnotthissystem. However,aswehaveseeninpreviouschapters,majorityruleisequitableinthesense thatallcitizensaretreatedequally.Thus,weagainfindatradeoffbetweenequity andefficiency.
EXERCISES
1. Anumberoffirmshavelocatedinthewesternportionofatownaftersinglefamily residencestookuptheeasternportion.Eachfirmproducesthesameproductand,inthe process,emitsnoxiousfumesthatadverselyaffecttheresidentsofthecommunity. a. Whyisthereanexternalitycreatedbythefirms? Noxious fumes created by firms enter the utility function of residents, and the residentshavenocontroloverthequantityofthefumes. Wecanassumethatthe fumesdecreasetheutilityoftheresidents(i.e.,theyareanegativeexternality)and lowerpropertyvalues. b. Doyouthinkthatprivatebargainingcanresolvetheproblem?Explain. Iftheresidentsanticipatedthelocationofthefirms,housingpricesshouldreflectthe disutilityofthefumes;theexternalitywouldhavebeeninternalizedbythehousing market in housing prices. If the noxious fumes were not anticipated, private bargainingcouldresolvetheproblemoftheexternalityonlyiftherearearelatively small number of parties (both firms and families) and property rights are well specified. Privatebargainingwouldrelyoneachfamilyswillingnesstopayforair quality,buttruthfulrevelationmightnotbepossible.Allthiswillbecomplicatedby theadaptabilityoftheproductiontechnologyknowntothefirmsandtheemployment relationsbetweenthefirmsandfamilies. Itisunlikelythatprivatebargainingwill resolvetheproblem. c. Howmightthecommunitydeterminetheefficientlevelofairquality? The community could determine the economically efficient level of air quality by
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Chapter18:ExternalitiesandPublicGoods aggregatingthefamilieswillingnesstopayandequatingitwiththemarginalcostof pollutionreduction.Bothstepsinvolvetheacquisitionoftruthfulinformation. 2.Acomputerprogrammerlobbiesagainstcopyrightingsoftware,arguingthateveryone should benefit from innovative programs written for personal computers and that exposure to a wide variety of computer programs will inspire young programmers to createevenmoreinnovativeprograms.Consideringthemarginalsocialbenefitspossibly gainedbythisproposal,doyouagreewiththisposition? Computersoftwareasinformationisaclassicexampleofapublicgood.Sinceitcan becostlesslycopied,themarginalcostofprovidingsoftwaretoanadditionaluseris nearzero. Therefore,softwareisnonrival. (Thefixedcostsofcreatingsoftwareare high, but the variable costs are low.) Furthermore, it is expensive to exclude consumers from copying and using software because copy protection schemes are availableonlyathighcostorhighinconveniencetousers.Therefore,softwareisalso nonexclusive. As both nonrival and nonexclusive, computer software suffers the problemsofpublicgoodsprovision: thepresence offreeriders makesitdifficult or impossible for markets to provide the efficient level of software. Rather than regulatingthismarketdirectly, thelegalsystemguaranteespropertyrightstothe creatorsofsoftware. Ifcopyrightprotectionwerenotenforced,itislikelythatthe softwaremarketwouldcollapse,orthattherewouldbeasignificantdecreaseinthe quantityofsoftwaredevelopedandsupplied,whichwouldreducethemarginalsocial benefits.Therefore,wedonotagreewiththecomputerprogrammer. 3. Assumethatscientificstudiesprovideyouwiththefollowinginformationconcerning thebenefitsandcostsofsulfurdioxideemissions: Benefitsofabating(reducing)emissions: Costsofabatingemissions: MB=50020A MC=200+5A
whereAisthequantityabatedinmillionsoftonsandthebenefitsandcostsaregivenin dollarsperton. a. Whatisthesociallyefficientlevelofemissionsabatement? Tofindthesociallyefficientlevelofemissionsabatement,setmarginalbenefitequal tomarginalcostandsolveforA: 50020A=200+5A A=12. b. What are the marginal benefit and marginal cost of abatement at the socially PlugA=12intothemarginalbenefitandmarginalcostfunctionstofindthebenefit efficientlevelofabatement? andcost: MB=50020(12)=260 MC=200+5(12)=260. c. Whathappenstonetsocialbenefits(benefitsminuscosts) ifyouabate1million moretonsthantheefficientlevel?1millionfewer? Net social benefits are the area under the marginal benefit curve minus the area underthemarginalcostcurve.Atthesociallyefficientlevelofabatementthisisequal toareaa+b+c+dinFigure18.3.cor 0.5(500200)(12)=1800milliondollars. Ifyouabate1millionmoretonsthenthenetsocialbenefitisareaa+b+c+deor
27
Chapter18:ExternalitiesandPublicGoods 18000.5(265240)(1)=180012.5=1787.5milliondollars. Ifyouabate1millionlesstonsthenthenetsocialbenefitisareaa+bor 0.5(500280)(11)+(280255)(11)+0.5(255200)(11)=1787.5milliondollars. d. Whyisitsociallyefficienttosetmarginalbenefitsequaltomarginalcostsrather thanabatinguntiltotalbenefitsequaltotalcosts? Itissociallyefficienttosetmarginalbenefitequaltomarginalcostratherthantotal benefitequaltototalcostbecausewewanttomaximizenetbenefits,whicharetotal benefitminustotalcost.Maximizingtotalbenefitminustotalcostmeansthatatthe margin,thelastunitabatedwillhaveanequalcostandbenefit.Choosingthepoint wheretotalbenefitisequaltototalcostwillresultintoomuchabatement,andwould beanalogoustochoosingtoproducewheretotalrevenuewasequaltototalcost. If totalrevenuewasalwaysequaltototalcostbychoice,thentherewouldneverbeany profit. Inthecaseofabatement,themoreweabate,thecostlieritis. Giventhat fundswilltendtobescarce,dollarsshouldbeallocatedtoabatementonlysolongas thebenefitofthelastunitofabatementisgreaterthanorequaltothecostofthelast unitofabatement.
$ MC 500
a c d b e
MB A 25
Figure18.3.c 4.Fourfirmslocatedatdifferentpointsonariverdumpvariousquantitiesofeffluentinto it. The effluent adversely affects the quality of swimming for homeowners who live downstream.Thesepeoplecanbuildswimmingpoolstoavoidswimmingintheriver,and firmscanpurchasefiltersthateliminateharmfulchemicalsinthematerialdumpedinthe river. Asapolicyadvisorforaregionalplanningorganization,howwouldyoucompare andcontrastthefollowingoptionsfordealingwiththeharmfuleffectoftheeffluent: a. Anequalrateeffluentfeeonfirmslocatedontheriver. First,oneneedstoknowthevaluetohomeownersofswimmingintheriver. This informationcanbedifficulttoobtain,becausehomeownerswillhaveanincentiveto
11 12 13
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Chapter18:ExternalitiesandPublicGoods overstatethisvalue.Asanupperboundary,iftherearenoconsiderationsotherthan swimming,onecouldusethecostofbuildingswimmingpools,eitherapoolforeach homeowner or a public pool for all homeowners. Next, one needs to know the marginal cost of abatement. If the abatement technology is well understood, this information should be readily obtainable. If the abatement technology is not understood,anestimatebasedonthefirmsknowledgemustbeused. The choice of a policy tool will depend on the marginal benefits and costs of abatement. If firms are charged an equalrate effluent fee, the firms will reduce effluentstothepointwherethemarginalcostofabatementisequaltothefee.Ifthis reduction is not high enough to permit swimming, the fee could be increased. Alternatively, revenue from the fees could be used to provide swimming facilities, reducingtheneedforeffluentreduction. b. Anequalstandardperfirmonthelevelofeffluentthateachcandump. Standards will be efficient only if the policy maker has complete information regardingthemarginalcostsandbenefitsofabatement,sothattheefficientlevelof thestandardcanbedetermined.Moreover,thestandardwillnotencouragefirmsto reduceeffluentsfurtherwhennewfilteringtechnologiesbecomeavailable. c. A transferable effluent permit system inwhich theaggregate level of effluent is fixedandallfirmsreceiveidenticalpermits. A transferable effluent permit system requires the policy maker to determine the efficienteffluentstandard.Oncethepermitsaredistributedandamarketdevelops, firmswithahighercostofabatementwillpurchasepermitsfromfirmswithlower abatement costs. However, unless permits are sold initially, rather than merely distributed,norevenuewillbegeneratedfortheregionalorganization. 5.Medicalresearchhasshownthenegativehealtheffectsofsecondhandsmoke.Recent socialtrendspointtogrowingintoleranceofsmokinginpublicareas.Ifyouareasmoker andyouwishtocontinuesmokingdespitetougherantismokinglaws,describetheeffect ofthefollowinglegislativeproposalsonyourbehavior.Asaresultoftheseprograms,do you,theindividualsmoker,benefit?Doessocietybenefitasawhole? Sincesmokinginpublicareasissimilartopollutingtheair,theprogramsproposed herearesimilartothoseexaminedforairpollution.Abilltolowertarandnicotine levelsissimilartoanemissionsstandard,andataxoncigarettesissimilartoan emissions fee. Requiring a smoking permit is similar to a system of emissions permits,assumingthatthepermitswouldnotbetransferable.Theindividualsmoker inalloftheseprogramsisbeingforcedtointernalizetheexternalityofsecondhand smokeandwillbeworseoff. Societywillbebetteroffifthebenefitsofaparticular proposaloutweighthecostofimplementingthatproposal.Unfortunately,thebenefits ofreducingsecondhandsmokeareuncertain,andassessingthosebenefitsiscostly. a. Abillisproposedthatwouldlowertarandnicotinelevelsinallcigarettes. The smoker will most likely try to maintain a constant level of consumption of nicotine, and will increase his or her consumption of cigarettes. Society may not benefitfromthisplanifthetotalamountoftarandnicotinereleasedintotheairis thesame. b. Ataxisleviedoneachpackofcigarettessold. Smokersmightturntocigars,pipes,ormightstartrollingtheirowncigarettes.The extent of the effect of a tax on cigarette consumption depends on the elasticity of demandforcigarettes.Again,itisquestionablewhethersocietywillbenefit. c. Smokers would be required to carry government issued smoking permits at all times.
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Chapter18:ExternalitiesandPublicGoods Smokingpermitswouldeffectivelytransferpropertyrightstocleanairfromsmokers tononsmokers.Themainobstacletosocietybenefitingfromsuchaproposalwould bethehighcostofenforcingasmokingpermitssystem. Inaddition,thecostofthe permitraisestheeffectivepriceofthecigarettesandtheresultingaffectonquantity smokedwilldependontheelasticityofdemand.
6. ThemarketforpaperinaparticularregionintheUnitedStatesischaracterizedby thefollowingdemandandsupplycurves
QD = 160, 000 2000P and QS = 40, 000 + 2000 P ,
where QD isthequantitydemandedofpaperin100lb.lots, QS isthequantitydemanded ofpaperin100lb.lots,and Pisthepriceper100lb.lotofpaper.Currentlythereisno attempttoregulatethedumpingofeffluentintostreamsandriversbythepapermills. Asaresult,dumpingiswidespread. Themarginalexternalcost( MEC)associatedwith theproductionofpaperisgivenbythecurve MEC = 0.0006QS . a. Calculate the output and price of paper if it is produced under competitive conditionsandnoattemptismadetomonitororregulatethedumpingofeffluent. The equilibrium price and output would be where quantity demand is equal to quantitysupplied: 160,0002000P=40,000+2000P 4000P=120,000 P=$30per100lb.lot Q=100,000lotsof100lb.each. b. Determinethesociallyefficientpriceandoutputofpaper. Tofindthesociallyefficientsolution,weneedtoconsidertheexternalcosts,asgivenby MEC = 0.0006QS , as well as the private costs, as given by QS = 40,000 + 2000P . Rewritingthesupplycurve,theprivatecostsareP=0.0005QS20=MC.Therefore, MSC=MC+MEC=0.0005QS20+0.0006QS MSC=0.0011QS20. Settingthemarginalsocialcostequaltothedemandcurve,orthemarginalbenefit, 0.0011Q20=800.0005Q Q=62,500lotsof100lb.each. P=$48.75per100lb.lot. c. Explainclearlywhytheanswersyoucalculatedinpartsaandbdiffer. Theequilibriumquantitydeclinedandtheequilibriumpriceroseinpartbbecause the external costs were considered. Ignoring some of the costs will result in too muchoutputbeingproducedandsoldattoolowofaprice. 7. In a market for dry cleaning, the inverse market demand function is given by P = 100 - Q andthe(private)marginalcostofproductionfortheaggregationofalldry cleaning firms is given by MC = 10 + Q . Finally, the pollution generated by the dry cleaning process creates external damages given by the marginal external cost curve MEC = Q .
30
a.
Chapter18:ExternalitiesandPublicGoods Calculatetheoutputandpriceofdrycleaningifitisproducedundercompetitive conditionsabsentregulation. Tofindtheanswer,setpriceequaltomarginalcost: 100Q=10+Q, Q=45,andP=55.
b.
Determinethesociallyefficientpriceandoutputofdrycleaning. Tofind the answer here, we must first calculate themarginal social cost (MSC), whichisequaltothemarginalexternalcostplustheprivatemarginalcost. Next, setMSCequaltothemarketdemandfunctiontosolveforpriceandquantity.When allcostsareincluded,thequantityproducedwillfallandthepricewillrise: MSC=MC+MEC=10+2Q=100Q, Q=30,andP=70.
c.
Determine the tax that would result in a competitive market producing the sociallyefficientoutput. Ifthereisaunittax,thenthenewmarginalprivatecostfunctionisMC=10+Q+tQ.Ifwe nowsetthisnewmarginalcostfunctionequaltothepriceof70andsubstitutein30forthe quantity,wecansolvefort: 10+Q+tQ=70 Q(1+t)=60 1+t=2 t=1. Thetaxshouldbe$1perunitoutput.Notethatwiththetaxequalto1,thenewprivatecost functionisthesameasthemarginalsocialcostfunction.
d.
Calculate the output and price of dry cleaning if it is produced under monopolisticconditionswithoutregulation. Themonopolistwillsetmarginalcostequaltomarginalrevenue.Recallthatthemarginal revenue curve has a slope that is twice the slope of the demand curve so MR=100 2Q=MC=10+Q.Therefore,Q=30andP=70.
e.
Determine the tax that would result in a monopolistic market producing the sociallyefficientoutput. Thetaxisequaltozerosincethemonopolistwillproduceatthesociallyefficientoutputin thiscase.
f.
Assuming that no attempt is made to monitor or regulate the pollution, which marketstructureyieldshighersocialwelfare?Discuss. Inthiscaseitisactuallythemonopolistthatyieldsthehigherlevelofsocialwelfareover thecompetitivemarketsincethemonopolistsprofitmaximizingpriceandquantityarethe sameasthesociallyefficientsolution.Sinceamonopolisttendstoproducelessoutputthan thecompetitiveequilibrium,itmayendupproducingclosertothesocialequilibriumwhena negativeexternalityispresent.
8.Abeekeeperlivesadjacenttoanappleorchard.Theorchardownerbenefitsfromthe beesbecauseeachhivepollinatesaboutoneacreofappletrees.Theorchardownerpays nothingforthisservice,however,becausethebeescometotheorchardwithouthishaving todoanything. Becausetherearenotenoughbeestopollinatetheentireorchard,the orchardownermustcompletethepollinationbyartificialmeans,atacostof$10peracre oftrees. BeekeepinghasamarginalcostofMC=10+5Q,whereQisthenumberofbeehives.Each
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Chapter18:ExternalitiesandPublicGoods hiveyields$40worthofhoney. a. Howmanybeehiveswillthebeekeepermaintain? Thebeekeepermaintainsthenumberofhivesthatmaximizesprofits,whenmarginal revenueisequaltomarginalcost.Withaconstantmarginalrevenueof$40(thereis no information that would lead us to believe that the beekeeper has any market power)andamarginalcostof10+5Q: 40=10+5Q,orQ=6.
b.
Isthistheeconomicallyefficientnumberofhives? Iftherearetoofewbeestopollinatetheorchard,thefarmermustpay$10peracrefor artificial pollination. Thus, the farmer would be willing to pay up to $10 to the beekeepertomaintaineachadditionalhive.So,themarginalsocialbenefit,MSB,of eachadditionalhiveis$50,whichisgreaterthanthemarginalprivatebenefitof$40. Assumingthattheprivatemarginalcostisequaltothesocialmarginalcost,weset MSB=MCtodeterminetheefficientnumberofhives: 50=10+5Q,orQ=8. Therefore,thebeekeepersprivatechoiceofQ=6isnotthesociallyefficientnumberof hives.
c.
Whatchangeswouldleadtothemoreefficientoperation? Themostradicalchangethatwouldleadtomoreefficientoperationswouldbethe mergerofthefarmersbusinesswiththebeekeepersbusiness. Thismergerwould internalizethepositiveexternalityofbeepollination. Shortofamerger,thefarmer andbeekeepershouldenterintoacontractforpollinationservices.
9.Therearethreegroupsinacommunity.Theirdemandcurvesforpublictelevisionin hoursofprogramming,T,aregivenrespectivelyby W1=$200T, W2=$240T, W3=$3202T. Suppose public television is a pure public good that can be produced at a constant marginalcostof$200perhour. a. Whatistheefficientnumberofhoursofpublictelevision? The efficient number of hours is the amount such that the sum of the marginal benefits is equal to marginal cost. Given the demand curves representing the marginal benefits to each individual, we sum these demand curves vertically to determinethesumofallmarginalbenefits. Fromthetablebelowonecanseethat MSB=MCatT=140hoursofprogramming. WillingnesstoPay Time 0 100 Group1 200 100 Group2 240 140 Group3 320 120 Vertical Sum 760 360
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120 140 160 180
Chapter18:ExternalitiesandPublicGoods 80 120 80 280 60 40 20 100 80 60 40 0 0 200 120 80
b.
Howmuchpublictelevisionwouldacompetitiveprivatemarketprovide? To find the number of hours that the private market would provide, we add the individualdemandcurveshorizontally.Theefficientnumberofhoursissuchthatthe privatemarginalcostisequaltotheprivatemarginalbenefit.Thedemandcurvefor group1liesbelow MC=$200forall T >0. Withmarginalcostequalto$200,only groups2and3wouldbewillingtopay$200.Atthatprice,100hoursofprogramming wouldbeprovided. QuantityDemanded Price 240 220 200 180 160 140 Group1 0 0 0 20 40 60 Group2 0 20 40 60 80 100 Group3 40 50 60 70 80 90 Horizontal Sum 40 70 100 150 200 250
10. ReconsiderthecommonresourceproblemasgivenbyExample18.5. Supposethat crawfishpopularitycontinuestoincrease,andthatthedemandcurveshiftsfromC=0.401 0.0064FtoC=0.500.0064F. Howdoesthisshiftindemandaffecttheactualcrawfish catch,theefficientcatch,andthesocialcostofcommonaccess?(Hint:Usethemarginal socialcostandprivatecostcurvesgivenintheexample.) Therelevantinformationisnowthefollowing: Demand: MSC: C=0.500.0064F C=5.645+0.6509F.
With an increase in demand, the demand curve for crawfish shifts upward, intersectingthepriceaxisat$0.50. Theprivatecostcurvehasapositiveslope,so additionaleffortmustbemadetoincreasethecatch.Sincethesocialcostcurvehasa positive slope, the socially efficient catch also increases. We may determine the sociallyefficientcatchbysolvingthefollowingtwoequationssimultaneously: 0.500.0064F=5.645+0.6509F,orF*=9.35. Todeterminethepricethatconsumersarewillingtopayforthisquantity,substitute F*intotheequationformarginalsocialcostandsolveforC: C=5.645+(0.6509)(9.35),orC=$0.44. Next,findtheactuallevelofproductionbysolvingtheseequationssimultaneously: Demand: C=0.500.0064F
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MPC:
Chapter18:ExternalitiesandPublicGoods C=0.357+0.0573F 0.500.0064F=0.357+0.0573F,orF**=13.45.
Todeterminethepricethatconsumersarewillingtopayforthisquantity,substitute F**intotheequationformarginalprivatecostandsolveforC: C=0.357+(0.0573)(13.45),orC=$0.41. Noticethatthemarginalsocialcostofproducing13.45unitsis MSC=5.645+(0.6509)(13.45)=$3.11. Withtheincreaseindemand,thesocialcostistheareaofatrianglewithabaseof4.1 millionpounds(13.459.35)andaheightof$2.70($3.110.41),or$5,535,000more thanthesocialcostoftheoriginaldemand. 11.TheGeorgesBank,ahighlyproductivefishingareaoffNewEngland,canbedivided intotwozonesintermsoffishpopulation. Zone1hasthehigherpopulationpersquare milebutissubjecttoseverediminishingreturnstofishingeffort.Thedailyfishcatch(in tons)inZone1is F1=200(X1)2(X1)2 whereX1isthenumberofboatsfishingthere.Zone2hasfewerfishpermilebutislarger, anddiminishingreturnsarelessofaproblem.Itsdailyfishcatchis F2=100(X2)(X2)2 whereX2isthenumberofboatsfishinginZone2.ThemarginalfishcatchMFCineach zonecanberepresentedas MFC1=2004(X1) MFC2=1002(X2). Thereare100boatsnowlicensedbytheU.S.governmenttofishinthesetwozones.The fisharesoldat$100perton. Totalcost(capitalandoperating)perboatisconstantat $1,000perday.Answerthefollowingquestionsaboutthissituation: a. Iftheboatsareallowedtofishwheretheywant,withnogovernmentrestriction, howmanywillfishineachzone?Whatwillbethegrossvalueofthecatch? Withoutrestrictions,theboatswilldividethemselvessothattheaveragecatch(AF1 and AF2)foreachboatisequalineachzone. (Iftheaveragecatchinonezoneis greaterthanintheother,boatswillleavethezonewiththelowercatchforthezone withthehighercatch.)Wesolvethefollowingsetofequations: AF1=AF2andX1+X2=100where 2 200X 1 2X 1 = 200 2X 1 and AF 1 = X1 AF 2 = Therefore,AF1=AF2implies
2 100X 2 X 2 = 100 X 2 . X2
2002X1=100X2,
2002(100X2)=100X2,or X 2 =
. FindthegrosscatchbysubstitutingthevalueofX1andX2intothecatchequations: and
100 and 3
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Chapter18:ExternalitiesandPublicGoods ThetotalcatchisF1+F2=6,666.Atthepriceof$100perton,thevalueofthecatchis $666,600.Theaveragecatchforeachofthe100boatsinthefishingfleetis66.66tons. Todeterminetheprofitperboat,subtracttotalcostfromtotalrevenue: =(100)(66.66)1,000,or=$5,666. Totalprofitforthefleetis$566,600. b. IftheU.S.governmentcanrestricttheboats,howmanyshouldbeallocatedtoeach zone?Whatwillbethegrossvalueofthecatch?Assumethetotalnumberofboats remainsat100. Assumethatthegovernmentwishestomaximizethenetsocialvalueofthefishcatch, i.e., the difference between the total social benefit and the total social cost. The governmentequatesthemarginalfishcatchinbothzones,subjecttotherestriction thatthenumberofboatsequals100: MFC1=MFC2andX1+X2=100, MFC1=2004X1andMFC2=1002X2. SettingMFC1=MFC2implies: 2004X1=1002X2,or2004(100X2)=1002X2,orX2=50and X1=10050=50. FindthegrosscatchbysubstitutingX1andX2intothecatchequations: F1=(200)(50)(2)(502)=10,0005,000=5,000and F2=(100)(50)502=5,0002,500=2,500. Thetotalcatchisequalto F1+F2=7,500.Atthemarketpriceof$100perton,the valueofthecatchis$750,000.Totalprofitis$650,000.Noticethattheprofitsarenot evenlydividedbetweenboatsinthetwozones. TheaveragecatchinZoneAis100 tonsperboat,whiletheaveragecatchinZoneBis50tonsperboat.Therefore,fishing inZoneAyieldsahigherprofitfortheindividualowneroftheboat. c. If additional fishermen want to buy boats and join the fishing fleet, should a governmentwishingtomaximizethenetvalueofthecatchgrantthemlicenses? Whyorwhynot? Toanswer thisquestion, first determinetheprofitmaximizing numberofboatsin eachzone.ProfitsinZoneAare
2 A = (100)(200 X1 2 X1 ) 1, 000 X , or A = 19, 000 X1 200 X12 .
TodeterminethechangeinprofitwithachangeinX1takethefirstderivativeofthe profitfunctionwithrespecttoX1: d A = 19,000 400X 1 . dX 1 Todeterminetheprofitmaximizinglevelofoutput,set forX1:
d A equaltozeroandsolve dX 1
19,000400X1=0,orX1=47.5.
SubstitutingX1intotheprofitequationforZoneAgives:
A = (100) (200)(47.5) (2)(47.52 ) (1, 000)(47.5) = $451, 250 .
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(
)
Chapter18:ExternalitiesandPublicGoods ForZoneBfollowasimilarprocedure.ProfitsinZoneBare
2 2 B = (100)( X2 X 2 ) 1, 000 X 2 , or B = 9, 000 X 2 100 X 2 . 100
TakingthederivativeoftheprofitfunctionwithrespecttoX2gives d B = 9,000 200X 2 . dX 2
Setting
d B equaltozerotofindtheprofitmaximizinglevelofoutputgives dX 2 9,000200X2=0,orX2=45.
SubstitutingX2intotheprofitequationforZoneBgives: B=(100)((100)(45)452)(1,000)(45)=$202,500. Totalprofitfrombothzonesis$653,750,with47.5boatsinZoneAand45boatsin Zone B. Because each additional boat above 92.5 decreases total profit, the governmentshouldnotgrantanymorelicenses.
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