Handout 11 key - Econ 101 Introductory Microeconomics...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Econ 101: Introductory Microeconomics DiscussionSection#11HandoutSolutions   Fall 2009     Dec9 11   Exercise 1: Externality Supposethatinthemarketforpaper,demandisP=100 Q.Themarginalprivatecostofproducingpaperis10+Q. However,pollutiongeneratedbytheproductionprocesscreatesaperunitexternalharm(i.e.,negativeexternality)equalto 0.5Q(i.e.,theleveloftheexternalityincreaseswiththequantityproduced).  a)Whatisthe(unregulated)marketequilibriumandquantityiftheexternalityisnotcorrectedforinthismarket?   Findtheintersectionoftheprivatecostcurveandthedemandcurve.  100–Q=10+Q Q=45.  ThemarketequilibriumpriceisP=55.   b)Whatisthesociallyoptimalquantityofpaperthatshouldbeproduced?       Findtheintersectionofthemarginalsocialcostcurveandthemarginalsocialbenefitcurve.  Thesocialcostisgivenby10+Q+0.5Q.  SincethereisnoconsumptionexternalitytheMSBcurve=demand.  Set100 Q=10+1.5QtofindthesociallyoptimalquantityisQ=36.  ThepriceisP=64.   c)Supposethatthegovernmentwantstoachievethesociallyoptimalquantitybyimposingataxonproducers.Whatwould bethesizeofthetaxperunitofpaper?  Thegovernmentcanimposeataxsothataftertaxmarketequilibriumcoincideswiththeequilibriumyou obtainedinpart(b).Toobtaintheverticaldifferencebetweenthenewandoldprivatecostcurves,notice thatthevalueofthenewprivatecostatQ=36is64.ThevalueoftheoldprivatecostatQ=36is46. Therefore,thesizeofthetaxshouldbe64 46=$18.      1  Exercise 2: Externality Watertownisasmalltownsurroundedbymanysmalllakes.WintersinWatertownareverycoldbut(forsomeunknown reason)peoplelovetoice fishonthelakesaroundWatertown.Peopletravelfromnearbycitiestoice fishinthewinter.The countycouncildecidestostartrequiringlicensestofishintheWatertownarea.Demandfortheselicensesis:P=250–Q andthemarginalcostofissuinglicensesisMC=Q.  a)Findthemarketequilibriumpriceandquantityforice fishingrights.   Tofindtheequilibrium,setP=250–QequaltoMC=Q.  ThisyieldsQ=125rightsatapriceofP=$125each.   b)Oneofthemembersofthecouncil,Mr.Smith,thinksthatthereareexternalcostsinvolvedwithsellingfishinglicenses. HeclaimsthatbeforelicenseswererequiredthereweremorepeoplecomingtoWatertownforicefishingandthiswasvery helpfulforthelocalmerchants.Heestimatesthatthelicensesdiscouragepeoplefromcomingtotownandthenetlossof merchantsamountsto10+Q.Consideringthemarketforice fishingrights,isthisaconsumptionexternalityoraproduction externality?   Sincewearetalkingaboutthemarketforicefishingrights,thisisanegativeproductionexternality.  Thecounty’scostofissuinglicensesdoesn’tincludethecostoffewertouristsinWatertown.  Sellinglicensesdiscouragesicefishingandreducesbusinessforlocalmerchants.   d)AssumingMr.Smith’sestimateiscorrect,findthesociallyefficientquantityandpriceoficefishingrights.   TofindthesociallyefficientoutcomeweneedtofindthequantitywhereMSC=MSB.  MSC=MPC+externality=Q+(10+Q)=2Q+10.  SincethereisnoconsumptionexternalityMSB=D.  SosetMSC=2Q+10=250–QandsolveforQ=80.  Thesociallyoptimalquantityoflicensesis80andthesociallyoptimalpriceis$170.    Exercise 3: Public Goods Consideraneconomywithtwoconsumers,BenandJoe.Thereispublicgoodinthiseconomyinaformoftornadosirens. Ben’sdemandfortornadosirensisgivenbyP=10 Q,andJoe’sdemandfortornadosirensisP=8 2Q.Marginalcostfor providingtornadosirensinthemarketsisconstant,MC=9.  a)Whichtwopropertiesmustbesatisfiedforsirenstobepublicgoods?   Publicgoodsmustbenon rivalandnon excludable   b)Aretornadosirensarenon rival?Explainyouranswer.  Yes.Ifonepersonusesit(i.e.shecanhearsirens),otherpeople’suseofthisgoodisnotaffected(other peoplecanhearthesirensaswell).   c)Aretornadosirensarenon exclusive?.Explainyouranswer.   Yes.Everyoneintheareawillbeabletohearthesiren,regardlessofwhethertheypaidforthisgood.   d)Isthereapotentialforfree riderproblem?  Yes.Thisisimpliedbythefactthatsirensarenon excludable,i.e.theremightbepeoplewhodidn’tpayfor theservicebutthesepeoplewillstillbeabletohearthesirens.Wecallthesepeoplefree riders. 2  e)Derivemarketdemandcurveforsirens.Drawthreegraphsonthetopofeachother–firstgraphforBen’sdemand,second graphforJoe’sdemand,andthethirdgraphformarketdemand.  ThemarketdemandcurvecanbederivedbyVERTICALsummation(nothorizontalasisthecasewith privategoods)oftheindividualdemandcurves.Ateachquantitylevel,weseethewillingnesstopayof eachindividualandthenestimatesociety’stotalwillingnesstopaybyaddingthewillingnesstopayofthe variousindividuals.       Atquantityof0sirens,Beniswillingtopay10dollars,andJoeiswillingtopay8dollars.Together, they’rewillingtopay18dollars.Atquantityof4sirens,Joeiswillingtopay0dollars,andBeniswilling topay6dollars.Toseethis,plugQ=4intoBen’sdemandcurve:P=10–Q=10 4=6).Atquantityof 10,bothconsumersarearen’twillingtopayanything(P=0).  Usetheinformationcalculatedabovetodrawmarketdemandcurve.Firstdrawthethreepoints(10,0), (4,6),(18,0),andthendrawlinearcurvebetweenthesepoints.You’llseethatthemarketdemandcurvehas akinkatpoint(4,6).Therefore,themarketdemandcurvehastwoparts:P=18 3QifP>=6,andP=10 Q ifP<=6.Note:youcancalculatederivethefirstpartfromthepoints(0,18)and(4,6)onthegraph–yousee thatthey interceptis18,andyoucancalculatetheslopefromthetwopoints.Thesecondpartisthesame asBen’sdemandcurve   3  f)Howmanysirenswillbeprovidedinthemarket?  DrawtheMConthegraphwithmarketdemandcurve(MC=9).YoucanseethatMCintersectsthe demandcurveintheupper.MC=demand=>9=18 3Q=>9=3Q=>Q=3(sotherewillbe3sirens providedinthemarket)   g)Whatwillbethepriceforthesesirens?  DrawadottedlineupatQ=3suchthatyouseewhereitintersectsBen’sandJoe’sdemandcurve.Plugging Q=3intotheirindividualcurves,yougetthatBeniswillingtopay$7andJoeiswillingtopay$2. Therefore,thepriceinthismarketforproviding3sirenswillbe$9.   h)Istheresultfrompreviousquestionrealistic?Discusshowgovernmentfundspublicgoods.  No,theresultisnotrealistic.Ourexampledescribesidealizedsituationinwhichwearegivendemand curvesofbothindividuals.However,thisisnotthecaseinthereallife,becauseinthereallife,wedon’t knowpeople’sdemandcurves.Inotherwords,peopledon’tpubliclyrevealhowmuchtheyarewillingto payforpublicservice.Infact,peopleareoftentryingtobecomefree ridersbyclaimingthattheydon’t actuallyneedtheservice.Thegovernmentcandobenefit costanalysisandchargeuserfees,forexample throughtaxes,orthroughentryfees. 4  ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online