SOLUTIONS TO TEXT PROBLEMSch8 doc.docx

SOLUTIONS TO TEXT PROBLEMSch8 doc.docx

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SOLUTIONSTOTEXTPROBLEMS:

QuickQuizzes

1.Figure8-1showsthesupplyanddemandcurvesforcookies,withequilibriumquantityQ1andequilibriumpriceP1.Whenthegovernmentimposesataxoncookies,thepricetobuyersrisestoPB,thepricereceivedbysellersdeclinestoPS,andtheequilibriumquantityfallstoQ2.ThedeadweightlossisthetriangularareabelowthedemandcurveandabovethesupplycurvebetweenquantitiesQ1andQ2.Thedeadweightlossshowsthefallintotalsurplusthatresultsfromthetax.

Figure8-1

2.Ataxonbeerwouldhavealargerdeadweightlossthanataxonmilk,sincethedemandforbeerismoreelasticthanthedemandformilkandthedeadweightlossofataxislargerthegreateristheelasticityofdemand.

3.Ifthegovernmentdoublesthetaxongasoline,therevenuefromthegasolinetaxcouldriseorfall,dependingonwherethetaxfallsontheLaffercurve.However,ifthegovernmentdoublesthetaxongasoline,youcanbesurethatthedeadweightlossofthetaxrises,sincedeadweightlossalwaysrisesasthetaxraterises.

QuestionsforReview

1.Whenthesaleofagoodistaxed,bothconsumersurplusandproducersurplusdecline.Thedeclineinconsumersurplusandproducersurplusexceedstheamountofgovernmentrevenuethat’sraised,sosociety’stotalsurplusdeclines.Thetaxdistortstheincentivesofbothbuyersandsellers,soresourcesareallocatedinefficiently.

2.Figure8-2illustratesthedeadweightlossandtaxrevenuefromataxonthesaleofagood.Withoutatax,theequilibriumquantitywouldbeQ1,theequilibriumpricewouldbeP1,consumersurpluswouldbeA+B+C,andproducersurpluswouldbeD+E+F.Theimpositionofataxplacesawedgebetweenthepricebuyerspay,PB,andthepricesellersreceive,PS,wherePB=PS+tax.TheequilibriumquantitydeclinestoQ2.NowconsumersurplusisA,producersurplusisF,andgovernmentrevenueisB+D.ThedeadweightlossofthetaxisC+E,sincethatareaislostbecauseofthedeclineinquantityfromQ1toQ2.

Figure8-2

3.Thegreatertheelasticitiesofdemandandsupply,thegreaterthedeadweightlossofatax.Sinceelasticitymeasurestheresponseofquantitytoachangeinprice,higherelasticitymeansthetaxinducesagreaterreductioninquantity,henceagreaterdistortiontothemarket.

4.Expertsdisagreeaboutwhetherlabortaxeshavesmallorlargedeadweightlossesbecausetheyhavedifferentviewsabouttheelasticityoflaborsupply.Somebelievethatlaborsupplyisinelastic,soataxonlaborhasasmalldeadweightloss.Butothersthinkthatworkerscanadjusttheirhoursworkedinvariousways,solaborsupplyiselastic,andthusataxonlaborhasalargedeadweightloss.

5.Thedeadweightlossofataxrisesmorethanproportionallyasthetaxrises.Taxrevenue,however,mayincreaseinitiallyasthetaxrises,butasthetaxrisesfurther,revenueriseslessthanproportionallyandeventuallydeclines.

ProblemsandApplications

1.a.Figure8-3illustratesthemarketforpizza.TheequilibriumpriceisP1,theequilibriumquantityisQ1,consumersurplusisareaA+B+C,andproducersurplusisareaD+E+F.Thereisnodeadweightloss,asallthepotentialgainsfromtradearerealized;totalsurplusistheentireareabetweenthedemandandsupplycurvesA+B+C+D+E+F.

Figure8-3

b.Witha$1taxoneachpizzasold,thepricepaidbybuyers,PB,isnowhigherthanthepricereceivedbysellers,PS,wherePB=PS+$1.ThequantitydeclinestoQ2,consumersurplusisareaA,producersurplusisareaF,governmentrevenueisareaB+D,anddeadweightlossisareaC+E.ConsumersurplusdeclinesbyB+C,producersurplusdeclinesbyD+E,governmentrevenueincreasesbyB+D,anddeadweightlossincreasesbyC+E.

c.IfthetaxwereremovedandconsumersandproducersvoluntarilytransferredB+Dtothegovernmenttomakeupforthelosttaxrevenue,theneveryonewouldbebetteroffthanwithoutthetax.TheequilibriumquantitywouldbeQ1,asinthecasewithoutthetax,andtheequilibriumpricewouldbeP1.ConsumersurpluswouldbeA+C,becauseconsumersgetsurplusofA+B+C,thenvoluntarilytransferBtothegovernment.ProducersurpluswouldbeE+F,sinceproducersgetsurplusofD+E+F,thenvoluntarilytransferDtothegovernment.Bothconsumersandproducersarebetteroffthanthecasewhenthetaxwasimposed.IfconsumersandproducersgavealittlebitmorethanB+Dtothegovernment,thenallthreeparties,includingthegovernment,wouldbebetteroff.Thisillustratestheinefficiencyoftaxation.

2.a.Thestatement,“Ifthegovernmenttaxesland,wealthylandownerswillpassthetaxontotheirpoorerrenters,”isincorrect.Withataxonland,landownerscannotpassthetaxon.Sincethesupplycurveoflandisperfectlyinelastic,landownersbeartheentireburdenofthetax.Renterswon’tbeaffectedatall.

b.Thestatement,“Ifthegovernmenttaxesapartmentbuildings,wealthylandownerswillpassthetaxontotheirpoorerrenters,”iscorrect.Withataxonapartmentbuildings,landownerscanmoreeasilypassthetaxon,thoughtheextenttowhichtheydothisdependsontheelasticitiesofsupplyanddemand.Inthiscase,thetaxisadirectadditiontothecostofrentalunits,sothesupplycurvewillshiftupbytheamountofthetax.Thetaxwillbesharedbyrentersandlandowners,dependingontheelasticitiesofdemandandsupply.

3.a.Thestatement,“Ataxthathasnodeadweightlosscannotraiseanyrevenueforthegovernment,”isincorrect.Anexampleisthecaseofataxwheneithersupplyordemandisperfectlyinelastic.Thetaxhasneitheraneffectonquantitynoranydeadweightloss,butitdoesraiserevenue.

b.Thestatement,“Ataxthatraisesnorevenueforthegovernmentcannothaveanydeadweightloss,”isincorrect.Anexampleisthecaseofa100percenttaximposedonsellers.Witha100percenttaxontheirsalesofthegood,sellerswon’tsupplyanyofthegood,sothetaxwillraisenorevenue.Yetthetaxhasalargedeadweightloss,sinceitreducesthequantitysoldtozero.

4.a.Withveryelasticsupplyandveryinelasticdemand,theburdenofthetaxonrubberbandswillbebornelargelybybuyers.AsFigure8-4shows,consumersurplusdeclinesconsiderably,byareaA+B,butproducersurplusdoesn’tfallmuchatall,justbyareaC+D.

Figure8-4

b.Withveryinelasticsupplyandveryelasticdemand,theburdenofthetaxonrubberbandswillbebornelargelybysellers.AsFigure8-5shows,consumersurplusdoesn’tdeclinemuch,justbyareaA+B,whileproducersurplusfallssubstantially,byareaC+D.Comparedtopart（a）,producersbearmuchmoreoftheburdenofthetax,andconsumersbearmuchless.

Figure8-5

5.a.Thedeadweightlossfromataxonheatingoilislikelytobegreaterinthefifthyearafteritisimposedratherthanthefirstyear.Inthefirstyear,theelasticityofdemandisfairlylow,aspeoplewhoownoilheatersaren’tlikelytogetridofthemrightaway.Butovertimetheymayswitchtootherenergysourcesandpeoplebuyingnewheatersfortheirhomeswillmorelikelychoosegasorelectric,sothetaxwillhaveagreaterimpactonquantity.

b.Thetaxrevenueislikelytobehigherinthefirstyearafteritisimposedthaninthefifthyear.Inthefirstyear,demandismoreinelastic,sothequantitydoesn’tdeclineasmuchandtaxrevenueisrelativelyhigh.Astimepassesandmorepeoplesubstituteawayfromoil,theequilibriumquantitydeclines,asdoestaxrevenue.

6.Sincethedemandforfoodisinelastic,ataxonfoodisagoodwaytoraiserevenuebecauseitdoesn’tleadtomuchofadeadweightloss;thustaxingfoodislessinefficientthantaxingotherthings.Butitisn’tagoodwaytoraiserevenuefromanequitypointofview,sincepoorerpeoplespendahigherproportionoftheirincomeonfood,sothetaxwouldhitthemharderthanitwouldhitwealthierpeople.

7.a.Thistaxhassuchahighratethatitisn’tlikelytoraisemuchrevenue.Becauseofthehightaxrate,theequilibriumquantityinthemarketislikelytobeatornearzero.

b.SenatorMoynihan’sgoalwasprobablytobantheuseofhollow-tippedbullets.Inthiscase,ataxisaseffectiveasanoutrightban.

8.a.Figure8-6illustratesthemarketforsocksandtheeffectsofthetax.Withoutatax,theequilibriumquantitywouldbeQ1,theequilibriumpricewouldbeP1,totalspendingbyconsumersequalstotalrevenueforproducers,whichisP1xQ1,whichequalsareaB+C+D+E+F,andgovernmentrevenueiszero.Theimpositionofataxplacesawedgebetweenthepricebuyerspay,PB,andthepricesellersreceive,PS,wherePB=PS+tax.TheequilibriumquantitydeclinestoQ2.NowtotalspendingbyconsumersisPBxQ2,whichequalsareaA+B+C+D,totalrevenueforproducersisPSxQ2,whichisareaC+D,andgovernmenttaxrevenueisQ2xtax,whichisareaA+B.

b.Thepricereceivedbyproducersfallsbecauseofthetax,unlesssupplyisperfectlyelastic.Totalreceiptsforproducersfall,sinceproducersloserevenueequaltoareaB+E+F.

Figure8-6

c.Thepricepaidbyconsumersrises,unlessdemandisperfectlyelastic.Whethertotalspendingbyconsumersrisesorfallsdependsonthepriceelasticityofdemand.Ifdemandiselastic,thepercentagedeclineinquantityexceedsthepercentageincreaseinprice,sototalspendingdeclines.Ifdemandisinelastic,thepercentagedeclineinquantityislessthanthepercentageincreaseinprice,sototalspendingrises.Whethertotalconsumerspendingfallsorrises,consumersurplusdeclinesbecauseoftheincreaseinpriceandreductioninquantity.

9.Sincethetaxongadgetswaseliminated,alltaxrevenuemustcomefromthetaxonwidgets.Thetaxrevenue