平狄克《微观经济学》课后答案 9

CHAPTER9

THEANALYSISOFCOMPETITIVEMARKETS

TEACHINGNOTES

WiththeexceptionofChapter1,Chapter9isthemoststraightforwardandeasilyunderstood

chapterinthetext.Thechapterbeginswithareviewofconsumerandproducersurplus.Ifyou

havepostponedthesetopics,youshouldcarefullyexplainthedefinitionofeach(refertoteaching

suggestionsinChapters4and8).WhileSection2discussesefficiencyincompetitivemarketsby

comparingcompetitiveoutcomeswiththoseundermarketfailure,moreanalyticdiscussionof

efficiencyisleftforChapter16.

Thepresentationineachsectionofthischapterfollowsthesameformat:thereisageneral

discussionofwhymarketinterventionleadstodeadweightloss,followedbythepresentationofan

importantpolicyexample.Eachsectionisdiscussedinonereviewquestionandappliedinatleast

oneexercise.Exercise(1)focusesonminimumwagespresentedinSection9.3.Exercises(4)and(5)

reinforcediscussionofpricesupportsandproductionquotasfromSection9.4.Theuseoftariffsand

quotas,presentedinSection9.5,canbefoundinExercises(3),(6),(7),(10),and(12).Taxesand

subsidies(Section9.6)arediscussedinExercises(2),(8),and(14).Exercise(9)reviewsnaturalgas

pricecontrolsinExample9.1,acontinuationofExample2.7.Exercise(4)maybecomparedto

Example9.4anddiscussedasanextensionofExample2.2.

REVIEWQUESTIONS

1.Deadweightlossreferstothebenefitslosttoeitherconsumersorproducerswhenmarketsdonot

operateefficiently.Thetermdeadweightdenotesthatthesearebenefitsunavailabletoanyparty.

Forexample,aneffectivepriceceilingreducesthepricebelowthemarketequilibriumprice.This

policycausesalossofbothconsumerandproducersurpluses.Consumersurplusdecreasesbecause

lessispurchasedandproducersdonotcaptureallofthisdecrease.Producersurplusdecreases

becauselessisproducedandconsumersdonotcaptureallofthisdecrease.Surplusnotcapturedby

marketparticipantsisdeadweightloss.

2.Whenthesupplycurveiscompletelyinelastic,theimpositionofaneffectivepriceceilingtransfers

alllossinproducersurplustoconsumers.Consumersurplusincreasesbythedifferencebetweenthe

market-clearingpriceandthepriceceilingtimesthemarket-clearingquantity.Consumerscapture

alldecreasesintotalrevenue.Therefore,nodeadweightlossoccurs.

3.Ifthesupplycurvewasperfectlyinelasticanddemandincreases,apriceceilingwillincrease

consumersurplus.

Ifthedemandcurveisinelastic,pricecontrolsmayresultinanetlossofconsumersurplusbecause

consumerswillingtopayahigherpriceareunabletopurchasetheprice-controlledgoodorservice.

Thelossofconsumersurplusisgreaterthanthetransferofproducersurplustoconsumers.

However,ifdemandiselastic(andsupplyisrelativelyinelastic)consumersintheaggregatewillenjoy

anincreaseinconsumersurplus.

4.Becauseahigherpriceincreasesrevenueanddecreasesdemand,someconsumersurplusis

transferredtoproducersbutsomeproducerrevenueislostbecauseconsumerspurchaseless.The

problemwithapricefloororminimumpriceisthatitsendsthewrongsignaltoproducers.Thinking

thatmoreshouldbeproducedasthepricegoesup,producersincurextracosttoproducemorethan

whatconsumersarewillingtopurchaseatthesehigherprices.Theseextracostscanoverwhelm

gainscapturedinincreasedrevenues.Thus,unlessallproducersdecreaseproduction,aminimum

pricecanmakeproducersasawholeworseoff.

5.Municipalauthoritiesusuallyregulatethenumberoftaxisthroughtheissuanceoflicenses.When

thenumberoftaxisisbelowthatwhichitwouldbewithoutregulation,thosetaxisinthemarketmay

chargeahigher-than-competitiveprice.

Stateauthoritiesusuallyregulatethenumberofliquorlicenses.Byrequiringthatanybaror

restaurantthatservesalcoholhavealiquorlicenseandthenlimitingthenumberoflicensesavailable,

theStatelimitsentrybynewbarsandrestaurants.Thislimitationallowsthoseestablishmentsthat

havelicensestochargeahigherpricefbralcoholicbeverages.

Federalauthoritiesusuallyregulatethenumberofacresofwheatorcorninproductionbycreating

acreagelimitationprogramsthatgivefarmersfinancialincentivestoleavesomeoftheiracreageidle.

Thisreducessupply,drivingupthepriceofwheatorcorn.

6.Pricesupportsandacreagelimitationscostsocietymorethanthedollarcostoftheseprograms

becauselessoutputisproduced,drivingpricesabovecompetitivelevels.Thissmalleroutput

decreasesconsumersurplusandleadstodeadweightloss.(Note:Thislossdoesnotincludepayments

tofarmers,becausethesepaymentsonlyredistributethesurplusfromnon-farmerstofarmers.Thus,

thereisnolosstosocietyasawholefromthetransferofsurplus.)

7.Changesindomesticconsumerandproducersurplusesarethesameunderimportquotasand

tariffs.Therewillbealossin(domestic)totalsurplusineithercase.However,withatariff,the

governmentcancollectrevenueequaltothetarifftimesthequantityofimportsandtheserevenues

canberedistributedinthedomesticeconomytooffsetthedomesticdeadweightlossby,fbrexample,

reducingtaxes.Thus,thereislessofalosstothedomesticsocietyasawhole.Withtheimport

quota,foreignproducerscancapturethedifferencebetweenthedomesticandworldpricetimesthe

quantityofimports.Therefore,withanimportquota,thereisalosstothedomesticsocietyasa

whole.Ifthenationalgovernmentistryingtoincreasewelfare,itshoulduseatariff.

8.Theburdenofataxandthebenefitsofasubsidydependontheelasticitiesofdemandandsupply.

Iftheratiooftheelasticityofdemandtotheelasticityofsupplyissmall,theburdenofthetaxfalls

mainlyonconsumers.Ontheotherhand,iftheratiooftheelasticityofdemandtotheelasticityof

supplyislarge,theburdenofthetaxfallsmainlyonproducers.Similarly,thebenefitofasubsidy

accruesmostlytoconsumers(producers)iftheratiooftheelasticityofdemandtotheelasticityof

supplyissmall(large).

9.Ataxcreatesdeadweightlossbyartificiallyincreasingpriceabovethefreemarketlevel,thus

reducingtheequilibriumquantity.Thisreductionindemandreducesconsumeraswellasproducer

surpluses.Thesizeofthedeadweightlossdependsontheelasticitiesofsupplyanddemand.Asthe

elasticityofdemandincreasesandtheelasticityofsupplydecreases,i.e.,assupplybecomesmore

inelastic,thedeadweightlossbecomeslarger.

EXERCISES

a.Inafree-marketequilibrium,Ls=LD.Solvingyieldsw=$4andLs=LD=40.Iftheminimum

wageis$5,thenLs=50andLD=30.Thenumberofpeopleemployedwillbegivenbythelabor

demand,soemployerswillhire30millionworkers.

Figure9.1.a

b.Letwdenotethewagereceivedbytheemployee.Thentheemployerreceivingthe$1subsidyper

workerhouronlypaysw-1foreachworkerhour.AsshowninFigure9.1.b,thelabordemandcurve

shiftsto:

LD=80-10(w-1)=90-lOw,

wherewrepresentsthewagereceivedbytheemployee.

Thenewequilibriumwillbegivenbytheintersectionoftheoldsupplycurvewiththenewdemand

curve:

Therefore,90-10w**=10w**,orW**=$4.5perhour

L**=10(4.5)=45millionpersonsemployed.

Figure9.1.b

2.a.Tofindtheequilibriumpriceandquantity,equatesupplyanddemandandsolveforQEQ：

10-Q=Q-4,orQEQ=7.

SubstituteQEQintoeitherthedemandequationorthesupplyequationtoobtain

PEQ

PEQ=10-7=3,

or

PEQ=7-4=3.

b.Withtheimpositionofa$1.00taxperunit,thedemandcurveforwidgetsshiftsinward.Ateach

price,theconsumerwishestobuyless.Algebraically,thenewdemandfunctionis:

尸=9-Q.

Thenewequilibriumquantityisfoundinthesamewayasin(2a):

9-Q=Q-4,orQ*=6.5.

*

Todeterminethepricethebuyerpays,,substituteQ*intothedemand

equation:

PB=10-6.5=$3.50.

*

Todeterminethepricethesellerreceives,P$,substituteQ*intothesupply

equation:

Ps=6.5-4=$2.50.

c.TheoriginalsupplycurveforwidgetswasP=Q-4.Withasubsidyof$1.00towidgetproducers,

thesupplycurveforwidgetsshiftsoutward.Rememberthatthesupplycurveforafirmisits

marginalcostcurve.Withasubsidy,themarginalcostcurveshiftsdownbytheamountofthe

subsidy.Thenewsupplyfunctionis:

P=Q-5.

Toobtainthenewequilibriumquantity,setthenewsupplycurveequaltothe

demandcurve:

Q-5=10-Q,orQ=7.5.

ThebuyerpaysP=$2.50,andthesellerreceivesthatpriceplusthesubsidy,i.e.,

$3.50.Withquantityof7,500andasubsidyof$1.00,thetotalcostofthesubsidyto

thegovernmentwillbe$7,500.

3.Figure9.3.ashowsthegainsandlossesfromaper-poundsubsidywithdomesticsupply,S,and

domesticdemand,D.Psisthesubsidizedprice,PBisthepricepaidbythebuyers,andPEQisthe

equilibriumpricewithoutthesubsidy,assumingnoimports.Withthesubsidy,buyersdemand

FarmersgainamountsequivalenttoareasAandB.Thisistheincreaseinproducersurplus.

ConsumersgainareasCandF.Thisistheincreaseinconsumersurplus.Deadweightlossisequal

totheareaE.ThegovernmentpaysasubsidyequaltoareasA+B+C+F+E.

Price

Figure9.3.a

Figure9.3.bshowsthegainsandlossesfromaper-poundtariff.Pwistheworldprice,andPEQisthe

equilibriumprice.Withthetariff,assumedtobeequaltoPEQ-PWibuyersdemandfarmers

supplyQo,andQT-QDisimported.FarmersgainasurplusequivalenttoareaA.Consumerslose

areasA,B,C;thisisthedecreaseinconsumersurplus.DeadweightlossisequaltotheareasBand

C.

Figure9.3.b

Withoutmoreinformationregardinggovernmentpolicy,itseemssensibletoassumethatthe

Japanesegovernmentwouldavoidpayingsubsidiesbychoosingatariff,butthericefarmerswould

preferthesubsidy.

4.a.Equatingdemandandsupply,Qr)=Qs,

28-2P=4+4尸,orP=4.

Todeterminetheequilibriumquantity,substituteP=4intoeitherthesupply

equationorthedemandequation:

QS=4+4⑷=20

and

Q°=28-2(4)=20.

b.Becausethefreemarketsupplybyfarmersis20billionbushels,the25percentreductionrequired

bythenewPayment-In-Kind(PIK)Programwouldimplythatthefarmersnowproduce15billion

bushels.Toencouragefarmerstowithdrawtheirlandfromcultivation,thegovernmentmustgive

them5billionbushels,whichtheysellonthemarket.

Becausethetotalsupplytothemarketisstill20billionbushels,themarketpricedoesnotchange;it

remainsat$4perbushel.Thefarmersgain$20billion,equalto($4)(5billionbushels),fromthePIK

Program,becausetheyincurnocostsinsupplyingthewheat(whichtheyreceivedfromthe

government)tothemarket.ThePIKprogramdoesnotaffectconsumersinthewheatmarket,

becausetheypurchasethesameamountatthesamepriceastheydidinthefreemarketcase.

c.Taxpayersgainbecausethegovernmentisnotrequiredtostorethewheat.Althougheveryone

seemstogainfromthePIKprogram,itcanonlylastwhiletherearegovernmentwheatreserves.The

PIKprogramassumesthatthelandremovedfromproductionmayberestoredtoproductionwhen

stockpilesareexhausted.Ifthiscannotbedone,consumersmayeventuallypaymorefor

wheat-basedproducts.Finally,farmersaretaxpayerstoo.Sinceproducingthewheatmusthave

costsomething,theprogramoffersthemawindfallprofit.

5.a.Ifthequantitiesdemandedandsuppliedareveryresponsivetopricechanges,thena

governmentprogramthatdoublesthepriceofjellybeanscouldeasilycostmorethan$50million.In

Figure9.5.a.i,theshadedrectangleisthecostoftheprogram.

Figure9.5.a.i

Ontheotherhand,ifthedemandandsupplycurvesareinelastic,thenitisconceivablethatthe

programcouldcostlessthan$50million.SeeFigure9.5.a.ii.

b.Whenthedemandcurveisperfectlyinelastic,thelossinconsumersurplusis$50million,equalto

($0.5)(100millionpounds).Thisrepresentsthehighestpossiblelossinconsumersurplus.

Therefore,ifthedemandcurvehasanyelasticityatall,thelossinconsumersurpluswouldbeless

then$50million.SeeFigure9.5.b.

Pricen

$1.25-(1

1.00---------------------

Lossin

0.75-Consumer

Surplus

0.50---------------------

0.25-

III।Quantity

50100MO200250emillions

Figure9.5.b

6.a.Tofindtheequationfordemand,weneedtofindalinearfunction,e.g.,

P=a+bQDt

suchthatthelineitrepresentspassesthroughtwoofthepointsinthetable,e.g.(15,10)and(12,16).

First,theslope,6,isequaltothe“rise”dividedbythe'iun；'

15-12_1

10-16--i'

Second,wesubstitutefbrbandonepoint,e.g.,(15,10),intoourlinearfunctiontosolvefbrthe

constant,a:

Therefore,P=20—Invertingtoobtainthedemandcurveinitsusual

form:

Qn=40-2P.

Similarly,wemaysolvefbrthesupplyequation:

P=c+dQSt

passingthroughtwopoints,e.g.,(6,4)and(3,2).

Theslope,d,is

6-33

4-2-2,

Solvingfbrc:

(3、

Therefore,P=I—IQS.Invertingtoobtainthesupplycurveinitsusualform:

Qs=?

o尸.

b.Thepriceelasticityofdemand,ED,isequalto

P丫乌

EDlejl

Here,一色isequaltotheslopeofthedemandequation,i.e.,-2.Fromthetableorthedemand

equationderivedinparta,atP=9,QD=22.Substitutingintotheequationforelasticityofdemand:

TodeterminetheelasticityofdemandatP=12,QD=16,followthesameprocedure:

c.Thepriceelasticityofsupply,Es,isequalto

於。s]

IQ〔△PJ

△Qs2

Here,isequaltotheslopeofthesupplyequation,i.e.,At尸=9,Qs=6.

3

Substitutingintotheequationfortheelasticityofsupply:

Atapriceof12,thequantitysuppliedisequalto8.Substitutingintotheformulafortheelasticityof

supply:

=1.

d.Iftherearenotraderestrictions,theworldpriceof$9.00willprevailintheU.S.Fromthetable,we

seethatat$9.00domesticsupplywillbe6millionpounds.Similarly,domesticdemandwillbe22

millionpounds.Importswillprovidethedifferencebetweendomesticdemandanddomesticsupply:

22-6=16millionpounds.

e.Witha$9.00tariff,theU.S.pricewillbe$15(thedomesticequilibriumprice),andtherewillbeno

imports.Becausetherearenoimports,thereisnorevenue.Thedeadweightlossisequalto

(0.5)(16millionpounds)($6.00)=$48million,

where16isthedifferenceatapriceof$9between22demandedand6supplied,and$6isthe

differencebetween$15and$9.

flWithanimportquotaof8millionpounds,thedomesticpricewillbe$12.At$12,thedifference

betweendomesticdemandanddomesticsupplyis8millionpounds,i.e.,16millionpoundsminus8

millionpounds.

ThecostofthequotatoconsumersisequaltotheareaofthetrapezoidABCEinFigure9.6.f.

(12-9)(16)+(0.5)(12-9)(22-16)=$57million.

ThegaintodomesticproducersisequaltotheareaofthetrapezoidAGFE.

Therefore,totaldomesticproducergainis

(12-9)(6)+(0.5)(9-6)(12-9)=$22.5million.

7.a.Witha$9tariff,thepriceoftheimportedmetalonU.S.marketswouldbe$18,thetariffplusthe

worldpriceof$9.Todeterminethedomesticequilibriumprice,equatedomesticsupplyanddomestic

demand:

|-P=40-2P,orP=$15.

Theequilibriumquantityisfoundbysubstitutingapriceof$15intoeitherthedemandorsupply

equations:

QD=40-(2X15)=10

and

Theequilibriumquantityis10millionounces.Becausethedomesticpriceof$15islessthanthe

worldpriceplusthetariff,$18,therewillbenoimports.

b.WiththeVoluntaryRestraintAgreement,thedifferencebetweendomesticsupplyanddomestic

demandwouldbelimitedto8millionounces,i.e.Q。-Q，=g.Todeterminethedomesticpriceofthe

metal,sety-Qs=SandsolveforP:

(40-2P)-|p=8,orF=$12.

Atapriceof$12,V=16andQ=8;thedifferenceof8millionounceswillbesuppliedbyimports.

8.a.Section9.6inthetextprovidesaformulaforthe“pass-through”fraction,i.e.,thefractionofthe

..Eq

taxbornebytheconsumer.Thisfractionis------------,whereEsistheown-priceelasticityofsupply

Es-ED

andEDistheown-priceelasticityofdemand.SubstitutingfbrEsandEDythepass-throughfractionis

44

—7——r=——«0.95.

4-(-0.2)4.2

Therefore,95percentofthetaxispassedthi'oughtotheconsumersbecausesupplyisrelativelyelastic

anddemandisrelativelyinelastic.

b.Withanincreaseinthepriceofliquor(fromthelargepass-throughoftheliquortax),consumerswill

substituteawayfromliquortobeer,shiftingthedemandcurvefbrbeeroutward.Withaninfinitely

elasticsupplyfbrbeer(aperfectlyflatsupplycurve),therewillbenochangeintheequilibriumpriceof

beer.

9.FromExample9.1,weknowthatthesupplyanddemandcurvesfbrnaturalgasinthe1970scan

beapproximatedasfollows:

Qs=14+2PG+0.25P°

and

QD=-5PG+3.75P°

wherePGisthepriceofgasandPoisthepriceofoil.

Withthepriceofoilat$12perbarrel,thesecurvesbecome,

Qs=17+2&

and

QD=45-5PG.

Settingquantitydemandedequaltoquantitysupplied,

17+2PG=45-5PG,orPG=$4.

Atthisprice,theequilibriumquantityis25thousandcubicfeet(Tcf).

Ifaceilingof$1isimposed,producerswouldsupply19Tcfandconsumerswoulddemand40Tcf.

ConsumersgainareaA-B=57-3.6=$53.4billioninthefigurebelow.Producerslosethearea-A-C

=-57-9=$66.0billion.DeadweightlossisequaltotheareaC+B,53.4-66=$12.6billion.

Figure9.9

10.a.WearegiventheequationsforthetotalmarketdemandforsugarintheU.S.andthesupply

ofU.S.producers:

QD=23.86-.25P

Qs=-8.19+1.07P.

Thedifferencebetweenthequantitydemandedandsupplied,QD-Qs,istheamountofsugar

importedwhichisrestrictedbythequota.

Ifthequotaisincreasedfrom3billionpoundsto4billionpounds,thenwewillhaveQD-Qs=4

andwecansolvefbrQsandPfrom:

Qs+4=23.86-.25P

Qs=-8.19+1.07P

So

23.86-.25P-4=-8.19+1.07PorP=28.05/1.32=21.25centsperpound

and

Qs=-8.19+(1.07)(21.25)=14.5billionpounds

QD=Qs+4=18.5billionpounds.

b.

14.515.3518.3518.5Q

Figure9.10.b

ThegaininconsumersurplusisthesumoftheareasAthroughDinFigure9.10.b.Ontheother

hand,domesticproducerssufferalossofproducersurplusequaltoareaA.

Numerically:

A=(.75)(14.5)+(.75)(15.35-14.5)/2=10.88+.32=11.20

B=(.75)(15.35-14.5)/2=.32

C=(.75)(18.5-18.35)/2=.06

D=(.75)3=2.25

Thesenumbersareinbillionsofcentsortensofmillionsofdollars.

Thus,consumersurplusincreasesbyA+B+C+D=13.83=$138.3million,whiledomesticproducer

surplusdecreasesbyA=11.2=$112million.

c.Whenthequotais3billionpounds,theprofitearnedbyforeignproducersarerepresentedbytheareasDandG

(theworldpricefbrsugarisassumedtobe12centsperpound).Whenthequotaincreasesto$4billion,these

profitsarethenrepresentedbytheareasE,F,andinFigure9.10.b.Thechangeinprofitstoforeignproducersis

thus(E+F+G)-(D+G)orE+F-D.

Numerically:

E+F=(21.25-12)[(15.35-14.5)+(18.5-18.35)]=9.25(intensofmillionsofdollars).

Thus,theprofitsearnedbyforeignproducersincreaseby9.25-2.25=7or$70million.

ThedeadweightlossofthequotadecreasesbyanamountequaltotheareasB+EandC+F.Deadweight

lossthusdecreasesby.32+.06+9.25=9.63or$96.3million.

11.a.

AtapriceP=22centsperpound,thequantitydemandedQDwouldbe23.86-(.25)(22)or18.36

billionpounds.ThequantitysuppliedbythedomesticproducersQswouldbe-5.19+(1.07)(22)or

18.35billionpoundswhichalmostmatchesthequantitydemanded.(Note:Thetrueequilibrium

pricewithnoimportsis22.007centsperpound.)UseP=22andQ=18.35intherestofthe

answer.

b.AtthepriceP=22,domesticdemandforsugarwillbe18.4billionpounds.Ifthegovernment

wantstoallow2.5billionpoundsofsugarimports,itmustconstrainthedomesticproducersto

supplynomorethan18.4-2.5=15.9billionpounds.Thisamountstoaquotaondomestic

producersof15.9billionpounds.Thedomesticsupplycurvewillthusbecomeverticalatthis

quantity(seeFigure9.11.b).

19.7

Figure

9.1l.b

Wenowcomparethecurrentcasewiththefreemarketequilibriumwherethepriceofsugarinthe

U.S.isequaltotheworldpriceof12centsperpound.Theextracosttoconsumersisthelossin

consumersurpluswhichisrepresentedbytheareasAthroughD.Thebenefittodomestic

producersistheincreaseinproducersurpluswhichisrepresentedbyareaA.Theprofitsofthe

foreignproducersincreasebyanamountrepresentedbyareaD.Finally,thedeadweightloss

associatedwiththecurrentoutcomeisrepresentedbyareasBandC.

Numerically:

B=(15.9-7.7)*(19.7-12)/2=31.57

C=(20.9-18.4)*(22-12)/2=12.5

D=2.5(22-12)=25

A=[15.9(22-12)]-B=159-31.57=127.43.

Thesenumbersareinbillionsofcentsortensofmillionsofdollars

Thelossinconsumersurplusis127.43+31.57+12.5+25=196.5or$1.97billion.

Thegainindomesticproducersurplusis127.43or$1.27billion.

Theincreaseinforeignproducersurplusis25or$250million.

Thedeadweightlossis12.5+31.57=44.07or$441million.

12.Toanalyzetheinfluenceofatariffonthedomestichulabeanmarket,startbysolvingfor

domesticequilibriumpriceandquantity.First,equatesupplyanddemandtodetermine

equilibriumquantity:

50+Q=200-2Q,orQEQ=50.

Thus,theequilibriumquantityis50millionpounds.SubstitutingQEQequals50intoeither

thesupplyordemandequationtodetermineprice,wefind:

Ps=50+50=100,

and

PD=200-(2)(50)=100.

TheequilibriumpricePis$1(100cents).

However,theworldmarketpriceis60cents.Atthisprice,thedomesticquantitysuppliedis

60=50-Qs，orQs=10.

Similarly,domesticdemandattheworldpriceis

60=200-2Qo,orQD=70.

Importsareequaltothedifferencebetweendomesticdemandandsupply,or60millionpounds.If

Congressimposesatariffof40cents,theeffectivepriceofimportsincreasesto$1.At$1,domestic

producerssatisfydomesticdemandandimportsfalltozero.

AsshowninFigure9.11,consumersurplusbeforetheimpositionofthetariffisequaltothearea

boundedbythedemandcurveandapriceof60cents.

(0.5)(200-60)(70)=4,900millioncentsor$49million.

Afterthetariff,thepricerisesto$1.00andconsumersurplusf