平狄克《微观经济学》课后答案 16

PARTIV

INFORMATION,MARKETFAILURE,

ANDTHEROLEOFGOVERNMENT

CHAPTER16

GENERALEQUILIBRIUMANDECONOMICEFFICIENCY

TEACHINGNOTES

ThischapterbringstogethermaterialfromChapters1,3,6-10,and14.Duetotheamountof

materialanditstheoreticalnature,therearefewerexamplesthaninpreviouschapters.Thethemeis

theefficiencyofcompetitivemarketsingeneralequilibrium.

Thedistinctionbetweenpartialandgeneralequilibriumisreadilyacceptedbystudents,but

theymightfindthegeometryofFigure16.1intimidating.Exercise(6)offersstudentspracticewiththe

algebraunderlyingFigure16.1.Althoughthisisnotacompletediscussionofgeneralequilibrium,

studentscanlearntoappreciatethelimitationsofapartialequilibriumanalysisandtheneedto

considerinteractionsamongmarkets.Stresstheimportanceofusingageneralequilibriumanalysisfor

economy-widepolicies,e.g.,raisingtheminimumwage.

Toprovideacontextforthediscussionofexchangeeconomies,youmightstartbydiscussing

twochildrentradingcookiesandpotatochipsatlunchtime.Foramoreseriousexample,seeRadford,

<4TheEconomicOrganizationofaPOWCamp,“Economica(November1945).Anotherapplicationis

providedinExercise(4).StudentsfindthedefinitionofParetooptimality(anallocationisPareto-

efficientifgoodscannotbereallocatedtomakesomeonebetteroffwithoutmakingsomeoneelseworse

off)confusingbecauseofits“doublenegative”expression(i.e.,“cannot”and“without“inthesame

sentence).Trytoexpressthesameideainotherways,e.g.,“AnallocationisnotPareto-efficientif

goodscanbetradedsothatonepersonisbetteroffandeveryoneelseisjustaswelloff."Alwaysask

yourstudentswhetherapointisParetoefficient.DefineaPareto-improvingtrade.Showwhy

movementstowardthecontractcurvearePareto-improving,whilemovementsalongthecontractcurve

arenotPareto-improving.PointoutthatallcompetitiveequilibriaarePareto-efficientbutnotall

Pareto-efficientpointsareinequilibrium.Emphasizethatthecompetitiveequilibriumdependsonthe

initialallocation,whichwillelucidatethedistinctionbetweenequityandfinalallocationina

distribution.

UsetheEdgeworthboxtoshowthedistinctionbetweenefficiencyandequity;e.g.,apointon

thecontractcurvenearonecornermightbelesspreferredbecauseofequityconsiderationsthanapoint

offthecurvebutnearertothemiddleofthebox.Thisconflictintroducestheproblemofdefiningequity

andincorporatingitintoaneconomicanalysis.Table16.2presentsfourdefinitionsofequity.After

discussingthem,asktheclasstovoteonwhichdefinitionisclosesttotheirconceptofequity.Thenask

thestudentstodefendtheirchoices,whichshouldleadtoaninterestingdiscussion.

TheanalysisinSection16.4followsfromSection16.2byintroducingstudentstoproductionin

anEdgeworthbox(seeExercise(6)).Thisanalysisleadstothedefinitionofinputefficiencyandthe

productioncontractcurve.Exercise(3)focusesoninputefficiencywithmonopsonyandmonopoly.

ApplythedefinitionofParetooptimalitytoproduction.Exercise(2)discussestheshapeofthe

production-possibilitiesfrontier,PPF.BeforediscussingthegeometryofFigure16.11,makesurethat

studentsknowtherequirementsforoutputefficiency.Unlessyouhaveintroducedtheinvestment­

possibilitiesfrontierandtheaccompanyinganalysisinChapter15,thegeometrywillbenew.An

alternativeapproachtoFigure16.10istodrawtheEdgeworthboxforexchangeinsidethePPFwith

oneoftheverticesatpointC.Showwherethemarginalratesofsubstitutionareequalforboth

individualsandalsoequaltothemarginalrateoftransformation.Section16.5introducescomparative

advantageandappliesgeneralequilibriumanalysistothegainsfrominternational(two-country)trade.

Section16.6servesasabridgebetweenChapter16andthefollowingtwochapters.

REVIEWQUESTIONS

1.Whycanfeedbackeffectsmakeageneralequilibriumanalysissubstantiallydifferent

fromapartialequilibriumanalysis?

Apartialequilibriumanalysisfocusesontheinteractionofsupplyanddemandforone

market.Itignorestheinfluencesthatshiftsinsupplyanddemandinonemarket

mighthaveonmarketsforcomplementsandsubstitutes.Ageneralequilibrium

analysisattemptstoaccountfortheinfluencesonrelatedmarketsthatcould,inturn,

influencethemarketofprimaryconcern.Ignoringthesefeedbackeffectscanleadto

inaccurateforecastsofthefullinfluenceofchangesineithersupplyordemand.

Althoughanalysisshouldincorporateallfeedbackeffects,onetaskoftheeconomistis

todeterminethemarketsthataremostcloselyrelatedtothemarketofprimary

concern.Attentionisdirectedtowardthesemarkets,thusenablingbetterforecastsof

changeinequilibriumpricesandquantities.

2.IntheEdgeworthboxdiagram,explainhowonepointcansimultaneouslyrepresentthe

marketbasketsownedbytwoconsumers.

TheEdgeworthboxdiagramallowsustorepresentthedistributionoftwogoods

betweentwoindividuals.Theboxisformedbyinvertingtheindifferencecui'vesofone

individualandsuperimposingtheseontheindifferencecurvesofanotherindividual.

Thesidesoftheboxrepresentthetotalamountsofthetwogoodsavailableto

consumers.Ontheverticalaxis,wereadofftheamounttoeachindividualasthe

differencebetweenthehorizontalaxisandthepoint.Foroneindividual,thisisthe

distancefromthebottomoftheboxtothetop,andfortheother,thisisthedistance

fromthetopoftheboxtothebottom.Similarly,thehorizontalaxisrepresentsamounts

ofasecondgooddistributedtothetwoindividuals.Eachpointintheboxrepresentsa

differentallocationofthetwogoodsbetweenthetwoindividuals.

3.IntheanalysisofexchangeusingtheEdgeworthboxdiagram,explainwhyboth

consumers9marginalratesofsubstitutionareequalateverypointonthecontractcurve.

Thecontractcurve,inthecontextofanEdgeworthboxdiagram,isthesetofpoints

wheretheindifferencecurvesofthetwoindividualsaretangent.Weknowthatthe

marginalrateofsubstitutionisequaltothe(negative)slopeoftheindifferencecurves.

Also,whentwocurvesaretangentatapoint,theirslopesareequalatthatpoint.Thus,

bydefiningthecontractcurveasasetofindifferencecurvetangencies,themarginal

ratesofsubstitutionbetweenthetwogoodsareequalforthetwoindividualsifwe

assumeconvexindifferencecurves.

4.“Sinceallpointsonacontractcurveareefficient,theyareallequallydesirablefroma

socialpointofview.”Doyouagreewiththisstatement?Explain.

Ifsocietyisonlyconcernedwithefficiencyandnotwithequity,thenallpointsonthe

contractcurveareequallydesirable.Sinceitisimpossibletomakecomparisonsof

utilitybetweenindividuals,economicsfocusesonefficiency.But,ifwearealso

concernedwithequity(i.e.,whetherthefinalallocationisfair),thenallpointsonthe

contractcurvearenotequallydesirable.

5.Howdoestheutilitypossibilitiesfrontierrelatetothecontractcurve?

SinceeachpointinanEdgeworthboxcanbecomparedtoeveryotherpointbyeach

individual,individualscanassignapreferenceorderingtoallpoints.Thispreference

orderingistheutilityfunction.Wecangraphthesepreferencewithlevelsof

satisfaction(utility)foroneindividualononeaxisandlevelsofsatisfactionforasecond

individualontheotheraxis.(Ofcourse,morethantwoindividualscanberepresented

withmoreaxes.)Theutility-possibilityfrontiershowsthelevelsofsatisfaction

achievedbyeachoftwoindividualswhentheyhavetradedtoanefficientoutcomeon

thecontractcurve.Whilepointsthatliebetweentheoriginandtheutility-possibility

frontierarefeasibletheyarenotefficientbecausefurthertradingwillleaveone

individualbetteroffwithoutmakingtheotherindividualworseoff.Pointsoutsidethe

frontierarenotfeasibleunlesstheindividualsaregivengreateramountsofoneorboth

goods.

6.IntheEdgeworthproductionboxdiagram,whatconditionsmustholdforanallocation

tobeontheproduction-contractcurve?Whyisacompetitiveequilibriumonthecontract

curve?

WhenconstructinganEdgeworthboxfortheproductionoftwogoodswithtwoinputs,

eachpointintheboxrepresentsanallocationofthetwoinputsbetweenthetwo

productionprocesses.Withproduction,eachpointcanbeorderedaccordingtothetotal

output.Thesepointslieonisoquantsinsteadofonindifferencecurves.Sinceeach

pointsimultaneouslyrepresentstheallocationofinputstotwoproductionprocesses,it

liesontwoisoquants,oneforeachproductionprocess.Theproductioncontractcurve

representsallcombinationsofinputsthataretechnicallyefficient.Thus,therewould

benowaytoincreasetheoutputofonegoodwithoutdecreasingtheoutputoftheother

good.

Acompetitiveequilibriumisonepointontheproduction-contractcurve.Itisthe

intersectionoftheproduction-contractcurveandalinepassingthroughtheinitial

allocationwithaslopeequaltotheratioofprices.(Theratioofpricesdictatestherates

atwhichinputscanbetradedinthemarket.)Foracompetitiveequilibriumtohold,

eachproducermustuseinputssothattheslopesoftheisoquantsareequaltoone

anotherandalsoequaltotheratioofthepricesofthetwoinputs.Therefore,the

competitiveequilibriumisefficientinproduction.(Thisequilibriumassumesconvex

indifferencecurves.)

7.Howistheproduction-possibilitiesfrontierrelatedtotheproductioncontractcurve?

Wecangraphthequantitiesofeachoutputproducedbyeachallocation(eachpointin

theEdgeworthbox)onatwo-dimensionalgraph,wheretheverticalaxisrepresentsthe

outputofoneprocessandthehorizontalaxisrepresentstheoutputoftheotherprocess.

Theproduction-contractcurveisrepresentedinthistwo-dimensionalgraphasthe

productionpossibilitiesfrontier.Pointsinsidethisfrontierarefeasiblebutinefficient.

Pointsoutsidethefrontierareinfeasibleandonlyattainablewhenmoreinputsbecome

availableorproductionprocessesbecomemoreefficient.

8.Whatisthemarginalrateoftransformation(MRT)?ExplainwhytheMRTofonegood

foranotherisequaltotheratioofthemarginalcostsofproducingthetwogoods.

Themarginalrateoftransformation,MRT,isequaltotheabsolutevalueoftheslopeof

theproductionpossibilitiesfrontier.(Sincetheslopeofthefrontierisnegative,we

prefertoworkwithpositivequantities;themagnitudeistheabsolutevalueofthe

slope.)TheMRTistherateatwhichwecantradeoneoutputforanother(insteadof

usinginputstoproduceanotherunitofoneoutput,wecouldusethemtoproduce

anotherunitoftheotheroutput).Also,weknowthatthetotalcostofallinputsisthe

sameateachpointbecauseweusethesametotalamountofeachinput.Inparticular,

alongtheproductionpossibilitiesfrontier,theratioofmarginalcostisequaltotheratio

ofchangesinthetwoinputs(themarginalrateoftransformation).Thus,theMRTis

equaltotheratioofmarginalcostsofproducingthetwogoods.

9.ExplainwhygoodswillnotbedistributedefficientlyamongconsumersiftheMRTisnot

equaltotheconsumers'marginalrateofsubstitution.

Ifthemarginalrateoftransformation,MRT,isnotequaltothemarginalrateof

substitution,MRS,wecouldreallocateinputsinproducingoutputtoleavethe

consumersbetteroff.WhereMRTMRS,theratioofmarginalcostwillnotbeequalto

theratioofprices.Wecouldincreasetheoutputofonegood,sellthisoutputinthe

market,andusetheproceedstoincreasetheproductionoftheothergoods,leavingthe

consumerbetteroffthanintheinitialposition.Therefore,theinitialallocationwasnot

Pareto-efficient.OnlywhenMRT=MRSwillconsumersbeleftworseoffwitha

reallocationofinputsbetweentheproductionprocesses.

10.Whycanfreetradebetweentwocountriesmakeconsumersofbothcountriesbetteroff?

Freetradebetweentwocountriesexpandseachcountry'seffectiveproduction

possibilitiesfrontier.Assumingeachcountryhasacomparativeadvantageinthe

productionofsomegoodorservice,tradeallowsacountrytospecializeinthearea

whereithasthisadvantage.Ittradestheseoutputsforthosemorecheaplyproducedin

anothercountry.Therefore,specializationbenefitsmanyconsumersinbothcountries.

11.Whatarethefourmajorsourcesofmarketfailure?Ineachcase,explainbrieflywhythe

competitivemarketdoesnotoperateefficiently.

Thefourmajorsourcesofmarketfailurearemarketpower,incompleteinformation,

externalities,andpublicgoods.Weknowfromthestudyofmarketstructuresthat

marketpowerleadstosituationswherepricedoesnotequalmarginalcost.Inthese

situations,theproducerisproducingtoolittle.Consumerscouldbemadebetteroffby

redirectinginputsintotheproductionofthegoodproducedunderacompetitivemarket

structure,therebyloweringpriceuntilpriceisequaltomarginalcost.Incomplete

informationimpliesthatpricesdonotreflecteitherthemarginalcostofproductionor

thechangeinutilityfromchangesinconsumption.Eithertoomuchortoolittle(atthe

extreme,none)isproducedandconsumed.Externalitiesoccurwhenaconsumptionor

productionactivityinfluencesotherconsumptionofproductionactivities,andthese

effectsarenotreflectedinmarketprices.Publicgoodsaregoodsthatcanbeconsumed

atpricesbelowmarginalcost(attheextreme,freely)becauseconsumerscannotbe

excluded.Inthesefourcases,pricesdonotsendthepropersignalstoeitherproducers

orconsumerstoincreaseordecreaseproductionorconsumption.Thus,themarket

mechanismcannotequatesocialmarginalcostswithsocialmarginalbenefits.

REVIEWEXERCISES

1.Intheanalysisofanexchangebetweentwopeople,supposebothpeoplehaveidentical

preferences.Willthecontractcurvebeastraightline?Explain.(Canyouthinkofa

counterexample?)

Giventhatthecontractcurveintersectstheoriginforeachindividual,astraightline

contractcurvewouldbeadiagonallinerunningfromoneorigintotheother.Theslope

Y

ofthislineis—,whereYisthetotalamountofthegoodontheverticalaxisandXis

thetotalamountofthegoodonthehorizontalaxis.G,力garetheamountsofthetwo

goodsallocatedtooneindividualandaretheamountsof

thetwogoodsallocatedtotheotherindividual;thecontractcurvemayberepresented

bytheequation

y书k

Weneedtoshowthatwhenthemarginalratesofsubstitutionforthetwoindividuals

areequal,MRS1=MRSandtheallocationliesonthecontractcurve.

Forexample,considertheutilityfunctionU=.Then

W=翳2工融2耿

IfMRS1equalsMRS2,then

2融融

Isthispointonthecontractcurve?Yes,because

x2=X-X1andy2=Y-y19

2国12皆一力

ra(r\nt-xYr^

Thismeansthat

""""Qy-M，orXX-y/i=y_yi，and

%1欠1

=y-%,or¥^=y，or%=后心.

WiththisutilityfunctionwefindMRS1=MRS,andthecontractcurveisastraight

line.However,ifthetwotradershaveidenticalpreferencesbutdifferentincomes,the

contractcurveisnotastraightlinewhenonegoodisinferior.

2.Giveanexampleofconditionswhentheproductionpossibilitiesfrontiermightnotbe

concave.

Mostoftheproduction-possibilitiesfrontiersare'"bowedoutward,"i.e.,theyarestrictly

concavetotheorigin.However,ifthetwogoodsareproducedwithidenticalproduction

functions,decreasingtheoutputofonewillincreasetheoutputoftheotherbyanequal

amount.Thentheproduction-possibilitiesfrontierisastraightline.

3.Amonopsonistbuyslaborforlessthanthecompetitivewage.Whattypeofinefficiency

willthisuseofmonopsonypowercause?Howwouldyouranswerchangeifthe

monopsonistinthelabormarketwerealsoamonopolistintheoutputmarket?

Whenmarketpowerexists,themarketwillnotallocateresourcesefficiently.Ifthe

wagepaidbyamonopsonistisbelowthecompetitivewage,toolittlelaborwillbeused

intheproductionprocess.However,outputmayincreasebecauseinputsaregenerally

lesscostly.Ifthefirmisamonopolistintheoutputmarket,outputwillbesuchthat

priceisabovemarginalcostandoutputwillclearlybeless.Withmonopsony,toomuch

maybeproduced;withmonopoly,toolittleisproduced.Theincentivetoproducetoo

littlecouldbelessthan,equalto,orgreaterthantheincentivetoproducetoomuch.

Onlyinaspecialconfigurationofmarginalexpenditureandmarginalrevenuewould

thetwoincentivesbeequal.

4.Janehas8litersofsoftdrinksand2sandwiches.Bob,ontheotherhand,has2litersof

softdrinksand4sandwiches.Withtheseendowments,Jane'smarginalrateofsubstitution

(MRS)ofsoftdrinksforsandwichesisthreeandBob'sMRSisequaltoone.Drawan

Edgeworthboxdiagramtoshowwhetherthisallocationofresourcesisefficient.Ifitis,

explainwhy.Ifitisnot,whatexchangeswillmakebothpartiesbetteroflf?

工

GiventhatMRS80bMRSJane,thecurrentallocationofresourcesisinefficient.Jane

andBobcouldtradetomakeoneofthembetteroffwithoutmakingtheotherworseoff.

ThisisrepresentedintheEdgeworthboxinFigure16.4.

AlthoughwedonotknowtheexactshapeofJane'sandBob'sindifferencecurves,wedo

knowtheslopeofbothindifferencecurvesatthecurrentallocation,becauseweknow

=

thatMRS加屣3andMRSBob=1.

AssumethattheindifferencecurvesshowninthefigurerepresentJane'sandBob's

preferences.Then,bothJaneandBobwouldbebetteroff(becausetheywouldbeon

indifferencecurveswithgreaterlevelsofsatisfaction)ifJanetraded1literfor1

sandwich,leavingherwith7litersand3sandwiches.Note:ifsoftdrinksand

sandwicheswereperfectcomplementsforbothJaneandBob,thistradewouldnot

leavethembetteroff.

Sandwiches

Bob

Drinks

5.TheAcmeCorporationproducesxandyunitsofgoodsAlphaandBeta,respectively.

a.Useaproductionpossibilityfrontiertoexplainhowthewillingnesstoproducemore

orlessAlphadependsonthemarginalrateoftransformationofAlphaorBeta.

Theproduction-possibilitiesfrontiershowsallefficientcombinationsofAlphaandBeta.

ThemarginalrateoftransformationofAlphaforBetaistheslopeoftheproduction­

possibilitiesfrontier.Theslopemeasuresthemarginalcostofproducingonegood

relativetothemarginalcostofproducingtheother.Toincreasex,theunitsofAlpha,

AcmemustreleaseinputsintheproductionofBetaandredirectthemtoproducing

Alpha.TherateatwhichitcanefficientlysubstituteawayfromBetatoAlphaisgiven

bythemarginalrateoftransformation.

b.Considertwocasesofproductionextremes:(i)AcmeproduceszerounitsofAlpha

initially,or(ii)AcmeproduceszerounitsofBetainitially.IfAcmealwaystriesto

stayonitsproduction-possibilityfrontier,describetheinitialpositionsofcases(i)

and(ii).WhathappensastheAcmeCorporationbeginstoproducebothgoods?

Thetwoextremesarecornersolutionstotheproblemofdeterminingefficientoutput,

givenmarketprices.Thesetwosolutionsarebothpossiblewithdifferentpriceratios,

whichcouldproducetangencieswithAcme'sendofthefrontier.Assumingthatthe

priceratiochangessothefirmwouldfinditefficienttoproducebothgoodsand,

assumingtheusualconcaveshapeofthefrontier,itislikelythatthefirmwillbeableto

decreasetheproductionofitsprimaryoutputbyasmallamountforalargergaininthe

outputoftheothergood.Thefirmshouldcontinuetoshiftproductionuntiltheratioof

marginalcosts(i.e.,theMRT)isequaltotheratioofmarketpricesforthetwooutputs.

6.InthecontextofouranalysisoftheEdgeworthproductionbox,supposeanewinvention

causesaconstant^returns-to-scaleproductionprocessforfoodtobecomeasharply-

increasing-returnsprocess.Howdoesthischangeaffecttheproduction-contractcurve?

InthecontextofanEdgeworthproductionbox,theproduction-contractcurveismade

upofthepointsoftangencybetweentheisoquantsofthetwoproductionprocesses.A

changefromaconstant-returns-to-scaleproductionprocesstoasharply-increasing-

returns-to-scaleproductionprocessdoesnotnecessarilyimplyachangeintheshapeof

theisoquants.Onecansimplyredefinethequantitiesassociatedwitheachisoquant

suchthatproportionalincreasesininputsyieldgreater-than-proportionalincreasesin

outputs.Underthisassumption,themarginal