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Itiscrucialtonotethattheimportdemandandexportsupplycurvesarenotthemselves
typicaldemandandsupplycurves.Eachofthemalreadyhaswithinitawholestructureof
productionanddemand.
RealIncomes,Production,ElasticitiesandtheTradePattern(appendix)
[ThefollowingisbasedontheappendicesofCavesandJones.]
Wewouldliketobeginbysettingoutthesourcesofwelfarecharges.Afirstexaminationshows
thatthesecancomeaboutdueto(1)changesinthetermsoftrade,or(2)endowmentchanges.
Therelevantexpression,whereRYreferstorealincomeinunitsoftheYgood:
Thisformidable-lookingexpressionactuallyhassomeintuitivecontent.Wehavechosento
measurewelfareintermsofyourrealconsumptionmeasuredinunitsoftheimportableYgood.
Notsurprisinglythen,thechangeinwelfareisgivenbythechangeinconsumptionthatis
attained--viz.PdDX+dDY(notethatthepriceconvertsunitsofXinto“real”terms,i.e.unitsof
Y).Thefinalexpressionofthishastwoterms.Thefirstisa“termsoftrade”effect.Notingthat
whenpˆ−1>0thenthepriceoftheimportablehasrisenrelatively,orequivalentlythetermsof
tradehaveworsened,wearenotsurprisedtofindthatthislowerswelfare.Thesecondtermis
lookingattheeffectsofsmallshiftsinourproductionbundle.Assumingth maintainfull
employment,soremainonthePPF,thefirstordereffectofthesechangesiszero.Thereasonis
thatwewerealreadyatanoptimum,soalongthePPFMRT=dY/dX=-P.Butsimply
multiplyingandrearrangingthenshowsPdX+dY=0.[Themoreadvancedstudentmay gnizethisasanexampleoftheWong/Vinerenvelopetheorem.]Whenthetermsoftradechange,whathappenstothedomesticdemandforimports?Thisisa
complicatedquestion.Wehavetoconsidersubstitutioneffectsandincomeeffectsindemand,as
wellasanyinducedeffectsonsupply.Theexpressionwhichwewillderivereflectsallofthese:
Ourdecisionsaboutimportsandexportsareintimatelylinkedbytherequirementof
balancedtrade.Whatdoesthissuggestabouttherelationoftheelasticities mportdemandand
exportsup Firstletusrecallthedefinitionsofeachoftheseterms:
ElasticityofimportdemandWewouldliketohaveanideahowthetermsoftradeadjusttoexogenouschanges
(anythingbutprices)inimportdemandsinthetwocountries.Theresultthatwewillderiveis
thatthetermsoftradewillturnagainstwhicheverhasthelargerproporti growthinimport
demandatunchangedprices:
III.TheRicardianModel Inth tchapterweestablishedanimportantprinciple:Ifautarkyrelativepricesdiffer,
itispossibleforcountriestotradeatanintermediatepriceratiosuchthatbothmaygain.Our
developmentoftheworldequilibriumwasinverygeneraltermsbasedondemandandsupplyin
eac ntry.Howeveritwasleftunexplainedwhyautarkypricesshoulddiffer.Thepresent
chapterdevelopstheRicardianmodeloftrade,andusestheconceptofcomparativeadvantage
asthebasisoftrade.WewillseethatintheRicardianmodel,thiscomparativeadvantagederives
fromunderlyingd encesinthetechnologyavailabletoeachcountry.
ivationoftheRicardianPPF
Onefactor(labor)infixedsupply
TwoGoods:XandY
Thetechnologyisfullydescribedbytheconstantunitlaborinputs:aLXandaLY
Factormarketclearingrequires:
MRT=aLX/aLYdefinesthemarginalrateoft ormation,whichtellshowmuchYmustb ucedtoproduceonemoreunitofX(notethatitisconstanthere).[seeFigure1]
AutarkyEquilibriuminaRicardianWorld
Wewillassumehomogeneoushomotheticpreferencessothatwecanusetheconstructofa
singlerepresentativeconsumer.
Assumingthatbothgoodsareprodu theoptimalityconditionsinacompetitiveeconomy
insurethat:AbilitytoTransform
MRS=[∂U/∂X]/[∂U/∂Y]
WillingnesstoSubstitute
Homogen erencesmeanseverybodyinthesocietyhasthesamepreferences.
HomotheticpreferencesmeanthatforagivenrelativepriceP,theproportioninwhichthegoods
areconsumedisindependentofthelevelofincome.[Theseallowustoputasideforthemoment
problemsofincomedistribution.]
RicardianSupplyandDemand
Thepricesof oodsproduceddependonlaborcosts.Ifanypricewasstrictlyaboveitslabor
costs,thenassumingagive eandfixedinputcoefficients,wecouldhaveinfiniteprofitsby
expandingproduct fthatgoodtoaninfinitelevel.Thustheassumptionofcompetitionand
finiteproduction lsinsuresthatthepricemustbelessthanorequaltothelaborcosts;thatis:
PX≤waLX
andPY≤waLY
(equalityifactuallyproduced)
Ifbothgoodsareproduced,itfollowsthat:
P=PX/PY=(waLX)/(waLY)=aLX/aLY=MRT
S candrawtheRicardianSupplyCurvesforXandY.Notethat,theautarkypricehasbeen
determinedevenbeforeconsideringdemand.Thedivisionofoutputbetweenthetwogoods,then
willcorrespondtothatdemandedatthesupply-determinedprice.ComparativeAdvantage
Whydocountriestrade?Whatdetermineswhichcountriesproducewhichgoods?Afirst
ideamightoccur:sincelaboristheonlyinput,homeshouldproducethosegoodswhichitcan
producewithlesslaborthantheforeigncountry.Itshouldimporttheothergoods.This heso-
calledPrincipleofAbsoluteAdvantage.Bythisprinciple,ifaLX<aLX*thenweshouldexport
goodX.Butisthisanadequatecharacterizationofthedeterminantsoftrade?Whatshould
happenifthehomecountryhasanabsoluteadvantageinproducingeverygood?Inthiscase,
aLi<aLi*forallgoodsi.Shouldtheytradeatall?
Toanswerthis,wemustturntothePrincipleofComparativeAdvantage.Thisis
arguablythemostimportantresultininternationaltradetheory,andsomustbestudiedclosely.
RecallthatwehavealreadydefinedthemarginalrateoftransformationasMRTaLX/aLY.
Wewillsaythathomehasacomparativeadvantageintheproducti goodXjust
when:Notethatintheautarkyequilibrium,wehadtheconditionthatP=MRT,soalsointheforeign
countrywehadP*=MRT*.Thus,recallingthatP=PX/PY,wehaveacomparativeadvantagein
goodXwhenP<P*,thatiswhenwehavealowerautarkyrelativepriceofgoodX.
Thismayseemabithardtofollow.Butthebasicideaissi Wearethe ively
efficientproducerofX.Whenourautarkypriceislower,thismeansthatwehavetogiveupless
YtogetonemoreunitofXthanistrueintheforeigncountry.Conversely,iftheforeigncountry
weret duceoneunitlessofX,theycouldusetheextralabortoproducemoreYthanwe
gaveup.Intuitively,thisextraamountofYcouldbedividedupandbothwouldbebetteroff.
ComparativeAdvantage:AnExample
Herehomehasanabsoluteadvantageineachgood(check!).Howeveritsco tiveadvantage
liesingoodX,since:Thusfromanautarkyposition,ifhomeproducedonelessY,itcouldproducetwomore
X.Ifforeignproducedonele itcouldproduce oreY.Thenetgaintotheworldof
shiftingthesiteofproductionisoneXandone-halfY.Bothcouldbemadebetteroff.
Note,then,absoluteadvantageisnotanadequatedeterminantofthepatternoftrade houghhomehasanabsoluteadvantageintheproductionofgoodY(aswellasgoodX),it
doesnotexportY.ThereasonisthatinspiteoftheabsoluteadvantageinY,ithasacomparative
disadvantageinY.
Derivati theRicardianWorldProductionPossibilitiesFrontier
TheworldPPFshowsthemaximum blecombinationsofXa giventhe
availabletechnologyandlaborsupplies.AcombinationofXandYissaidtobethemaximum
feasibleifitisnotpossibletoproducemoreofonewithoutproducinglessoftheother.Theseare
alsocalledpointso ductionefficiency.
IfeachcountryisonitsPPF,doesitfollowthattheworldisontheworldPPF?No!It
maybethatthedistributionofproductionacrosscountriesisaccomplishedinefficiently.Insuch
acase,byshiftingthesiteofproductionofeachgoodtothecountrywithcomparativeadvantage
ofthatgood,wecanincreasetheavailabilityofsomegoodswithoutreducingtheavailabilityof
others.Thatis,wecanmovetowardsapointofworldproductionefficiency.
WewouldliketoderivetheworldPPF.Twopointsareeasilyderivable,namelythose
whenbothcountriesproduceonlyX,oronlyY.Inthiscase:
Toproceed,wemustknowthepatternofcomparativeadvantage.Suppose,asbefore,thathome
has parativeadvantageingoodX.ThenMRT<MRT*.ThusifanyXatallshouldbe
produced,itshouldbeproducedinthehomecountry.Thus,startingfromapositionwhereonly
Y roduced,havethehomecountryproduceoneunitofX;theamountofYwehavetogive
upisexactlyMRT(recallthatishowwedefinedit!).Itisobviousthatwewouldhavethehome
startproducingXfirst,sincethefactthatithasalowerMRT sthatwehavetogiveupless
YforthatfirstunitofX.Note,though,thatsi helaborinp quirementsareconstantfor
eachcountry,thesamemustbetrueoftheirratio,theMRT.Thatis,foreachextraXwe
produce,wehavetogiveupMRTunitsofY.Thiscontinuestobetrueupuntilthepointthat
homeiscompletelyspecializedinX.IfwewanttheworldtoproduceyetmoreX,thenthe
foreigncountrywillhavetostartproducingit.But,nowthattheforeigncountrystartstoproduce
it,wehavetogiveu eYtogetaunitofX,sinceMRT*>MRT.
NotethatifactualproductionistotheleftofthekinkintheworldPPF,thentheprice
undertradeisequaltothehomeautarkyprice:PT=PA=MRT.Ifweactuallyproducetothe
rightofthekink,thenPT=PA*=MRT*.Ifweactuallyproduceatthekink,thenallthatwecan
sayisthatthetradepriceisintherange:PT∈[PA,PA*].TodeterminetheactualpointontheworldPPFwherewewillproduce,wehavetolook
atworlddemandandsupply.Asbefore,assumeMRT<MRT*,andthepricesarePPX/PY.
Notethattheworldsupplycurveisinthenatureofastepfunction.Thiscorrespondstothe
conditionthatacountrywillproducebothgoodsonlyifP=MRTinthatcountry.Thusthe
horizontalsectionsoccuratthelevelsatwhichP=MRTintherespectivecountries.Wecanthen
definethreeregionsinwhichbothgoodsaresupplied.Atapriceequaltothehomeautarky
price,PT=MRTonlyhomewillproduceX(althoughitmayproducesomeY ll);foreign
willspecializeinY.AtapricesuchthatMRT<PT<MRT*,bothcountriesspecialize--homein
goodXandforeigningoodY.AtatradepricesuchthatPT=MRT*thehomecountrywill
specializeingoodXandtheforeignwillbewillingtoproduceanyfeasiblecombinationofgood
XandY.Ofcourse,giventhesupplyconditions,thepricesandquantitiesdependonthedemand
conditions.However,notethatsmallshiftsindemandaffectproductionlevelsonlywhenoneof
thecountriesisproducingbothgoods.Further,inthiscase,thepriceiswhollyunaffected.Onthe
otherhand,ifbothcountriesarecompletelyspecialized,thensmallshiftsindemandleadtono
changeinproductionlevels,onlyach inthepricelevel!RicardianGainsFromTrade
Solongasthetradepricesdifferfromautarkyprices,therearegainstotrade.Ingeneral,
thegainswillbelargerthelargerthedivergence.
RelativeWagesinaRicardianWorld
TheRicardianmodelcanbeusedtotakeafistlookatwhatmightgiverisetothe
observeddistributionofwagesintheworld.
Ifbothcountriesspecialize,whichoccurswhenMRT<PT<MRT*,itmustbetruethat
PX=waLXandPY=w*aLY*.
Thisimpliesthatw/w*=[PX(1/ /[PY(1/aLY*)].Notethat1/aLXisthemarginal
productoflabor,soPX(1/aLX)givesthevalueofthemarginalproductforgoodX.Thustheratio
ofwagesbetweenthetwocountriesequalstheratioofthevalueoftherespectivemarginal
products.NotethatashiftofdemandthatraisedP=PX/PYyetstillleftproductioncompletely
specializedwouldraisehomerelativewages.
Wecansayabitmoreaboutrelativewagesinthisfirstcase.Solongasthetradeprices
are(weakly)betweentheautarkyprices,wecangiveaboundforrelativewages(alsoknownas
thefactoraltermsoftrade):Ifhomespecialized,butforeig not,thenitmustbethecasethat:
PX=waLX=w*aLX*andsow/w*=aLX*/aLX.
Thatis,hererelativewagesarefixedwhollybythetechnicaldifferencesinthegoodproducedin
common.This uesolongasonedoesnotspecialize.
SmallRicardianEconomyCapableofProducingNGoods
Bydefinition,asmallRicardianeconomyfacesfixedpricesforitsoutput.Evenifitis
capableofproducingNgoods,itwillspecializeinone(orseveralintheknife-edgecaseofatie)
forwhichthereisthelargestvalueofthemarginalproduct:Pi(1/aLi)=VMPi(recall1/aLiisthe
marginalproductinthei'thgood.TherewillbeatieifandonlyifPi/Pj=aLi/aLj.
NoticethatthissuggeststhatifweactuallylivedinaRicardianworldtherewouldlikely
beaver hdegreeofspecialization.AsalwaysinaRicardianmodel,wehavethetechnical
coefficients(herethelaborinputrequirements)independentofthelevelofoutput o assumedtobehomogeneousandperfectlymobiledomestically.
TechnicalProgressinaRicardianModel&DistributionoftheGains
Bydefinition,asmallRicardianeconomyfacesfixedpricesforitsoutput.Evenifitis
capableofproducingNgoods,itwillspecializeinone(orseveralintheknife-edgecaseofatie)
forwhichthereisthelargestvalueofthemarginalproduct:Pi(1/aLi)=VMPi(recall1/aLiisthe
marginalproductinthei'thgood.TherewillbeatieifandonlyifPi/Pj=aLi/aLj.
NoticethatthissuggeststhatifweactuallylivedinaRicardianworldtherewouldlikely
beaveryhighdegreeofspecialization.AsalwaysinaRicardianmodel,wehavethetechnical
coefficients(herethelaborinputrequirements)independentofthelevelofoutput.Laboris
assumedtobehomogeneousandperfectlymobiledomestically.
TechnicalProgressinaRicardianModel&Distribu