The Simple Analytics of Trade Creation and Diversion - Ford ......2019/06/14 · Trade creation...
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RESEARCH SEMINAR IN INTERNATIONAL ECONOMICS
Gerald R. Ford School of Public Policy The University of Michigan
Ann Arbor, Michigan 48109-3091
Discussion Paper No. 670
The Simple Analytics of Trade Creation and Diversion
Alan V. Deardorff University of Michigan
Rishi R. Sharma Colgate University
June 14, 2019
Recent RSIE Discussion Papers are available on the World Wide Web at: http://www.fordschool.umich.edu/rsie/workingpapers/wp.html
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The Simple Analytics of Trade Creation and Diversion
Alan V. Deardorff The University of Michigan
and
Rishi R. Sharma
Colgate University
June 14, 2019
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Paper: TCTD06142019.docx
ABSTRACT
The Simple Analytics of Trade Creation and Diversion
Alan V. Deardorff The University of Michigan
and Rishi R. Sharma
Colgate University
Thispaperconductsanalysisofafreetradeagreementwithinasimplemodelofpartialequilibrium,linearsupplyanddemand,andcircumstancessuchthattradeflowsarepositiveinallequilibriaconsidered.Theresultsillustratethecloseconnection,ontheonehand,betweentradecreationandthebenefittotheFTA-formingcountriesandtotheworld,and,ontheotherhand,theequallycloseconnectionbetweentradediversionandtheharmtooutsidecountriesandpotentiallyboththeparticipatingcountriesandtheworld.Inaddition,byconsideringasecondcaseinwhichacountrythatalreadyhasoneFTAaddsanother,weshowthatthenewFTAcausestradetobedivertedfromitspriorpartner,aneffectthatwecalltradereversion.Itturnsoutthattradereversioncausesneitherharmnorbenefittotheimportingcountry,andwhenwelookatworldwelfare,iftradereversionisequaltotradediversiontheirtwoeffectscancelout,leadingtheeffectonworldwelfaretobeasimplefunctionoftheamountoftradecreationandthesizeofthetariff. Keywords: FTAs Correspondence: Trade creation Alan V. Deardorff Trade diversion Ford School of Public Policy JEL Subject Code: F13 Commercial Pol. University of Michigan Ann Arbor, MI 48109-3091 Tel. 734-764-6817 Fax. 734-763-9181 E-mail: [email protected] http://www-personal.umich.edu/~alandear/
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June 14, 2019
The Simple Analytics of Trade Creation and Diversion*
Alan V. Deardorff The University of Michigan
and Rishi R. Sharma
Colgate University
I. Introduction
In this paper we lay out a simple model of trade creation and trade diversion caused by a
Free Trade Agreement (FTA). These concepts, introduced by Viner (1950) for a customs
union, are most simply explained in terms of the cost of producing a good in a potential
partner country compared either to the cost of producing it at home or producing it
abroad, in a country from which imports continue to be subject to a tariff. However,
market responses to FTAs will often, especially in the short run, cause costs to change
and even become equal at the margin, as suppliers move up and down their supply
curves. The analysis here allows for that, so that the welfare effects of trade creation and
trade diversion cannot be easily inferred from marginal costs as they appear in
equilibrium. These welfare effects are nonetheless quite easy to derive using the standard
*This paper began as the theoretical basis for Deardorff and Sharma (2018), in which we ask how the sectors that countries exempt from their FTAs are related to whether they would be subject to trade creation or trade diversion. Our development of the model was prompted in part by comments from Peter Neary on an early version of that paper. The current extension of the analysis to include a fourth country, and what we are calling trade reversion, was prompted by comments from a referee on that other paper.
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tools of consumer and producer surplus, and they conform well with the expectations of
Viner.
Viner’s analysis was conceived at a time when FTAs and customs unions were
not common. Today, there are hundreds of FTAs reported to the World Trade
Organization, so that when two countries form a new FTA, it is likely that each has other
trading partners with which it already trades freely under a separate FTA. Viner’s
concepts can be applied to such situations as well, but now a new FTA diverts trade not
just from outside countries but also from inside countries – those with which the
importing country trades freely under the separate FTA. While such trade may be viewed
as literally being diverted, the welfare effects are not the same as trade diversion from an
outside country, and we will give it the different name of “trade reversion.”1 Our
thinking is that this is trade that had previously been diverted in the conventional sense
when the prior FTA was formed, and the diversion due to the new FTA is really just
reversing that earlier trade diversion.
In section II we lay out our market assumptions and the notation that we use
throughout the paper. In section III we provide a graphical analysis of a simple 3-country
case, in which one country forms an FTA with a second country, while keeping its tariff
on the entire rest of the world unchanged. The essence of this graphical analysis is not
new, adapting and building on WTO (2011). It shows clearly how the welfare effects of
the FTA are related to trade creation and trade diversion, and how these concepts make
sense even though costs in each country change with the formation of the FTA.
1A search for this term in prior literature also found it, with the same meaning, in Silva (1986) and Deardorff (2014).
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Section IV provides the algebraic analysis of both the model of section III and of
a 4-country model that includes a pre-existing FTA. The latter model is then examined
graphically in section V. Each of sections III-V present steps in analysis that may be less
than obvious without breaking them into smaller steps. These smaller steps are laid out
in appendices.
II. Model Assumptions and Notation
Ours is a partial equilibrium, perfectly competitive analysis of a single product that is
imported by a focus country, A, and that is exported to it by two or more other countries,
B, C, and, in section V, D. Demands and supplies are linear, as are their differences,
exports of countries B-D, and imports of country A:
Exports: !" = $"%&" − ("),, = -, ., /,012&" ≥ (" (1)
Imports: 45 = $5((5 − &5),012&5 ≤ (5 (2)
Here, $" > 0, , = ;, -, .,/, are the constant slopes of the excess supply and demand
functions, and (" > 0, , = ;, -, .,/, are the autarky prices at which trade in this product
would be zero. We will confine our attention to only cases in which all of the quantities
traded are nonnegative, and thus2
&" = (" + !"/$",, = -, ., / (3)
&5 = (5 −45/$5 (4)
2 We discuss the importance of this assumption, and how it might be dropped in section VI.
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Astheonlycountryimportingthisgood,countryAleviesspecifictariffs,>",
, = -, ., /,onitsimportsfromtheotherthree,anyofwhichmaybezero.In
equilibrium
45 = !? + !@ + !A (5)
For any trade flow (since they are assumed positive), prices differ by the size of the tariff:
&" = &5 − >",, = -, .,/ (6)
TherevenueofcountryA(theonlycountrylevyingatariffinthismarket)is
B5 = >?!? + >@!@ + >A!A (7)
SolutionoftheModel:
Substituting(1),(2),and(6)into(5):
$5((5 − &5) = ∑ D$"%&5 − >" − (")EA"F? (8)
whichrearrangesto
G + ∑ $">"A"F? = H&5 (9)
where
H = $5 + $? + $@ + $A (10)
G = $5(5 + $?(? + $@(@ + $A(A (11)
Aswillbeseenbelow,underadditionalassumptionsthe$" reflectcountrysize,and
thereforewedefine
I" = $" H⁄ (12)
whichcanthenbeinterpretedascountryi’ssizeasashareoftheworldeconomy.
From(9),theequilibriumpriceincountryAisthen
&5 = KL+ ∑ I">"A
"F? (13)
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Welfare
Whenpriceinacountrychanges,wewillidentifythewelfareeffectofthe
pricechangebythetradeanalogueofproducer/consumersurplus.Forthe
importingcountry,A,thechangeinwelfarewillalsoincludeanychangeintariff
revenue,plusthechangeinnetsurplusoftheprivatesector(domesticsuppliersand
domesticdemanders):
∆NO5 = −4P5∆&5 + Q
R$5(∆&5)R (14)
Fortheexporters
∆NO" = !P"∆&" +QR$"%∆&")R,, = -, .,/ (15)
CountrySize
Todealwithcountrysize,weaddthefollowingassumptionaboutthe
compositionofindustriesineachcountry:Lettheindustryineachcountry, =
;, -, .,/becomposedofalargenumberS"ofcompetitivesuppliers,eachwiththe
samesupplycurveT%&" − U").Thustheslopeparameterofallfirmsinallcountries
isassumedtobethesame,T,andthefirmsdifferacrosscountriesonlyintheircost
intercept,U".Theindustrydomesticsupplycurveincountryiistherefore
O" = S"T%&" − U"),&" ≥ U" (16)
Assumetoothatdemandersinallcountriesialsoshareasingleslopeparameter,V,
andthattheytoodifferacrosscountriesonlyintheirintercepts,W".Assumefinally
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thatthenumberofdemandersineachcountryisacommonmultiple,Γ,ofthe
numberoffirms,S".Thentheindustrydomesticdemandcurveis
/" = ΓS"V%W" − &"),&" ≤ W" (17)
Withtheseassumptions,theautarkypriceincountryicanbederivedas
(" = YZ[\]^_[
Y\]^ (18)
whichisindependentofthenumbersoffirmsanddemanders,andthusof
industry/countrysize.Theslopeparameteroftheexportandimportfunctions,
however,doesdependoncountrysize.Thesefunctionscanbederivedas
!" = S"(T + ΓV)%&" − ("),, = -, .,/, &" ≥ (" (19)
45 = S5(T + ΓV)((5 − &5),&5 ≤ (5 (20)
Thustheslopeparametersare,
$" = S"(T + ΓV),, = ;,-, ., / (21)
andthe$" differacrosscountriesonlybycountrysize.Lettheunitsof
measurementofgoods,money,firms,anddemandersbechosensothatT + ΓV = 1.
Thenwecaninterpret$" = S" asmeasuringthesizeofcountryi,andI" = $" H⁄ as
therelativesizeofcountryicomparedtoalltogether.3
3 The assumption above that numbers of demanders are proportional to numbers of firms may strain credulity even more than the other assumptions here, since one expects exporters to have more firms on average, relative to population, than importers. This error might be minimized if trade itself is small compared to domestic supply and demand, but even that is a stretch. This association of the b’s with country size is therefore only intended as a very rough heuristic, and even then is better for comparing exporters than comparing an exporter to the importer.
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III. Analysis of a First FTA
InthissectionweapplythemodelofsectionIItotheformationofasingleFTA
betweencountryAandcountryB,withcountryCrepresentingtheentirerestofthe
worldwithwhichcountryAcontinuestohaveacommonMFNtariff,t.Weignore
countryD,forwhichweassume$A, IA = 0.Theanalysisinthissectionisgraphical,
usingthesameassumptionsofsectionII,withoneadditionalassumption:thatthe
twoexportingcountries,BandC,areidentical.Thisassumptionallowsusto
representthemwithacommonexportsupplycurve.Itsimportanceisminimalin
the3-countrycase,butitwillbemoreimportantwhenweaddafourthcountry,as
wewillseelater.
Figure1showstheequilibriabeforeandaftertheformationoftheFTA.On
theleftarethecommonexportsupplycurvesforcountriesBandCasfunctionsof
thepriceincountryA,&5,withthesuperscriptfwhentheyarenotsubjecttoatariff
bycountryAandthesuperscripttwhentheyaresubjecttothecommonspecific
tarifft.ThepanelontherightshowstheimportdemandcurveofcountryA,45.
Equilibriumisfoundbyintersectingthiswiththehorizontalsumofthetwoexport
supplycurves.
PriortotheFTA,bothexportersaresubjecttothesametariff,sothis
horizontalsumhasthesameinterceptasthetwowith-tariffexportsupplycurves,
andhalftheirslope.Theequilibriumhasprice&P5incountryAandquantityof
imports4P5,whichissplitevenlybetweenthetwoexporters.
WiththeFTA,countryB’sexportsupplycurveisnowthelowerone,!?a,and
itisabletoexportatpricesbelowtheautarkypriceofcountryC.Theimportsupply
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curveontherightthereforeisidenticaltocountryB’sexportsupplycurveforprices
below(@ + >.Onlyabovethatlevelarethetwoexportsupplycurvesadded
together,resultinginthekinkshownatthatprice.Becauseweassumethroughout
thispaperthatalltradeflowsremainpositive,weshowthenewequilibriumas
abovethatkink,althoughitwouldn’thavetobeifthetariffwerelargeenough.
Comparingthetwoequilibria,weseethatcountryA’stotalimportsrisefrom
4P5to4Q
5,whilepartnercountryB’sexportsriseevenmore,from!P? to!Q? .This
happensbecausetheexportsoftheoutsidecountry,C,fall,from!P@ to!Q@ .This,of
course,isthetradediversionthatVinertaughtus,thoughinthiscaseitdoesnot
arisebecauseofanyexantedifferencebetweencountriesBandC,sinceweassumed
themtobeidentical.We’llseeshortlywhythistradediversioniscostlyinspiteof
that.
Figure1labelstheriseinimportsofcountryAastradecreation,TC,andthe
fallinexportsofcountryCastradediversion,TD.Theincreaseinexportsofpartner
countryBmustofcoursebethesumofthesetwo(asrequiredbyequation(5)since
countryDisabsent),anditwillbeconvenientthereforetoshowTDandTCalsoas
makingupthegapbetween!P? and!Q? .
NowconsiderthewelfareeffectsofthisFTA.TheseareshowninFigure2for
theimportingcountryA,inFigure3forthebothexportingcountries,BandC,andin
Figure4fortheworld.InFigure2,CountryAlosesallofitsprevioustariffrevenue
fromcountryB,anditalsolosesthetariffrevenueonthoseimportsfromcountryC
thatnolongeroccur.Ontheotherhand,countryA’sdomesticdemandersofthe
goodgainfromitsfallinprice,andtheirgainexceedsthelosstodomesticsuppliers
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bytheamountshownontherightofFigure2.Forexpositionalconvenience,wewill
refertothisasthegaintocountryA’snetdemanders,andspeaksimilarlyofthe
welfareoftheexportingcountries’netsuppliers.
CountryAmaythereforelosefromtheFTAifthelossoftariffrevenueis
greaterthanthegaintothedomesticprivatesector.AsindicatedinFigure2,the
lossisassociatedwiththeamountoftradediversionandthegainwiththeamount
oftradecreation.Thelatteristruebecausenotonlythesmalltrianglebutalsothe
muchlargerrectangleofgaindependinsizeontheamountoftradecreation,since
thepricechangeandquantitychangearerelatedbytheslopeparameter,$5 .
However,itisnotthecasethatonecansimplycomparethetwoquantitiesoftrade
creationandtradediversioninordertoinferwhethertheFTAisoverallbeneficial
tocountryA.ThatdependsalsoontheheightoftheareasinFigure2plusthe
amountofinitialtradewithcountryB,onwhichalltariffrevenueislost.
ThewelfareeffectsonthetwoexportingcountriesareshowninFigure3as
verysimplytheareastotheleftofthetwoexportsupplycurvesbetweentheirtwo
prices,countryBgainingandcountryClosing.Asdrawn,theformerexceedsthe
latter,butthatwouldnoneedtobethecaseifBandCwerenotidentical.What
mattersforbothisthesizeanddirectionofitschangeinexports,andtheprice
changesthatcausethem.However,itisclearfromthefigurethatthelosstocountry
Cdependsdirectly,andalmostsolely,ontheamountoftradediversion.Thepartner
countryB,ontheotherhand,gainsfrombothtradecreationandtradediversion.
Figure4includesalloftheeffectsshownfromFigures2and3,withtheloss
oftariffrevenueforcountryAsuperimposedonthegainofcountryB.Itmaynotbe
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obvioushowthesepositiveandnegativeeffectsnetout,buttheresult(shownin
severalstepsinAppendixA)isinFigure5.Thisshowsclearlythatallofthegainfor
theworldisduetotradecreation(thegreentriangle),andallofthelossisdueto
tradediversion(theredrectangle).Again,however,onecannotsimplycomparethe
quantitiesofthesetwochangesintradetodeterminewhetherworldwelfarerises
orfalls,sincetheareasdependontheirverticaldimensionsaswellasthe
horizontal.Theverticaldimensionsdependonthesizeofthetariff,butthatmatters
forboththegainandthelosssimilarly.Moreimportantaretheslopesofthecurves,
whichwesawintheequationsofsectionIItoberelatedtothesizesofthecountries.
Wewillneedthealgebratosortthatoutmorefully,whichwewilldoinsectionIV.
Whatthegraphicalanalysisdoesallowustodo,however,istoseemore
clearlywhytradecreationandespeciallytradediversionhavethewelfareeffects
thattheydo.Fortradecreation,thegreentriangleinFigure5tellsthefamiliar
story:astradeexpands,netdemanderspurchaseunitsofthegoodthatareworth
moretothem(theheightofthedemandcurve)thantheirmarginalcostof
productionabroad(theheightofthesupplycurve).4Thegreentrianglecaptures
theintegralofthisdifference,asthemarginalbenefitandmarginalcostaremoved
togetherbynewtrade.
Fortradediversion,welookmorecarefullyatcostsinthetwoexporting
countriesinFigure6.Initially,becausetheyfacethesameprice,suppliersinthe
4More fully, by “net demanders purchase” we mean domestic demanders increase their purchases of goods worth more to them than their cost from abroad at the same time that domestic suppliers reduce their sales of goods that cost them more to produce than they can be obtained from abroad.
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twocountrieshavethesamemarginalcost.Butastradediversioncausesoutputto
riseinthecountryB,itsmarginalcostgoesupalongB‘ssupplycurve,andatthe
sametimeoutputfallsincountryC,causingitsmarginalcosttofall.Thusafterthe
firstunitoftradediversion,whichreplacesoneexportwithanotheratthesame
cost,alladditionalunitsofdivertedtradereplaceunitsofexportswithothersat
highermarginalcost.ThetwoaddedtrapezoidsinFigure6integratethesecost
changes,andtheirdifferenceinareaisequaltothesmallrectangleofworld
efficiencylossshownabovethemasthelossfromtradediversion.
Asthissuggests,theefficiencycostperunitoftradediversioninthismodel
withupwardslopingsuppliesincreaseswithitsquantity.Indeed,likethe
deadweightlossinsimplemodelsoftariffs,itriseswiththesquareofthequantityof
tradediversion,sincethemoretradeisdiverted,thegreaterwillbethemarginal
costdifferencebetweenthetwosuppliers.
IV. Model Solutions
WenowapplythemodelofSectionIItoasituationinwhichcountryAinitiallyhas
anFTAwithonlycountryD,thenformsanFTAwithcountryBaswell.Thuswe
haveaninitialequilibriumwithacommontariff,t,onbothBandCbutazerotariff
onD.ThesecondequilibriumhasthetariffsettozeroonBaswellasD,keepingthe
MFNtarifftoncountryConly.The solution is also valid for the case of a first FTA as
well, by just setting IA , reflecting the size of country D, to zero.
From (13) we have the initial and final price in country A:
&P5 =KL+ I?>? + I@>@ (22)
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&Q5 =KL+ I@>@ (23)
ThereforethepricechangeintheimportingcountryA,whichisalsotheprice
changeincountriesCandDsincetheirpricescontinuetoequal&5 − >,is
∆&5 = ∆&@ = ∆&A = −I?>? < 0 (24)
Notefromthisthatthedropinpriceintheimportingcountryislargerthelargeris
thenewpartnercountry,bothrelativetotherestofworldandrelativetoitsexisting
partner,sinceI? reflectscountryB’sshareofthemarketsofallfourcountries
combined.
Using (1), (2), and (24) it is straightforward to derive the changes in trade:
∆45 = I?$5> > 0 (25)
∆!? = I?($5 + $@ + (A)> > 0 (26)
∆!@ = −I?$c> < 0 (27)
∆!A = −I?$d> < 0 (28)
Thus the formation of an FTA between countries A and B causes trade between them to
increase in (25-26), while reducing the exports in (27-28) from both the outside country
C and the country D with which country A already had an FTA. These two declines in
exports, since they are matched by an increase in exports by country B, might both be
called trade diversion. However, because their welfare implications turn out to be
different, we will call only the first trade diversion TD (from country C) and refer to the
second as trade reversion TR (from country D). The reason for that name is that this can
be viewed as a partial reversal of the trade diversion that had previously occurred when
country A formed its FTA with country D, although we have not looked at that explicitly
here.
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Thus these changes in trade give us formulas for trade creation, trade diversion,
and trade reversion:
e. = I?$5> > 0 (29)
e/ = I?$c> > 0 (30)
eB = I?$d> > 0 (31)
Note that, while the increase in exports from country B does not have a name, it is equal
to the sum of the other three:
∆!? = e. + e/ + eB > 0 (32)
Welfare Effects
In country A, the government loses the entire tariff revenue on its prior imports
from the new partner country B, and it also loses the tariff revenue on the trade that is
diverted from country C to country B (TD). It does not lose anything from the decline in
imports from the existing partner country D, since the tariff on it was already zero. Thus
∆B5 = −>!P? − >e/ (33)
Ontheotherhand,countryAgainsfromthefallinprice,sinceitisanetimporter,
anditsdomesticdemandersthereforegainmorethanitsdomesticsuppliers.This
gaininnetsurplus(∆NO5),canbecalculatedfromtheimportdemandcurveasthe
followingtrapezoid:
∆NO5 = −fgh\fih
R∆&5 (34)
Withsomemanipulation,showninAppendixB,thiscanbetransformedtothe
following,
∆NO5 = (4P5/$5 + I?>/2)e. (35)
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whichwecombinewith(33)togettheneteffectonthewelfareofcountryA:
∆k5 = (4P5/$5 + I?>/2)e. − >e/ − >!P? (36)
WelfareofcountriesB,C,andDcanbefoundsimilarlyfromtheirpricechangesand
theirexportsupplyfunctions:
∆NO" = lg[\li[
R∆&" = !P"∆&" +
m[
R%∆&")R,, = -, ., / (37)
To apply this to country B we need its price change, which is a rise from &P5 − >
to &Q5:
∆&? = &Q5 − (&P5 − >) = ∆&5 + > = (1 − I?)> (38)
fromwhich(37)giveus
∆NO? = !P?(1 − I?)> +mn
R(1 − I?)R>R (39)
InAppendixBthisismanipulatedtoget
∆k? = ∆NO? = o!P? +QR(e. + e/ + eB)p (1 − I?)> (40)
CountriesCandD,withconstantandzerotariffsrespectively,experiencethe
samepricechangeascountryA:∆&@ = ∆&A = ∆&5.Thereforeasimilaranalysis,
alsodetailedinAppendixB,leadsto
∆k@ = o−!P@ +qARp I?> (41)
∆kA = o−!PA +qrRp I?> (42)
Interestingly,whilethefactsoftradediversionandtradereversionareharmfulto
thesecountries,thesereductionsintheirexportsreducetheirlossbelowwhat
wouldhaveoccurredfromtheirpricechangealonehadtheirexportsnotdeclined.
Thisisanalogoustothefamiliarresultthatthelossofproducersurplusfromafall
inpriceissmallerthanthelossinrevenuethatwouldhaveoccurredifsuppliers
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wereunabletoreduceoutput.Withaslopingsupplycurve,theylimitthatloss
somewhatbyceasingtoproduceunitsofthegoodthatwouldcostthemmorethan
thenewlowerprice.
Finally,weaskhowtheFTAaffectsthewelfareofallfourcountries
combined.Adding(36),(40),(41),and(42)weget
∆ks = tfih
mh+ unv
Rw e. − >e/ − >!P?
+ x!P? +12(e. + e/ + eB)y (1 − I?)>
+o−!P@ +qARp I?> + o−!PA +
qrRp I?> (43)
WithmoremanipulationshowninAppendixB,thisreducestothefollowing:
∆ks = QRe.> + Q
R(eB − e/)> (44)
Thus,theworldasawholegainsfromtradecreationandtradereversion,butloses
fromtradediversion.
V. Analysis of a Second FTA
Wenowturntoagraphicalanalysisofthe4-countrymodelthatincludestrade
reversion.TheapproachisexactlythesameasinsectionIII,butwiththreeidentical
exportingcountriesinsteadoftwo.Figure7showsthreeequilibriaintheright-
handpanel,zP, zQ, andzR,forcountryAhavingFTAswithnocountry,withone
country(D),andwithtwocountries(BandD)respectively.Eachistheintersection
ofimportdemandwithexportsupplies,wherethelatterarethesumsofthe
appropriateindividualexportsuppliesshownontheleft.AsinsectionII,countries
B,C,andDareassumedtosharethesameexportsupplycurve(aswasnotassumed
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inthemathofsectionIV).Theexportsupplyasafunctionofthecountry-Aprice,P,
isshownwiththesuperscriptf(forfreetrade)ifthereisnotariffonthoseexports,
andwiththesuperscripttiftheexportsfacethetarifftforsalesintocountryA.
Importsupplycurve∑!Pisthehorizontalsumofthoseidenticalupperthree
supplycurves.Curve∑!Qiswhatwetakeasourinitialsupplycurve,withtariffonB
andC,butnotonD.ItduplicatesjustcountryD’sexportsupplycurveuptothe
priceatwhichtheothertwocountriesbegintoexport,beyondwhichitisflatter,
parallelto∑!P.Curve∑!RshowsimportsupplywhenbothcountriesBandDfacea
zerotariff,anditthereforehashalftheslopeof∑!Quptoitskink.Asbeforewe
havedrawnthefigureundertheassumptionthatallthreecountriesexportinboth
equilibria.
TheformationofanFTAbetweencountriesAandBinthepresenceofaprior
FTAbetweenAandDcausesmovementfromequilibriumzQtozR.Thusitcauses
importsofcountryAtoexpandby∆45,exportsofcountryBtoexpandby∆!? ,and
exportsofcountriesCandDtofallby∆!@ and∆!A respectively.Sincetheselast
twochangesaremovementsalongparallelsupplycurvesrespondingtothesame
fallinprice,theymustbethesame:∆!@ = ∆!A.
Asbeforeweidentify∆45astradecreation,TC.Therearenowtwo
countrieswhoseexportsdeclineandarereplacedbyadditionaladdedexportsfrom
countryB,sobothmightreasonablybenamedtradediversion.However,because
weknow(buthavenotshown)thatcountryDmusthavebeenthebeneficiaryof
earliertradediversionwhenitsownFTAwithcountryAwasformed,wename∆!A
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tradereversion,TR,instead.OnlythedropinexportsofthestillexcludedcountryC
getsthenametradediversion,TD.Theselabelsarealsoshowninthefigure.
InsectionIIIitwasusefultonotealsothatthechangeinexportsofthe
partnercountryBcouldalsobelabeledwithTCandTD.Thesameistrueherefor
thenewpartnerB,whose∆!?equalsthesumofTC,TD,andTR.Weshowthisas
wellinthefigure,asitwillbeusefulinoursubsequentinterpretation.
Figures8-11showthewelfareeffectsofcountryA’snewFTAwithcountryB.
TheirconstructionparallelswhatwasseeninFigures2-4sufficientlythatno
additionalexplanationshouldbeneeded.Themainnewfeatureisthelossofnet
surplusincountryDduetotradereversion.Figure12thenshowsallfoursetsof
effectstogether,togettheeffectontheworld.
ThegainsandlossesshowninFigure12arenottrivialtomanipulatesoasto
findtheneteffectontheworld,butitcanbedoneinanumberofstepsshownin
AppendixC.TheresultistheperhapssurprisinglysimpleFigure13.Thenetofall
thegainsandlossesshowninFigure12turnsouttobeanunambiguousgain,equal
toasimpletrianglethebaseofwhichisthetariffandtheheightofwhich(measured
horizontally)istheamountoftradecreation.
Thissurprisingresult–thatthetradediversionandreversionofasecond
FTAdonothurttheworld–isanartifactofanassumptionthatwemadeinorderto
simplifythediagrams:thatcountriesCandDareidentical.Thisassumptionledto
thequantitiesoftradediversionandtradereversionbeingthesame.Lookingback
atequation(44),withe/ = eBitbecomes
∆ks = QRe.> (45)
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whichispreciselywhatisshowninFigure13.Withoutthatassumption,thesecond
FTAwouldraiseworldwelfareevenmorethanin(45)andinFigure13ifeB > e/.
Alternatively,ifeB < e/–asofcourseitmustbeifthereisnopriorFTA–then
worldwelfarewillrisebylessandmayfall.
VI. Other Cases
Zerotrade
We’veassumedthroughoutthateverycountry’sexportsarepositiveboth
beforeandaftertheFTA.Withourlinearexportsupplies,thatmaynotbethecase,
asapricemaystartorendbelowtheinterceptoftheexportsupplycurve.Thenew
partnercountry,B,mayinitiallynotexport,buttheFTAmayallowitto.And
countriesCandD,fromwhomtradeisdiverted,mayreducetheirexportstozero.
Wewillnotaddressanyofthesecasesexplicitly,excepttonotethatwhenan
FTAcausesapricetocrossacountry’sautarkyprice,thecasecanbebrokeninto
twoparts,onepartwiththatcountrysupplyingzeroandthereforenotincludedin
theanalysis,andasecondpartwhereitbehavesaswehavemodeledthecountries
here.Sinceouranalysisincludescasesinwhichacountryisabsent(aswasthecase
ofcountryDinsectionIII),themodeleasilyaccommodatessuchcases.Mostof
whatwehavefoundherewillholdinsuchhybridcases,withtheobviousexception
thatonceacountry’sexportsaredriventozero,nofurthertradediversionor
reversionispossibleforit.
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Non-identicalexporters
Weassumedidenticalsupplyfunctionsforallexportersonlyinthegraphical
analysisofsectionsIIIandV,sothealgebraofsectionIVallowsarbitrarydifferences
amongthem.However,ourargumentthattheslopeparameters$" wouldreflect
countrysizealsorequiredthatthecountriesbeidentical.Itremainstruethat,other
thingsequal,alargercountrywillhavealargervalueof$" ,butmanyotherthings
maymatterforthe$" aswellascountrysize.
Also,itisnotablethattheparameters(" haveplayednoroleinouranalysis,
eventhoughthesewouldnormallybethoughttoreflectcomparativeadvantageand
thecostdifferencesthatdriveournormalunderstandingofthecostsoftrade
diversion.Thereasonisagainourassumptionthatallexportsarepositiveboth
beforeandaftertheFTA.Itfollowsthatalleffectsaremovementsalongthesupply
curves,sothatonlytheirslopesmatter.
However,ifitisthecasethattheexportingcountriesdifferintheirautarky
prices(" ,thencountrieswithlowervaluesforthisparameterwillbeexporting
moreatgivenpricesevenwiththesame$" ,sothatagainourassociationof$" with
countrysizewillnotbevalid.
Otherimporters
We’vealsoassumedonlyasingleimporterforthegood.Therestofthe
worldoutsideanyFTAofcountryAcanofcourseincludeothercountriesthat
importthegood,sincetheywilljustbepartofthedomesticdemandofcountryC.
Whatwillcomplicatethingsforus,however,isifcountryAisalreadyinanFTAwith
anothercountrythatalsoimportsthegood.WhencountryAlowersitstariffon
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countryCandthisreducesthepriceofthegoodincountryA,thatotherimporter
willalsobenefitfromthelowerpriceeventhoughitdoesnotreduceitsowntariff.
Thatisacomplicationthatisnotcoveredbytheanalysishere.
Conclusion
Thispaperhasconductedanalysisofafreetradeagreementwithinasimplemodel
ofpartialequilibrium,linearsuppliesanddemands,andcircumstancessuchthat
tradeflowsarepositiveinallequilibriaconsidered.Theresultsillustratetheclose
connectionbetweentradecreationandthebenefittotheFTA-formingcountriesand
totheworld,andtheequallycloseconnectionbetweentradediversionandthe
harmtooutsidecountriesandpotentiallyboththeparticipatingcountriesandthe
world.Inaddition,byconsideringasecondcaseinwhichacountrythatalreadyhas
oneFTAaddsanother,wesawthatthenewFTAcausestradetobedivertedfromits
priorpartner,aneffectthatwecalledtradereversion.Itturnsoutthattrade
reversioncausesneitherharmnorbenefittotheimportingcountry,andwhenwe
lookatworldwelfare,inthespecialcasewheretradereversionisequaltotrade
diversion,theirtwoeffectscancelout,leadingtheeffectonworldwelfaretobea
simplefunctionoftheamountoftradecreationandthesizeofthetariff.More
generally,tradereversionwillincreasetheworldbenefitsfromthenewFTAifitis
greaterthantradediversion.
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References
Deardorff, Alan V. 2014. “Trade Implications of the Trans-Pacific Partnership for ASEAN and Other Asian Countries, Asian Development Review 31(2), pp.1–20.
Deardorff, Alan V. and Rishi R. Sharma 2018. “Exempted Sectors in Free Trade Agreements,” Research Seminar and International Economics, Discussion Paper #665, October 19.
Silva, Armindo Patrício da. 1986. "An analysis of the effects of preferential trade policies through the estimation of quantitative models: the case of Portugal," Tese de Doutoramento. University of Reading.
Viner, Jacob. 1950. The Customs Union Issue, New York: Carnegie Endowment for International Peace.
World Trade Organization, "Causes and Effects of PTAs: Is it all about preferences?", Ch. C: World Trade Report 2011, pp. 92-121
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Figure 1
FTA with a Single Country
𝑝"
Q Q
𝑋$%, 𝑋(%
𝑀"
𝑋*$ 𝑀+" 𝑀*
"
𝑡
𝑋$% + 𝑋(%
𝑋$. + 𝑋(%
𝑋$., 𝑋(. 𝑝+"
𝑝*"
TD TC
TD TC
Export Supplies Import Market
𝑋+$ = 𝑋+(
𝑋*(
𝑎$ = 𝑎(
𝑝"
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23
Figure 2
Change in Welfare of Country A Due to FTA with a Single Country
Q
Export Supplies
Q
𝑋$%, 𝑋(%
𝑀"
𝑋*$ 𝑀+" 𝑀*
"
Tariff revenue lost
from B C
Net gain of A’s private sector
𝑡
𝑋$% + 𝑋(%
𝑋$. + 𝑋(%
𝑋$., 𝑋(. 𝑝+"
𝑝*"
TD TC
TD TC
Import Market
𝑋+$ = 𝑋+(
𝑋*(
∆𝑊" = 6𝑎" +𝑏$𝑡2𝛽 :𝑇𝐶 − 𝑡𝑇𝐷 − 𝑡𝑋+
$
𝑝" 𝑝"
𝑎$ = 𝑎(
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24
Figure 3
Change in Welfare of Countries B and C Due to A’s FTA with a Single Country
Q Q
𝑋$%, 𝑋(%
𝑀"
𝑋*$ 𝑀+" 𝑀*
"
𝑡
𝑋$% + 𝑋(%
𝑋$. + 𝑋(%
𝑋$., 𝑋(. 𝑝+"
𝑝*"
TD TC
TD TC
Export Supplies Import Market
𝑋+$ = 𝑋+(
𝑋*(
Gain by partner country B
Loss by outside country C
𝑝" 𝑝"
𝑎$ = 𝑎(
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25
Figure 4
Change in Welfare of the World Due to A’s FTA with a Single Country
Q Q
𝑋$%, 𝑋(%
𝑀"
𝑋*$ 𝑀+" 𝑀*
"
𝑡
𝑋$% + 𝑋(%
𝑋$. + 𝑋(%
𝑋$., 𝑋(. 𝑝+"
𝑝*"
TD TC
TD TC
Export Supplies Import Market
𝑋+$ = 𝑋+(
𝑋*(
𝑝" 𝑝"
𝑎$ = 𝑎(
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26
Figure 5
Change in Welfare of the World Due to A’s FTA with a Single Country
(after some cancellation of losses and gains)
Q Q
𝑋$%, 𝑋(%
𝑀"
𝑋*$ 𝑀+" 𝑀*
"
𝑡
𝑋$% + 𝑋(%
𝑋$. + 𝑋(%
𝑋$., 𝑋(. 𝑝+"
𝑝*"
TD TC
TD TC
Export Supplies Import Market
𝑋+$ = 𝑋+(
𝑋*(
Loss from trade
diversion
Gain from trade creation
𝑝" 𝑝"
𝑎$ = 𝑎(
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27
Figure 6
Why the Loss from Trade Diversion
Q Q
𝑋$%, 𝑋(%
𝑀"
𝑋*$ 𝑀+" 𝑀*
"
𝑡
𝑋$% + 𝑋(%
𝑋$. + 𝑋(%
𝑋$., 𝑋(. 𝑝+"
𝑝*"
TD TC
TD TC
Export Supplies Import Market
𝑋+$ = 𝑋+(
𝑋*(
Loss from trade
diversion
C’s fall in cost
B’s rise in cost
𝑝" 𝑝"
𝑎$ = 𝑎(
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28
Figure 7 Adding a Second FTA
(By A with B after First FTA with D)
P
𝑋$., 𝑋(.,𝑋?.
Q Q
ImportMarket
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋?
TR
∆𝑋(
TD
∆𝑀"
TC
TR
ExportSupplies
∑𝑋+ 𝐸+
𝐸*
𝐸A
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29
Figure 8 Welfare Effects on A of Adding a Second FTA
P
Q Q
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋? ∆𝑋(
TD
∆𝑀"
TC
Tariffrevenuelost
from
B C
NetgainofA’sprivatesector
TR
TR
ImportMarket ExportSupplies
𝑋$., 𝑋(.,𝑋?.
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30
Figure 9 Welfare Effects on B of Adding a Second FTA
P
Q Q
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋? ∆𝑋(
TD
∆𝑀"
TC
NetgainofB’sprivatesector
TR
TR
ImportMarket ExportSupplies
𝑋$., 𝑋(.,𝑋?.
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31
Figure 10 Welfare Effects on C of Adding a Second FTA
P
Q Q
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋? ∆𝑋(
TD
∆𝑀"
TC
NetlossofC’sprivatesector
TR
TR
ImportMarket ExportSupplies
𝑋$., 𝑋(.,𝑋?.
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Figure 11 Welfare Effects on D of Adding a Second FTA
P
𝑋$., 𝑋(.,𝑋?.
Q Q
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋? ∆𝑋(
TD
∆𝑀"
TC
NetlossofD’sprivatesector
TR
TR
ImportMarket ExportSupplies
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Figure 12 Welfare Effects on World of Adding a Second FTA
P
𝑋$., 𝑋(.,𝑋?.
Q Q
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋? ∆𝑋(
TD
∆𝑀"
TC TR
TR
ImportMarket ExportSupplies
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Figure 13 Welfare Effects on World of Adding a Second FTA
(after cancellations)
P
𝑋$., 𝑋(.,𝑋?.
Q
ExportSupplies
Q
𝑋$%, 𝑋(%, 𝑋?% P
𝑡
∑𝑋*
∑𝑋A
𝑀"
∆𝑋$ ∆𝑀" ∆𝑋( ∆𝑋?
TD TC
∆𝑋? ∆𝑋(
TD
∆𝑀"
TC
𝑋*?
𝑋*$ = 𝑋*(
𝑋*$ 𝑋*( 𝑋*?
TR
TR
ImportMarket
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Appendix A
Derivation of Figure 5 from Figure 4
Figure 4 Change in Welfare of the World Due to A’s FTA with a Single Country
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
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36
Figure 4.1 Cancel overlap of lost tariff revenue with supplier gain to County B
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
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37
Figure 4.2 Re-shade remaining lost tariff revenue
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
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38
Figure 4.3 Move small red triangle to complete red rectangle
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
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39
Figure 4.4 Note that green rectangle on right is the sum of two red rectangles on left,
since 𝑀*( = 𝑋*" + 𝑋*&
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
=
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40
Figure 4.5 Cancel red and green rectangles
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
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41
Figure 4.6 Move small green triangle to left
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
𝑝( 𝑝(
𝑎" = 𝑎&
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42
Figure 5 Change in Welfare of the World Due to A’s FTA with a Single Country
(After cancelations)
Q Q
𝑋"#, 𝑋&#
𝑀(
𝑋)" 𝑀*( 𝑀)
(
𝑡
𝑋"# + 𝑋&#
𝑋"- + 𝑋&#
𝑋"-, 𝑋&- 𝑝*(
𝑝)(
TD TC
TD TC
Export Supplies Import Market
𝑋*" = 𝑋*&
𝑋)&
Loss from trade
diversion
Gain from trade creation
𝑝( 𝑝(
𝑎" = 𝑎&
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43
Appendix B: Steps deriving welfare changes in Section IV Derivation of (35) from (34):
∆𝑁𝑆$ = −'()*'+)
,∆𝑝$ (34)
= −.)/0)12()3*.)/0)12+)3,
∆𝑝$ from(2)
= −.)/0)12()*2+)12+)3*.)/0)12+)3,
∆𝑝$
= −𝑏$(𝑎$ − 𝑝7$)∆𝑝$ +.)/∆2)3
:
,
= 𝑏$(𝑎$ − 𝑝7$)𝜃<𝑡 +.)
,(𝜃<𝑡), from(24)
= (𝑎$ − 𝑝7$)𝑏$𝜃<𝑡 +>?@,𝑏$𝜃<𝑡
= (𝑀7$/𝑏$)𝑇𝐶 + >?@
,𝑇𝐶 from(2)&(29)
= (𝑀7
$/𝑏$ + 𝜃<𝑡/2)𝑇𝐶 (35)Derivation of (40) from (39): ∆𝑁𝑆< = 𝑋7<(1 − 𝜃<)𝑡 +
.?
,(1 − 𝜃<),𝑡, (39)
= H𝑋7< +.?
,(1 − 𝜃<)𝑡I (1 − 𝜃<)𝑡
= H𝑋7< +.?
,𝑡 − .?
,𝜃<𝑡I (1 − 𝜃<)𝑡
= H𝑋7< +.?
,𝑡 − J1.)1.K1.L
,𝜃<𝑡I (1 − 𝜃<)𝑡 from(10)
= H𝑋7< +.?
,𝑡 − J
,𝜃<𝑡 + .)>?@*.K>?@*.L>?@
,I (1 − 𝜃<)𝑡
= H𝑋7< +.?
,𝑡 − .?
,𝑡 + NO*NP*NQ
,I (1 − 𝜃<)𝑡 from(29-31)
= H𝑋7< +.?
,𝑡 − .?
,𝑡 + NO*NP*NQ
,I (1 − 𝜃<)𝑡 from(12)
∆𝑊< = ∆𝑁𝑆< = H𝑋7< +S,(𝑇𝐶 + 𝑇𝐷 + 𝑇𝑅)I (1 − 𝜃<)𝑡 (40)
Derivation of (41-42) from (37): For𝑖 = 𝐶,𝐷: ∆𝑁𝑆X = 𝑋7X∆𝑝X +
.Y
,/∆𝑝X3
, (37)
= −𝑋7X𝜃<𝑡< +.Y
,(𝜃<𝑡<), from(24)
= H−𝑋7X +.Y
,𝜃<𝑡<I 𝜃<𝑡<
∆𝑁𝑆O = H−𝑋7O +.K>?@?
,I 𝜃<𝑡<
= H−𝑋7O +NP,I 𝜃<𝑡< from(30)
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44
∆𝑊O = ∆𝑁𝑆O = H−𝑋7O +NP,I 𝜃<𝑡< (41)
∆𝑁𝑆P = H−𝑋7P +.L>?@?
,I 𝜃<𝑡<
= H−𝑋7P +NQ,I 𝜃<𝑡< from(31)
∆𝑊P = ∆𝑁𝑆P = H−𝑋7P +NP,I 𝜃<𝑡< (42)
Derivation of (44) from (43): ∆𝑊Z = ['+
)
.)+ >?@
,\ 𝑇𝐶 − 𝑡𝑇𝐷 − 𝑡𝑋7<
+ ]𝑋7< +12(𝑇𝐶 + 𝑇𝐷 + 𝑇𝑅)^ (1 − 𝜃<)𝑡
+H−𝑋7O +NP,I 𝜃<𝑡 + H−𝑋7P +
NQ,I 𝜃<𝑡 (43)
= '+)
.)𝑇𝐶 + >?@
,𝑇𝐶 − 𝑡𝑇𝐷 − 𝑡𝑋7<
+𝑋7< +12(𝑇𝐶 + 𝑇𝐷 + 𝑇𝑅)𝑡
−𝑋7<𝜃<𝑡 −𝜃<𝑡2 𝑇𝐶 −
𝜃<𝑡2 𝑇𝐷 −
𝜃<𝑡2 𝑇𝑅
−𝑋7O𝜃<𝑡 +NP,𝜃<𝑡 − 𝑋7P𝜃<𝑡 +
NQ,𝜃<𝑡
= '+)
.)𝑇𝐶 − 𝑡𝑇𝐷 + S
,(𝑇𝐶 + 𝑇𝐷 + 𝑇𝑅)𝑡
−𝑋7<𝜃<𝑡 − 𝑋7O𝜃<𝑡 − 𝑋7P𝜃<𝑡 = '+)
.)𝑇𝐶 − 𝑡𝑇𝐷 + S
,(𝑇𝐶 + 𝑇𝐷 + 𝑇𝑅)𝑡
−(𝑋7< + 𝑋7O + 𝑋7P)𝜃<𝑡 = '+)
.)𝑇𝐶 − 𝑡𝑇𝐷 + S
,(𝑇𝐶 + 𝑇𝐷 + 𝑇𝑅)𝑡 −𝑀7
$𝜃<𝑡 from(5)
= '+)
.)(𝑇𝐶 − 𝑏$𝜃<𝑡) + S
,𝑇𝐶𝑡 + S
,𝑇𝑅𝑡 − S
,𝑇𝐷𝑡
= S,𝑇𝐶𝑡 + S
,𝑇𝑅𝑡 − S
,𝑇𝐷𝑡 from(29)
∆𝑊Z = S,𝑇𝐶𝑡 + S
,(𝑇𝑅 − 𝑇𝐷)𝑡 (44)
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45
Appendix C: Derivation of Figure 13 from Figure 12
Figure 12 Welfare Effects on World of Adding a Second FTA
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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46
Figure 12.1 Cancel overlap of lost tariff revenue with supplier gain to County B.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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47
Figure 12,2 Re-shade triangle of remaining lost tariff revenue.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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48
Figure 12.3 Move small red triangle to complete red rectangle.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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49
Figure 12.4 Split and move red-bordered rectangle.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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50
Figure 12.5 Replace small red-bordered rectangle with shaded triangle of equal size.
Note sizes of rectangles.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
𝑋-$ = 𝑋-(
𝑋-( 𝑋-) 𝑋-) 𝑋-$
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51
Figure 12.6 Cancel equal rectangles.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
𝑋-$ = 𝑋-(
𝑋-( 𝑋-) 𝑋-) 𝑋-$
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52
Figure 12.7 Remove size of red triangle from green triangle
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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53
Figure 12.8 Move small green triangle right to left.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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54
Figure 12.9 Convert trapezoid to triangle by moving a triangle up.
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.
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55
Figure 13 Welfare Effects on World of Adding a Second FTA
(after cancelations)
𝑃"
𝑋$%, 𝑋(%,𝑋)%
Q Q
𝑋$*, 𝑋(*, 𝑋)*
𝑡
∑𝑋-
∑𝑋.
𝑀"
TD TC TC TR
ExportSupplies ImportMarket
TD TR
𝑃"
𝐸-
𝐸.