E ± c iency G ainsfrom M ultilateralT rad e Agreem ents
C
»aglar OÄ z d en¤
E m ory U niversity
A bstract
Itis widely accepted thatthe G A T T regime has been quite e®ective in alleviating
theproblemsfacedbytradeliberalizatione®ortsofthepast.T hereisnodoubtthatthe
institutionalframeworkandtheG A T T principleshavebeenamongthemajorcausesof
this success.U singageneralbargaininggameframeworkbetween governments acting
intheirselfinterest,weshowthatmultilateralnegotiationsprovidetwodistinctsources
ofe±ciencygains comparedtoanetworkofbilateralnegotiations.T hee±ciencygains
ofmultilateralism arise from the ability (1 )to provide P areto superioroutcomes in
marketwith largenumberofparticipants compared toseveralsmallerones and (2)to
internalizetheexternalities imposed bydiscriminatoryarrangements on third parties.
¤
D epartment ofEconomics, Emory U niversity, A tlanta, G A 30 322. E-mail:cozden@ emory.
edu. T his
paperis based on chapter2 ofmy dissertation atStanford U niversity.I would like tothankA nneKrueger
forencouragementand guidance,R obertStaiger, D ouglas B ernheim,A vnerG reif,P aulKrugman,R onald
M cKinnon, Steven T adelis, P ravin Krishna, participants at the European Economic A ssociation A nnual
Congress and departmentworkshops atStanford, Emory, Y ale, B rown, U niversity ofT exas atA ustin for
comments and theO lin Foundation for¯nancialsupport.A llerrors aremine.
1
1
In
trod uc tion
T he period since the Sec ond nW orld W ar w itnessed a rapid lib eralizationofinternational
trad e d uring w hic h the average tari® rate onnon-agric ulturalprod uc tsam ong ind ustrialized c ountriesd ropped f
rom 4 5% to 4 % . T here islittle d ispute ab out the role played b y
the num erousmultilateralround sofnegotiationsc ond uc ted at the auspic esofthe G eneral
Agreem ent onT ari®sand T rad e (G AT T ).M ore rec ently, b ilateraland regionalagreem ents
have b eengaining im portance interm softrad e polic y d eterm ination. Since m emb ership
inthese negotiationf
orum sisvoluntary, w hy d o c ountries¯nd it intheir self
-interest to
partic ipate insuc h regimesand ab id e b y their rules? W e are not the ¯rst onesto ask this
question.
O ne strand ofthe literature id enti¯ed the ine± c ienciesofunilaterally d eterm ined tari®s
and the role ofthe trad e negotiationsinim plem entingP areto superior outc om es,espec ially
inthe presence ofterm s-of
-trad e m otivations.J ohnson's[1953/54 ] sem inalw ork isa m ain
example ofthisliterature.T he m aininsight w e gainf
rom these papersisthat inthe ab sence
ofnegotiationsb etw eengovernm entsto low er their respec tive protec tionist m easures, the
negative externalitiesc aused b y unilateralac tionsw illlead to P areto inf
erior outc om es1.
M ost ofthe papersthat estab lish the w elf
are im provingpropertiesoflib eraliz atione®ortsd o
not d istinguish b etw eend i®erent typesoftrad e agreem ents.T he analysisism ostly c arried
out ina tw o-c ountry f
ram ew ork and israrely extend ed to a multi-c ountry c ase,m ainly d ue
to tec hnic ald i± c ulties.Another strand ofthe literature aim sto c om pare regionaland multilateralarrangem entsand triesto answ er w hether they are c om plem entsor sub stituteson
the path to glob alf
ree trad e2 How ever,the negotiationaspec t oftrad e polic y d eterm ination
isignored and the f
oc usisplac ed uponunilateralac tionsinb oth regional(c oalitional) and
1
T headjustmentprocesscanconvergetoaunique¯naloutcomeoratari®cycleneitherwhicharesocially
e±cient.
2
U nfortunately, this question has turned outtobe very di±culttoformalize and asystematicanalysis
has notyetemerged.T hestandardapproachhas beentocomparethewelfareproperties ofdi®erentregimes
and theanswers seem todepend criticallyon theassumptions overtheunderlyingeconomicenvironment.
2
multilateralsettings.
Inthispaper,our aim isto answ er the f
ollow ingquestions:Canw e c om pare the w elf
are
implic ationsofmultilateraland b ilateral/regionalapproachesto trad e polic y f
ormulation?
Ifw e c an, isit also possib le to id entif
y the sourc esofthe d i®erencesinresulting w elf
are
levels? T he answ er to the b oth questionsisyes.W e w illid entif
y tw o d istinct sourc esofe± c iency gainsthat only multilateralnegotiationsc anprovid e w henc om pared to a netw orkof
b ilateralnegotiations3.T hese e± c iency gainsresult f
rom the f
unctioningofany negotiation
round (b ilateralor multilateral) asanexc hange m arket f
or tari®sover w hich the ind ivid ual
c ountries' payo®sare d e¯ned . Inthisf
ram ew ork, the ¯rst sourc e ofe± c iency gainsarises
f
rom the ab ility to provid e superior outc om esina m arket w ith large numb er ofpartic ipants(c om pared to severalsm aller ones) through w elf
are arb itrage ac rosspartic ipants.T his
generalequilib rium result m anif
estsitselfinthe f
orm oftrad ing oftari® c oncessionsac ross
c ountriesinthe G AT T negotiations.A sec ond sourc e ofe± c iencygainsarise f
rom the ab ility
to internaliz e the negative externalitiesim posed b yd isc rim inatoryarrangem ents.\M arkets"
f
or tari®sd i®er f
rom other simple exc hange ec onom iesina signi¯c ant w ay since the tari®
rate b etw eentw o c ountriesentersthe payo® f
unctionofother c ountriesand thusc reates
anexternality. For example, b ilateraltrad e lib eralizationb etw eenc ountry A and c ountry
B w illnot only increase their w elf
are levels, b ut it w illalso low er the w elf
are ofc ountry
C through the w ell-know ntrad e d iversione®ec t. M ultilateralnegotiationsprovid e P areto
superior outc omesthrough the eliminationofthe negative externalitiesc aused b y d isc rim inatory arrangem ents(b etw eena group ofc ountries) onthird parties.Havingid enti¯ed the
potentialw elf
are gainsc reated b y multilateraltrad e b argaining, w e exam ine the rulesim plem ented inthe G AT T negotiationround s(rec iproc ity,unanim ity and non-d isc rim ination)
to realize these gainsinthe next c hapter.
M any papershave id enti¯ed the ine± c ienciesassoc iated w ith unilateralac tionsinthe
3
Inthenextchapter,wewillanalyzehowtheG A T T negotiationrounds werestructured and whatrules
(reciprocity, unanimity and non-discrimination orthe M ostFavored N ation-M FN )were adopted torealize
thee±ciencygains from multilateralism.
3
internationaltrad e literature, asw e stated earlier. E xtend ing J ohnson'sw ork onb ilateral
trad e relationships,M ayer [1981] id enti¯ed the set ofP areto e± c ient tari® levelsand asked
w hether ifc ertainG AT T lib eralizationrulesc anlead to the e± c ient points.Againinb ilateral
f
ram ew ork,R iezm an[19 82 ] asksifthe Nash b argaining solutionc anim plem ent ane± c ient
outc ome4 .
Ina series ofrec ent papers, B agw elland Staiger [19 96, 19 97a, b , c ] look at sim ilar
issuesand f
oc usonthe ine± c ienciesc aused b y term s-of
-trad e and /or politic ally m otivated
unilateralstrategies.InB agw elland Staiger [1996],they em phasiz e the P risoners'Dilem m a
nature ofunilaterallyd etermined trad e polic iesw here term s-of
-trad e m otivationsare present.
T hisc reatesthe m otivationf
or rec iproc allow eringoftrad e restric tionsina b ilateralsetting.
T heyextend their analysisto a verystyliz ed multilateralsettingto see ifthere isany role f
or
non-d isc rim inationrulesinthe optim aloutc om e.How ever, they d o not set up anexam ple
w here they c anexplic itly c om pare the w elf
are c onsequencesofmultilateraland netw ork of
b ilateralnegotiations.Inallofthese papers,their m ainc ontrib utionisem phasiz ingthe link
b etw eenthe institutionalrulesofthe G AT T and ec onom ic e± c iency w hic h w e w illad d ress
inm ore d etailinthe next c hapter.
T here are variousstud iesanalyz ingc ertainad vantagesofmultilateralism inthe literature.
B hagw ati [1990 , 1991a] m entionsthe d istrib utionalargum entsam ong the m ainb ene¯tsof
multilateralnegotiations.Inmultilateralsettings,sm allc ountriesw illhave m ore b argaining
pow er against b igc ountriesand w illb e ab le to im prove their w elf
are.M aggi[19 96]show sthat
multilateralism enhancese± c iencyd ue to increasesinenf
orc em ent pow er ina repeated gam e
setting.Since,there are unilateralincentivesto d eviate f
rom agreed tari® levelsinany trad e
agreem ent,a threat m ec hanism innec essary to d eter governm entsf
rom cheating.O ne ofthe
rolesofthe G AT T b ec om esto d issem inate inf
orm ationand c oord inate punishm ents.Inthis
paper,w e ignore enf
orc ement issuesand assum e that allagreem entsare enf
orc eab le.R ather,
4
A related question has been the enforcementofe±cientoutcomes. D ixit[1 987]and a series ofother
papers identify the P risoners'D ilemma N ature of the trade negotiations and the role of the treaties in
enforcinge±cientagreements.
4
w ef
oc usonhow c ountriesac hieve a c ertainoutc om e.Asm entioned b yHoekm an[1993,199 6],
ac hieving anoutc om e and enf
orc ing it ina negotiationare c om plem entary issuesf
ac ed b y
polic y-makers.T heref
ore M aggi'spaper and thispaper should b e seenasc om plem entssince
they point out to d istinctive and c om plem entary gainsf
rom multilateralism 5. K ow alcz yk
and Sjostrom [19 94 ] analyz e the w elf
are enhancingb ene¯tsofsid e paym entsinmultilateral
negotiations,w hic h w e also ad d ressinthispaper.
T hispaper hasstrongim plic ationsf
or the regionalism vs.multilateralism d eb ate.T hese
issueshave b eenonthe researc h agend a ofthe internationaltrad e ec onom istsf
or d ec ad es
and it isim possib le to sum m arize allofthe argum ents.Starting w ith Viner's[1950 ] trad e
c reationvs.d iversiond istinctionand c ontinuing w ith K rugm an's[199 1a, 1991b ] in°uential
trad ingb loc ksmod el,the stand ard approac h hasb eento f
oc usonunilateralac tionsofagents
inregionalor multilateralsettings.T he c ontroversialU -shaped relationship b etw eenw elf
are
and numb er oftrad ing b loc ksinthe K rugm anm od elsisthe result ofthe analysisb eing
solely b ased onunilateralstrategies.How ever c ountriesengage innegotiationsto avoid the
externalitiesc aused b y unilateraland c oalitionalpolic ies. W henthisob servationistaken
into ac c ount,som e ofthe resultsare likely to change.
T his paper d i®ers inone ¯nalrespec t f
rom the previous papers since w e present all
ofour resultsina very general(yet f
orm al) b argainingf
ram ew ork.E c onom ists' trad itional
perc eptionofinternationaltrad e d ivergesf
rom that ofpolic ym akersinim portant d im ensions.
For ec onom ists,internationaltrad e isone ofthe m ost ob viousm echanism sto increase w elf
are
and the existence oftrad e b arriersisa typic alexam ple ofthe role ofpolitic sinec onom ic
polic y-making(see G rossmanand Helpm an[199 4 ,19 95a,19 95b ]f
or anextensive m od elthat
introd uc esa politic altari® d eterm inationproc ess). Although there are m any theoretic al
m od elsinw hic h trad e b arriersincrease w elf
are, m ost ec onom istsstrongly b elieve that f
ree
trad e isthe b est polic y, evenifit isim plem ented unilaterally6.T heref
ore there isno room
5
A ninterestingextension wouldbetoanalyzetheroleoftheG A T T principles,especiallytheM FN rule,
intheenforcementmechanism.
6
See H elpman and Krugman (1 983)and H elpman (1 984)forextensive surveys ofthis in° uentialstrand
5
f
or trad e negotiationsinthisperspec tive.
O nthe other hand , governm ent o± c ialsw ho hand le the long and c umb ersom e negotiationshave d i®erent perc eptions. Aselec ted o± c ialsor b ureauc ratsappointed b y elec ted
politic ians, their incentivesare in°uenced b y the interestsofthe ec onom ic ac torsintheir
c ountry.T heref
ore,it isim portant to ¯nd c om prom isesthat w ould m ake every governm ent
b etter o® c om pared to the d ef
ault optionsw ithinthe politic alc onstraints.T ari® negotiationsw orkasmec hanismsw here tari® c oncessions(or other protec tive m easuresthat impose
externalitiesonthe trad ing partners) are exchanged such that the new outc om e im proves
the w elf
are ofallofthe governm entsw hich isb ased onpolitic alm otivations. Inad d ition
to re°ec ting the f
orm ationoftrad e polic iesina multilateralenvironm ent, the b argaining
f
ram ew ork explainsthe m erc antilist approach ofgovernm ents. (See K rugm an[199 1] f
or a
m od ernversionofmerc antilism.)
T he next sec tionw illoutline the und erlying the generalequilib rium m od elw e w illb e
using.T henw e w illestab lish the trad e polic yd eterm inationgam e asa b argaininggam e.T he
e± c ient payo® f
rontier w hic h w illf
orm the m ainf
oc usofanalysisinthe f
ollow ingsec tionsw ill
b e d e¯ned .Next, w e show the e± c iency gainsf
rom multilateralism through c ross-c ountry
trad es. T hen, the multilateralsetting w here b ilateraltreatiesim pose externalitiesonthe
outsid er through trad e d iversionw illb e introd uc ed .U nd er these c irc um stances,there w illb e
f
urther P areto gainsto b e ob tained via multilateralnegotiationsthrough the internaliz ation
ofthese externalities.T he c onclusionf
ollow s.
2
T he B asic Setup
T hissec tionw illintrod uc e a b enchm ark m od el. W e w illd e¯ne the d em and and supply
f
unctionsthat und erlie the nationalec onom iesand the governm ents' ob jec tive f
unctions.
Asymm etriesinthe supplyf
unctions(d ue to end ow m entsofthe sec tor spec i¯c inputs) w illb e
ofliterature.
6
the reasonsf
or trad e b etw eenc ountries.T he strategiesavailab le to the governm entsc onsist
oftari®sonthe im ports7 and w e w illd e¯ne the payo®softhe governm entsasf
unctionsof
the tari® rates.
T he b enchm arkmod elissim ilar to the one used b yG rossm anand Helpm an[199 4 ].E ach
c ountry ispopulated b y id entic alind ivid ualsw ho m axim ize a utility f
unctiongivenb y
uA = u(x0 ) +
X
i2H
w here H
A
u(xi)
A
d enotesthe set ofgood sd em and ed inc ountry A and xi isthe c onsum ptionof
good i.T hese ind ivid uald emand f
unctionsare increasing,d i®erentiab le and c oncave.G ood
0 servesasthe numeraire w ith pric e set to 1:It ism anuf
ac tured only w ith lab or using a
c onstant returnsto sc ale prod uc tiontechnology w hich lead sto a w age rate of1 and the
end ow m ent oflab or islarge enough to guarantee a positive supply ofgood 0 :Lab or and an
inelastic ally-supplied sec tor-spec i¯c f
ac tor are used inthe prod uc tionofthe other good s.T he
prod uc tiontec hnology ofeac h good hasc onstant returnsto sc ale and d im inishing returns
w ith respec t to lab or. T he mainad vantage ofthis f
ram ew ork isthat the rew ard to the
prod uc ersofany non-num eraire good and the c onsum er d em and f
or it d epend only onits
d om estic pric e w hile the numeraire good ab sorb sallofthe exc esssupply and d em and .T his
generalequilib rium f
ram ew ork w ith the resid ualnum eraire good isintend ed to rationalize
the partialequilib rium approac h intrad e theoryand hasb eensuc c essf
ullyused inG rossm an
and Helpm an[199 4 ,199 5a,199 5b ]to explaintrad e polic yd eterm inationina politic alsetting.
T hroughout the paper, w e w illassum e that there isonly one c ountry w ho im portsa good
w hile one or m ore c ountriesm ight export it.
W e w illnow f
oc us ontw o good s, i and j; (w here i;j 6
= 0 ) that are trad ed b etw een
7
W e willassume thatexporttaxes and subsidies are notavailable.Exporttari®s are banned in many
countries, including the U S, and subsidies are outlawed in G A T T (with fewexceptions forR &D and environmentalpurposes.
) H owever, the results ofthis paperwillnotchange as long as monetary transfers
between the governmentand the ¯rms create deadweightlosses in the economy. Some examples are the
costs incurredinthecollectionsystem oftaxes topayforthesubsidies andthedistortions oftari®s.A more
detailed discussion ofexportpolicies is in thenextsection.
7
tw o c ountries, A and B . G ood i(j) isthe naturalexport good f
or c ountry A (B ) d ue to
end ow m entsofthe sec tor-spec i¯c f
ac tors.Neither inor jisprod uc ed or d em and ed inany
other c ountry.W e w illlet p xi d enote the pric e ofgood iinthe exporting c ountry, and p mi ;
the pric e inthe importingc ountry.T he tari® levelis¿i w here
¿i = p mi ¡p xi
(1)
W e w illim pose no restric tionsonthe value of¿i inord er to allow im port sub sid ies.D (p)
and S(p) w illd enote c ountry-w id e d em and and supply f
unctions. For sim plic ity, w e w ill
assum e that d em and and supply are linear and ,theref
ore,the c onsum er surplus,© (p),and
the prod uc er surplus, ¦ (p), are quad ratic inpric es8 .T he equilib rium pric esf
or good iin
b oth c ountriesw illb e d etermined b yequation(1) together w ith the f
ollow ingm arket c learing
c ond ition:
D A (p xi) + DB (p mi ) = SA (p xi) + SB (p mi )
(2 )
W ith these tw o equations, w e c and eterm ine b oth export and im port pric esasf
unctionsof
the tari® leveland the exogenousend ow m entsofthe inputs.Sim ilar equationshold f
or good
j.
Inc ountry A,the payo® d ue to the c onsum ptionofthe export good is
UAx (¿i) = © A (p xi (¿i)) + ¦ A (p xi (¿i))
and the payo® f
rom the im port good is
³
´
³
´
n
³
´
³
´o
UAm (¿j) = © A p mj (¿j) + ® A¦ A p mj (¿j) + ¿j D A p mj (¿j) ¡SA p mj (¿j)
8
T helinearityassumptionis notnecessaryforanyoftheresults inthis paper.H owever,itmakes lifeand
drawinggraphs much easier.Simple quasi-concavityassumption is su±cient.
8
w here the last term isthe tari® revenue9 ,10 and ® ¸ 1 d ue to lob b ying pow ersofimport
c om peting ind ustries11 .Inthese d e¯nitions, the param eter ® isthe w eight attached b y the
government to prod uc er surplusinthe im port sec tor w hic h isa stand ard w ay ofintrod uc ing
politic alec onomy c oncernsofany governm ent into the analysis(see B ald w in[??],G rossm an
and Helpm an[199 4 ,19 95,199 6]).It isstraightf
orw ard to show that
@U x
@ 2 UAm
@UAm
@ 2 UAx
j¿j< ¿jN > 0 ; A j¿i= 0 < 0 ;
<
0
;
> 0
@¿j
@¿i
@¿j2
@¿i2
(3)
G iventhese tw o f
unctions,w e c and e¯ne the payo®sto each c ountry as12 ,13:
UA (¿i;¿j) =
UAm (¿j) + U Ax (¿i)
UB (¿i;¿j) =
UBm (¿i) + UBx (¿j)
(4 )
Note that ¿j isa d ec isionvariab le f
or c ountry A and ¿i f
or c ountry B :T he task f
ac ed b y
the tw o governm ents is to d eterm ine the tari® levels, ¿i;¿j, giventheir respec tive payo®
f
unctions.W e w illref
er to thisasthe tari® d eterm inationgam e.
9
D uring this paper, we willsustain the assumption thatthe directtransfers between governments are
not allowed and some of the results depend on this assumption. H owever, this standard assumption in
internationaltrademodels (seeD ixit[1 985])mightseem unjusti¯edtheoreticallysinceweallowtheobjective
functions tobe linearin monetarypayo®s,i.
e.tari®s.W e can stillmake theclaim thatunlimited transfers
are notfeasible due topoliticalreasons.O rwe can modify the modelsuch thatthe governmentpayo®is
aconcave function oftari®revenue due toine±ciencies in the domestictaxation and distribution systems
which would preserve allofourresults.
10
W eshouldactuallydenotetheproducersurplusincountryA forgoodi as¦A ;i (px
entgoods
i )sincedi®er
and countries willhave di®erentproduction functions.H owever,fornotationalsimplicity,we willsuppress
the¯rstsubscript\ ¶
{".
11
In G rossman and H elpman [1 994], there is an ® ¸ 1 attached to the producersurplus in the payo®
function ofthe exportsector. Since, we do notallow exportpolicies, there would be no lobbying e®orts
(assumingtheowners ofthespeci¯cinputofxi areasmallportionofthepopulation)andwecanset® = 1 .
N evertheless, the qualitative nature ofthe results would notchange ifthe weights were di®erentin each
payo®function.
12
A ctually,U m (:)is strictly concave and U x(:)is strictly convex because ofthe linearity assumption on
theunderlyingdemand and supplyfunction.
13 N
¿j
is unilateralN ash tari®levelde¯ned inthenextparagraph.
9
3 B argain
ingFram ew ork
W e now f
ormulate the tw o-c ountry tari® d eterm inationgam e asa b argaining gam e. T he
f
orm ald e¯nitionofthe b argainingprob lem ,asgivenb yO sb orne and R ub instein(199 0 ),c an
b e stated asthe f
ollow ing:
De¯n
ition
:A bargainingproblem isd e¯ned asthe pair (S;d ) w here S½R +2 isc om pac t
and c onvex,d 2 S,and there existssom e s 2 S such that si > d i f
or alli= 1;2 .
Inthissetting,S isthe f
easib le payo® set,d isthe d isagreem ent point and s isany point
w hic h im provesupond f
or allplayers.T he d isagreem ent point w illb e givenb y the unilaterally d eterm ined tari®sthat result inthe (unique) Nash E quilib rium ofthe simultaneous
m ove tari® setting game w here payo®sare givenb y equation(4 ). T hese unilateralNash
tari®sw illb e d enoted as¿jN and ¿iN and they are d eterm ined b y simultaneously solving:
³
´
¿jN = argm¿axUA ¿iN ;¿j
j
³
¿iN = argm¿axUB ¿i;¿jN
i
´
G ivenc ond itionsin(3) and quad ratic payo® f
unctions,the Nash tari® levelsw illb e positive
and unique.T he payo®sc orrespond ingto the unilateraltari®s,d enoted asUAN and UBN ,w ill
b e the low est levelsthat w e assum e w illoc c ur inthisenvironm ent.T he tari® settinggam e,
w henplayed unilaterally asa single stage gam e w ithout b argaining, w illhave the nature
ofa P risoner'sDilem m a game14 .T he f
easib le P areto superior outc om esare not supported
b y a Nash E quilib rium ina single stage, static gam e15. W e b elieve that one ofthe m ost
14
T heP risoners'D ilemmanatureofthetari®settinggamehasbeennotedbymanyauthorsintheliterature
and is the main motivation fortheuse ofrepeated game techniques toavoid P aretoinferiorequilibria.See
D ixit[1 987]fordiscusssion.
15
H owever,theseequilibriacan besupportedinarepeated settingthroughtriggerstrategies as shownby
various FolkT heorems.T hese theorems areexistenceresults and in mostcases pointtoan in¯nite number
ofequilibria.
10
important rolesoftrad e negotiationsisto id entif
y the set ofP areto Superior outc om esand
selec t anelement ofthisset asthe equilib rium .
T he next step isto d e¯ne the P areto Superior set S. InF igure 1, the c urvesUAN and
UBN represent the pairsoftari® levelsat w hich each c ountry hasthe sam e levelofpayo® as
the one attained w ith the Nash tari® levels.T his¯gure im pliesthat any pair oftari® levels
insid e the tw o c urvesimprovesw elf
are f
or b oth c ountries.Inthissetting,a trad e agreem ent
w illb e e± c ient if
"
#
d ¿i
d ¿j
=
d U A= 0
"
#
d ¿i
d ¿j
(5)
d UB = 0
or sim ply w hentw o ind i®erence c urvesare tangent to eac h other inthe tari® spac e.Since
h
i
d ¿i
d ¿j d U = 0
A
= 0 and
h
i
d ¿i
d ¿j d U = 0
B
³
´
= 1 at ¿iN ;¿jN ; the unilateralNash tari® levelsare not
e± c ient and there existsopportunitiesf
or P areto im provem ents16.Inother w ord s,the set S
isnot em pty.
T he f
easib le and e± c ient f
rontier c analso b e c harac teriz ed asthe set ofpoints(UA;UB ):
8
9
>
>
>
< (UA;UB ) :UA = max U A (¿i;¿j) + ¸ [ UB (¿i;¿j) ¡UB ]; >
=
>
>
:
¿i;¿j;¸
UA ¸UAN
(6)
>
>
;
;UB ¸UBN
w here ¸ is the Lagrange multiplier. W e c ansim ply d e¯ne the e± c ient f
rontier w ith the
equationUA = f (UB )17:T he tari® pairs (¿i;¿j) that solve the c onstrained optim iz ation
prob lem f
or a givenUB ind e¯nition(6) w illsatisf
y equation(5).W e now c harac teriz e the
f
unctionUA = f (UB ):
³
´
T he ind i®erence c urvesc orrespond ingto UAm ax = f UBN and UAN = f (U Bm ax) inthe tari®
spac e are d raw ninF igure 2 .Am ax and B m ax are respec tively the pointsat w hic h c ountry A
and c ountry B attaintheir maximum payo®s18 .
16
W eborrowedthis notationforthede¯nition ofe±ciencybyB agwellandStaiger[1 996]
.
17
W ealsohavethe restrictions U A ¸U AN and U B ¸U BN on the function.
18
T he e±cienttari®locus (orsimplythe contractcurve)is the dotted line between A max and B
its properties willbeestablished later.
11
max
and
T he ¯rst ob servationisthat the e± c ient payo® f
rontier,UA = f (UB ) isstric tlyd ow nw ard
sloping and stric tly c oncave. T hisisa d irec t c onsequence ofthe envelope theorem w here
f0(UB ) = ¡¸ < 0 (f
or UB < UBm ax) and the d i®erentiationofthe ¯rst ord er c ond ition
f00(UB ) = ¡d dU¸B · 0 . W ith the shape ofthe e± c ient payo® f
rontier estab lished , w e c an
state the f
ollow ing:
P rop osition1 : T he tari® settinggam e betw eentw o countries is a stand ard B argaining
P roblem, asd e¯ ned above.
P roof
:T he proofisstraightf
orw ard . W e have d e¯ned the d isagreem ent point and existence ofP areto superior outc om es.T he e± c ient payo® f
rontier, UA = f (UB ), d e¯nesthe
b ound ary ofthe payo® set over w hich the governm entsw illb argain. Since it isc oncave,
d ow nw ard slopingand d e¯ned over UBN ·UB ·UBm ax, the f
easib le set S isc losed ,b ound ed
and c onvex.Q.
E .D.
T he e± c ient payo® f
rontier w ith the d ef
ault (unilateralNash) outc om esd e¯nesour b argaininggam e.E ± c iency inanyb argaininggam e requiresthat the outc om e isloc ated onthe
b ound ary ofthe f
easib le set w hic h isgivenb y the e± c ient payo® f
rontier,(UA;U B ):It isno
c oincid ence that e± c iency inthe trad e-theoretic sense and b argainingsense are equivalent.
T hisequivalence isac tually the reasonthat enab lesusto treat the trad e negotiationgam e
asa stand ard b argaininggam e.
Another f
unctionto b e d e¯ned isthe e± c ient contrac t c urve (¿i;¿j) w hich isthe d otted
line b etw eenAm ax and B m ax inF igure 2 . T he f
ollow ing propositionestab lishesitsm ain
properties.
P rop osition2 : T he e± c ient contrac t c urve inthe tari® space is stric tly concave and
d ow nw ard sloping.
P roof
: See the append ix
12
T his propositionim plies that w e c and enote the e± c ient c ontrac t c urve as a f
unction¿i = g (¿j). Also, w e c anestab lish a very im portant relationship b etw eenthe pairs
(f (UB );UB ) and (g (¿j);¿j):Since b oth are nic ely b ehavingf
unctions,there isa one-to-one
c orrespond ence b etw eenthem .Asw e m ove alongthe graph of(g (¿j);¿j) inthe tari® spac e,
¿j (¿i) ism onotonic ally increasing (d ec reasing) w hich im pliesUA (UB ) isstric tly increasing
(d ec reasing).Since f (:) isd ow nw ard sloping,increasinga c ountry'spayo® requiresd ec reasingthe other'spayo®.Inord er to increase (d ec rease) c ountry A'spayo®,the tari® charged
onher im portsmust increase (d ec rease) and the tari® charged to her exportsmust d ec rease
(increase) simultaneously alongthe e± c ient payo® f
rontier.For c om pleteness,w e w illm ake
the f
ollow ingd e¯nitionsw hic h w illb e used inthe rest ofthe paper:
De¯n
ition
:Ane± c ient outcome ofthe tari® settinggam e (and the equivalent b argaining
prob lem) isa tari® pair (¿i;¿j) w hic h isonthe e± c ient c ontrac t c urve (g (¿j);¿j)and w hich
lead sto payo® levels (U A;UB ) that are onthe e± c ient payo® f
rontier (f (UB );UB ). An
e± c ient bargainingprocesslead sto a unique e± c ient outc om e.
T hisd e¯nition(or thissec tion) d oesnot m ake any pred ic tionsab out the outc om e ofthe
b argaininggam e.How ever,the c laim isthat a m ore f
avorab le outc om e f
or a c ountry im plies
a monotonic d ec rease inthe tari®sf
ac ed b y her exportsand m onotonic increase inthe tari®
employed tow ard sher imports. So, ifw e ob serve tw o c ountriesmutually d ec reasing their
tari® levelsc om pared to a previousagreem ent, w e c anc onclud e that either (1) they w ere
previouslynot onthe e± c iencyf
rontier or (2 ) som e exogenousparam eter,suc h aspref
erences
or end ow m ents,shif
ted the e± c iency f
rontier.T hisone-to-one c orrespond ence b etw eenthe
payo® levels and the tari®s m akes the f
ollow ing analysis very easy since it im plies that
b argainingover tari®s(w hic h w e see inG AT T negotiations) isequivalent to b argainingover
payo®s(w hic h w e see inthe theoretic alb argainingm od els).For the rest ofthe paper,w e w ill
f
oc usonthe e± c ient payo® f
rontier d e¯ned b y the f
unctionf (UB ) w hich im plic itly d epend s
onexogenousparam eters.O nce w e choose a spec i¯c point onthisf
rontier, w e c ango b ack
and d eterm ine the e± c ient tari® levelsthat lead to that payo® pair.
13
T he mainresultsofthissec tionare that (1) unilateralNash polic iesare ine± c ient and (2 )
trad e agreements(w hether they are b ilateralor m ultilateral) play a unique role inreaching
e± c ient tari® levels. T his point is not new and has b eenm entioned repeated ly inthe
literature.T he im plied rec iproc ity inthisproc essisone ofthe m aininsightsofthe B agw ell
and Staiger [1996] paper, asw e m entioned b ef
ore. How ever, asc anb e seeninF igure 3,
there are anin¯nite numb er ofe± c ient trad e agreem entsavailab le to the c ountriesand they
c aneasily b e P areto ranked f
rom each governm ent'sperspec tive.T hus, the sec ond role of
the trad e negotiations(other thanreac hingane± c ient tari® level) b ec om esto d eterm ine at
w hic h e± c ient tari® levelthe playersw illend up.
3.
1
Sid e Note onthe R ol
e ofE xport P ol
ic ies
E xport taxesand sub sid iesare not availab le aspolic ytoolsto the governm entsinthismod el.
T hisassum ptionw asb ased onthe lac kofw id espread use ofthese polic iesb ythe governments
and the G AT T polic iesinthisregard .A m ore c om plete m od elw ould d erive thisob servation
asanequilib rium outc om e b ut thisisb eyond the sc ope ofthispaper19 .How ever,the ab sence
ofthe export polic ieshasstrong im plic ationsf
or the m od elw hic h need to b e ad d ressed at
thispoint.
T he simultaneouspresence ofexport and im port polic iesenab lesgovernm entsto set the
w orld pric e that maxim iz e their joint w elf
are and use their respec tive polic iesto transf
er
w elf
are f
rom eac h other2 0 . Inother w ord s, the prob lem sim pli¯es to solving the w orld
pric e that m aximiz esthe joint w elf
are ofthe tw o governm ents,takingthe politic alec onomy
d istortionsinto ac c ount. Inthe b argaining prob lem , the e± c ient payo® f
rontier b ec om es
linear (instead ofthe stric tly c oncave shape w e have) and c ountriesnegotiate over a ¯xed
pie. Inother w ord s, the availab ility ofexport polic iesalongsid e im port polic iesb ec om es
19
See R odrik[1 995]foradetailed explanation on why the e±cientpolicy tools mightnotbe used in the
equilibrium ofagame where thechoice ofthepolicytoolis alsoendogenous.
.
20
Inthefollowingpapers [1 996,1 997b],B agwellandStaigertakeadvantageofthis propertyand focus on
thenettari®s instead oftheactualtari®s.
14
equivalent to havinga c ostlesstransf
er m echanism .T he ab sence ofexport polic ies,theref
ore,
hasnegative w elf
are im plic ationssince m ost outc om esw illim ply glob alw elf
are lossesf
rom
the governm ents'perspec tive and shrinkingofthe f
easib le payo® set.T he sam e result w ould
b e ob tained ina generalequilib rium setting w ith tw o good sand only im port polic iesd ue
to the Lerner symm etry theorem .Inthe f
ollow ing sec tions, w e w illshow that multilateral
b argaining b ec omesevenm ore im portant b ec ause ofthe unavailab ility ofexport polic ies.
Nevertheless, f
urther researc h isneed ed to point out other c osts ofim plem enting export
polic iesthat outw eigh the ab ove m entioned e± c iency b ene¯ts.
4
M ul
tic oun
try Negotiations
O ne ofthe d e¯ningc harac teristic softhe past G AT T negotiationround sistheir multilateralism.Ineac h round ,more c ountriesnegotiated over m ore issuesf
or longer period softim e.
M any ec onom istsand polic ymakersc laim that the multilateralnature ofthe trad e negotiationsc ontrib uted to the suc c essinred uc ingtari® levelsand increasingw elf
are f
or allofthe
m emb er c ountriesinthe last ¯f
ty years. W e w illtry to show the theoretic alf
ound ations
ofthisob servations¯rst through a three c ountry c ase. T he c laim w illb e that w elf
are in
trilateralnegotiationishigher thanthe settingw ith three b ilateralnegotiations.
T he b asic b uild ingb loc ksofthe m od elw illb e sim ilar to the onesinthe previoussec tion.
T here are three c ountriesand six good s. Any pair ofc ountriestrad e tw o d istinct good s
w hic h are neither c onsumed or prod uc ed inthe third c ountry and , theref
ore, none ofthe
b ilateralnegotiations im pose externalitiesonthe outsid ers. fab (UB ) d e¯nesthe e± c ient
payo® f
rontier ofthe b ilateralb argaininggam e b etw eenc ountryA and B :fab (UB ) isc oncave
and d ow nw ard sloping. fac(UC ) and fbc(UC ) are sim ilarly d e¯ned f
or the gam esb etw een
A & C and B & C respec tively. T he e± c ient payo® f
rontier f
or the trilateralb argaining
15
c onsistsofthe points(UA;UB ;UC ) and w illb e charac terized asthe f
ollow ing:
8
>
>
>
>
>
<
(UA;UB ;UC ) :UA = m axUA (¿ab;¿ba ) + UA (¿ac;¿ca)
+ ¸ B [ UB (¿ab;¿ba ) + U B (¿cb;¿bc) ¡UB ]+ ¸ C [ UC (¿ac;¿ca) + UC (¿cb;¿bc) ¡UC ];
>
>
>
>
>
:
UA ¸UAN ;U B ¸UBN ;UC ¸UCN
9
>
>
>
>
>
=
>
>
>
>
>
;
(7)
w here ¿ab isthe tari® im posed b y c ountry A onc ountry B :Sim ilarly, w e c and e¯ne this
e± c iency f
rontier ofthe f
easib le payo® set w ith the equationUA = F (UB ;UC ) w ith the
c ond itionsthat UA ¸UAN ;UB ¸U BN and UC ¸UCN :T he d e¯nitionofthe B argaining gam e
c anb e easily extend ed to the three c ountry c ase w ith d =
ofS isd e¯ned b y the f
unctionUA = F (U B ;UC ).
³
UAN ;UBN ;UCN
´
and the b ound ary
³
´
³
´
Suppose the b ilateralb argaininggam e outc om e b etw eenc ountry A and B is UAab;UBab
³
´
w here UAab = fab UBab :T hisoutc om e isuniquely d eterm ined asa result ofa b argaining
game d esc rib ed inthe previoussec tion.Again,w e sim ilarly d e¯ne (UAac;U Cac) and UBbc;U Cbc
¤
¤
asoutc omesofthe other tw o b argaininggam es.W e w illlet (¿ab
;¿ba
;::) d enote the tari® levels
ofthese b ilateraloutc om esand w illlet UA¤ = U Aab + UAac; UB¤ = UBab + UBbc;UC¤ = UCbc+ UCacb e
the totalpayo®s.T he f
ollow ing propositionw illhighlight the m ainb ene¯t ofmultilateral
b argaininggame d espite the f
ac t that the ind ivid ualb ilateralgam esare ind epend ent ofeach
other.
P rop osition3 :T here isa point onthe e± c ient payo® frontier oftri-lateralbargainingthat
P areto d om inatesany outcome ofthe netw orkof(three ind epend ent) bilateralnegotiations.
P roof
: See the append ix.
T his propositionsaysthat the outc om e ofthe netw ork ofb ilateralb argaining gam es
m ight not b e onthe e± c iency f
rontier ofthe trilateralgam e and ,theref
ore,P areto superior
outc omesw illb e availab le ina multilateralgam e2 1 .T hisresult isid entic alto the e± c iency
21
M aggi [1 996]has asimilarresultwhich shows in aN ash B argainingframework,multilateralbargaining
providesP aretosuperioroutcomescomparedtoanetworkofbilateralgamesonlywhenthereareasymmetries
acrosscountries.O urresultismuchmoregeneralandshowsthatgivenanyenvironmentunderanybargaining
framework,foranybilateraloutcome thereis aP aretosuperiormultilateralone.
16
requirementsina generalequilib rium ec onomy w ith exchange.E ± c iency requiresthat, at
the optimum,everyb od y'srelative m arginalvaluationsofany tw o good sthat they c onsum e
(the tari® ratesinthisc ase) are equal.At the sam e tim e,there are no triangular arb itrage
opportunitiesso
d UA d UA
=
d UC d UB
=
d UB
d UC
issatis¯ed . Ifthislast requirem ent d oesnot hold , then
there are opportunitiesf
or \b arter"ac rossgovernm ents(or triangular arb itrage),and w elf
are
improvem entsf
or allgovernm entsare possib le.Since there are no assum ptionsinherent in
the b argaininggame that guarantee thisthrough the b ilateralnegotiations,w e w ill(almost)
alw aysb e b etter o® (and never w orse o® ) c ond uc tingmultilateralnegotiationsto realiz e all
e± c iency gains.
T hisresult m ight seem surprising at ¯rst, since none ofthe b ilateralb argaining gam es
e®ec t any other governmentsand the tw o tari® ratesthat tw o governm entsare negotiating
over d o not enter the payo® f
unctionsofother governm entsd ue to the very strong ind epend ence assum ptionw e m ad e.E venthough governm entsc annot im prove their payo®sin
eac h b ilateralgam e (since they are onthe e± c iency f
rontier),trilateralb argainingprovid es
f
urther opportunities.T histype oftrad ing ac rossc ountriesisextensive d uring the G AT T
negotiationsasd oc um ented b y m any authorssuch asHoekm an[19 95].Anextrem e exam ple
w ould b e the c ase w here A only importsf
rom B w ho only im portsf
rom C w ho only im ports
f
rom A.Inthisc ase,b ilateralnegotiationsw illnot b ringany trad e lib eraliz ationsince none
ofthe c ountrieshasanythingto o®er f
or their im porter (they have nothingto exc hange f
or
the good theyw ant) .How ever,through trilateralnegotiations,it ispossib le to ac hieve low er
tari®sand w elf
are gains2 2 .
Anim portant extensionofthispropositionw ould b e to the \N "c ountry c ase.Suppose
that N ¡1 c ountriesnegotiate multilaterally and reac h a point ontheir joint e± c ient payo®
22
A s A vnerG reifpointed out,ifA andB couldsignabilateralcontractover¿ab and¿ba thatestablished
thesetari®rates as functions oftheoutcomes oftheotherbilateralagreements (ratherthansinglenumbers),
thenthise±ciencygainsfrom multilateralism couldbecapturedthroughbilateralnegotiations.H owever,this
conditionalbilateralnegotiationframeworkis exactlyhowmostofthemultilateralnegotiations arehandled!
T hus,themain di®erencebetweenmultilateralandbilateralnegotiations (in theabsenceofexternalities)is
theabilitytowrite conditionalcontracts.I would liketothankA vnerforthis clari¯cation.
17
f
rontier,thusexploit allpossib ilitiesofw elf
are im provem ent.Also,allofthem have b ilateral
relationshipsw ith anN
th
c ountry. Now , thisc ountry w antsto jointhe multilateraltrad e
negotiations.T he f
ollow ingpropositionestab lishesthe w elf
are c onsequencesofthisac tion.
Corol
l
ary 4 : T he entry ofa new governm ent to anexistingm ultilateralnegotiationw ill
result inP areto gainsfor allcountries.
P roof
: See the append ix
T hispropositionstatesthat the totaland ind ivid ualw elf
aresare increasinginthe numb er
ofgovernm entspartic ipatinginthe negotiations.W henm ore governm entsare present,there
w illb e m ore opportunitiesf
or trad e ac rossc ountries. F inally, the f
ollow ing c orollary isa
d irec t implic ationofthe ab ove result.
Corol
l
ary 5 : T he highest payo® w illbe realized w henallgovernm entsnegotiate jointly.
P roof
: It f
ollow sd irec tly f
rom the ab ove result.
Asexpec ted , multilateralb argaining w ith the highest numb er ofpartic ipantsm axim ize
ind ivid ualand totalw elf
are. T his sec tionid enti¯ed w hy w e see trad ing ofissues ac ross
c ountriesand how thisa®ec tsw elf
are ofthe partic ipants.T hissim ple setting allow susto
ob serve the propertiesofmultilateralnegotiationsthat increase w elf
are.O ne im plic ationof
the ab ove resultsisthat trad e polic iesw illb e renegotiated once a new m emb er joinsthe group
since it w illb ring more opportunitiesf
or trad e, (evenb etw eenthe old m emb ers) and the
e± c ient payo® f
rontier w illshif
t out.T he ever-c ontinuingnature ofthe G AT T negotiations
m ight b e partly d ue to thisreason; c ountries renegotiate trad e polic ies(m ostly d ec rease
trad e b arriers) to take ad vantage ofnew entries.Another im plic ationisthat c ountriesw ill
m ove tow ard sf
ree trad e outc om e asm ore c ountriesjoin.Alltari® levelsw illnot d ec rease
b ut the generalm ovem ent w illb e inthat d irec tionto estab lish higher payo®s.
18
4.
1
E xport P ol
ic ies,O n
c e Again
P reviously,w e had mentioned that the presence ofexport polic iesisequivalent to the transf
orm ationofthe e± c ient payo® f
rontier to a linear f
orm , c om pared to itsstric tly c oncave
shape. W henthisf
rontier islinear, w e w illhave
d UA
d UB
= 1f
or allb ilateralnegotiationsf
or
alle± c ient outc om es.T hisimpliesthere w illb e no opportunitiesf
or \triangular arb itrage"
b etw eenc ountriesand no c ross-c ountry exchanges.T here w illb e no reasonto hold multilateralnegotiationssince there w illb e no possib le P areto gains.Inother w ord s,the ab sence
ofexport polic iesb ec omesone ofthe m ost im portant reasonsf
or hold ingmultilateraltalks.
How ever,the next sec tionw illpoint out f
urther b ene¯tsofmultilateralism .
5 M ul
tic oun
try Negotiationsw ith E xternal
ities
So f
ar, w e assum ed that the trad e relationship b etw eentw o c ountriesd id not d irec tly af
f
ec t the w elf
are ofany other c ountry.T hisind epend ence, though it sim pli¯ed the analysis
c onsid erab ly, isf
ar f
rom reality inm od erntrad e relationships.Any trad e c reatingb ilateral
agreem ent b etw eentw o c ountriesw illhave im plic ationsonother c ountriesthrough trad e
d iversione®ec ts(that are m ost likely to b e negative externalities.) Inthissec tion, w e w ill
argue that the other mainreasonf
or hold ingm ultilateraltrad e negotiationsisto internalize
these externalitiesthrough the b argainingproc essand provid e f
urther e± c iency gains.
T o analyz e thissourc e ofe± c iency,w e w illuse a stylized three c ountryc ase w hose results
c anb e easily generalized to the N ¡c ountry c ase. F irst, inthissec tion, f
or sim plic ity, w e
w illassume that ® A = ® B = ® C = 1 so the governm entsaim to m axim iz e the soc ialsurplus
w ith no politic almotivations.T here are three good sw hich are d enoted b y a;b and c
.G ood
a isprod uc ed b y c ountriesB and C and c onsum ed b y only c ountry A:T he end ow m entsof
the sec tor-spec i¯c f
ac tor f
or good a are id entic alinc ountriesB and C ; thusthe supply and
prod uc er surplusf
unctionsare id entic al.T he sam e setup appliesto good sb and c
:T heref
ore,
inequilib rium ,c ountryA im portsgood a f
rom one or b oth ofthe other c ountriesand exports
19
good b to c ountry B and good cto c ountry C :
W e w illlet ¿ab b e the tari® rate im posed b y c ountry A onc ountry B . Anequilib rium
involvesthe d eterminationofsix such tari® ratesb etw eenthree c ountries. T he payo® f
or
c ountry A isthe sum ofthe payo®sf
rom tw o export sec torsand anim port sec tor. T he
export sec tor payo®sf
or good sb and c
, d enoted asU X (¿ba ;¿bc) and U X (¿ca;¿cb), are the
sum s ofc onsumer surplusand the prod uc er surplus. T he im port sec tor payo®, d enoted
as U M (¿ab;¿ac), is c omprised ofc onsum er surplus, prod uc er surplus and tari® revenues.
W henthe supply and d em and f
unctionsare linear, the payo® f
unctionsd e¯ned ab ove w ill
b e quad ratic intheir param eters.Also,b ec ause ofthe sym m etric struc ture ofthe m od el,the
f
unctionsw illb e symm etric intheir param etersasw ell. T hus, the overallpayo® f
unction
f
or c ountry A isgivenb y
U A (¿ab;¿ac;¿ba ;¿bc;¿ca;¿cb) = U M (¿ab;¿ac) + U X (¿ba ;¿bc) + U X (¿ca;¿cb)
(8)
W e c and e¯ne the ob jec tive f
unctionsf
or the c ountriesina sim ilar w ay.(¿ab;¿ac) are d ec ision
variab lesf
or c ountry A,(¿ba ;¿bc) f
or c ountry B and (¿ca;¿cb) f
or c ountry C .
It isstraightf
orw ard to show that the unilateralNash tari® ratesim posed b y a c ountry
tow ard sthe trad ing partnersw illb e equal,satisf
yingthe M F N requirem ent.How ever, this
isd ue to the very strong sym metric nature ofthe m od el.Sim ilar to previoussec tions, the
Nash tari® ratesare ine± c ient and there are P areto gainsto b e achieved through rec iproc al
low eringoftari® rates.Still,there isno reasonto assum e that the resultingtari® ratesw ill
satisf
y the M F N c riteria w henthe c ountriesengage intrad e negotiationsto im prove their
w elf
are .T o c om pare the implic ationsofthe M F N requirem ent w hich isof
tenob served in
multilateraltrad e agreem ents,w e w illanalyz e severald i®erent regim es.T he ¯rst one isthe
m ost generalc ase w here there are no restric tionsonthe tari® rate.Asinthe previousc ase,
20
the P areto f
rontier c onsistsofthe points(UA;UB ;U C ) such that
8
>
>
(UA;U B ;UC ) :UA = m axUA (¿ab;¿ac;¿ba ;¿bc;¿ca ;¿cb)
>
>
>
>
>
>
<
>
>
>
>
>
>
>
>
:
+ ¸ B [UB (¿ab;¿ac;¿ba ;¿bc;¿ca;¿cb) ¡UB ]
+ ¸ C [UC (¿ab;¿ac;¿ba ;¿bc;¿ca;¿cb) ¡U C ];
UA ¸UAN ;UB ¸U BN ;UC ¸UCN
9
>
>
>
>
>
>
>
>
=
>
>
>
>
>
>
>
>
;
(9)
T hen,w e c anw rite the P areto f
rontier asa f
unctionUA = F G en (UB ;UC ) w here w e have the
requirement that UA ¸UAN ; UB ¸UBN ,UC ¸UCN :T he P areto e± c ient f
rontier inthisregim e
hasthe similar propertiesofthe previoussec tion.T he f
rontier isc oncave and increasingin
one d imensionrequiresd ec reasesinthe other tw o d im ensions;thusthe f
easib le set isc onvex.
T he sec ond regim e isthe w eb of(three) b ilateralnegotiationsb etw eenthe three c ountries. Ineac h b ilateralnegotiation, the partiestake the outc om esofthe other (tw o) negotiationsasgivenand reac h a pair ofe± c ient tari® rates. For exam ple, ifA and B are
negotiating over (¿ab;¿ba ), the e± c ient outc om e w illb e a f
unctionofthe other f
our tari®
rates. T he equilib rium point ofthisnetw ork ofb ilateralnegotiationsw illb e a vec tor of
tari®s¿ B =
³
´
B
B
B
B
B
B
¿ab
;¿ac
;¿ba
;¿bc
;¿c
uch that they solve the f
ollow ing system ofequations
a ;¿c
b s
simultaneously:
8 ³
´
h
³
´i® h
³
´i1¡®
>
B
B
B
B
B
B
B
B
B
B
>
>
¿
;¿
=
argm
ax
U
¿
;¿
;¿
;¿
;¿
;¿
U
¿
;¿
;¿
;¿
;¿
;¿
A
ab
ba
B
ab
ba
>
ab ba
ac bc c
a c
b
ac bc c
a c
b
>
< ³
´
h
³
´i¯ h
³
´i1¡¯
B
B
B
B
B
B
B
B
B
B
¿ac
;¿c
;¿ca;¿ab
;¿ba
;¿bc
;¿c
U C ¿ac;¿ca ;¿ab
;¿ba
;¿bc
;¿c
a = argm ax U A ¿ac
b
b
>
>
³
´
h
³
´i°h
³
´i1¡°
>
>
>
B
B
B
B
: ¿ B ;¿ B = argm ax UB ¿bc;¿cb;¿ B ;¿ B ;¿ B ;¿ B
U
¿
;¿
;¿
;¿
;¿
;¿
C
bc
c
b
bc c
b
ab ba ac c
a
ab ba ac c
a
9
>
>
>
>
>
=
>
>
>
>
>
;
(10 )
f
or some ® ;¯ ;°(w here 0 > ® > 1;0 > ¯ > 1;0 > °> 1)2 3. T hese param eterslead to
ane± c ient outc ome ineac h ind ivid ualb argaining gam e giventhe outc om esofthe other
b argaininggam es.Depend ingonthe und erlyingpayo® f
unctions,there c anb e multiple set
ofsolutionsf
or thisset ofequationsor no solutionsat all.For the rest ofthe paper w e w ill
assum e that at least one equilib rium exists.At the equilib rium point, no pair ofc ountries
23
W e assume thatthese inequalities are stricttoavoid some technicalproblems.T hey donote®ectthe
results inanyway,butsomeproofs would becomemoreelaborate.
21
w illhave the incentive to renegotiate their b ilateraloutc om e since they w ould b e alread y on
the (b ilateral) e± c iency f
rontier.T he f
ollow ingpropositionestab lishesthe glob ale± c iency
propertiesofthe equilib rium pointsinsuc h a netw ork ofb ilateralnegotiations:
P rop osition6 : No equilibrium outcom e ofthe netw ork ofbilateralnegotiations w illbe
globally P areto e± c ient.Inother w ord s, no solutionto the equations(10 ) w illbe inthe set
givenby (9).
P roof
:See the append ix.
Inthe previoussec tionw here the b ilateraltrad e relationshipsd id not im pose externalities
onthe third c ountry, it w as possib le, b ut not guaranteed , that the netw ork ofb ilateral
negotiationsc ould implement a glob ally e± c ient outc om e.Inthisc ase, w here the b ilateral
treatiesc reate trad e d iversione®ec ts,thisno longer ispossib le.A netw orkofb ilateraltreaties
never im plem entsa glob allye± c ient outc om e and thisb ec om esthe other m ainm otivationf
or
hold ing multilateralnegotiations.E ac h b ilateralnegotiationim posesnegative externalities
onthe outsid e c ountry and there existsa m ultilateraloutc om e that isP areto superior to any
b ilateralnetw ork outc ome.
T he ab ove result d oesnot require the tari®sim posed b y A onB and C (¿ab;¿ac) to b e
equalto each other,inother w ord s,d isc rim inatorytari®sare allow ed .How ever,one c om m on
f
eature ofmultilateraltrad e agreementsisthe non-d isc rim inationor the M ost Favored Nation
(M F N) c lause w hic h memb er c ountriesf
rom im posingd i®erent tari®sonid entic alprod uc ts
c om ingf
rom tw o d i®erent sourc es.Ina m athem atic alsense,these are f
urther c onstraintson
the P areto f
rontier given(9).T he new P areto f
rontier ofthe multilateralb argainingsetting
w ith the M F N requirem ent w illb e givenb y the f
ollow ingset ofpoints:
8
>
>
>
>
>
<
(UA;UB ;UC ) :UA = m axUA (¿a ;¿b;¿c)
+ ¸ B [ UB (¿a ;¿b;¿c) ¡UB ]+ ¸ C [U C (¿a ;¿b;¿c) ¡UC ];
>
>
>
>
>
:
UA ¸UAN ;UB ¸U BN ;UC ¸UCN
22
9
>
>
>
>
>
=
>
>
>
>
>
;
w here ¿a isthe tari® im posed b y c ountry A onher im portsregard lessoforigin.UA (¿a ;¿b;¿c)
c anb e ob tained f
rom equation(8) w ith the appropriate sub stitutions.W e w illd enote this
P areto f
rontier asUA = F M
FN
(U B ;UC ). T hisf
rontier hasthe sam e propertiesasU A =
F G en (UB ;UC ) w hic h c anb e show nusing the sam e argum entsinthe previousproposition.
O ur ¯rst aim isto c om pare these f
easib le setscharac teriz ed b y the P areto f
rontiers:
P rop osition7 T he feasible set ofthe M F N m ultilateralbargainingisa subset ofthe feasible
set ofthe generalbargaining.Inother w ord s, the m ultilateralnegotiationsw ith no restric tions
P areto d om inatesthe M F N negotiations.
P roof
: See the append ix.
T he propositionshow sthat f
or any e± c ient M F N tari® c on¯guration, there isa nonM F N one that P areto d ominates it. Sim ply put, the M F N requirem ent inmultilateral
trad e negotiationsc reatese± c iency losseseveninthisextrem ely sym m etric m od el. T his
result isnot surprisingsince introd uc tionofad d ed c onstraintsw illalw aysresult ina sm aller
f
easib le setsand the M F N requirement sim plyim posesextra c onstraintsonthe optim iz ation
prob lem.Ina b argaining sense, im positionofthe M F N rule d istortsthe e± c ient exchange
ofc oncessions.T he result ofthispropositionc anb e seeninF igure 5 w here higher (low er)
surf
ac e c orrespond sto the e± c ient payo® f
rontier ofthe general(M F N) negotiations.T he
tw o surf
ac esintersec t at one point w hich c orrespond sto the f
ree trad e payo®s.G iventhis
lossofe± c iency d ue to the M F N rule, it isim portant to know w hy it issuch anintegral
part ofmultilateraltrad e agreem ents.W e w illd elay the analysisofthisquestionuntilthe
next c hapter and w e w illtake the M F N rule asgivenat thisstage.
6 M FN R egim e vs.B il
ateralR egim e
T he ¯nalquestionto b e asked isw hether the governm entsw ould pref
er a multilateralnegotiationenvironm ent w ith the M F Nc lause or a b ilateralenvironm ent that allow sd isc rim inatory
23
tari®s. W ith the im positionofthe M F N rule, w e c annot d irec tly c laim that multilateral
negotiationsc anprovid e a P areto superior outc om e und er allc irc um stances.T he answ er w ill
d epend onw hic h equilib rium outc om e provid esthe higher w elf
are levels.M ore spec i¯c ally,
the M F Nregim e w illd e¯nitelyb e c hosenifallgovernm entsare b etter o® inthat equilib rium .
T hisquestionisd i± c ult to answ er since w e im posed no restric tionsso f
ar onthe shapesof
the payo® f
unctionsand other param etersother thansom e very generalassum ptions.It is
quite c onceivab le that M F N regim e c anb e pref
erred , and thusenf
orc eab le, und er c ertain
c ond itions.
Inthissec tion,w e w illprovid e one such exam ple w ith som e restric tive assum ptionsw hich
are ac tually im posed quite of
teninthe internationaltrad e literature.W e w illassum e that
the c ountriesare symm etric inevery sense possib le:
(1) T he im port payo® f
unctionUAM (¿ab;¿ac) w illb e sym m etric inb oth param etersand
thishold sf
or other governm ents.
(2 ) T he export f
unctionsf
or A f
or b oth export good s,UAX (¿ba ;¿bc) and U AX (¿ca;¿cb) w ill
b e id entic aland thisw illhold f
or other governm ents.
(3) For A and B w ho c ompete to export good cto c ountry C ; their export f
unction
UAX (¿ca ;¿cb) and UBX (¿cb;¿ca) w illb e id entic al.
T hese c ond itionsw ould b e met iftw o c ountriesexporting the sam e good had the sam e
end ow m ents and the supply f
unctions f
or allgood s w ere id entic al. Form these, w e w ill
assum e that the equilib rium outc om es are id entic alas w ell. Inother w ord s, the tari®s,
¿B =
³
´
B
B
B
B
B
B
¿ab
;¿ac
;¿ba
;¿bc
;¿c
tab lished inthe netw orkofb ilateralgam esw illb e equalto
a ;¿c
b ; es
eac h other.T he questionb ec omesifthere isanequilib rium outc om e ofa m ultilateralM F N
b argaining game that P areto im provesuponthe b ilateraloutc om e. T he f
ollow ing result
answ ersthisquestion:
P rop osition8 : Inthe symmetric case, there isanM F N outcom e that isP areto superior
to the bilateralnetw orkoutcome.
24
P roof
:See the append ix.
T hisexample show sthat the M F N c ase P areto im provesuponthe b ilateralc ase.Since
allgovernm entsare b etter o®.none w illw ant to d eviate f
rom the M F N rule w hich w ould
imply returningto the d isc riminatory b ilateralregim e.
7 Con
cl
usions
T hispaper approac hesthe w orld trad ingsystem f
rom a verygeneralb argainingperspec tive as
it isd one b y m any polic ym akersand governm ent o± c ials.T hisapproach hasthe ad vantage
ofexplainingmanyob servationssuc h asthe m erc antilist b ehavior ofthe governm entsd uring
the negotiationround s.How ever,our m ainaim isto d eterm ine the sourc esofe± c iencygains
inmultilateralnegotiationssuc h asthe G AT T /W T O sponsored negotiationround s.
T he ¯rst sourc e ofe± c iencygainsarisessince multilateralism allow sthe negotiatingpartiesto equate the ratiosoftheir marginalpayo®s.T hisisw hat agentsw ould d o ina general
equilib rium exc hange ec onomy to reach P areto superior outc om es.M ultilateralism provid es
thisgainevenw henthe trad e regim e isc om posed ofind epend ent b ilateralrelationships.
T he sec ond sourc e ofgainsarisessince m ultilateralism allow sc ountriesto internaliz e the
(negative) externalitiesim posed b y (m ostly trad e d iverting) b ilateral/regionalagreements
onthird parties.T hisissim ilar to the e± c iency gainsthat b ilateralagreem entsprovid e over
unilateralac tions.Although,the M F N rule lim itsthe w elf
are gainsthat w ould b e availab le
ina generalf
ram ew ork,w e show that ina sym m etric c ase,m ultilateralM F N outc om esare
stillsuperior to b ilateraloutc om es.
Inshort, multilateralnegotiationsallow (1) trad ing oftari®sand other b arriersac ross
c ountriesthrough b argaining and (2 ) internaliz ationofallunilateraland c oalitionalexternalities. E ± c iency gainsare ob tained through anexpansionofthe f
easib le set to includ e
P areto superior outc om es(c ompared to unilateraland b ilateraloutc om es).W e show that,
w ith no transac tionc osts, the ind ivid ualand totalw elf
are are m onotonic ally increasing in
25
the numb er ofc ountries.B est outc om esare ob tained w henallissuesare negotiated simultaneously amongallofthe c ountries.Certainextensionsto ac c om m od ate politic alec onomy
e®ec tsare includ ed to explainw hy w e never see c om pletely f
ree trad e.
W e d em onstrated the ab ove resultsusing a very spec ializ ed generalequilib rium m od el
since it sim pli¯ed the analysis c onsid erab ly. How ever, the results c anb e easily c arried
to other settings, espec ially strategic trad e m od els. T he im portant step is to introd uc e
the e®ec ts ofb ilateraland /or multilateralb argaining and to c om pare these to outc om es
w ith unilateralac tions. Since, the w orld trad ing system is c harac teriz ed b y c ontinuous
negotiations,w e b elieve it isc ruc ialto analyz e trad e polic iesina b argainingf
ram ew ork.
T he e± c iencygainsf
rom multilateralism arise f
rom the nature ofthe und erlyingec onom ic
environm ent and trad e relationships.How ever, asw e stated earlier, suc c essf
ulmultilateral
negotiationshave b eenonly estab lished inthe post-w ar era w ithinthe G AT T regim e.T he
f
ailure to exploit the P areto superior outc om es provid ed b y multilateralnegotiations in
the past, w e b elieve, is d ue to the institutionalf
ram ew ork inw hic h trad e polic ies w ere
f
ormulated .inthe next c hapter, w e w illanalyz e the negotiationprinciplesand other rules
w ithinthe G AT T system that enab led the m em b er c ountries to estab lish and sustaina
suc c essf
ulmultilateralregim e.
F inally,thisanalysishelpsusto id entif
y the strengthsofG AT T /W T O w hich isa c ruc ial
task at this stage. G AT T /W T O b ased non-d isc rim inatory m ultilateralsystem is f
ac ing
seriousc hallengesand going through m ajor institutionalc hanges.Correc t id enti¯c ationof
strengthsand w eaknessesofthe trad ing system w ould enab le usto d esignm ore e± c ient
and °exib le rulesand a negotiationf
ram ew orkto hand le the c om plic ated issuesonthe trad e
agend a.W e b elieve G AT T /W T O should b e the pillar ofthe w orld trad ingsystem since nond isc rim inatorymultilateralism hasthe potentialto d eliver the m axim um payo®sto c ountries
and avoid possib le ine± c iencies.It isc ruc ialto end ow the W T O w ith the right m ec hanism s
since the next d ec ad e w illd etermine itsand the w orld trad ingsystem 'sf
uture.
26
8
Append ix
P roofofP rop osition2 : T he e± c iency oftrad e agreem entsrequiresthat equation(5)
hold s. T hisim pliesthat
d U A=d ¿j
d U A=d ¿i
=
d U B =d ¿j
:De¯ne
d U B =d ¿i
f
unctionW (¿i;¿j) =
d UA d UB
d ¿j d ¿i
¡ ddU¿Ai ddU¿Bj :
Lookat the loc usW (¿i;¿j) = 0 w hich im plic itlyd e¯nesthe e± c ient tari® pointsonthe c ontrac t c urve.Since the d emand f
unctionsare linear and the c onsum er surplusesare quad ratic ,
eac h d erivative inW (¿i;¿j) islinear initsargum ent.T henw e c anw rite
d UA
d ¿i
d UB
d ¿i
d UA
d ¿j
= a ¡b¿j and
= c
¿i ¡d w here a;b;c
;d are allpositive c onstants.B ec ause ofsym m etry, w e w illhave
= a ¡b¿i and
d UB
d ¿j
= c
¿j¡d .T henf
or the tari® pointssatisf
yingW (¿i;¿j) = 0 ; w e c an
d eterm ine dd ¿¿ji,the slope ofthe e± c iencyloc us.Af
ter sub stitutingthe ab ove linear equations,
w e ¯nd that
³
h
i
d ¿i
d ¿j W (¿ ;¿ )= 0
i j
< 0 and
·
¸
d 2 ¿i
2
d ¿j
W (¿i;¿j)= 0
< 0 f
or alle± c ient pairs(¿i;¿j).
P roofofP rop osition3: Let ¸ b e the Lagrange m ultiplier at the optim alpoint
´
UAab;UBab ofthe b ilateralb argaining gam e b etw eenA and B . Sim ilarly d e¯ne ¹ f
or
³
´
(UAac;UCac) and ´ f
or UBbc;U Cbc :Suppose ´ ·¹=¸.Note that ¸ isalso the rate oftransf
or-
m ationb etw eenthe payo®sofc ountry A and B b y d e¯nition.T he sam e hold sf
or ´ and ¹ :
Inthe trilateralb argaininggam e,w e have £ asthe rate oftransf
orm ationb etw eenpayo®sof
c ountriesA and B and ¢ f
or c ountriesA and C asgivenb y expression7.Furtherm ore,on
the e± c ient f
rontier w e need to have ¢ =£ asthe rate oftransf
orm ationb etw eenc ountries
B and C .Since, ´ · ¹ =¸, the outc om e ofb ilateralnegotiationsc annot b e onthe payo®
f
rontier oftrilateralnegotiations.T hus,givenany outc om e ofb ilateralnegotiations,w e c an
¯nd a trilateralnegotiationoutc ome that P areto d om inatesit.
P roofofCorol
l
ary 4 : Since the initialc ountriesare onthe f
rontier,there are no b arter
trad e opportunitiesofthe sort d esc rib ed previously.Let sab d enote the slope ofthe b ilateral
payo® f
rontier b etw eenc ountry A and B at the outc om e d ec id ed d uring the multilateral
negotiations.san d enotesthe slope ofthe b ilateralpayo® f
rontier b etw eenc ountry A and N
at their b ilateralagreem ent point.Let abc
d :::k d enote anord ering oflength K ofsom e of
the c ountriesinmultilateralnegotiationinitially.Suppose sabsbc:::skn ·san .T henusingthe
trad ingm ethod d esc rib ed ab ove,it ispossib le im prove any c ountry'spayo® w ithout hurting
27
the other ones. T husinclusionofc ountry N increasesthe siz e ofthe P areto f
rontier and
c reatesopportunitiesto improve the w elf
are ofallc ountries.
P roofofP roposition6:Suppose ¿ B =
³
´
B
B
B
B
B
B
¿ab
;¿ba
;¿ac
;¿bc
;¿c
ob ale± a ;¿c
b isonthe gl
c iency f
rontier d e¯ned b y (9).T henit should b e the solutionto a m axim iz ationprob lem of
the f
ollow ingtype:
¿ B = argmax[U A (¿)]p [UB (¿)]q [UC (¿)]1¡p¡q
(11)
w here 1 > p > 0 ;1 > q > 0 ;1 > p + q > 0 :Inother w ord s, suc h p and q should exist.W e
know that the f
ollow inghold at ¿ B f
rom the ¯rst-ord er c ond itionsofequation(10 ):
d UB =d ¿ab
d U A=d ¿ab
+ (1 ¡® )
=
UA
UB
d U A=d ¿ba
d UB =d ¿ba
(® )
+ (1 ¡® )
=
UA
UB
(® )
0;
0
Also,the f
ollow inghold at ¿ B f
rom the ¯rst ord er c ond itionofequation(11):
d UB =d ¿ab
d UC =d ¿ab
d UA=d ¿ab
+ (q)
+ (1 ¡p ¡q)
=
UA
UB
UC
d UA=d ¿ba
d UB =d ¿ba
d UC =d ¿ba
(p)
+ (q)
+ (1 ¡p ¡q)
=
UA
UB
UC
0
(p)
0
R earrangingthe ab ove equationsand sub stitutionyield s
µ
¶
1 ¡® d UB =d ¿ab
d UC =d ¿ab
q ¡p
+ (1 ¡p ¡q)
=
®
UB
UC
µ
¶
1 ¡® d UB =d ¿ba
d UC =d ¿ba
q ¡p
+ (1 ¡p ¡q)
=
®
UB
UC
0
0
W e know that d UC =d ¿ab > 0 ;d UB =d ¿ab < 0 and (1 ¡p ¡q) > 0 .So the ¯rst equationrequires
³
that q ¡p 1¡®
®
´
³
> 0 :Also, d UC =d ¿ba > 0 and d UB =d ¿ba > 0 w hich im plies q ¡p 1¡®
®
´
< 0:
B ut thisisnot possib le, so no suc h (p;q) c anexist and theref
ore ¿ B il c annot b e glob ally
e± c ient.
P roofofP rop osition7: Since the optim izationprob lem ofthe M F N c ase hasthe
same ob jec tive f
unctionw ith ad d itionalc onstraints,the outc om e hasa low er value.Inother
28
w ord sF G e n (U B ;U C ) ¸F M
FN
(U B ;U C ) f
or allpairsof(U B ;U C ):T heref
ore,the outc om e of
negotiationsw ith no restric tionsP areto d om inatesthe outc om e ofnegotiationsw ith M F N
c onstraint.
P roofofP roposition8: Anoutc om e,¿ M
FN
; ofthe multilateralM F Nb argaininggam e
hasto b e a solutionto the f
ollow ingprob lem :
¿M
FN
= argm ax[UA (¿)]® [UB (¿)]¯ [UC (¿)]1¡® ¡¯
w here 1 > ¯ > 0 ;1 > ® > 0 ;1 > ® + ¯ > 0 :T o c om plete the proof
, w e need to show that
one pair of(® ;¯ )existsw hic h satisf
y the ab ove equation.Let ® = ¯ = 1=3.T henthe ¯rst
c ond itions(w hen¿a = ¿aM
"
d UA
d ¿a
#
FN
) b ec ome
+
¿a = ¿aM
FN
"
d UB
d ¿a
#
+
¿a = ¿aM
FN
"
d UC
d ¿a
#
= 0
¿a = ¿aM
FN
d ue to the f
ac t that UA = UB = UC . Sam e hold s f
or other tari® rates as w ell. Since
tari® ratesinthe b ilateralc ase are equal,w e c anassum e that the c ountriesare at the Nash
b argaining solution. T he ¯rst ord er c ond itionsf
or ¿ab inthe b ilateralnetw ork c ase (w hen
B
¿ab = ¿ab
) is:
"
d UA
d ¿ab
#
+
¿ab=
BIL
¿ab
"
d UA
d ¿ab
B
Since d UC =d ¿a < 0 , w e must have that ¿ab
> ¿aM
#
= 0
¿ab=
FN
B IL
¿ab
B
. Since thishold sf
or ¿ab
, it w illhold
f
or alltari® rates. T his w ould imply that the payo®s ofallc ountries inthe M F N c ase
³
UAM F N ;UBM
FN
;UCM
FN
´
³
´
ishigher thanthe payo®sinthe b ilateralnetw orkc ase U AB il;UBB il;UCB il .
29
R ef
erences
[1] B agw ell, K yle and R ob ert Staiger [19 96], \R ec iproc alT rad e Lib eraliz ation," NB E R
W orkingP aper #54 88.
[2 ] B agw ell,K yle and R ob ert Staiger [199 7a],\G AT T -T hink,"m im eo.
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