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The Simple Analytics of Trade Creation and Diversion
Alan V. DeardorffUniversity of Michigan
Rishi R. SharmaColgate University
For presentation at
Conference on International Economic Integration: Firms, Workers, and Policies
Universität Tübingen May 22-23, 2019
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To Willi
• Known since his year at Michigan in the 1980s
• Visited him and Gabi in Essen, Linz, and Tübingen
• Have admired his work throughout• Delighted to be here to honor him
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My Topic
• FTAs• Willi has touched on these throughout his
career, as have most of us in the trade field
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Outline
• Background• 3-country case, in graphs• Somewhat more general case, in equations• 4-country case, in graphs
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Background
• Viner’s (1950) trade creation and trade
diversion are usually illustrated with
– Constant costs
– 2-country FTA or CU plus rest of world
• We’ll look here at cases with
– Upward sloping supplies
– And in the last case, an FTA with pre-existing
other FTA
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3-country case*
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• Three countries, importer A, and exporters B, and C
• Export supply and import demands are linear• Countries B and C are identical• Two equilibria
– 0: MFN specific tariff t on exports of both B and C– 1: FTA of A and B:
• tariff t on exports of C; • zero tariff on exports of B
For
simplicity
*Much of this is an elaboration of material in 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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P
!" = !$
Q
Export Supplies of B and C
Q
Exports to Country A
%"&, %$& P %"& + %$&
%") + %$&
*
Export Supplies
%"), %$)
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P
!"#, !%#
Q Q
Import Market
!"&, !%& P
'(
!)" = !)% ')( = !)" +!)%
MFN Equilibrium
," = ,%-
!"& + !%&
!"# + !%&.)(
Export Supplies
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P
Q Q
!"#, !%# P
&'
!("= !(%
!*%
FTA Equilibrium
!*" &(' &*'
+" = +%,
!"# + !%#
!". + !%#/('/*'
!"., !%.
Export Supplies Import Market
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Trade Creation and Diversion
P
Q Q
!"#, !%# P
&'
!(" &)' &('
*" =*%
,
!"# + !%#
!". + !%#!"., !%.
/)'/('
TD TC
Export Supplies Import Market
!)"= !)%
!(%
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TC & TD, another View
!"
Q Q
#$%, #'%
("
#)$ (*" ()"
+
#$% + #'%
#$- + #'%#$-, #'-
!*"!)"
TD TCTDTC
Export Supplies Import Market
#*$= #*'
#)'2$ =2'
!"
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Welfare Effects on Country A
Q
Export Supplies
Q
!"#, !%#
&'
!(" &)' &('
Tariff revenue lost fromB C
Net gain of A’s private sector
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Import Market
!)"= !)%
!(%
-' -'
2"= 2%
See immediately that country A• Gains from trade creation• Loses from trade diversion• As well as from lost revenue from country B
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Welfare Effects on Countries B and C
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
Gain by partner country B
Loss by outside country C
-' -'
2"= 2%
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Welfare Effects on the World
These add up, with much cancellation to yield the following:
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
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Welfare Effects on the World
These add up, with much cancellation to yield the following:
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
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Welfare Effects on the World
These add up, with much cancellation to yield the following:
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
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Welfare Effects on the World
These add up, with much cancellation to yield the following:
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
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Welfare Effects on the World
These add up, with much cancellation to yield the following:
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
=
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These add up, with much cancellation to yield the following:
Welfare Effects on the World
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
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These add up, with much cancellation to yield the following:
Welfare Effects on the World
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
-' -'
2"= 2%
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Welfare Effects on the World
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
Loss from trade diversion
Gain from trade creation
-' -'
2" =2%
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Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
Why the Loss from Trade Diversion
C’s fall in cost
B’s rise in cost
-' -'
2" =2%
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Welfare Effects on the World
Q Q
!"#, !%#
&'
!(" &)' &('
*
!"# + !%#
!", + !%#!",, !%,
-)'-('
TD TCTDTC
Export Supplies Import Market
!)"= !)%
!(%
Loss from trade diversion
Gain from trade creation
-' -'
2" =2%
• Loss is an area, product of the price change and the quantity of trade diversion, with the latter depending on the former.
• So the loss rises with the square of trade diversion.
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The Model
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• Four countries:
– Importer A
– Exporters B, C, and D
• Export supply and import demands are linear
• Three equilibria
– 0: MFN tariff t on exports of B, C, and D
– 1: FTA of A and D:
• Tariff t on exports of B and C;
• Zero tariff on exports of D
– 2: FTA of A with B, keeping FTA with D
• Tariff t on exports of C only
• Zero tariff on exports of B and D
• Consider only cases with !" > 0, & = (, ), *
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The Model
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Exports:
Imports:
Equilibrium:
!" = $" %" − '" , ) = *, +, ,, %" ≥ '"
./ = $/ '/ − %/ , %/ ≤ '/
./ = !1 + !3 + !4
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The Model
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Let:
Then solution is:!" = $ + &'(' + &)() + &*(*
+ = ," + ,' + ,) + ,*
$ = &"-" + &'-' + &)-) + &*-*&. = ⁄,. +
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The Model
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• With more assumptions, !" are proportional to country size– (See paper)
• Therefore #" is country i’s share of world economy– (This is not really right, as it assumes both
demanders and suppliers in proportion to population. Exporters will in fact have more firms, and thus greater weight, than importers.)
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The Model
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Effect of new FTA between A and B (in presence of A’s FTA with D)
Let ∆ be change from equilibrium 1 to equilibrium 2
Thus price in A falls by a fraction of the tariff, in proportion to size of new partner compared to world.
Country B’s price rises by the rest of the tariff
Because A’s tariff on C and D does not change
∆"# = −&'(
∆"' = (1 − &')(
∆", = ∆"- = ∆"# = −&'(
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The Model
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From the price changes, one derives the following changes in quantities of trade:
∆"#= %&'#( > 0∆+&= %& '# + '- + ./ ( > 0
∆+-= −%&'1( < 0
∆+/= −%&'3( < 0
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The Model
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As must be from market equilibrium
Thus the added exports of the partner country include the new imports of country A plus the reduced exports of countries C and D. The latter trade may be said to be “diverted,” but we label
and
because it is reversal of trade diversion from the prior FTA.
∆"#= ∆%& − ∆"( −∆")
−∆"( as “trade diversion”
−∆") as “trade reversion”
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The Model
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Thus
!"#$% &"%#'()* = !& = ,-./' > 0
!"#$% 2%3%"4()* = !2 = ,-.5' > 0
!"#$% 6(3%"4()* = !6 = ,-.7' > 0
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The Model
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Welfare effects of new FTA
Country A (home):
Country B (new partner):
Country C (outside world):
Country D (old partner):
∆"#= ⁄&'# (# + *+ ⁄, 2 ./ − ,.1 − ,2'+
∆"+= ∆34+= 2'+ +12 ./ + .1 + .6 1 − *+ ,
∆"7= −2'7 +.12 *+,
∆"8= −2'8 +.62 *+,
Lost tariff revenue
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The Model
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Welfare effects of new FTA on the World
World (A+B+C+D):
∆"#= 12'() +
12 '+ − '- )
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4-country case
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• Three countries, importer A, and exporters B, C, and D
• Export supply and import demands are linear
• Countries B, C, and D are identical
• Two equilibria
– 1: MFN tariff t on exports of both B and C• Zero tariff on exports of old FTA partner D
– 2: New FTA of A and B:
• tariff t on exports of C only;
• zero tariff on exports of two FTA partners B and D
For simplicity
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P
!" =!$ =!% Q
Export Supplies of B, C, and D
Q
Export Supplies to Country B
&"', &$', &%' P
∑&* = &"* + &$* +&%*,
Export Supplies
∑&- = &"* + &$' +&%*
∑&. = &"' + &$' +&%*
/" = /$ = /%
∑&0 = &"' + &$' +&%'&"*, &$*, &%*
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P
Q
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P
Equilibrium 1: A has FTA with 1 country, D
∑!(
∑!)*+
!("= !(%
!(& *(+
= !(" +!(% + !(&
!"., !%., !&.
/
Import Market
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P
Q
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
!("= !(%
!(& *(+
Equilibrium 2: A has FTA with 2 countries, B & D
!)% !)"= !)&
*)+
!"-, !%-, !&-
.
Import Market
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P
Q
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
!("= !(%
!(& *(+
Changes in Trade from expanding FTA to Country B
!)% !)"= !)&
∆*+∆!% ∆!&
*)+
!"., !%., !&.
/
Import Market
∆!"
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Trade Creation
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P
Q
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
∆!" ∆*+∆!% ∆!&TD TR TC
Trade Creation (TC), Diversion (TD), and Reversion (TR)
!"1, !%1, !&1
2
Import Market
Trade CreationTrade Diversion Trade Reversion
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P
Q
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Trade Creation (TC), Diversion (TD), and Reversion (TR)
∆!" ∆*+∆!% ∆!&
TRTDTCNote that ∆!", while a gain to Country B, is the sum of TC, TD, & TR, since ∆!"= ∆*+ − ∆!% − ∆!&
!"2, !%2, !&2
3
Import Market
TD TR TC
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on Country ATariff
revenue lost from
B CNet gain of A’s private sector
Note that trade reversion does not appear to affect A’s welfare. I suspect this is an artifact of making export supplies from B and D the same.
!",, !%,, !&,
-
Import Market
Q
∆!" ∆*+∆!% ∆!&
∆!&TR
∆!%TD∆*+
TC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on Country B
!",, !%,, !&,Net gain of B’s private sector
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on Country C
Net loss of C’s private sector
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on Country D
!",, !%,, !&,Net loss of D’s private sector
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
I claim that these gains and losses mostly cancel out to reduce to the following:
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!(" !(% !(&!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
!("= !(%
!(&
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!(" !(% !(&!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
!("= !(%
!(&
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
!("= !(%
!(&!(" !(% !(&
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effects on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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P
Export Supplies of B, C, and D
Q
!"#, !%#, !&# P ∑!(
∑!)*+
Welfare Effect on World
!",, !%,, !&,
-
Import Market
QTRTDTC
TR TCTD
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4-country case
64
• Result:– World welfare rises with second FTA, by amount
depending on trade creation and the tariff• Recall from model:
• Here, because we’ve assumed countries B and D are the same, TR=TD
∆"#= 12'() +
12 '+ − '- )
∆"#= 12'()
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4-country case
65
• In general, !" ≠ !$• Which is larger depends just on country size, size
both face the same price change.
• If the new partner is smaller than the old, !" > !$ , and world gain will be larger
• If new partner is bigger than old, then !" < !$and world gain will be smaller and perhaps a loss.
∆45= 12!9: +
12 !" − !$ :
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Conclusion
• Analysis of FTAs shouldn’t treat each independently of FTAs that already exist
• Sequencing of FTAs can matter.
66
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