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Tariff De-Escalation
with Successive Oligopoly
Ian Sheldon
Short Course - Lecture 2
Catholic University of Milan
Cremona, Italy
June 11-22, 2012
Tariff Escalation
● Tariff escalation long-recognized issue in trade policy
literature, (Corden, 1966; Ethier, 1977; Anderson, 1998)
● Cadot et al. (2004) report nominal protection escalates
with degree of processing in both industrial and
agricultural goods
● Extent of tariff escalation highlighted as key issue
affecting developing country exports (UNCTAD, 2002;
World Bank, 2003; FAO, 2007)
● Provides rationale for formula approaches to reducing
tariffs, i.e., percentage reduction in higher tariffs
exceeds that for lower tariffs (Francois and Martin,
2003) – essentially in draft WTO modalities (WTO, 2009)
EU Japan US
Cocoa Primary
Processed
0
17
0
43.0
0
13
Coffee Primary
Processed
4
8
0
12
0
2
Sugar Primary
Processed
406
36
397
80
90
55
Fruits Primary
Processed
8
19
9
19
5
11
Oilseeds Primary
Processed
0
29
60
6
18
5
Grains Primary
Processed
30
34
67
153
1
3
Rice Primary
Processed
40
60
702
847
2
5
End-Uruguay Round Bound Tariffs (FAO, 2007)
Basic Result
● In vertically-related market, simultaneous and equal
reduction of upstream and downstream tariffs has non-
equivalent effects on upstream and downstream firms’
profits
● Result due to within (horizontal) stage and between
(vertical) stage impact of tariff cuts, where latter is
made up of pass-through and pass-back effects
● To extent firms are concerned about relative
profitability, outcome provides potential source of
opposition to tariff reductions
● Generates strong argument for tariff de-escalation
Literature
● Relates to literature on cascading contingent protection
where upstream tariffs have spillover effect, increasing
chance of tariffs downstream (Hoekman and Leidy,
1992; Sleuwaegen et al., 1998)
● Feinberg and Kaplan (1997) in analyzing US anti-
dumping cases found levels of protection upstream
have an impact on protection downstream
● Different, however, to literature on optimal tariffs in
vertically-related markets (Spencer and Jones, 1991,
1992; Ishikawa and Spencer, 1999)
● Paper also abstracts from explicit political economy
considerations in order to focus on mechanisms arising
with simultaneous tariff reductions
ux1
ux2Upstream:
Domestic Imports
x1Downstream: x2
Policy
Final Demand
Tariff - ut
Tariff - dtd ut t>
Stage
u
u u u
x x
x x x
1
1 2
=
= +
Technology:
Vertical Market Structure
Equilibrium
● Three-stage game:
(1) Government commits to ut and dt
(2)/(3) Nash equilibria upstream and downstream,
● Downstream revenue functions:
R x x1 1 2( , ) (1)
R x x2 1 2( , ) (2)
● Downstream profit functions:
dπ x x cR x1 111 1 2= ( , ) - (3)
d dπ x x t xcR x2 222 1 2 2= ( , ) - - (4)
Equilibrium
● First-order conditions are:
cR1,1 1 = (5)
2,2 2 = + dtcR (6)
● Nash equilibrium downstream:
1,11 1,12 1 1
2,21 2,22 2 2
=
c +
u
d
dpR R dx
d dtR R dx (7)
● Slopes of reaction functions:
1,121
1
2 1,11
= = - Rdx
rRdx
(8)
2,212
2
1 2,22
= = - Rdx
rRdx
(9)
Substitutes (complements), i,ijR < 0(> 0), ri < 0(> 0)
Figure 2: Strategic Substitutes vs. Strategic Complements*
X2 X2
X1 X1
N N
R2
R1
R2
R1
R2'
N'
R2'
N'
Strategic Substitutes Strategic Complements
* Bulow, Geanakoplos, and Klemperer (1985)
Equilibrium
● Solution found by re-arranging and inverting (7), and
simplifying notation:
1 2 1-1
2 2 1 2
- = Δ
- + d
a b dpdx
b a dc dtdx
1
u
(10)
where: 1,11 2,221 2 = = a aR R
1,12 2,211 2 = = b bR R ,
and for stability, i < 0a , and -1
1 2 1 2Δ = ( - ) > 0a a b b
● From (8) and (9), substitute i i i= -( ) /r b a into (10):
11 2 1 1-1
22 2 1 2
= Δ
+
u
d
dpdx a a r
dc dtdx a ar (11)
Equilibrium
● Upstream firms’ profits are:
1 1 1 2 1 1= ( , ) -u u u u u uπ R x x c x (12)
u u u u u u u uπ R x x c x t x2 2 1 2 2 2 2= ( , ) - - (13)
● Given technology, upstream Nash equilibrium is:
12 11 -1 1
22 12 2
( )Δ
uU U UU
U
uU UUU U
dca a rdx =
dta ardx dc + (14)
where for stability < 0u
ia , -1(Δ ) > 0u ,and also >u
i ia a ,
i.e., perceived marginal revenue steeper upstream
(see Lemma 1)
Incidence of Tariff Reductions
● To identify market access effects, assume initially that
(i) u ddt dt> 0, = 0, and then (ii) u ddt dt= 0, > 0:
■ Pass-through of udt :
1 1,1 1 2 1,1= ( + ) =u u u u u udp dt p dx dx p D
where 1 1,1/ < 0u u udp dx = p , and -1
1 1= {(Δ ) [ (1+ )]} < 0u u uD a r
Likely that 1,1 < 1up D , i.e., under-shifting of reduction in
upstream tariff (linear or weakly convex demand curve generates this result, Fullerton and Metcalf, 2002)
Incidence of Tariff Reductions
■ Pass-back of ddt :
u u uu1
d u u d
dp dp d x xa r p
dt d x + x dt
u-11 1 2
1 1 1,1
1 2
( + )= = Δ (1+ )
( )
(a) -1
1 1 1,1Δ (1+ ) > 0 if < 0u
ia r p r - substitutes
(b) -1
1 1 1,1Δ (1+ ) < 0 if > 0u
ia r p r - complements
● Pass-through and pass-back effects not equivalent:
u u u u up a r a r p-1 -1
1,1 1 1 1 1 1,1(Δ ) [ (1+ )] Δ (1+ )
(see Lemma 2)
Tariff Reductions and Market Access
● Effect of lowering ut on market access:
-121= (Δ ) < 0
uu u
u
dxa
dt
(16)
■ Imports of intermediate good increase
-1 -1 u u u2 2 12 2 1,1 1 1
1
= = (Δ ) [(Δ ) (a (1+r ))]u
u
u u u
dx dx dpa r p
dt dp dt
(17)
u
dx > r
dt2
20 if < 0 or u
dx < r
dt2
20 if > 0
■ Imports of final good fall (increase) depending on
whether final goods are substitutes (complements)
Tariff Reductions and Market Access
● Effect of lowering dt on market access:
d
dxa a r r p
dt
-1 -1 u21 2 1 2 1,1= Δ [1+ Δ (1+ )] < 0
(18)
■ Imports of final good increase
-1 -12
1 1 2 1,1= (Δ ) [1+ Δ (1+ )]u
u
d
dxs a r a p
dt (19)
1 1 2= ( + )u udx d x x , so 2 1 1 1( / ) =1- ( / ) =u udx dx dx dx s
u
d
dx > r
dt2
10 if < 0 or u
d
dx < r
dt2
10 if > 0
■ Imports of intermediate good fall (increase) if final
goods are substitutes (complements)
Tariff Reductions and Market Access
● Net effect on market access of lowering ut and dt :
u uu u u
u d
dx dxa s a r a p
dt dt
-1 -1 -12 21 1 1 2 1,1+ = (Δ ) + (Δ ) [1+ Δ (1+ )] < 0
(20)
■ Imports of intermediate good increase, partly offset
by decline in derived demand downstream
u u u u
u d
u
dx dxa r p a r
dt dt
a a r r p
-1 -12 22 2 1,1 1 1
-1 -1
1 2 1 2 1,1
+ = (Δ ) (Δ ) [ (1+ )]
+ Δ [1+ Δ (1+ )] < 0
(21)
■ Imports of final good increase, as long as vertical
effect of upstream tariff reduction is not too great
Tariff Reductions and Market Access
● Which stage is most affected by change in access?
u d
u u u u u
u u u u
dt dt
a r p a r a a r r pdx
dx a s a r a p
-1 -1 -1
2 2 1,1 1 1 1 2 1 2 1,12
-1 -1 -1
2 1 1 1 2 1,1+
Δ (Δ ) [ (1+ )]+ [1+ Δ (1+ )]= <1
(Δ ) + Δ (1+ (1+ )Δ )
(22)
■ Final good imports likely to increase by less than
increase in imports of intermediate good (see Proposition 1)
● Result rationalizes why some firms may take a
different stance on trade liberalization, reinforcing need for formula reductions in tariffs
Tariff Changes and Profits
● By how much would dt have to change, given unit
reduction in ut , in order to keep change in domestic
firms’ profits equal between stages?
● Tariff rule is to find ˆddt such that:
ˆ
1 1
1 1
+
=
+
d uu
u u
d
d u
d d
dπ dπdt
dt dtdt
dπ dπ
dt dt
(23)
1 1 1 1> 0, > 0, < 0, > 0d u d u
d d u u
dπ dπ dπ dπ
dt dt dt dt
Tariff Changes and Profits
● (i) If ˆ d udt / dt de -escalation>1, implies tariff
(ii) If ˆ d udt / dt escalation0 < <1, implies tariff
■ Result (i) means percentage reduction in downstream
tariff should exceed that for upstream tariff
■ Result (ii) means percentage reduction in downstream
tariff should be less than that for upstream tariff
● When vertical effects coupled with horizontal effects,
effects of simultaneous tariff reductions may not have an equal effect on profits of firms located at upstream and downstream stages
Policy Implications
● Equal reduction in tariffs in vertically-related market
may result in greater impact on upstream (downstream)
firm(s) compared to downstream (upstream) firm(s)
● To extent vested interests oppose trade liberalization,
lobbying likely to come from upstream (downstream) –
not just because profits fall, but as profits fall by more
than downstream (upstream)
● Important justification for formula approaches to tariff
reduction – not just simpler negotiations, but also
formal basis in mechanisms arising in vertically-related
markets
● Potentially beneficial to developing country exporters