HIAS-E-57

Backfiring with Backhaul Problems:
Trade and Industrial Policies with Endogenous
Transport Costs(Revised Version of HIAS-E-12)
Jota Ishikawa
Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan
RIETI

Norio Tarui
Department of Economics, University of Hawaii at Manoa and the University of Hawaii Economic Research
Organization (UHERO), 2424 Maile Way, Saunders Hall 542, Honolulu, HI 96822, U.S.A

October 2017

Hitotsubashi Institute for Advanced Study, Hitotsubashi University
2-1, Naka, Kunitachi, Tokyo 186-8601, Japan
tel:+81 42 580 8604
http://hias.ad.hit-u.ac.jp/
HIAS discussion papers can be downloaded without charge from:http://hdl.handle.net/10086/27202
https://ideas.repec.org/s/hit/hiasdp.html

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Manuscript
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Backfiring with Backhaul Problems⇤
Trade and Industrial Policies with Endogenous Transport Costs

Jota Ishikawa†and Nori Tarui‡
July 2017

Abstract
Trade barriers due to transport costs are as large as those due to tari↵s. This
paper incorporates the transport sector into a standard model of international tradeand studies the e↵ects of trade and industrial policies. Transport firms need to commit
to a shipping capacity sufficient for a round trip, with a possible imbalance of shipping
volumes in two directions. This imbalance is known as the “backhaul problem.” Astransport firms attempt to avoid this problem, a tari↵ in one sector may a↵ect otherindependent import and/or export sectors. In particular, domestic tari↵s may backfire:domestic exports may also decrease, harming domestic export sectors and the domestic
economy. This finding contributes to the literature on how import liberalization may
generate a positive e↵ect on the liberalizing country’s exports by identifying a newchannel through endogenous changes in transport costs given the backhaul problem.
JEL Codes: F12, F13, R40
Key words: Transport sector; transport cost; backhaul problems; international shipping; tari↵s⇤

We wish to thank two anonymous referees, Lorenzo Rotunno, Frederic Warzynski, and participants atthe conferences and workshops held at Australian National University, Hitotsubashi University, Keimyung
University, Kobe University, National Taiwan University, National University of Singapore, Singapore Management University, Sogang University, Université Paris 1 Panthéon-Sorbonne, University of Bari, Universityof Hawaii, University of Sydney, and the 2015 WEAI Conference for their helpful comments and suggestions.
We also thank Kazunobu Hayakawa for consultations on trade data. Jota Ishikawa acknowledges financial
support from the Japan Society for the Promotion of Science through the Grant-in-Aid for Scientific Research(S), Grant Number 26220503.
†
Faculty of Economics, Hitotsubashi University, Kunitachi, Tokyo 186-8601, Japan & RIETI; E-mail:jota@econ.hit-u.ac.jp.
‡
Department of Economics, University of Hawaii at Manoa and the University of Hawaii Economic Research Organization (UHERO), 2424 Maile Way, Saunders Hall 542, Honolulu, HI 96822, U.S.A; E-mail:nori@hawaii.edu.

1Introduction

The recent literature on international trade documents the important role of transport costsin terms of both magnitude and economic significance (Estevadeordal et al., 2003; Anderson
and van Wincoop, 2004; Hummels, 2007). According to Hummels (2007), studies examining
customs data consistently find that transport costs pose a barrier to trade at least as large
as, and frequently larger than, tari↵s.1 Hummels (2007) also argues that, “[a]s tari↵s becomea less important barrier to trade, the contribution of transportation to total trade costs—
shipping plus tari↵s—is rising.”
Despite such clear presence in international trade, the analytical treatment of transport
costs tends to be ad hoc. The standard way to incorporate transport costs is to apply theiceberg specification (Samuelson, 1952): the cost of transporting a good is a fraction of thegood, where the fraction is given exogenously. Thus this specification implicitly assumes thattransport costs are exogenous and symmetric across countries. However, several trade facts
indicate that such assumptions are not ideal when studying the impacts of transport costs on
international trade. In particular, market power in the transport sector and the asymmetryof trade costs are key characteristics of international transport, as detailed below.
Among the various modes of transport, maritime (sea) transport is the most dominant.2
Liner shipping, which accounts for about two-thirds of U.S. waterborne foreign trade byvalue (Fink et al., 2002), is oligopolistic. The top three firms account for more than 40% of
the global liner fleet capacity.3 Liner shipping firms form “conferences,” where they agree on
the freight rates to be charged on any given route.4 An empirical investigation by Hummels
et al. (2009) find that ocean cargo carriers charge higher prices when transporting goods withhigher product prices, lower import demand elasticities, and higher tari↵s, and when facing
fewer competitors on a trade route—all indicating market power in the shipping industry.5
Air cargo, whose share in the value of global trade has been increasing, is also oligopolistic(Weiher et al., 2002).6 The prediction of standard trade theory without a transport sector,
1

Anderson and van Wincoop (2004) estimate that the ad-valorem tax equivalent of freight costs forindustrialized countries is 10.7 percent while that of tari↵s and nontari↵s is 7.7 percent.
2
For example, waterborne transport accounted for more than 75% in volume (46% in value) of U.S.
international merchandise trade in 2011 (U.S. Department of Transportation, 2013, Figure 3-4). Globally,
maritime transport handles over 80% (70%) of the total volume (value) of global trade (United Nations,2012, p.44).
3
Based on the Alphaliner Top 100, www.alphaliner.com/top100/.
4De Palma et al. (2011) provide evidence of market power in various transportation sectors.
5
Regulations may also be responsible for enhancing transport firms’ market power. Under the MerchantMarine Act (also known as the Jones Act) of 1920 in the United States, for example, vessels that transportcargo or passengers between two U.S. ports must be U.S. flagged, U.S. crewed, U.S. owned and U.S. built.
Debates exist over the impact of the Act on the U.S. ocean shipping costs.
6
Top 25 air cargo carriers are found in http://www.aircargonews.net/news/airlines/single-view/news/top-1

with exogenous transport costs, may be altered once we consider the markets for transportation explicitly by taking into account the market power of transport firms in influencing
shipping costs.7
Trade costs exhibit asymmetry in several dimensions. First, developing countries pay
substantially higher transport costs than developed nations (Hummels et al., 2009; Waugh,2010). Second, depending on the direction of shipments, freight charges di↵er on the sameroute. For example, the market average freight rates for shipping from Asia to the UnitedStates was about 1.5 times the rates for shipping from the United States to Asia in 2009
(United Nations Conference on Trade and Development, 2010).8 This fact is also at odds
with the assumption of iceberg transport costs in the standard trade theory.
Such asymmetry of transport costs may have substantial economic consequences. For
example, Waugh’s (2010) empirical analysis suggests that “[t]he systematic asymmetry in
trade costs is so punitive that removing it takes the economy from basically autarky to over
50 percent of the way relative to frictionless trade” (p.2095). Asymmetric transport costs
are associated with the “backhaul problem,” a widely known issue regarding transportation:
shipping is constrained by the capacity (e.g., the number of containers) of each transport
firm, and hence firms need to commit to the capacity necessary for the maximum load of around-trip. This implies an opportunity cost associated with a trip (the backhaul trip) withcargo that is under-capacity.9 To avoid the backhaul problem, that is, to have the balancein shipping volume in both directions, transport firms adjust shipping capacities and freightrates.
Attempts to incorporate transportation in general equilibrium trade models show thechallenges associated with defining simultaneous market clearing for the goods to be traded
and the transport services to be required (Kemp, 1964; Wegge, 1993; Woodland, 1968). They
assume a competitive transport sector without explicit attention to shipping capacity constraints. Thus, neither the market power in the transport sector nor the backhaul problems
are considered.
Several recent studies have developed trade models that incorporate an explicit transport
sector in a tractable manner. Behrens and Picard (2011) apply a new economic geographymodel to show that, because a region that is a net exporter of manufactured goods faces
a higher transportation costs due to the backhaul problem, the agglomeration forces are
25-air-cargo-carriers-fedex-maintains-top-spot.html
7
Deardor↵ (2014) demonstrates that, even without an explicit transport sector, considering transport
costs may alter the pattern of trade.
8
Takahashi (2011) and Behrens and Picard (2011) provide several examples where freight costs exhibit
asymmetry.
9
Dejax and Crainic (1987) provide an early survey of the research on backhaul problems in transportation
studies.

2

weakened given endogenous transport costs. While they assume a perfectly competitivetransport sector with explicit shipping capacity, several other studies consider market powerin the transport sector (without taking into account the constraint on the shipping capacity).
Behrens et al. (2009), Takahashi (2011) and Forslid and Okubo (2015) address the implicationof endogenous transport costs on agglomeration and dispersion forces. Abe et al. (2014)
focus on pollution from international shipping and analyze the optimal pollution regulation.
Takauchi (2015) examines the relationship between freight rates and R&D efficiency.
Existing studies have not investigated the impacts of trade and industrial policies in thepresence of a transport sector with backhaul problems (or with its capacity constraint). Our
point of departure is an investigation of how the e↵ects of trade and industrial policies change
once the transport sector and its decision making are considered explicitly.
For this purpose, we incorporate a transport sector into a standard model of international
trade with perfectly competitive markets of traded goods. In the basic model, we assume amonopolistic transport firm to capture market power in a simple manner.10 We investigate
the e↵ects of tari↵s and a tax on the transport firm on trade and welfare. We do so by
taking into account how each policy influences the volume of trade and the freight rates
endogenously, with the backhaul problem being considered explicitly.11
Our model with an explicit transport sector with market power illustrates how transport
costs are determined endogenously, with possible asymmetry between domestic and foreigncountries. In particular, when a gap in the demand size exists between the two countries,
the country with the lower demand faces higher freight costs on shipping (provided the priceelasticity of shipping demand is not too di↵erent between the two countries). This theoreticalprediction is consistent with Waugh’s (2010) finding that countries with lower income tend
to face higher export costs. Furthermore, when a gap in the price elasticity of shipping
demand exists between the two countries, the country with the higher elasticity faces higher
freight costs on shipping (provided the demand for shipping is not too di↵erent between thetwo countries).
Our analysis demonstrates that an explicit consideration of a transport sector changes
10

In fact, a monopolistic transport firm can be justified by Hummels et al. (2009). They report: “In
the fourth quarter 2006 one in six importer–exporter pairs world-wide was served by a single direct liner“service”, meaning that only one ship was operating on that route. Over half of importer–exporter pairs
were served by three or fewer ships, and in many cases all of the ships on a route were owned by a single
carrier”.
11
As Demirel et al. (2010) argue, most studies that consider the backhaul problem assume that the transportation sector is competitive and hence predict that the equilibrium backhaul price is zero when there is
imbalance in shipping volume in both directions over a given route. This is the case for Behrens and Picard(2011). Demirel et al. (2010) o↵er a matching model to generate equilibrium transport prices that may di↵er
but are positive for both directions. Our model, with the transportation firms having market power, also
supports positive equilibrium transport prices.

3the prediction of the e↵ects of trade policies based on standard trade models. In particular, acountry’s trade policy may backfire: domestic import restrictions may also decrease domestic
exports and harm the domestic export sectors while benefiting the foreign import sectors.
These results are due to transport firm’s endogenous response to trade policy. A transport
firm with market power makes decisions on two margins: the freight rate to be charged
for each direction and the capacity for transport. With changes in trade restrictions, thetransport firm makes adjustments only in the freight rates, or in both the freight rates andthe capacity, depending on the stringency of the trade policy. When the transport firm
avoids the backhaul problem, a policy that a↵ects one trip may influence the return trip
through a linkage due to endogenous transport. Thus an increase in a country’s import tari↵
can reduce its exports, thereby generating the backfiring e↵ect described above. We also
demonstrate such policy linkages when the transport sector’s shipping capacity is taxed.
The backfiring e↵ects of tari↵s also imply that a country that reduces its import tari↵s
may enhance not only its imports but its exports. Thus this paper contributes to the literature on how import liberalization may generate a positive e↵ect on the liberalizing country’s
exports (e.g., Cruz and Bussolo 2015) by identifying a new route, i.e., via endogenous changes
in the transport costs given backhaul problems.
Our basic model consists of a monopolistic transport firm, a single export sector and asingle import sector in each country. Investigating this simple case allows us to explain theeconomic intuitions of our main results (Propositions 2-3) in a transparent manner. We thenconsider extensions and check the robustness of our results. In one extension, we investigate
a case with multiple transport firms. In another extension, we consider multiple exportable
goods. In these extensions, besides the backfiring e↵ects, we obtain a few additional results.
Most importantly, we confirm that the main backfiring results that we find with a monopolistic transport firm hold with oligopolistic transport firms. Indeed, the result is moregeneralized: as long as one of the transport firms avoids the backhaul problem, an increasedtari↵ by a trading partner could decrease both exports and imports. The basic welfare
impacts remain the same as in the base case because the total shipping volume (insteadof shipping by individual transport firms) matters for computing changes in consumer andproducer surpluses. The e↵ect of taxes on shipping capacity is also the same qualitatively
when there are multiple shipping firms. In the case of multiple exportable goods, a tari↵in one sector may a↵ect other sectors even when the goods are independent (i.e., neither
substitutes nor complements). In particular, a domestic tari↵ in one sector could hurt theother domestic import sectors and benefit the other foreign export sectors.
In what follows, Section 2 describes our trade model with an endogenous transport sector.
Section 3 studies the impacts of tari↵s and taxes on shipping capacity on trade volume and4welfare. We provide extensions of our analysis when there are multiple carriers (Section 4)
and when there are multiple exportable goods (Section 5). Section 6 discusses alternativeinternational product market structures and the case of India’s trade liberalization in the
1990s to see whether our theoretical results are consistent with it. Section 7 concludes thepaper with a discussion on further research.

2

A trade model with a transport sector

There are two countries A and B. A single transport firm (firm T ) supplies transport services
between the two countries.12 Firm T faces the following inverse demand:
TAB = ⌦B

µB xAB , TBA = ⌦A

µA xBA ,(1)

where Tij and xij are respectively the freight rate when shipping goods from country i tocountry j and the quantity demanded for transport services from country i to country j.
The parameters ⌦A , ⌦B , µA ,and µB are all positive scalars. We assume that both ⌦A and ⌦Bare large enough to have both xAB > 0 and xBA > 0 in the rest of the analysis. We assume
that the freight rate is linear and additive by following the empirical findings supporting thisspecification.13
The costs of firm T , C, are given by
C = f + r,
where r, f, and  are, respectively, the marginal cost (MC) of operating a means of transport
such as vessels or containers, the fixed cost (FC), and the capacity (or, the maximum load,i.e., max{xAB , xBA } = ). In the following analysis, the MC plays a crucial role while the
FC does not. Thus, we assume r > 0 and f = 0 for simplicity. Firm T chooses the shipping
capacity  and the freight rates TAB and TBA in order to maximize its profit:⇧T = TAB xAB + TBA xBAr.

The profit maximization generates three cases. First, if xAB > xBA holds in equilibrium
12
Firm T may be located in country A, country B, or a third country. The location becomes crucial whenanalyzing welfare.
13
Using multi-country bilateral trade data at the 6-digit HS classification, Hummels and Skiba (2004)
find that shipping technology for a single homogeneous shipment more closely resembles per unit, rather
than ad-valorem, transport costs. Using Norwegian data on quantities and prices for exports at thefirm/product/destination level, Irarrazabal et al. (2015) find the presence of additive (as opposed to iceberg) trade costs for a large majority of product-destination pairs.

5

(this case is referred to as type 1 in the following), then we have
⇧T = TAB xAB + TBA xBA

rxAB = (⌦BµB xAB )xAB + (⌦AµA xBA )xBA

rxAB .

The equilibrium (type-1 equilibrium) under free trade is given by
F1
TAB
=

⌦B + r⌦A F 1⌦B r F 1
⌦A
F1
, TBA
=
, xAB =, xBA =
.
2
2
2µB
2µA

1
1
The condition for type 1 is xFAB
> xFBA, which is µA (⌦B r) > µB ⌦A . Both XBA and thefreight rate from country B to country A, TBA , are independent of the MC of operating ameans of transport, r, in this case.
Second, if xAB < xBA holds in equilibrium (this case is referred to as type 3 in thefollowing), then we have
⇧T = TAB xAB + TBA xBA rxBA .

Type-3 equilibrium is
F3
TAB
=

⌦B
⌦A + r F 3
⌦B
⌦A r
F3
3
, TBA
=
, xAB =, xFBA
=
.
2
2
2µB
2µA

The condition for type 3 is µB (⌦A r) > µA ⌦B . In this case, both XAB and TAB are
independent of r.
Lastly, if xAB = xBA holds in equilibrium (this case is referred to as type 2 in thefollowing), which arises when both µA (⌦B r)  µB ⌦A and µB (⌦A r)  µA ⌦B hold (i.e.,µA ⌦B µA r  µB ⌦A  µA ⌦B + µB r holds), then we have
⇧T = TAB xAB + TBA xAB

rxAB .

Type-2 equilibrium is given by1(rµB ⌦A µB + 2⌦B µA + ⌦B µB ) ,2 (µA + µB )1=
(rµA + ⌦A µA + 2⌦A µB ⌦B µA ) ,2 (µA + µB )⌦A + ⌦ B r
2= xFBA=.
2(µA + µB )

F2
TAB
=
F2
TBA
2
xFAB

In contrast to type-1 and type-3 equilibria, both TAB and TBA depend on r. However, they
are not equal in general.
In the following analysis, we assume xAB xBA without loss of generality. There are two
6

types of equilibrium with xAB
xBA . In type 1, there is a large demand gap between thetwo countries, implying an excess shipping capacity from country B to country A. That is,a full load is not realized for shipping from country B to country A. In type 2, the demand
gap is relatively small. Thus, firm T adjusts its freight rates so that it does not have an
excess shipping capacity, i.e., it realizes a full load in both directions. Obviously, type-2
equilibrium arises if the two markets are identical. Firm T faces the backhaul problem inthe type-1 equilibrium but avoids the problem in the type-2 equilibrium.
Our result is consistent with Hummels et al. (2009), who find that freight rates are higher
as the market size of importing countries becomes larger and as the price elasticity of importdemand becomes lower. Observe from the type-1 equilibrium that a larger ⌦i (i = A, B)
means a larger market, indicating that the freight rate for shipping to a country with a
F1
F1
1
1
larger ⌦i tends to be higher. However, TAB< TBA
could arise even if xFAB
> xFBA, that is,
the freight rate could be higher even with excess shipping capacity. This stems from thedi↵erence in the price elasticities of the demand for shipping (which are characterized by µi ,i = A, B, and are positively correlated with the price elasticity of import demand). Even if
the demand for shipping is relatively large, firm T may set a low freight rate when its priceelasticity is relatively large.
Figure 1 here
Since we started with the derived demand for transportation, the above result holds
regardless of product market competition. Figure 1 specifically depicts the case of perfectcompetition.14 Suppose that country i exports good i (i = A, B). For simplicity, we assume
that goods are neither substitutes nor complements and that shipping one unit of good i
requires one unit of shipping capacity. In Figure 1, the upper panel shows the export supply
curve of good A, EXA , which is excess supply of good A in country A, and the importdemand curve of good A, IMA , which is excess demand for good A in country B. With
these two curves, noting one unit of shipping capacity is required to export one unit of goodA from country A to country B, we can draw the demand for transportation services fromcountry A to country B, DDAB , which is a gap between IMA and EXA (see the lowerFpanel). Facing this demand curve (i.e., (1)), firm T determines the freight rate, TAB, and theshipping load, xFAB .15 The prices of good A in country A and in country B are, respectively,
F
F
F
F
F
F
given by PAA
and PAB. The gap between the two prices is TAB, i.e., TAB
= PAB
PAA
.
14

We analyze the case of an international oligopoly in the product market in detail elsewhere (Ishikawa
and Tarui, 2015). See Section 6.1.
15
F1
In type-1 equilibrium, point FB is the midpoint on the demand curve, because TBA
does not depend on
the MC, r. Point FA is located to the upper left of the midpoint.

7

Recalling shipping one unit of good requires one unit of shipping capacity, we can easily
verify who gains or loses from free trade by checking how producer surplus and consumer
surplus change. In country i (i = A, B), free trade benefits producers of good i but harms
consumers of good i. In Figure 1, the net gain in the product market of good A in countryF
A is given by dcPAA. In country B, free trade harms producers of good A but benefits
consumers of good A. The net gain in the product market of good A in country B is givenFby abPAB. The revenue of firm T from shipping good A from country A to country B isF
Fgiven by bcPAA
PAB.
Figure 2 here
Type-2 equilibrium is shown in Figure 2. The upper panel and the lower panel show
trade in good A and trade in good B, respectively. Firm T adjusts freight rates, TAB and
TBA so as to have a full load in both directions (i.e., xFAB = xFBA ). We can easily confirm thenet gains from free trade in goods A and B and the revenue of firm T in the figures.

3

Trade and Industrial Policies

In this section, we first explore the e↵ects of import tari↵s on the freight rates and theequilibrium welfare of the trading countries.16 Then we examine taxes on shipping capacity
as an example of industrial policies because taxing imports and shipping capacity exhibit
similar performance. Without loss of generality, we still assume that xAB xBA holds underfree trade.

3.1

Tari↵sWe begin with import tari↵s on goods. We assume that product markets are perfectlycompetitive and that country i exports good i (i = A, B). Suppose that a specific tari↵,
the rate of which is ⌧ i (i = A, B), is imposed by country i. Then the inverse demand curve
shifts downward by ⌧ i :where ⌦⌧B ⌘ ⌦B
16

TAB = (⌦B

⌧ B)

µB xAB = ⌦⌧BµB xAB ,TBA = (⌦A⌧ A)

µA xBA = ⌦⌧AµA xBA ,⌧ B and ⌦⌧A ⌘ ⌦A

⌧ A.

The e↵ects of import quotas are similar to those of tari↵s. See Ishikawa and Tarui (2015).

8

Type-1 equilibrium with tari↵s is given by⌧ B) + r⌦⌧ + r(⌦A ⌧ A )
⌦⌧
⌧1
= B
, TBA
=
= A,
2
2
2
2
(⌦B ⌧ B ) r⌦⌧B r ⌧ 1(⌦A ⌧ A )⌦⌧A==
, xBA =
=
.
2µB
2µB
2µA
2µA
(⌦B

⌧1
TAB
=
1
x⌧AB

An increase in ⌧ i decreases xji and increases xii (i, j = A, B, i 6= j), but a↵ects neither xij
nor xjj . This is the conventional e↵ects of tari↵s when goods A and B are neither substitutes
nor complements. An increase in ⌧ i decreases Tji but the total trade costs from country j
to country i, which equal Tji + ⌧ i , increase.
Type-2 equilibrium with tari↵s is given by1(rµB ⌦⌧A µB + 2⌦⌧B µA + ⌦⌧B µB ) ,2 (µA + µB )1=
(rµA + ⌦⌧A µA + 2⌦⌧A µB ⌦⌧B µA ) ,2 (µA + µB )⌦⌧ + ⌦⌧B r
2= x⌧BA= A.
2(µA + µB )

⌧2
TAB
=

(2)

⌧2
TBA

(3)

2
x⌧AB

(4)

In this equilibrium, the shipping capacity is binding in both directions. We can easily verify
that an increase in ⌧ i increases the trade costs not only from country j to country i, Tji + ⌧ i ,but also from country i to country j, Tij . Thus, both xji and xij decrease and both xii
and xjj increase (i, j = A, B, i 6= j). This is in contrast to type-1 equilibrium, in which anincrease in ⌧ i a↵ects the supplies only in country i, that is, an increase in ⌧ i decreases xji
and increases xii . An increase in ⌧ i decreases xji in both types of equilibrium. In type-2
equilibrium, however, the shipping capacity is reduced to be equal to xji and hence xij also
decreases. Thus an increase in the import tari↵ generates a “backfiring e↵ect” on the export
quantity.
Even if xAB
xBA holds under free trade, xAB < xBA may arise with tari↵s. That is,tari↵s may shift the equilibrium from type 1 to type 3 or from type 2 to type 3. Type-3
equilibrium with tari↵s is given by
⌧3
TAB
=

⌦⌧B ⌧ 3⌦⌧ + r ⌧ 3
⌦⌧
⌦⌧ r
3
, TBA = A
, xAB = B , x⌧BA
= A
.
2
2
2µB
2µA

As in type-1 equilibrium, an increase in ⌧ i in type-3 equilibrium decreases xji and increasesxii (i, j = A, B, i 6= j), but a↵ects neither xij nor xjj .
Figure 3 here
The above cases are illustrated in Figure 3. The figure shows the relationship between
9⌧ B and the volumes of trade, i.e. xAB and xBA , with ⌧ A = 0.17 The free trade equilibrium
is given by FA and FB in Figure 3 (a) and by F in Figure 3 (b). In Figure 3 (a), as⌧ B increases, only xAB decreases with 0  ⌧ B < µ1 (⌦B µA ⌦A µB rµA ). Both withA
0  ⌧ B < µ1 (⌦B µA ⌦A µB rµA ) and with µ1 (⌦B µA ⌦A µB + rµA ) < ⌧ B < ⌦B , xBA
AA
is independent of ⌧ B . With µ1 (⌦B µA ⌦A µB rµA )  ⌧ B  µ1 (⌦B µA ⌦A µB + rµA ),A
AxAB = xBA holds and an increase in ⌧ B reduces both xAB and xBA . In Figure 3 (b), with0  ⌧ B  µ1 (⌦B µA ⌦A µB + rµA ), both xAB and xBA decrease together as ⌧ B increases.
A
With µ1 (⌦B µA ⌦A µB + rµA ) < ⌧ B < ⌦B , when ⌧ B rises, xAB falls but xBA is constant.
A
In Figure 3, the equilibrium shifts from type 1 to type 2 and then to type 3 or fromtype 2 to type 3. Type-1 equilibrium arises if 0 < ⌧ B < µ1 (⌦B µA ⌦A µB rµA ), type-2
Aequilibrium arises if max{0, µ1 (⌦B µA ⌦A µB rµA )}  ⌧ B  µ1 (⌦B µA ⌦A µB + rµA ),A
Aand type-3 equilibrium arises if µ1 (⌦B µA ⌦A µB + rµA ) < ⌧ B < ⌦B .
A
The above results are summarized in the following proposition.
Proposition 1 If country i imposes a tari↵, ⌧ i , firm T lowers the freight rate from country
j to country i, Tji (i, j = A, B, i 6= j) and mitigates the e↵ects of the tari↵. However, thetrade costs, ⌧ i + Tji , increase and country j’s shipping quantity decreases.
Proposition 2 Suppose xAB > xBA holds under the free-trade equilibrium. Any tari↵ ofcountry B, which leads to xAB  xBA , increases the freight rate from country B to country A
and decreases not only country B’s imports but also country B’s exports. Suppose xAB = xBA
holds under the free-trade equilibrium. Then any tari↵ of country B(A) increases the freightrate from country B(A) to country A(B) and decreases country B(A)’s exports as well as
country B(A)’s imports.
It should be pointed out that linear demands are not crucial for the above propositions.
dT
Appendix A shows (i) d⌧jii < 0 holds if demand for shipping from country j to country i isd(Tji +d⌧ i )dT
not very convex, (ii)
> 0 necessarily holds, and (iii) d⌧iji = 0 holds in type-1 andd⌧ idTtype-3 equilibria while d⌧iji > 0 holds in type-2 equilibrium. Thus, regardless of demanddT
specifications, the backfiring e↵ect of a tari↵ (i.e., d⌧iji > 0) necessarily arises in type-2
equilibrium.
The e↵ects of country B’s tari↵ are shown in Figure 1. When a specific tari↵, ⌧ B ,is imposed, the import demand curve of good A, IMA , and hence the demand curve oftransport services from country A to country B, DDAB , shift down by ⌧ B . Then the freightrate and the capacity are now given by point ⌧ in the lower panel. The freight rate decreases.
17

If xAB = xBA holds with free trade, the relationship between ⌧ A and the volumes of trade with ⌧ B = 0
is similar to Figure 3 (b). If xAB > xBA holds with free trade, however, an increase in ⌧ A simply decreases
xBA without a↵ecting xAB at all.

10

However, the decrease in the freight rate is less than the tari↵ rate, implying that the total
trade costs from country A to country B increase and the shipping-load decreases. The totalt⌧trade costs from country A to country B are given by TAB(= TAB+⌧ B ). Therefore, as shownFin the upper panel, the price of good A in country B (importing country) rises from PAB
to⌧F⌧
PAB and the price of good A in country A (exporting country) falls from PAA to PAA .
Next we examine the welfare e↵ects of country B’s tari↵s with the aid of Figure 1.18
Welfare is measured by the total surplus (i.e., the sum of consumer surplus, producer surplus
and tari↵ revenue). We begin with the case in which the profits of firm T are not included
in welfare.19 Compared with autarky, free trade increases the total surplus in the market ofFF
good A by the area abPAB
in country B and by the area cdPAA
in country A. When thetari↵, ⌧ B , is imposed under free trade, the sum of consumer surplus and producer surplus
F⌧in the market of good A decreases by the area b0 bPAB
PAB
in country B and by the area
0 ⌧F
cc PAA PAA in country A. The tari↵ also generates tari↵ revenue, T RB for country B and
improves the terms of trade of country B. In the market of good A in country B, the total
surplus increases as long as the tari↵ rate is small. In the market of good A in country
A, the total surplus decreases. These changes in surpluses are basically the conventional
optimal-tari↵ argument and they are the only changes if type-1 equilibrium is realized withthe tari↵.
If type-2 or type 3 equilibrium arises with country B’s tari↵, we have to take the othermarket (i.e., the market of good B) into account when analyzing welfare. Because of adecrease in the shipping capacity, country B’s tari↵ decreases not only exports of good A
from country A to country B but also exports of good B from country B to country A. As aresult, the price of good B in country B falls. This benefits consumers of good B in country
B and producers of good B in country A but harms producers of good B in country B
and consumers of good B in country A. In fact, the sum of consumer surplus and producer
surplus in the market of good B decreases in both countries. Country B’s tari↵ may not
improve country B’s terms of trade. For country A, the deterioration of its terms of tradeis magnified because not only the export price falls but also the import price rises.
Figure 2 shows the case where type-2 equilibrium arises with and without the tari↵.20 As
shown in the lower panel of Figure 2, the tari↵ decreases the total surplus in the market ofgood B by the area in country B and by the area " in country A. In country B, therefore,
the total surplus in the market of good A increases if the area is greater than the area
, but the total surplus in the market B necessarily decreases. The net change in the total
18

The welfare e↵ects of country A’s tari↵s are analogous to those of country B’s tari↵s.
This is the case if the transport firms are located in a third country.
20
If type-3 equilibrium arises as a result of country B’s tari↵, xBA > xAB holds but the qualitative results
would not change.
19

11

surplus, or, welfare, which is the area (), may be negative. The analysis here
indicates another backfiring e↵ect: an increase in country B’s import tari↵ harms its export
sector and hence may reduce country B’s welfare even if the tari↵ is small. In country A,
the total surplus decreases by the area (↵ + ").
We now consider the changes in the profits of firm T . It is obvious that firm T loses fromany tari↵, because tari↵s reduce the demand for transport services. Thus, the location offirm T is crucial for welfare evaluation. In particular, even if a tari↵ set by country B underfree trade is small, country B’s welfare necessarily deteriorates when it includes firm T ’s
profits (see Appendix B for the proof). It is obvious that country B’s tari↵s worsen country
A’s welfare farther when it includes firm T ’s profits.
Thus, we can establish the following proposition.
Proposition 3 Suppose that country B(A) sets a small tari↵ under free trade. In the casewhere xAB > xBA holds under both free trade and the tari↵, country B(A)’s welfare improves
if and only if firm T is not located in country B(A). However, in the other cases, country
B(A)’s welfare may not improve even if firm T is not located in country B(A). In both cases,
country A(B) always loses form country B(A)’s tari↵.

3.2

Taxes on Shipping Capacity

In this subsection, we compare a specific tax, t, on shipping capacity with tari↵s.21
With the tax, the e↵ective MC for firm T becomes r+t. In type-1 equilibrium, an increasein the e↵ective MC a↵ects only TAB and xAB . TAB increases and xAB decreases. We canverify that if country B sets a tax on shipping capacity, the tax is basically equivalent tot1⌧1
country B’s tari↵ on good A in type-1 equilibrium. With t = ⌧ B , we have TAB
6= TAB(wheret1⌧1
t stands for the tax equilibrium) but the trade costs are the same, i.e., TAB = TAB + ⌧ B and⌧1hence xt1
AB = xAB holds. In Figure 1, the freight rate and the capacity are indicated by pointt in the lower panel. Thus, country B’s tax on shipping capacity is equivalent to country B’stari↵ on good A. If country A sets the tax instead, its e↵ects on consumers, producers andfirm T are the same with the e↵ects of country B’s tari↵ but tax revenue accrues to country
A’s government.
We should note that the e↵ects of country A’s tari↵ on good B are di↵erent from thoseof a shipping-capacity tax in type-1 equilibrium, because in type-1 equilibrium, ⌧ A a↵ects
only TBA and xBA while t a↵ects only TAB and xAB . It is straightforward that in type-3
equilibrium, country A’s shipping-capacity tax and country A’s tari↵ are equivalent with
21
When country i imposes a tax on shipping capacity of firm T , we implicitly assume that firm T is locatedin country i.

12t = ⌧ A but the equivalence does not hold between country B’s shipping-capacity tax andcountry B’s tari↵.22
In type-2 equilibrium, a specific tax on shipping capacity increases both TAB and TBA
t2
⌧2
t2
⌧2
and decreases xAB and xBA . We can easily verify that TAB= TAB+ ⌧ B and TBA= TBA+ ⌧ A.
Also the e↵ects on xji are the same between a shipping-capacity tax and country i’s tari↵,⌧ i (i, j = 1, 2; i 6= j). Thus, we obtain the following proposition.
Proposition 4 Country B’s shipping-capacity tax and country B’s tari↵ set at the samelevels are equivalent in type-1 and type-2 equilibria. Similarly, country A’s shipping-capacity
tax and country A’s tari↵ set at the same levels are equivalent in type-2 and type-3 equilibria.
The above proposition implies that in type-1(type-3) and type-2 equilibria, country B(A)can substitute the tax for a tari↵ if country B(A) can impose the tax on firm T .

4

Multiple Carriers

In this section, we extend the basic model to the case with multiple carriers and investigate
how the results in the basic model (i.e., the case with a single carrier) are modified. We
assume that there are two transport firms: firm T1 and firm T2 and that these firms areengaged in Cournot competition. Without loss of generality, we assume that 0 < r1  r2 ,where rh (h = 1, 2) is the MC of operating a means of transport for firm Th . In (1), we havexAB = x1AB + x2AB and xBA = x1BA + x2BA . We focus on the case in which both firms T1
and T2 supply positive transport services.
Appendix C shows that there are five possible equilibria with r1 < r2 , which are statedin the following lemma (see the upper panel of Figure 4).
Lemma 1 Type 1) x1AB > x1BA and x2AB > x2BA hold if ⇤ (⌘ ⌦⌧A µB ⌦⌧B µA ) < µA (r1 2r2 );Type 2) x1AB = x1BA and x2AB = x2BA hold if µA r1  ⇤  µB r1 ; Type 3) x1AB < x1BA
and x2AB < x2BA hold if µB (2r2 r1 ) < ⇤; Type 4) x1AB > x1BA and x2AB = x2BA
hold if µA (r1 2r2 )  ⇤ < µA r1 ; and Type 5) x1AB < x1BA and x2AB = x2BA hold ifµB r1 < ⇤  µB (2r2 r1 ).
Figure 4 here
22

Since we have assumed xAB xBA with free trade, type-3 equilibrium does not arise with country A’stari↵ alone. We implicitly assume that country B also imposes a tari↵ in the analysis of country A’s tari↵in type-3 equilibrium.

13

If r1 = r2 , only three types of equilibrium are possible, i.e., x1AB > x1BA and x2AB > x2BA
(type 1), x1AB = x1BA and x2AB = x2BA (type 2), and x1AB < x1BA and x2AB < x2BA (type3). If r1 < r2 , we have two more types, i.e., x1AB > x1BA and x2AB = x2BA (type 4) andx1AB < x1BA and x2AB = x2BA (type 5). This implies that firm T1 is more likely to operate
without a full load in equilibrium. With given r2 , as r1 becomes smaller, the range of type-2
equilibrium becomes smaller and the ranges of type-4 and type-5 equilibria become larger.
Thus, as r1 becomes small relative to r2 , the range in which firm T1 has a full load becomes
smaller while the range in which firm T2 has a full load becomes larger. The economic
intuition behind this result is as follows. The MC of operating a means of transport is lower
for firm T1 than for firm T2 , implying that the cost to operate shipping without a full load
is lower for firm T1 than for firm T2 . Thus, firm T1 has less incentive to adjust freight rates
to have a full load in both directions. The following proposition is immediate.
Proposition 5 With r1 < r2 , the range of parameterization for operating without a full load
is larger for firm T1 than for firm T2 .
Figure 4 (the middle panel) also shows the relationship between five types of equilibrium
and country B’s tari↵ rates (with ⌧ A = 0). Since x1ij > 0 and x2ij > 0 (i, j = A, B), ⌧ B mustsatisfy 0  ⌧ B < ⌦B . The free trade equilibrium is determined by ⌧ B = 0. For example,
if µ1 (⌦A µB ⌦B µA µA r1 + 2µA r2 ) < 0 < µ1 (⌦A µB ⌦B µA + µA r1 ) holds, then theAAfree trade equilibrium (i.e., ⌧ B = ⌧ A = 0) is type 4. We can obtain a similar relationship forcountry A’s tari↵ rates (see the bottom panel in Figure 4). We should note that neither type3 equilibrium nor type-5 equilibrium arises with country A’s tari↵ alone, because xAB xBA
is assumed under free trade. As in the case of country B’s tari↵, ⌧ A must satisfy 0  ⌧ A < ⌦Aand ⌧ A = 0 determines the free trade equilibrium. If µ1 (⌦A µB ⌦B µA + µA r1 ) > 0, forB
example, the free trade equilibrium is type 2. In this case, as ⌧ A increases, equilibrium shifts
from type 2 to type 4 and then to type 1.
We now compare the above five types of equilibrium with the three types of equilibriumwith a single carrier. With x1AB > x1BA and x2AB > x2BA , the equilibrium is given by
1 ⌧1C1(⌦B + r1 + r2 ) , TBA= ⌦⌧A ,
(5)
3
3
1
1
1 ⌧
C1
=
(⌦⌧B 2r1 + r2 ) , xC1(⌦⌧B 2r2 + r1 ) , xC1⌦ ,(6)
2AB =
1BA = x2BA =
3µB
3µB
3µA A
1
2 ⌧
C1
C1
C1
= xC1
(2⌦⌧B r1 r2 ) , xC1⌦ .
(7)
1AB + x2AB =BA = x1BA + x2BA =
3µB
3µA A

C1
TAB
=

xC1
1AB
xC1
AB

The characteristics of this equilibrium are essentially the same with those of type-1 equilibrium with a single carrier. A change in ⌧ i a↵ects only shipping from country j to i, x1ji and14

x2ji . It should be noted that we have x1AB > x2AB but x1BA = x2BA , that is, x1BA = x2BA
holds even if x1AB 6= x2AB . This is because TBA is independent of r1 and r2 .
Similarly, with x1AB < x1BA and x2AB < x2BA , we have (A7)-(A9). The equilibrium
characteristics are essentially the same with those of type-3 equilibrium with a single carrier.
A change in ⌧ i a↵ects only shipping from country j to i, x1ji and x2ji . With x1AB = x1BA
and x2AB = x2BA , we have (A1)-(A6). The characteristics of this equilibrium are also thesame with those of type-2 equilibrium with a single carrier. A change in ⌧ i (i = 1, 2) equallya↵ects all shipping volumes (i.e., x1AB , x2AB , x1BA and x2BA ).
With x1AB > x1BA and x2AB = x2BA , we have
C4
TAB
=
C4
TBA
=

xC4
1AB =
xC4
1BA =
C4
x2AB
=

xC4
AB =
xC4
BA =

1
(3⌦⌧B µA ⌦⌧A µB + 2⌦⌧B µB + 3µA r1 + 2µB r1 + 2µB r2 ) ,(8)
6 (µA + µB )1
(2⌦⌧A µA + 3⌦⌧A µB ⌦⌧B µA µA r1 + 2µA r2 ) ,(9)
6 (µA + µB )1(⌦⌧ µ3⌦⌧B µA 2⌦⌧B µB + 3µA r1 2µB r2 + 4µB r1 ) , (10)6µB (µA + µB ) A B
1(2⌦⌧A µA + 3⌦⌧A µB ⌦⌧B µA + 2µA r2 µA r1 ) ,(11)
6µA (µA + µB )1
xC4(⌦⌧ + ⌦⌧B 2r2 + r1 ) ,
(12)
2BA =
3 (µA + µB ) A
1(⌦⌧ µ + 3⌦⌧B µA + 4⌦⌧B µB 3µA r1 2µB r1 2µB r2 ) , (13)6µB (µA + µB ) A B
1(4⌦⌧A µA + 3⌦⌧A µB + ⌦⌧B µA + µA r1 2µA r2 ) .
(14)
6µA (µA + µB )Although xAB > xBA holds, the characteristics of this equilibrium are di↵erent fromthose of type-1 equilibrium with a single carrier. In this equilibrium, a change in ⌧ i (i = 1, 2)a↵ects both xAB and xBA , which does not occur in type-1 equilibrium with a single carrier.
In particular, we should note that a change in ⌧ i a↵ects both x1AB and x1BA even thoughx1AB > x1BA holds. This stems from x2AB = x2BA . The direct e↵ect of an increase in ⌧ i isto decrease x1ji and x2ji . The indirect e↵ect is to decrease x2ij because x2ji = x2ij , which inturn increases x1ij as x1ij and x2ij are strategic substitutes with x1ji 6= x1ij . The decrease inx2ij dominates the increase in x1ij and hence xij falls. An increase in ⌧ i also decreases Tji
and increases Tij .

15

With x1AB < x1BA and x2AB = x2BA , we have
C5
TAB
=
C5
TBA
=

xC5
1AB =
xC5
1BA =
xC5
2AB =
xC5
AB =
xC5
BA =

1
(3⌦⌧B µA ⌦⌧A µB + 2⌦⌧B µB µB r1 + 2µB r2 ) ,(15)
6 (µA + µB )1
(2⌦⌧A µA + 3⌦⌧A µB ⌦⌧B µA + 2µA r1 + 2µA r2 + 3µB r1 ) ,(16)
6 (µA + µB )1
(3⌦⌧B µA ⌦⌧A µB + 2⌦⌧B µB µB r1 + 2µB r2 ) ,(17)
6µB (µA + µB )1(⌦⌧B µA 3⌦⌧A µB 2⌦⌧A µA + 4µA r1 2µA r2 + 3µB r1 ) , (18)6µA (µA + µB )1
xC5(⌦⌧ + ⌦⌧B 2r2 + r1 ) ,
(19)
2BA =
3 (µA + µB ) A
1(⌦⌧ µ + 3⌦⌧B µA + 4⌦⌧B µB + µB r1 2µB r2 ) ,(20)
6µB (µA + µB ) A B
1(4⌦⌧A µA + 3⌦⌧A µB + ⌦⌧B µA 2µA r1 2µA r2 3µB r1 ) . (21)6µA (µA + µB )Although xAB < xBA holds, the characteristics of this equilibrium are di↵erent from thoseof type-3 equilibrium with a single carrier. As in type-4 equilibrium above, a change in ⌧ i(i = 1, 2) a↵ects both x1AB and x1BA even though x1AB < x1BA holds. Also Tij increases
and xij decreases.
Figure 5 here
Figure 6 here
Figure 5 illustrates the relationship between shipping volumes and country B’s tari↵ rates
when type-1 equilibrium arises with free trade (i.e., when ⌦A µB ⌦B µA µA r1 + 2µA r2 < 0holds).23 The upper panel and the lower panel show shipping volumes of firm T1 and thoseof firm T2 , respectively. The lower panel is similar to Figure 3 (a): x2AB monotonicallydecreases as ⌧ B rises. x2BA is constant in type-1 and type-3 equilibria but decreases with ⌧ Bin type-2, type-4 and type-5 equilibria. In the upper panel, x1AB monotonically decreases,
while x1BA does not. In type-4 and type-5 equilibria, an increase in ⌧ B increases x1BA . Thus,
when country B introduces a tari↵ under free trade, firm T1 ’s shipping volume from country
A to country B necessarily decreases but that from country B to country A may increase.
In particular, it is easy to verify that x1BA in type-1 equilibrium is less than x1BA in
type-5 and type-3 equilibria if 2µA r1 µA r2 + µB r1 < 0 and that x1BA in type-1 and tpye-4
equilibria is less than x1BA in type-3 equilibrium if µA r1 + 2µB r1 µB r2 < 0. These cases are23

As was mentioned above, the free trade equilibrium is determined by the location of ⌧ B = 0 in Figure 5.
Setting the vertical axis at ⌧ B = 0, we can easily analyze the cases in which the other types of equilibrium
arise under free trade.

16

more likely to occur when r1 is much smaller than r2 , that is, the range of type-2 equilibrium
is much smaller than the ranges of type-4 and type-5 equilibria. A small r1 relative to r2
implies that firm T1 can increase a means of transport less costly than firm T2 .
Figure 6 illustrates the relationship between shipping volumes and country A’s tari↵ rates
when type-2 equilibrium arises with free trade (i.e., when µ1 (⌦A µB ⌦B µA + µA r1 ) > 0
Bholds).24 As in Figure 5, the upper panel and the lower panel show shipping volumes of firm
T1 and those of firm T2 , respectively. Since x1AB increases with ⌧ A in type-4 equilibrium,a tari↵ under free trade decreases the “total” shipping volumes in both directions but may
increase firm T1 ’s shipping volume from country A to country B. In particular, x1AB in
type-1 equilibrium is greater than x1AB in type-2 and type-4 equilibria if ⌦B µA ⌦A µB
2µA r1 + µA r2 > 0 holds.
In type-4 and type-5 equilibria, ⌧ B decreases firm T1 ’s profits from shipping the good fromcountry A to country B but increases firm T1 ’s profits from shipping the good from country
B to country A. The negative e↵ect on firm T1 ’s profits is relatively stronger (weaker)
than the positive e↵ect in type-4 equilibrium (type-5 equilibrium), because x1AB > x1BA
(x1AB < x1BA ) holds. Appendix D proves that an increase in ⌧ B decreases firm T1 ’s total
profits in type-4 equilibrium, but could increase firm T1 ’s total profits in type-5 equilibrium.
Firm T1 gains from an increase in ⌧ B only if the gap between x1AB and x1BA is large. When
x1BA is much larger than x1AB , the positive e↵ect of the increase in x1BA on firm T1 ’s profits
could dominate the negative e↵ect of the decrease in x1AB on firm T1 ’s profits.
Similarly, in type-4 equilibrium, ⌧ A decreases firm T1 ’s profits from shipping the goodfrom country B to country A but increases firm T1 ’s profits from shipping the good fromcountry A to country B. Appendix D also shows that in type-4 equilibrium, an increase in⌧ A could raise firm T1 ’s total profits. Again, firm T1 gains from an increase in ⌧ A only if thegap between x1AB and x1BA is large.
With respect to the e↵ects of tari↵s on each transport firm, the following proposition canbe established.
Proposition 6 Suppose 0 < r1 < r2 and ⌧ i increases. In type-2, type-4 and type-5 equilibria, Tij increases and xij decreases (the backfiring e↵ect). However, in type-4 and type-5
equilibria, x1ij increases. Firm T2 necessarily loses but firm T1 may gain from an increasein ⌧ B in type-5 equilibrium and from an increase in ⌧ A in type-4 equilibrium.
The changes in firm T1 ’s shipping volume caused by tari↵s are not simple, but the e↵ects oftari↵s on the “total” shipping quantities from one country ton the other are similar to Proposiotion 2. That is, any tari↵ of country B, which satisfies max 0, µ1 (⌦A µB ⌦B µA µA r1 + 2µA r2 )A

24

If type-1 equilibrium arises with free trade, an increase in ⌧ A simply decreases x1BA and x2BA withouta↵ecting x1AB and x2AB .

17

< ⌧ B < ⌦B , increases the freight rate from country B to country A and decreases country
B’s exports as well as country B’s imports; and any tari↵ of country A increases the freightrate from country A to country B and decreases country A’s exports as well as country A’s
imports if 0 < µ1 (⌦A µB ⌦B µA µA r1 + 2µA r2 ) holds.
B
The e↵ects of tari↵s on the sum of consumer surplus and producer surplus depend not on
the shipping volumes of each transport firm but on the total volumes of shipping coming inand out from the country. This implies that as long as the profits of transport firms are notincluded in welfare, the analysis of the welfare e↵ects of tari↵s with a single carrier remains
valid with multiple carriers. Thus, Proposition 3 holds for the case of multiple carriers as
well.
Next we examine the e↵ects of taxes on shipping capacity and compare them with thoseof tari↵s. For this, we specifically consider the case in which the same specific tax rate, t,
applies to both firms T1 and T2 . It is straightforward to confirm that in type-1 (type-3)
equilibrium, x1AB (x1BA ) and x2AB (x2BA ) decrease but x1BA (x1AB ) and x2BA (x2AB ) areconstant; in type-2 equilibrium, all shipping volumes, x1AB , x2AB , x1BA , and x2BA , decrease;and in type-4 (type-5) equilibrium, x1AB (x1BA ), x2AB , x2BA , xAB and xBA decrease but x1BA
(x1AB ) increases.
In fact, country B’s shipping-capacity tax and country B’s tari↵ set at the same levels
are equivalent in type-4 equilibrium as well as in type-1 and type-2 equilibria. Similarly,
country A’s shipping-capacity tax and country A’s tari↵ set at the same levels are equivalent
in type-5 equilibrium as well as in type-2 and type-3 equilibria. Whereas xAB xBA holds
in type-1, type-2, and type-4 equilibria, xAB  xBA holds in type-2, type-3, and type-5
equilibria. Thus, the e↵ects of taxes on shipping capacity with multiple carriers are basicallythe same with those with a single carrier.

5

Multiple Exportable Goods

In this section, we extend the basic model to the case with multiple exportable goods andexamine the e↵ects of tari↵s. For this, we consider a model with three goods: A1 , A2 , and
B. Country A exports goods A1 and A2 to country B while country B exports good B tocountry A. Firm T faces the following inverse demand for shipping good Ak from country
A to country B:k⌧k Ak
TAB = ⌦A
µA
k = 1, 2,(22)
B
B xAB ,kwhere xA
AB is the quantity demanded for shipping good Ak from country A to country B. Ask⌧kin the previous section, the intercepts are inclusive of tari↵s: ⌦A⌘ ⌦A⌧ kB (k = 1, 2)
BB

18

where ⌧ kB is country B’s specific tari↵ on good Ak . Regarding the shipping from country B
to country A, firm T remains to face (1). Arranging (22), we obtain
k
xA
AB =

1 ⇣ Ak ⌧
⌦B
k
µA
B

⌘
TAB , k = 1, 2.

The total demand for transport services from country A to country B and its inverse demand
are given by
A2
1
xAB = xA
AB + xAB =

TAB =

1
A2
1
µA
B + µB

1
1 A2
µA
B µB

A2 ⌧ A1
1 ⌧ A2⌦A
B µB + ⌦ B µB

A2 ⌧ A1
1 ⌧ A2⌦A
B µB + ⌦ B µB

1
µA
B TAB

2
µA
B TAB ,1 A2µA
B µB xAB .

A2
1
Again we have three cases with profit maximization. If xAB (= xA
AB + xAB ) > xBA holds,
we haveA2 ⌧ A1
A1
A2
1 ⌧ A2⌦⌧A⌦A
M1
B µB + ⌦B µB + r(µB + µB )
,
T
=
,
BA
A2
1
2
2 µA
B + µB
1
A1
A2
2 ⌧ A11 ⌧ A2
1 ⌧ A1
⌦A
⌦A
=
2⌦A
,
B µB
B µB
B µB + rµB + rµB
A1A1A22µB µB + µB
1A1A2
1 ⌧ A22 ⌧ A1
2 ⌧ A2
=
⌦A
⌦A
2⌦A
,
B µB
B µB
B µB + rµB + rµB
A2A1
22µB µB + µA
B
1⌦⌧A
A1 ⌧ A2A2 ⌧ A1
A1
A2
M1
=
⌦
µ
+
⌦
µ
rµ
rµ
,
x
=
.
BA
B
B
B
B
B
B
1 A2
2µA
2µA
B µB

M1
TAB
=
1M 1
xA
AB

2M 1
xA
AB

1
xM
AB

If xAB < xBA holds instead, we haveA2 ⌧ A1
1 ⌧ A2⌦⌧A + r⌦A
M3
B µB + ⌦ B µB
,
T
=
,
BA
A2
1
2
2 µA
B + µB
1
2 ⌧ A11 ⌧ A2
1 ⌧ A1
=
⌦A
⌦A
2⌦A
,
B µB
B µB
B µB
A1
A1
2
2µB µB + µA
B1
1 ⌧ A22 ⌧ A1
2 ⌧ A2
=
⌦A
⌦A
2⌦A
,
B µB
B µB
B µB
A2
A1
A2
2µB µB + µB
1⌦⌧A r
A1 ⌧ A2A2 ⌧ A1
M3
=
⌦
µ
+
⌦
µ
,
x
=
.
BA
B
B
B
B
1 A2
2µA
2µA
B µB

M3
TAB
=
1M 3
xA
AB

2M 3
xA
AB

3
xM
AB

In both cases, an increase in ⌧ 1B or ⌧ 2B decreases TAB , while an increase in ⌧ A decreases
TBA . Thus, a tari↵ on good Ak a↵ects not only the market of good Ak but also the market ofgood Al (k, l = 1, 2; k 6= l) through a change in the freight rate. That is, a tari↵ on good Akkhas a spillover e↵ect on the the market of good Al . An increase in ⌧ kB directly decreases xA
AB
19

A1
A2
l
but indirectly increases xA
AB . The total load from country A to country B, xAB = xAB +xAB ,decreases, because the direct e↵ect dominates the indirect e↵ect.
If xAB = xBA holds, then we have another spillover e↵ect. In type-2 equilibrium, we
obtain
M2
TAB
=

M2
TBA
=

A2
A1
A2
1 A2
1 A2
1
{µA
µA
µA
⌦⌧A
B µB r(µB + µB )B µB
B + µB
A2
1
µA
+
µ
B
B
A2
A2
A1
A1 ⌧
A1
A1
A2
A2 ⌧
1 A2
1 A2
+µB µAµA
B µB + 2µB µA + 2µB µA ⌦B + µB
B µB + 2µB µA + 2µB µA ⌦B },
A2
A1 A2
A1
A2
⌧
1
{rµA (µA
B + µB ) + 2µB µB + µB µA + µB µA ⌦A

A1 ⌧ A2A2 ⌧ A1
A1
A2
2
M2
⌧
xM
AB = xBA = {⌦B µB + ⌦B µB + (µB + µB )⌦A

A2 ⌧
1
µA
B µA ⌦ B

A1 ⌧2µA
B µA ⌦B },

A2
1
r(µA
B + µB )},

A1
A2
1 A2
where ⌘ 1/ 2 µA
. An increase in ⌧ kB (k = 1, 2) decreases TAB
B µB + µB µA + µB µA
Aklbut increases TBA . As a result, xAB and xBA decrease but xA
AB increases (k, l = 1, 2; k 6= l).
Al
A1
A2
k
Since the decrease in xA
AB dominates the increase in xAB , xAB + xAB = xBA decreases.
The economic intuition behind the spillover e↵ects is as follows. When ⌧ kB rises, to keep afull load in both directions, firm T decreases the reduction of the load from country A tocountry B by lowering TAB and decreases the load from country B to country A by raising
TBA . Similarly, when the load from country B to country A falls because of an increase in⌧ A , firm T increases TAB to reduce the load from country A to country B.
Alk
In any equilibrium, an increase in ⌧ kB (k, l = 1, 2; k 6= l) decreases xA
AB but increase xAB .
Thus, an increase in ⌧ kB harms producers of good Ak but benefits producers of good Al incountry A and vice versa in country B. In both countries, the sum of producer surplus andconsumer surplus decreases in the market of good Ak but increases in the market of good
Al . The latter increase may exceed the former decrease. This implies that a small tari↵ ongood Ak set by country B under free trade may benefit country A.
The above results are summarized in the following proposition.25

Proposition 7 Suppose xAB
xBA holds under the free-trade equilibrium. Any tari↵ ongood Ak set by country B lowers the freight rate from country A to country B, decreases
25

A

With ⌧ A = 0, we have type-1 equilibrium if 0 < ⌧ kB <

type

2

equilibrium

if

AA⌦A µB1 µB2A⌦A µB1 µB2A ⌧A⌦B1 µA µB2

A ⌧

A

A
µA µBl
A ⌧
A
A ⌧
A
A
A
⌦B1 µA µB2 ⌦B2 µA µB1 +rµA (µB1 +µB2 )AµA µBl

A
A
A ⌧
A
A ⌧
A
A
A
⌦A µB1 µB2 +⌦B1 µA µB2 +⌦B2 µA µB1 +rµB1 µB2
Al
µA µB
A
A
A ⌧
A
A ⌧
A
A
A
⌦A µB1 µB2 +⌦B1 µA µB2 +⌦B2 µA µB1 +rµB1 µB2
Al
µA µB
A
A
A ⌧
A
⌦A µB1 µB2 ⌦B1 µA µB2

andtype-3equilibrium

AA⌦B2 µA µB1 +rµA (µB1 +µB2 )

<
if

⌧ kB
⌧ kB

,

<
>

(k, l = 1, 2; k 6= l). With ⌧ B = 0, we have type-2 equi-

librium if 0
⌧ A > max{0,

<

⌧A

A
A
⌦A µB1 µB2

A ⌧
A
A
A
⌦B2 µA µB1 +rµA µB1 +rµA µB2
A 1 A2
µB µB
A ⌧
A
A ⌧
A
A
A
⌦B1 µA µB2 ⌦B2 µA µB1 +rµA µB1 +rµA µB2
A1 A 2
µB µB

<

}.

20

and type-1 equilibrium if

country B’s imports of good Ak , and increases country B’s imports of good Al (k, l = 1, 2; k 6=l). Any tari↵ of country B, which results in xAB  xBA , increases the freight rate fromcountry B to country A and decreases country B’s exports.
When country B sets a tari↵ on good Ak (k = 1, 2), firm T lowers the freight rate TAB
and its profits decrease. Thus, firm T may stop shipping good Ak when ⌧ kB is large enough.
Appendix E shows that this case actually occurs under some parameter values.
Thus, we obtain the following proposition.
Proposition 8 An increase in ⌧ 1B (⌧ 2B ) may lead firm T to stop shipping good A1 (goodA2 ). This may increase TBA .
It may seem that the above analyses crucially depend on the assumption that firm T setsa single freight rate for shipping from country A to country B even though there are multiple
exportable goods. In the following, therefore, we briefly consider the case in which firm T
can price-discriminate between goods A1 and A2 . With price discrimination, the profits offirm T become
A1 A1
A2 A2
⇧T = TABxAB + TABxAB + TBA xBA r,
Ak
A1
where TAB
is the freight rate of good Ak (k = 1, 2). Firm T sets three freight rates, TAB,
A2
TAB and TBA . With profit maximization, type-1 equilibrium is given by

1
1 1⌧
A1 m1
,
TAB
= r + ⌦A
2
2 B

1
1 2⌧
A2 m1
TAB
= r + ⌦A
,
2
2 B

1
m1
TBA
= ⌦⌧A .
2

Type-3 equilibrium is
1 1⌧
A1 m3
TAB
= ⌦A
,
2 B

1 2⌧
A2 m3
TAB
= ⌦A
,
2 B

1
1
m3
TBA
= r + ⌦⌧A .
2
2

Ak
Al
In type-1 and type-3 equilibria, a change in ⌧ kB lowers TAB
but a↵ects neither TAB
nor TBA(k, l = 1, 2; k 6= l). Intuitively, the spillover e↵ects through a single freight rate disappear,
because firm T can set the di↵erent freight rates between goods A1 and A2 .
If xAB = xBA , firm T ’s profit maximization is given by:
A1 A1
A2 A2
max ⇧T = max{TAB
xAB + TABxAB + TBA xBA
A2
1
s.t. xBA = xA
AB + xAB .

21

rxBA }

Type-2 equilibrium is
A1 m2
TAB
=

m

A1 ⌧ A2A2 ⌧ A1A1 ⌧
1 ⌧ A1
2⌦A
B µB + ⌦ B µB + ⌦ B µB + ⌦ B µA

1
⌦A µ1 + rµA
B µA ,

A2 m2
TAB
=

m

A2 ⌧ A1A2 ⌧ A2A2 ⌧1 ⌧ A2⌦A
B µB + ⌦B µB + 2⌦B µB + ⌦B µA

A2
2
⌦A µA
B + rµB µA ,

m2
TBA
=

m

1
⌦ A µA
B

1⌧
⌦A
B µA

A2
A1
A2
2⌧
⌦A
B µA + ⌦A µB + 2⌦A µA + rµB µA + rµB µA ,A2
A1
1
where m ⌘ 1/ 2 µA
. An increase in ⌧ 1B or ⌧ 2B decreases both TAB
and
B + µB + µA
A2
A1A2
TAB and increases TBA while an increase in ⌧ A increases both TAB and TAB and decreases
TBA . In contrast to the case with xAB 6= xBA , therefore, firm T adjusts all freight rates
to keep a full load in both directions. That is, when ⌧ 1B or ⌧ 2B rises, firm T avoids theA1
A2
reduction in the load from country A to country B by lowering TAB
and TABand decrease
the load from country B to country A by raising TBA . Analogously, when the load from
A1
country B to country A falls because of an increase in ⌧ A , firm T increases both TAB
andA2
TAB to reduce the load from country A to country B. In type-2 equilibrium, therefore, evenif firm T can set di↵erent freight rates among di↵erent exportable goods, the e↵ects of tari↵s
are qualitatively similar to those of tari↵s in the case where firm T sets a single freight ratefrom one country to the other country.

6

Discussion

Here we discuss the robustness of our findings regarding competition in the output markets
and empirical relevance of our main results.

6.1

Product market competition

In our basic model, we have assumed that the product market is perfectly competitive.
Most of our main results would survive under various kinds of international product market
competition. In particular, domestic import tari↵s could decrease not only domestic imports
but also domestic exports given other types of product market competition.
In Ishikawa and Tarui (2015), the case of an international duopoly in the product market
is explored. In the model, there is a single manufacturing firm in each country and thetwo firms engage in Cournot competition in the segmented domestic and foreign markets.
When domestic import tari↵s decrease both domestic imports and exports, consumers inboth countries lose because of higher consumer prices. There are two conflicting e↵ects oftari↵s on the firms, the direct e↵ect and the indirect e↵ect, the sizes of which depend on
parameter values in the model. The direct e↵ect is conventional, that is, domestic import22

tari↵s benefit the domestic firm at the cost of the foreign firm. The indirect e↵ect stemmingfrom a decrease in domestic exports benefits the foreign firm at the cost of the domestic firm.
As a result, domestic import tari↵s could harm the domestic firm and benefit the foreign
firm. It is also possible that both firms gain. In this case, the decrease in the domestic
imports and the decrease in the domestic exports caused by a domestic tari↵ strengthen themarket power in the firm’s home market, that is, for both firms, the gain from the decreasein imports dominates the loss from the decrease in exports.
In the case of a standard model of monopolistic competition in the product market,
tari↵s are also detrimental to consumers because they face both higher consumer prices andless varieties. Import tari↵s do not a↵ect the profits of producers, which always equal zero
because of free entry and exit.

6.2

Suggestive evidence

Our main result implies that domestic tari↵ reductions may increase domestic exports.
Whether removing import restrictions (such as reducing tari↵s) may enhance exports has
been a subject of trade policy research in the literature. Previous studies have identified a
few channels through which an import tari↵ reduction may influence export. Though earlystudies indicate a negative e↵ect of liberalizing imports on exports (e.g., restricting import
could enhance export when the protected industry exhibits increasing returns to scale, Krugman, 1984), more recent studies identify positive e↵ects. For example, a tari↵ reduction onintermediate goods may expand the sectors that use those goods as inputs, enabling themto increase their exports (Cruz and Bussolo, 2015). This e↵ect via supply chain may bethrough direct e↵ects on production costs (that drop due to lower input costs) or indirecte↵ects through more intense import competition and resulting productivity increases forthe a↵ected firms (Trefler, 2004; Amiti and Konings, 2007). Our study identifies anotherchannel—endogenous transport costs—through which import liberalization has a positivee↵ect on the country’s exports—an empirical question of high policy relevance.
Which channels are present or have larger e↵ects in magnitude than others? Answering
this question would require careful empirical investigations. India’s trade liberalization in the
1990s presents a suitable case study for our purpose because India reduced its trade barriers
unilaterally in this period (see, e.g., Topalova and Khandelwal, 2011).26 One may wonder
if India’s container imports and exports have been balanced.27 However, multiple carriers
26
We thank the referees for encouraging us to investigate this case study to support our theoretical results
discussed in this subsection.
27
India’s container exports were 1.90 million TEUs in 2010, 2.95 million TEUs in 2013, and 3.07 million
TEUs in 2014 while India’s container imports were 2.00 million TEUs in 2010, 2.21 million TEUs in 2013,
and 2.39 million TEUs in 2014 (http://www.worldshipping.org/about-the-industry/global-trade/23

have been operating between India and the ROW. As the analysis on our multiple-carriermodel indicates, the backfiring e↵ects may occur even with imbalance between imported andexported containers.
The United States has been a major destination of India’s exports (with its share about
20% as of 2000). Figure 7 describes the trend of India’s average import tari↵ rates andthe real unit (per kg) transportation costs of exports from India to the United States. It
compares those with the tari↵ rates and the transport costs to the United States fromJapan and the European Union.28 The figure demonstrates that India’s average tari↵ rates
decreased substantially while those of EU and Japan changed little over the period. The
trends in the transport costs of exports from the three economies show a contrast in a
way consistent with our theoretical prediction and are not explained by a factor that may
influence transports on all routes uniformly (such as across-the-board technological change).
Unlike EU’s and Japan’s transport costs, which did not decrease between 1991 and 2003,
India’s transport costs decreased by about 40% over the same period. A closer look at thefigure reveals that the transport costs decreased for EU’s and Japan’s exports as well from1995 to 1998. Indeed, these declines are likely due to a drop in the fuel costs as lower fuelcosts can translate into lower transport costs. The real crude oil prices, which are highly
correlated with bunker fuel prices, decreased over the same years as shown in Figure 7.
It is notable that, when the oil prices increased substantially between 1998 and 2000 (by118%), the transport costs of Japan’s (EU’s) exports increased by 165% (25%) while India’stransport costs did not increase as much (by 15%). This may be another indication of a link
between India’s declining import tari↵s and its lower transport costs despite a substantial
increase in the fuel costs.29
While the United States was India’s top trading partner during the period, our theory
predicts that the decline in transport costs should apply to all other trading partners as welltrade-statistics#1). Thus, India was a net importer of containers from the the rest of the world (ROW)in 2010, but a net exporter of containers to the ROW in 2013 and 2014.
28
The figure displays the weighted average unit transport costs of all 2-digit HS code products that are
subject to containerized trade, where the weights are based on the export quantity in weights by HS code.
The transport costs are taken from OECD Maritime Transport Costs (MTC) database (Korinek, 2008). All
values are normalized so that the 1991 values equal one. European Union refers to the member countries as of
1995-2004, i.e., Austria, Belgium, Denmark, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg,
Netherlands, Portugal, Spain, Sweden, and United Kingdom. The tari↵ rates refer to weighted average MFN
rates.
29
Our theory also predicts that the transport costs of India’s imports from the United States increase as
India’s import tari↵s decrease. This result is due to the transport firms’ market power and does not dependon their capacity constraints or the associated backhaul problem. Because the transport costs of India’s
imports in the 1990s are not available at OECD’s Maritime Transport Costs data (except for cereals, which
are shipped via clean bulk carriers and not containers), we do not have a figure similar to Figure 7 on India’s
imports.

24

given India’s unilateral tari↵ rate reductions. Figure 8 displays India’s average unit transport
costs on the exports to the United States, Australia, and New Zealand.30 It illustrates asimilar, substantial reduction in the transport costs across destinations. A more careful
econometric study would be necessary to quantify the impacts of trade liberalization on thetransport costs, taking into account other time-varying factors such as technological change
specific to trade routes. However, the figures indicate that countries with di↵erent trends inimport tari↵s experience di↵erent changes in the transport costs and the changes apply tomultiple importers of the exporter with reduced tari↵ rates.
Figures 7 and 8 here

7

Conclusion

This paper explicitly incorporated the transport sector into a standard international trademodel and studied the e↵ects of trade policies when transport costs are endogenously determined. Our model captures key stylized facts about international shipping: market power bytransport firms and asymmetric transport costs across countries. Furthermore, we explicitly
took into account “backhaul problems” that have not been paid much attention in the international trade literature. Transport firms need to commit to a shipping capacity sufficient
for a round trip. This may lead to imbalance in shipping volume in two directions, that
is, an opportunity cost associated with returning without a full load. Given such backhaul
problems, we demonstrated how the freight rate from one country to another, as well as thefreight rate of the return trip, is determined and explored the e↵ects of import tari↵s ontransported goods and taxes on shipping capacity.
Our analysis reveals that domestic tari↵s reduce domestic exports as well as domestic
imports when transport firms try to avoid the backhaul problem. Domestic tari↵s, which
benefit the domestic import sector and harm the foreign export sector in a standard model ofinternational trade, can also harm the domestic export sector and benefit the foreign importsector. Thus, a domestic tari↵ may not improve domestic welfare even if the tari↵ rate issmall. These unconventional results, i.e., the “backfiring e↵ects,” occur because transport
firms choose their shipping capacity levels, subject to backhaul problems, while the export
sector cannot export beyond the transport firm’s shipping capacity. Clearly, tari↵s reduce
the transport firms’ profits.
A tax on shipping capacity could be equivalent to an import tari↵ on shipped goods.
This implies that the subsidies on shipping capacity may work as a substitute for an export
30

Australia and New Zealand are the only countries other than the United States for which we can obtain
the Indian exports data for 1991-2003 from the same data base.

25

subsidy on shipped goods. If a foreign country hesitates to lower its tari↵s, the domestic
country can increase its exports by providing export subsidies. However, export subsidies
are prohibited by the WTO and countervailing duties may be applied. Alternatively, thedomestic country could increase its exports by providing subsidies to carriers. The subsidies
may also increase domestic imports (i.e., foreign exports).
The extensions of our basic model revealed that the non-conventional impacts of trade
policies discussed above also arise in richer contexts under less restrictive assumptions. In
particular, in the presence of multiple carriers, even if the shipping volumes are not balanced
between the two directions, a tari↵ could decrease the shipping volumes in both directions.
We also obtained additional results in the extensions. When multiple exportable goods are
considered, a tari↵ a↵ects not only the targeted sector but also other independent importsectors (i.e., goods that are neither substitutes nor complements of the targeted good).
For simplicity, we focused on a two-country model. In reality, a carrier may call atseveral places en route. In our analysis, we can regard one of the two countries as the ROW.
However, a promising direction for future research is to explicitly investigate the case withmore than two countries.31
We investigated how India’s unilateral trade liberalization in the 1990s a↵ected its freightrates. According to our main results, India’s freight rates for imports should increase and its
freight rates for exports should decrease. Although data on India’s freight rates for imports
are not available, India’s freight rates for exports show declining trends. We should mention
that this is just a suggestive evidence consistent with our results. More rigorous empiricalanalysis is left for the future research.

Appendix A
This appendix shows that Propositions 1 and 2 hold with more general demand functionsxAB =AB (TAB + ⌧ B ), xBA =BA (TBA + ⌧ A ),which are twice continuously di↵erentiable. In this appendix, we focus on the case where ⌧ Bchanges with ⌧ A = 0.
First, we consider the case with xAB > xBA . In this case, firm T maximizes its profits⇧T = TAB xAB + TBA xBA
31

rxAB .

See Higashida (2015) for a three-country shipping model with capacity choice by transport firms withmarket power.

26

The first order conditions (FOCs) arer) 0AB = 0,

AB + (TAB0
BA + TBA BA = 0.

We assume that the second order conditions (SOCs) are satisfied:
0
AB (2

0
BA (2

"AB ) < 0,

"BA ) < 0,00

where "ij ⌘ ( ij0 )ij2 (i, j = A, B; i 6= j) is the elasticity of the slope of demand curve of shippingij
services from country i to country j. The demand curve is convex if 0  "ij (< 2) and isconcave if "ij  0. Totally di↵erentiating the FOCs, we have
0
AB (2

"AB )

0
0
BA (2

0

"BA )

!

dTAB
dTBA

!

0

!

=

0
AB (1

"AB )

0

!

d⌧ B ,

Then we obtain
dTAB
dTBA

!

1

=

0
AB (2

"AB )

1

0

0
BA (2

"BA )

0
AB (1

!

"AB )

0

d⌧ B .

ABBA
AB
Thus, dT= 12 ""ABand dT= 0. Noting the SOCs, dT< 0 if and only if "AB < 1. We
d⌧ B
d⌧ B
d⌧ B
AB
d(TAB +⌧ B )dTAB
also have= 1 + d⌧ B > 0. These results are basically the same with Brander andd⌧ B
Spencer (1984).
Next, we consider the case with xAB = xBA . In this case, firm T maximizes it profits
subject to xAB = xBA . Using the Lagrange multiplier method, the FOCs are

AB + (TAB

where
0
B
@

r + ) 0AB = 0,

) 0BA = 0,

BA + (TBA

BA = 0,AB

is the Lagrange multiplier. Totally di↵erentiating the FOCs, we have
0
AB (2

"AB )
0
0
AB

0
0
BA (2

"BA )
0
BA

10

1

0

0
dTAB
AB
CB
C B
0
BA A @ dTBA A = @

0

0
AB (1

"AB )

0
0
AB

d

1

C
A d⌧ Band then
1 0 0BA
0
dTAB
AB
B
C B
B
@ dTBA A = @ 1
2 "BA
d
0

1
0
AB
0
BA
2 "AB

2 "BA
2 "AB
(2 "AB )(2 "BA )

27

10
CB
C@
A

0
AB (1

"AB )

0
0
AB

1

C
A d⌧ B ,where

⌘

0
BA (2

AB
"AB )+ 0AB (2 "BA ) < 0. Thus, we obtain dT
=
d⌧ B

0
BA (1

"AB )+ 0AB (2 "BA ))

,

0
AB

BA
AB
which is negative if "AB < 1, and dT=> 0. 1 + dT
> 0 also holds.
d⌧ B
d⌧ B
In both cases, therefore, if the demand for shipping is not very convex, country B’stari↵ decreases the freight rate from country A to country B. Country B’s tari↵ necessarily
increases the trade costs from country A to country B and decreases country B’s imports.
Moreover, with xAB = xBA , country B’s tari↵ necessarily increases the freight rate fromcountry B to country A and decreases country B’s exports.

Appendix B
In this appendix, we prove that even if the equilibrium remains to be type 1 after a smalltari↵ set by country B, country B’s welfare deteriorates when it includes firm T ’s profits.
In the upper panel of Figure 1, free trade increases the total surplus in the market ofF
good A by the area abPAB
relative to autarky in country B. Free trade also generates firm
T ’s profits. The profits from shipping good A from country A to country B are given by its
FF
revenue bcPAA
PAB
minus its costs to ship xFAB units, rxFAB . In the lower panel of Figure 1,
point F gives the largest profits on the derived demand curve DDAB .
When a tari↵ is imposed, an increase in the total surplus in the market of good A relative⌧
to autarky is given by the area ab0 PAB
plus the tari↵ revenue T RB in the upper panel. Firm
T ’s profits from shipping good A from country A to country B are given by its revenue⌧⌧ x⌧AB OTAB
minus its costs to ship x⌧AB units in the lower panel. In the lower panel, the sumtof the tari↵ revenue and firm T ’s profits is given by tx⌧AB OTAB
minus firm T ’s costs, which⌧
actually equals firm T ’s profits minus its costs to ship xAB units at point t without any tari↵.
Since point F gives the largest profits of firm T along DDAB , the sum of the tari↵ revenue
and firm T ’s profits is smaller than firm T ’s profits under free trade.
Thus, in terms of the net change in surplus relative to autarky, the sum of the surplus in
the market of good A and firm T ’s profits from shipping good A from country A to country⌧
B with the tari↵, which equals the area ab0 c0 PAA
minus firm T ’s costs to ship x⌧AB units, isFless than that without the tari↵, which equals the area abcPAA
minus firm T ’s costs to shipF
xAB units.

Appendix C
In this appendix, we show Lemma 1.
There are nine possible combinations: i) x1AB > x1BA and x2AB > x2BA ; ii) x1AB > x1BA
and x2AB = x2BA ; iii) x1AB > x1BA and x2AB < x2BA ; iv) x1AB = x1BA and x2AB > x2BA ; v)
x1AB = x1BA and x2AB = x2BA ; vi) x1AB = x1BA and x2AB < x2BA ; vii) x1AB < x1BA andx2AB > x2BA ; viii) x1AB < x1BA and x2AB = x2BA ; and ix) x1AB < x1BA and x2AB < x2BA .
As shown below, however, only five combinations arise in equilibrium.
28

We start by characterizing each equilibrium. First, suppose that x1AB > x1BA andx2AB > x2BA hold in equilibrium. Then the profits of firms T1 and T2 are given by⇧1 = TAB x1AB + TBA x1BA

r1 x1AB , ⇧2 = TAB x2AB + TBA x2BA

r2 x2AB .

In equilibrium, we have (6) - (7).
Second, suppose that x1AB = x1BA and x2AB = x2BA hold in equilibrium. Then
⇧1 = (TAB + TBA )x1AB

r1 x1AB , ⇧2 = (TAB + TBA )x2AB

r2 x2AB .

In equilibrium, we have
C2
TAB
=
C2
TBA
=

xC2
1AB =
xC2
2AB =
xC2
AB =
xC2
BA =

1
(3⌦⌧B µA 2⌦⌧A µB + ⌦⌧B µB + µB r1 + µB r2 ) ,3 (µA + µB )1(⌦⌧ µ + 3⌦⌧A µB 2⌦⌧B µA + µA r1 + µA r2 ) ,3 (µA + µB ) A A
1xC2(⌦⌧ + ⌦⌧B 2r1 + r2 ) ,
1BA =
3 (µA + µB ) A
1
xC2(⌦⌧ + ⌦⌧B + r1 2r2 )2BA =
3 (µA + µB ) A
1(2⌦⌧A + 2⌦⌧B r1 r2 ) ,3 (µA + µB )1
(2⌦⌧A + 2⌦⌧B r1 r2 ) .
3 (µA + µB )

(A1)
(A2)
(A3)
(A4)
(A5)
(A6)

Third, suppose that x1AB < x1BA and x2AB < x2BA hold in equilibrium. Then the profits
of firms T1 and T2 are given by⇧1 = TAB x1AB + TBA x1BA

r1 x1BA , ⇧2 = TAB x2AB + TBA x2BA

r2 x2BA .

In equilibrium, we have
1 ⌧(⌦ + r1 + r2 ) ,(A7)
3 A
1 ⌧ C3
1
1
= xC3
⌦ ,x
=
(⌦⌧ 2r1 + r2 ) , xC3(⌦⌧ + r1 2r2 )(A8)
,
2AB =
2BA =
3µB B 1BA 3µA A
3µA A
12 ⌧ C3C3
C3= x1AB+ xC3⌦B , xBA = xC3(2⌦⌧A r1 r2 ) .
(A9)
2AB =
1BA + x2BA =
3µB
3µA

C3
TAB
=

xC3
1AB
xC3
AB

1 ⌧
⌦ ,
3 B

C3
TBA
=

Fourth, suppose that x1AB > x1BA and x2AB = x2BA hold in equilibrium. Then
⇧1 = TAB x1AB + TBA x1BA

r1 x1AB , ⇧2 = (TAB + TBA )x2AB29

r2 x2AB .

In equilibrium, we have (8) - (14).
Fifth, suppose that x1AB < x1BA and x2AB = x2BA hold in equilibrium. Then
⇧1 = TAB x1AB + TBA x1BA

r1 x1AB , , ⇧2 = (TAB + TBA )x2AB

r2 x2AB .

In equilibrium, we have (15) - (21).
Sixth, suppose that x1AB = x1BA and x2AB > x2BA hold in equilibrium. Then
⇧1 = (TAB + TBA )x1AB

r1 x1AB , ⇧2 = TAB x2AB + TBA x2BA

r2 x2AB .

In equilibrium, we have1(⌦⌧ + ⌦⌧B 2r1 + r2 ) ,3 (µA + µB ) A
1
=
(⌦⌧ µ
3⌦⌧B µA 2⌦⌧B µB + 3µA r2 2µB r1 + 4µB r2 ) ,6µB (µA + µB ) A B
1=(2⌦⌧A µA + 3⌦⌧A µB ⌦⌧B µA + 2µA r1 µA r2 ) .
6µA (µA + µB )

C6
x1AB
= xC6
1BA =
C6
x2AB

xC6
2BA

Seventh, suppose that x1AB = x1BA and x2AB < x2BA hold in equilibrium. Then
⇧1 = (TAB + TBA )x1AB

r1 x1AB , ⇧2 = TAB x2AB + TBA x2BA

r2 x2AB .

In equilibrium, we have
C7xC7
1AB = x1BA =1(⌦⌧ + ⌦⌧B
3 (µA + µB ) A

1(3⌦⌧B µA
6µB (µA + µB )
1
=
(⌦⌧ µ
6µA (µA + µB ) B A

2r1 + r2 ) ,

xC7
2AB =

⌦⌧A µB + 2⌦⌧B µB + 2µB r1

xC7
2BA

3⌦⌧A µB

2⌦⌧A µAµB r 2 ) ,2µA r1 + 4µA r2 + 3µB r2 ) .

It should be pointed out that the combination of x1AB > x1BA and x2AB < x2BA neverarises in equilibrium. To show this, suppose in contradiction that the combination arises inequilibrium. Then we should have1
1(⌦⌧B 2r1 ) , x2AB =(⌦⌧ + r1 ) ,
3µB
3µB B
1
1
=
(⌦⌧A + r2 ) , x2BA =(⌦⌧ 2r2 ) .
3µA
3µA A

x1AB =x1BA
We need x1AB x1BA =1(⌦⌧A µB
3µA µB⌦⌧B µA + 2µA r1 + µB r2 ) > 0, which implies ⌦⌧A µB <30

⌦⌧B µA . However, we also need x2BA x2AB = 3µ 1µ (⌦⌧B µA ⌦⌧A µB + µA r1 + 2µB r2 ) > 0,A Bwhich implies ⌦⌧A µB > ⌦⌧B µA . Thus, the combination of x1AB > x1BA and x2AB < x2BA
never arises. Similarly, the combination of x1AB < x1BA and x2AB > x2BA never arises.
We next examine the conditions under which the above equilibria are actually realized
as Nash equilibria.
The condition under which x2AB > x2BA arises given x1AB > x1BA is that x2AB (=1(⌦⌧B 2r2 + r1 )) > x2BA (= 3µ1 ⌦⌧A ), which becomes ⌦⌧A µB ⌦⌧B µA µA r1 + 2µA r2 < 0,3µB
Ai.e., ⇤ (⌘ ⌦⌧A µB ⌦⌧B µA ) < µA (r1 2r2 ). Now the condition under which x1AB > x1BA arises
given x2AB > x2BA is that x1AB (= 3µ1 (⌦⌧B 2r1 + r2 )) > x1BA (= 3µ1 ⌦⌧A ), which becomesB
A⌦⌧A µB ⌦⌧B µA + 2µA r1 µA r2 < 0, i.e., ⇤ < µA (r2 2r1 ). Since µA (r1 2r2 ) < µA (r2 2r1 )with r1 < r2 , the combination of x2AB > x2BA and x1AB > x1BA arises as a Nash equilibrium
if ⇤ < µA (r1 2r2 ).
The condition under which x2AB = x2BA arises given x1AB = x1BA is that neither x2AB >x2BA nor x2AB < x2BA holds given x1AB = x1BA . Suppose x2AB > x2BA given x1AB = x1BA .
Then
✓
◆
1
⌧
⌧
⌧
x2AB =(⌦ µ
3⌦B µA 2⌦B µB + 3µA r2 2µB r1 + 4µB r2 )6µB (µA + µB ) A B✓> x2BA =1
6µA (µA + µB )(2⌦⌧A µA + 3⌦⌧A µB⌦⌧B µA + 2µA r1◆µA r 2 ) .

Thus, the condition under which x2AB > x2BA does not hold given x1AB = x1BA is x2AB
x2BA  0, i.e., ⇤µA r2 . Suppose 2AB < x2BA given x1AB = x1BA . Then✓

x2AB =✓

1
6µB (µA + µB )1

< x2BA =6µA (µA + µB )(3⌦⌧B µA(⌦⌧B µA⌦⌧A µB + 2⌦⌧B µB + 2µB r1

3⌦⌧A µB

2⌦⌧A µAµB r 2 )◆◆2µA r1 + 4µA r2 + 3µB r2 ) .

Thus, the condition under which x2AB < x2BA does not hold given x1AB = x1BA is x2AB
x2BA 0, i.e., ⇤  µB r2 . The condition under which x1AB = x1BA arises given x2AB = x2BA
is that neither x1AB > x1BA nor x1AB < x1BA holds given x2AB = x2BA . Suppose x1AB > x1BA
given x2AB = x2BA . Then✓

x1AB =

1
6µB (µA + µB )

> xC4
1BA

✓

=

(⌦⌧A µB

1
6µA (µA + µB )3⌦⌧B µA

2⌦⌧B µB + 3µA r1(2⌦⌧A µA + 3⌦⌧A µB

31

2µB r2 + 4µB r1 )⌦⌧B µA + 2µA r2◆µA r 1 ) .

◆Thus, the condition under which x1AB > x1BA does not hold given x2AB = x2BA is x1AB 
x1BA , i.e., ⇤µA r1 . Suppose x1AB < x1BA given x2AB = x2BA . Then✓

x1AB =✓

 x1BA =1
6µB (µA + µB )1

6µA (µA + µB )(3⌦⌧B µA(⌦⌧B µA⌦⌧A µB + 2⌦⌧B µB

3⌦⌧A µBµB r1 + 2µB r2 )2⌦⌧A µA + 4µA r1◆◆

2µA r2 + 3µB r1 ) .

Thus, the condition under which x1AB < x1BA does not hold given x2AB = x2BA is x1AB
x1BA , i.e., ⇤  µB r1 . Therefore, the combination of x1AB = x1BA and x2AB = x2BA arises asa Nash equilibrium if µA r1 < ⇤ < µB r1 .
The condition under which x2AB < x2BA arises given x1AB < x1BA is that x2AB (=1(⌦⌧B )) < x2BA (= 3µ1 (⌦⌧A + r1 2r2 )), which becomes ⌦⌧A µB ⌦⌧B µA +µB r1 2µB r2 > 0.
3µB
AThis condition is equivalent to ⇤ > µB (2r2 r1 ). Now the condition under which x1AB < x1BA
arises given x2AB < x2BA is that x1AB (= 3µ1 ⌦⌧B ) > x1BA (= 3µ1 (⌦⌧A 2r1 + r2 )), which beBAcomes (⌦⌧A µB ⌦⌧B µA 2µB r1 + µB r2 ) > 0. This condition is equivalent to ⇤ > µB (2r1
r2 ). Since r1 < r2 , the combination of x2AB > x2BA and x1AB > x1BA arises as a Nashequilibrium if ⇤ > µB (2r2 r1 ).
The condition under which x2AB = x2BA arises given x1AB > x1BA is that neither x2AB >x2BA nor x2AB < x2BA holds given x1AB > x1BA . Suppose x2AB > x2BA holds given x1AB >x1BA . Then we have x2AB (= 3µ1 (⌦⌧B 2r2 + r1 )) > x2BA (= 3µ1 (⌦⌧A )). As pointed out
BAabove, the combination of x2AB < x2BA and x1AB > x1BA never occurs. Thus, the condition
under which x2AB = x2BA arises given x1AB > x1BA is that 3µ1 (⌦⌧B 2r2 + r1 ) < 3µ1 ⌦⌧A
B
Aholds, that is, (⌦⌧A µB ⌦⌧B µA µA r1 + 2µA r2 ) > 0 holds. Thus, the condition becomesµA (r1 2r2 ) < ⇤. Now the condition under which x1AB > x1BA arises given x2AB = x2BA is
that
✓
◆
1
⌧
⌧
⌧
x1AB =(⌦ µ
3⌦B µA 2⌦B µB + 3µA r1 2µB r2 + 4µB r1 )6µB (µA + µB ) A B✓> x1BA =1
6µA (µA + µB )(2⌦⌧A µA + 3⌦⌧A µB⌦⌧B µA + 2µA r2◆µA r 1 ) ,which becomes (⌦⌧A µB ⌦⌧B µA + µA r1 ) < 0. This condition is equivalent to ⇤ < µA r1 .Thus,
the combination of x2AB = x2BA and x1AB > x1BA arises as a Nash equilibrium if µA (r1 2r2 ) <⇤ < µA r 1 .
The condition under which x2AB = x2BA arises given x1AB < x1BA is that neither x2AB >x2BA nor x2AB < x2BA holds given x1AB < x1BA . The combination of x2AB > x2BA andx1AB < x1BA never occurs. Suppose that x2AB < x2BA holds given x1AB < x1BA . Then32

⇣⌘
we have x2AB = 3µ1 ⌦⌧B ) < x2BA (= 3µ1 (⌦⌧A 2r2 + r1 ) . Thus, the condition under which
B
A
x2AB = x2BA arises given x1AB < x1BA is that 3µ1 ⌦⌧B > 3µ1 (⌦⌧A 2r2 + r1 ) holds, that is,
B
A(⌦⌧A µB ⌦⌧B µA + µB r1 2µB r2 ) < 0 holds. Thus, the condition becomes ⇤ < µB (2r2 r1 ).
Now the condition under which x1AB < x1BA arises given x2AB = x2BA is that✓x1AB =✓< x1BA =1
6µB (µA + µB )1

6µA (µA + µB )(3⌦⌧B µA(⌦⌧B µA⌦⌧A µB + 2⌦⌧B µB

3⌦⌧A µBµB r1 + 2µB r2 )2⌦⌧A µA + 4µA r1◆◆

2µA r2 + 3µB r1 ) ,which becomes (⌦⌧B µA ⌦⌧A µB + µB r1 ) < 0. This condition is equivalent to ⇤ > µB r1 .
Thus, the combination of x2AB = x2BA and x1AB < x1BA arises as a Nash equilibrium ifµB r1 < ⇤ < µB (2r2 r1 ).
The condition under which x1AB = x1BA arises given x2AB > x2BA is that neither
x1AB > x1BA nor x1AB < x1BA holds given
x2AB > x2BA . Supposex2AB⇣⌘⇣ > x2BA⌘ holds
1⌧
given x1AB > x1BA . Then we have x1AB = 3µ (⌦B 2r1 + r2 ) > x1BA = 3µ1 ⌦⌧A . The
B
A
combination of x1AB < x1BA and x2AB > x2BA never occurs. Thus, the condition under which x1AB = x1BA arises given x2AB > x2BA is that 3µ1 (⌦⌧B 2r1 + r2 ) < 3µ1 ⌦⌧A
B
Aholds, that is, (⌦⌧A µB ⌦⌧B µA µA r2 + 2µA r1 ) > 0 holds. Thus, the condition becomes
2µA (r2 2r1 ) < ⇤. Now the condition under which x2AB > x2BA arises given x1AB = x1BA
is that✓◆1⌧⌧⌧x2AB =(⌦ µ
3⌦B µA 2⌦B µB + 3µA r2 2µB r1 + 4µB r2 )6µB (µA + µB ) A B✓> x2BA =1
6µA (µA + µB )(2⌦⌧A µA + 3⌦⌧A µB⌦⌧B µA + 2µA r1◆µA r 2 ) ,which becomes (⌦⌧A µB ⌦⌧B µA + µA r2 ) < 0. This condition is equivalent to ⇤ < µA r2 .
Since µA r2 < 2µA (r2 2r1 ) with r1 < r2 , the combination of x2AB = x2BA and x1AB >x1BA never arises as a Nash equilibrium.
The condition under which x1AB = x1BA arises given x2AB < x2BA is that neither x1AB >x1BA nor x1AB < x1BA holds given x2AB < x2BA . The combination of x1AB > x1BA andx2AB < x2BA
occurs. Suppose
x1AB < x1BA holds
given x2AB < x2BA . Then we⇣ never ⌘⇣⌘11have x1AB = 3µ ⌦⌧B < x1BA = 3µ (⌦⌧A 2r1 + r2 ) . Thus, the condition under which
B
A
x1AB = x1BA arises given x2AB < x2BA is that 3µ1 ⌦⌧B > 3µ1 (⌦⌧A 2r1 + r2 ) holds, that is,
B
A(⌦⌧A µB ⌦⌧B µA 2µB r1 + µB r2 ) < 0 holds. Thus, the condition becomes ⇤ < µB (2r1 r2 ).

33

Now the condition under which x2AB < x2BA arises given x1AB = x1BA is that✓x2AB =✓< x2BA =1
6µB (µA + µB )1

6µA (µA + µB )(3⌦⌧B µA(⌦⌧B µA⌦⌧A µB + 2⌦⌧B µB + 2µB r1

3⌦⌧A µB

2⌦⌧A µAµB r 2 )◆◆2µA r1 + 4µA r2 + 3µB r2 ) ,which becomes (⌦⌧B µA ⌦⌧A µB + µB r2 ) < 0. This condition is equivalent to ⇤ > µB r2 . SinceµB (2r1 r2 ) < µB r2 with r1 < r2 , the combination of x1AB = x1BA and x2AB > x2BA neverarises as a Nash equilibrium.

Appendix D
In this appendix, we first prove that an increase in ⌧ B decreases firm T1 ’s total profits in
type-4 equilibrium and then show that an increase in ⌧ A may increase firm T1 ’s total profits
in type-4 equilibrium and an increase in ⌧ B may increase firm T1 ’s total profits in type-5
equilibrium.
C4 2
C4 2
Firm T1 ’s total profits in type-4 equilibrium is given by ⇧C4
1 = µB (x1AB ) + µA (x1BA ) .
Di↵erentiating this with respect to ⌧ i (i = A, B), we have
C4
d⇧C4
dxC4
1
1AB
C4 dx1BA= 2µB xC4
+
2µ
x
.
A 1BA
1AB
d⌧ i
d⌧ i
d⌧ i
dxC4

C4
1AB
In type-4 equilibrium, xC4
1AB > x1BA with ⌧ A = 0. Since µB d⌧ B =d⇧C4µA, we obtain d⌧1B < 0 in type-4 equilibrium.
6(µA +µB )dxC4
3µA +2µB
and µA d⌧1BA=6(µA +µB )B

Next we consider the e↵ect of an increase in ⌧ A on firm T1 ’s total profits in type-4
dxC4
dxC4
µB
C4
1AB
1BA
equilibrium. With ⌧ B = 0, xC4
1AB > x1BA . We have µB d⌧ A = 6(µ +µ ) and µA d⌧ A =A

2µA +3µB.
6(µA +µB )

B

d⇧C4

C4
1
Thus, as long as the gap between xC4
1AB and x1BA is small, we obtain d⌧ A < 0.

The gap becomes the largest with ⌧ A =for example,⌦A µB ⌦B µA µA r1 +2µA r2. Thus, if the following holds,
µB

C1
C4
xC4
1AB ⌧ = ⌦A µB ⌦B µA µA r1 +2µA r2 ( = x1AB ) < 3 x1BA ⌧ = ⌦A µB ⌦B µA µA r1 +2µA r2
A

A

µB

, 2⌦B + 5r1

7r2 > 0,

µB

(A10)

d⇧C4

then we have d⌧1A < 0 in type-4 equilibrium. We can easily find a set of parameter values,
C4
C4
C4⌦A , ⌦B , µA , µB , r1 and r2 , which satisfies (A10), TAB> 0, TBA> 0, xC4
1AB > x1BA > 0, and
C4
C4
C4
xC4
2AB = x2BA > 0. The condition (A10) is likely to hold if the gap between x1AB and x1BA
C4
d⇧is small, or, the gap between r1 and r2 is small. However, if the gap is large, d⌧1A > 0 couldd⇧C4hold. To see this, suppose µA = µB . Then we have d⌧1A > 0 for ⌧ A the range of which is34

close enough to⌦A µB ⌦B µA µA r1 +2µA r2µB

if the following holds:

C1
C4
xC4
1AB ⌧ = ⌦A µB ⌦B µA µA r1 +2µA r2 ( = x1AB ) > 5 x1BA ⌧ = ⌦A µB ⌦B µA µA r1 +2µA r2
A

A

µB

, 4⌦B + 7r1µB

11r2 < 0.

(A11)

We consider the conditions under which (A11) holds. Setting ⌦B = ar1 and r2 = br2 , (A11) is⌦B +r1C4
equivalent to 4a+7 11b < 0. For xC4, 2b < a+1.
1AB > 0 and x2AB > 0, we need r2 <2Once we find a pair (a, b) which satisfies both 4a 11b < 7 and a 2b > 1, it is easy to
C4find a set of parameter values, ⌦A , ⌦B , µA , µB , r1 and r2 , which satisfies (A11), TAB
> 0,
C4
C4
C4
C4
TBA
> 0, xC4
1AB > x1BA > 0, and x2AB = x2BA > 0. For example, ⌦A = 30, ⌦B = 20, µA = 1,
µB = 1, r1 = 11 and r2 = 15 are such a set of parameters.
Lastly, we consider the e↵ect of an increase in ⌧ B on firm T1 ’s total profits in type-5
C5 2
C5 2
equilibrium, which is given by given by ⇧C5
1 = µB (x1AB ) + µA (x1BA ) . Di↵erentiating thiswith respect to ⌧ B , we have
d⇧C5
dxC4
dxC5
1
1AB
1BA
= 2µB xC5
+ 2µA xC5
.
1AB
1BA
d⌧ B
d⌧ B
d⌧ B
dxC5

dxC5
3µA +2µB
1BA
A
and
µ
= 6(µ µ+µ
. Thus,A
6(µA +µB )
d⌧ B
A
B)
C5
d⇧1
C5
C5
as long as the gap between x1AB and x1BA is small, we obtain d⌧ B < 0. The gap becomes⌦ µ +⌦ µµ r +2µ r
the largest with ⌧ B = A B B µA B 1 B 2 . For example, if the following holds:
A
C5
1AB
With ⌧ A = 0, xC5
1AB < x1BA . We have µB d⌧ B =

C3
C5
xC5
1AB ⌧ = ⌦A µB +⌦B µA µB r1 +2µB r2 ( = x1AB ) < 3 x1BA ⌧ = ⌦A µB +⌦B µA µB r1 +2µB r2
B

A

µA

, 2⌦A + 5r1µA

7r2 > 0,

(A12)

d⇧C5

then we have d⌧1B < 0 in type-5 equilibrium. The di↵erence between (A10) and (A12) isthat ⌦B in (A10) is replaced by ⌦A in (A12). It is easy to find a set of parameter values,
C5C5C5⌦A , ⌦B , µA , µB , r1 and r2 , which satisfies (A12), TAB> 0, TBA> 0, xC5
1BA > x1AB > 0,
C5
d⇧1
C5
and xC5
2AB = x2BA > 0. Similarly, we have d⌧ B > 0 for ⌧ B which is close enough to⌦A µB +⌦B µA µB r1 +2µB r2
if
µ
A

xC5
1AB ⌧ = ⌦A µB +⌦B µA µB r1 +2µB r2
BµA> 5 xC3
1AB ⌧ = ⌦A µB +⌦B µA µB r1 +2µB r2
B, 4⌦A + 7r1µA

11r2 < 0(A13)

holds. The di↵erence between (A11) and (A13) is that ⌦B in (A11) is replaced by ⌦A in(A13). Thus, we can find a set of parameter values, ⌦A , ⌦B , µA , µB , r1 and r2 , which
C5
C5
C5
C5
C5
satisfies (A13), TAB> 0, TBA> 0, xC5
1BA > x1AB > 0, and x2AB = x2BA > 0.
35

Appendix E
In this appendix, we show Proposition 8!. For this, we find a case in which an increasein ⌧ 1B (⌧ 2B ) actually leads firm T to stop shipping good A1 (good A2 ). For simplicity, we
A2
1
assume ⌧ 1B > 0, ⌧ 2B = 0 and xA
AB + xAB < xBA . Then we have
M3
TAB
=

A2 ⌧ A1
1 ⌧ A2⌦A
B µB + ⌦ B µB
,
A2
1
2 µA
B + µBkxA
AB =1 ⇣ Ak ⌧
⌦B
k
µA
B

⌘
TAB .

2

(⌦AB1 ⌧ µAB2 +⌦AB2 ⌧ µAB1 ). WhenA
A
A
A
4µB2 µB1 (µB1 +µB2 )2⌧firm T ships only good A2 , we have
TAB = 12 ⌦A
and the profitsB✓◆ from shipping only good A2q
A2 ⌧ 2
A1 ⌧
(⌦
)
⌦
A2
2⌧
1
1
1
are BA2 . Thus, if ⌦A> BA1 µA
µA
µA
, then the profits from shippingB
B +B
B + µBThe profits of firm T from shipping both goods A1 and A2 are

4µB

µB

only firm A2 are greater than those from shipping both goods A1 and A2 . It should be notedthat even if xAB > xBA initially holds, stopping shipping good A1 may lead to xAB  xBA
1(where xA
AB = 0). If this is the case, TBA increases.

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39

Figures

Pτ

PA
AB

Figure 1: Import demand and export supply
curves and freight rate

a

b’

PFAB

b”

Pτ AB -τB
TτAB

TRB

b

TFAB

PFAA
Pτ AA

c’

d

TAB

xτ

EXA
IMA
τB

c

F
AB x AB

xAB

τB
t

TtAB

F

TFAB
TτAB

O

DDAB

τ
xτ

F
AB x ABxAB

Figure 2: Type-2 equilibrium

PA

γ

Pτ AB

PF AB
β
Pτ AB -τB

ESA

Pτ

IMA
τB

TFAB
PF AA

AA

α

xτAB xFAB

PB
PF

Pτ BA
BA

xAB

ε

ESB

δ

IMB

TFBA
PF BB
Pτ BB

xτBA xFBA

xBA

Figure 3 (a): Tariffs set by country B(xAB > xBA with free trade)xAB, xBA(ΩB-r)/2µB

ΩA/2µA

FA

xBA

FB

B’

(ΩA-r)/2µA

xAB
A’
Type 1B

Type 2B

Type 3B

τB

O(ΩBµA- ΩAµB-rµA)/ µA(ΩBµA- ΩAµB+rµB)/ µA

Figure 3 (b): Tariffs set by country B(xAB = xBA with free trade)xAB, xBA(ΩA+ΩB-r)/2(µA +µB)

F

xBA
B’

(ΩA-r)/2µA

xAB
Type 2B
O

Type 3B(ΩBµA- ΩAµB+rµB)/ µA

A’τBFigure 4: Multiple transport firms(with r1 <r2)Type 1x1AB>x1BA
x2AB>x2BA

Type 2x1AB=x1BA
x2AB=x2BA

Type 4x1AB>x1BA
x2AB=x2BAµA(r1-2r2)-µAr1

Type 5x1AB<x1BAτB
x2AB=x2BAµBr1

Type 3x1AB<x1BA
x2AB<x2BA
Λ(≡ΩτAµB- ΩτBµA)µB(2r2-r1)

τB(with τA=0)-(ΩAµB- ΩBµA+µBr1-2µBr2)/µA-(ΩAµB- ΩBµA+µAr1)/µA-(ΩAµB- ΩBµA-µAr1+2µAr2)/µA(-ΩAµB+ ΩBµA+µBr1)/µA

τA

ΩA(with τB=0)(ΩAµB- ΩBµA+µAr1)/µB(ΩAµB- ΩBµA-µAr1+2µAr2)/µB

ΩB

x1AB, x1BA

Figure 5: Country B’s tariffs and shipping volumes
x1AB
x1BA

-(ΩAµB- ΩBµA-µAr1+2µAr2)/µA

x2AB, x2BA(-ΩAµB+ ΩBµA+µBr1)/µA-(ΩAµB- ΩBµA+µAr1)/µA

τB-(ΩAµB- ΩBµA+µBr1-2µBr2)/µA

x2AB

x2BA

Type-1B

Type-4B

Type-2B

Type-5B

x1AB>x1BA
x2AB>x2BA

x1AB>x1BA
x2AB=x2BA

x1AB=x1BA
x2AB=x2BA

x1AB<x1BA x1AB<x1BA
x2AB=x2BA x2AB<x2BA

Type-3B

τB

x1AB, x1BA

Figure 6: Country A’s tariffs and shipping volumes
x1AB
x1BA

(ΩAµB- ΩBµA+µAr1)/µB

τA

x2AB, x2BA

(ΩAµB- ΩBµA-µAr1+2µAr2)/µB

x2AB
x2BA
Type-2A

Type-4A

x1AB=x1BA
x2AB=x2BA

x1AB>x1BA
x2AB=x2BA

Type-1A

x1AB>x1BA
x2AB>x2BA

τA

Figure 7: Import tariffs and transport costs onexports to the United States, 1991-2003
Unit transport costs andcrude oil price (1991=1)
2.5
India to US

Tariff rates (%)
200

Japan to US

180

EU to US
2.0

160

Crude oil price (2017USD/barrel)
Tariff rates (India), right axis

140

Tariff rates (Japan), right axis
Tariff rates (EU), right axis

1.5

120
100
80

1.0

60
40

0.5

20
0

0.0
1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Note: Average unit transport costs (in 1990 US dollars) for all 2-digit HS code products
subject to container transport from OECD Maritime Transport Costs database (adjustedwith US GDP deflator). Tariff rates refer to the weighted average of each country’s MFN
rates from the World Development Indicators.

Figure 8 : India’s transport costs on exports to theUnited States, Australia, and New Zealand
Unit transport costs(1991=1)
1.2

1.0

0.8

0.6

0.4

India to US
India to Australia

0.2
India to New Zealand

0.0
1991

1992

1993

1994

1995

1996

1997

1998

1999

2000

2001

2002

2003

Note: Average unit transport costs (in 1990 US dollars) for all 2-digit HS code products
subject to container transport from OECD Maritime Transport Costs database (adjustedwith importing countries’ GDP deflator). Tariff rates refer to the weighted average of eachcountry’s MFN rates from the World Development Indicators.