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Backfiring with Backhaul Problems∗
Trade and Industrial Policies with Endogenous Transport Costs

Jota Ishikawa†and Nori Tarui‡
November 2016

Abstract
Trade barriers due to transport costs are as large as those due to tariffs. This
paper incorporates the transport sector into a standard model of international tradeand studies the effects 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. Because of this “backhaul problem,” a tariff in one sector
may affect other independent import and/or export sectors. In particular, domestic
tariffs may backfire: domestic exports may also decrease, harming domestic export
sectors and the domestic economy.
JEL Codes: F12, F13, R40
Key words: Transport sector; transport cost; backhaul problems; international shipping; tariffs∗

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, tariffs.1 Hummels (2007) also argues that, “[a]s tariffs becomea less important barrier to trade, the contribution of transportation to total trade costs—
shipping plus tariffs—is rising.”
Despite such clear presence in international trade, the treatment of transport costs tends
to be ad hoc. The standard way to incorporate transport costs is to apply the iceberg
specification (Samuelson, 1952): the cost of transporting a good is a fraction of the good,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 five firms account for more than 45% 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 tariffs, 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 oligopolisticwith two major alliances (SkyTeam Cargo and WOW Alliance) exerting market power in
the air shipping markets (Weiher et al., 2002). The prediction of standard trade theory
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 tariffs and nontariffs 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.

1without a transport sector, with exogenously fixed transport costs, may be altered once weconsider the markets for transportation explicitly by taking into account the market powerof transport firms in influencing shipping costs.6
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 differ 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).7 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 ships) of each transport firm,
and hence firms need to commit to the maximum capacity required for a round-trip. Thisimplies an opportunity cost associated with a trip (the backhaul trip) with cargo that isunder-capacity.8 To avoid the backhaul problem, that is, to have the balance in shipping
volume in both directions, transport firms adjust shipping capacities and freight rates.
This paper explicitly incorporates the transport sector with market power into a standard
model of international trade. This allows us to study how trade and industrial policies
perform given endogenous, and possibly asymmetric, transport costs in the presence of thebackhaul problems.
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
6

Deardorff (2014) demonstrates that, even without an explicit transport sector, considering transport
costs may alter the pattern of trade.
7
Takahashi (2011) and Behrens and Picard (2011) provide several examples where freight costs exhibit
asymmetry.
8
Dejax and Crainic (1987) provide an early survey of the research on backhaul problems in transportation
studies.

2

sector in a tractable manner. Behrens and Picard (2011) apply a new economic geographymodel with monopolistic competition in the output sector in order to study how the spatial
distribution of economic activities is altered when the freight rates for shipping goods acrosstwo regions are determined endogenously, subject to backhaul problems. However, they
assume perfect competition in the transport sector. On the other hand, the following studies
explicitly consider market power in the transport sector but ignore the constraint on the
shopping capacity. Behrens et al. (2009), Takahashi (2011) and Forslid and Okubo (2015)
address the implication of 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 andR&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 effects 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. In the basic model, we assume a monopolistictransport firm to capture market power in a simple manner.9 We investigate the effects oftariffs and a tax on the transport firm on trade and welfare. We do so by taking into accounthow each policy influences the volume of trade and the freight rates endogenously, with thebackhaul problem being considered explicitly.10
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 different 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
9

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”.
10
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) offer a matching model to generate equilibrium transport prices that may differ
but are positive for both directions. Our model, with the transportation firms having market power, also
supports positive equilibrium transport prices.

3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 different between thetwo countries).
Our analysis demonstrates that an explicit consideration of a transport sector changes
the prediction of the effects 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 the freight rates and thecapacity, depending on the stringency of the trade policy. When the transport firm avoids
the backhaul problem, a policy that affects one trip may influence the return trip through alinkage due to endogenous transport. Thus an increase in a country’s import tariff can reduce
its exports, thereby generating the backfiring effect described above. We also demonstratesuch policy linkages when the transport sector’s shipping capacity is taxed.
Our basic model consists of a monopolistic transport firm, a single export sector anda single import sector in each country. Investigating this simple case allows us to explain
the economic intuitions of our main results (Propositions 1-3) in a transparent manner. We
then consider 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 effects, we obtain a few additional results. Most importantly, we confirm that the main backfiring results that we findwith a monopolistic transport firm hold with oligopolistic transport firms. Indeed, the result
is more generalized: as long as one of the transport firms avoids the backhaul problem, anincreased tariff 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 effect of taxes on shipping capacity is also the same qualitatively
when there are multiple shipping firms. In the case of multiple exportable goods, a tariff
in one sector may affect other sectors even when the goods are independent (i.e., neither
substitutes nor complements). In particular, a domestic tariff 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 tariffs and taxes on shipping capacity on trade volume andwelfare. We provide extensions of our analysis when there are multiple carriers (Section 4)4and when there are multiple exportable goods (Section 5). Section 7 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 8 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.11 Firm T faces the following inverse demand:
TAB = ΩB − µB xAB , TBA = ΩA − 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 ΩA , ΩB , µA ,and µB are all positive scalars. We assume that both ΩA and ΩBare 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.12
The costs of firm T , C, are given by
C = f + rk,
where r, f, and k are, respectively, the marginal cost (MC) of operating a means of transport such as vessels, the fixed cost (FC), and the capacity (or, the maximum load, i.e.,max{xAB , xBA } = k). In the following analysis, the MC plays a crucial role while the FC
does not. Thus, we assume r > 0 and f = 0. Firm T chooses the shipping capacity k andthe freight rates TAB and TBA in order to maximize its profit:ΠT = TAB xAB + TBA xBA − rk.
The profit maximization generates three cases. First, if xAB > xBA holds in equilibrium
11
Firm T may be located in country A, country B, or a third country. The location becomes crucial whenanalyzing welfare.
12
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 haveΠT = TAB xAB + TBA xBA − rxAB = (ΩB − µB xAB )xAB + (ΩA − µA xBA )xBA − rxAB .
The equilibrium (type-1 equilibrium) under free trade is given by
F1
=
TAB

ΩA F 1ΩB − r F 1ΩAΩB + r F 1, TBA =, xAB =, xBA =
.
2
2
2µB
2µA

1
1
The condition for type 1 is xFAB
> xFBA, which is µA (ΩB − r) > µB ΩA .
Second, if xAB < xBA holds in equilibrium (this case is referred to as type 3 in thefollowing), then we haveΠT = TAB xAB + TBA xBA − rxBA .

Type-3 equilibrium is
F3
TAB
=

ΩA + r F 3ΩB F 3ΩA − rΩB F 3, TBA =, xAB =, xBA =
.
2
2
2µB
2µA

The condition for type 3 is µB (ΩA − r) > µA ΩB .
Lastly, if xAB = xBA holds in equilibrium (this case is referred to as type 2 in thefollowing), which arises when both µA (ΩB − r) ≤ µB ΩA and µB (ΩA − r) ≤ µA ΩB hold (i.e.,µA ΩB − µA r ≤ µB ΩA ≤ µA ΩB + µB r holds), then we haveΠT = TAB xAB + TBA xAB − rxAB .
Type-2 equilibrium is given by1(rµB − ΩA µB + 2ΩB µA + ΩB µB ) ,2 (µA + µB )1=
(rµA + ΩA µA + 2ΩA µB − ΩB µA ) ,2 (µA + µB )
ΩA + Ω B − r
2= xFBA=.
2(µA + µB )

F2
TAB
=
F2
TBA
2
xFAB

In the following analysis, we assume xAB ≥ xBA without loss of generality. There are two
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
6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 Ωi (i = A, B)
means a larger market, indicating that the freight rate for shipping to a country with a
F1
F1
1
1
larger Ωi 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 thedifference 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.
The following proposition summarizes the above analysis.
Proposition 1 When the demand for transportation in country B is sufficiently larger thanthe demand for transportation in country A (i.e., if µA (ΩB − r) > µB ΩA ), the equilibrium
shipping quantity to country B, XAB , exceeds the equilibrium shipping quantity to country A,
XBA , with excess shipping capacity from country B to country A. Both XBA and the freightrate from country B to country A, TBA , are independent of the MC of operating a meansof transport, r, in this case. Even with excess shipping capacity, TBA may be higher than
the freight rate from country A to country B, TAB .When the demands of the two countries
are close enough (i.e., if µA ΩB − µA r ≤ µB ΩA ≤ µA ΩB + µB r), there is no excess shipping
capacity but the equilibrium freight rates are not necessarily the same.
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.13 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 i, EXi , which is excess supply of good i in country i, and the import demand
curve of good i, IMi , which is excess demand for good i in country j. With these two
curves, we can draw the demand for transportation services, DDij , which is a gap between
IMi and EXi (see the lower panel). Facing this demand curve (i.e., (1)), firm T determines
13

We analyze the case of an international oligopoly in the product market in detail elsewhere (Ishikawa
and Tarui, 2015). See Section 6.1.

7the freight rate, TijF , and the shipping load, xFij .14 The prices of good i in country i and incountry j are, respectively, given by PiiF and PijF . The gap between the two prices is TijF , i.e.,
TijF = PijF − PiiF . In country i, free trade benefits producers of good i but harms consumersof good i. The net gain in the product market of good i in country i is given by dcPiiF in
Figure 1. In country j, free trade harms producers of good i but benefits consumers of goodi. The net gain in the product market of good i in country j is given by abPijF . The revenueof firm T from shipping good i from country i to country j is given by bcPiiF PijF .
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 effects of import tariffs on the freight rates and theequilibrium welfare of the trading countries.15 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

Tariffs

We begin with import tariffs on goods. We assume that product markets are perfectlycompetitive and that country i exports good i (i = A, B). Suppose that a specific tariff,
the rate of which is τ i (i = A, B), is imposed by country i. Then the inverse demand curve
shifts downward by τ i :16
TAB = (ΩB − τ B ) − µB xAB = ΩτB − µB xAB ,TBA = (ΩA − τ A ) − µA xBA = ΩτA − µA xBA ,where ΩτB ≡ ΩB − τ B and ΩτA ≡ ΩA − τ A .
14

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.
15
The effects of import quotas are similar to those of tariffs. See Ishikawa and Tarui (2015).
16
If products markets are not perfectly competitive, the downward shifts are not simply given by τ i . See
Ishikawa and Tarui (2015).

8

Type-1 equilibrium with tariffs is given byΩτ + r τ 1(ΩA − τ A )Ωτ(ΩB − τ B ) + r= B, TBA =
= A,
2
2
2
2
τ
(ΩB − τ B ) − rΩB − r τ 1(ΩA − τ A )ΩτA==, xBA =
=
.
2µB
2µB
2µA
2µA

τ1
TAB
=
1
xτAB

An increase in τ i decreases xji and increases xii (i, j = A, B, i 6= j), but affects neither xij
nor xjj . This is the conventional effects of tariffs when goods A and B are neither substitutes
nor complements. An increase in τ i decreases Tji but the total trade costs from country j
to country i, which equal Tji + τ i , increase.
Type-2 equilibrium with tariffs is given by1(rµB − ΩτA µB + 2ΩτB µA + ΩτB µB ) ,2 (µA + µB )1=
(rµA + ΩτA µA + 2ΩτA µB − ΩτB µA ) ,2 (µA + µB )
ΩτA + ΩτB − r
τ2.
= xBA =
2(µA + µB )

τ2
TAB
=

(2)

τ2
TBA

(3)

2
xτAB

(4)

In this equilibrium, the shipping capacity is binding in both directions. We can easily verify
that an increase in τ i increases the trade costs not only from country j to country i, Tji + τ i ,but also from country i to country j, Tij . Thus, both xji and xij decrease and both xii andxjj increase (i, j = A, B, i 6= j). This is in contrast with type-1 equilibrium, in which anincrease in τ i affects the supplies only in country i, that is, an increase in τ i decreases xji
and increases xii . An increase in τ 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.
Even if xAB ≥ xBA holds under free trade, xAB < xBA may arise with tariffs. That is,
tariffs may shift the equilibrium from type 1 to type 3 or from type 2 to type 3. Type-3
equilibrium with tariffs is given by
τ3
TAB
=

ΩτB τ 3Ωτ + r τ 3ΩτΩτ − r3, TBA = A
, xAB = B , xτBA
= A
.
2
2
2µB
2µA

As in type-1 equilibrium, an increase in τ i in type-3 equilibrium decreases xji and increasesxii (i, j = A, B, i 6= j), but affects neither xij nor xjj .
Figure 3 here
Figure 4 here

9The above cases are illustrated in Figures 3 and 4. Figure 3 (Figure 4) shows the relationship between τ B (τ A ) and the volumes of trade, i.e. xAB and xBA , with τ A = 0(τ B = 0). The free trade equilibrium is given by FA and FB in Figure 3 (a) and Figure 4 (a) and by F in Figure 3 (b) and Figure 4 (b). In Figure 3 (a), as τ B increases,
only xAB decreases with 0 ≤ τ B < µ1 (ΩB µA − ΩA µB − rµA ). Both with 0 ≤ τ B <
A
1
1
(Ω
µ
−
Ω
µ
−
rµ
)
and
with
(Ω
A
B A
A B
B µA − ΩA µB + rµA ) < τ B < ΩB , xBA is indepenµAµA
1
dent of τ B . With µ (ΩB µA − ΩA µB − rµA ) ≤ τ B ≤ µ1 (ΩB µA − ΩA µB + rµA ), xAB = xBAAA
holds and an increase in τ B reduces both xAB and xBA . In Figure 3 (b), with 0 ≤ τ B ≤1(ΩB µA − ΩA µB + rµA ), both xAB and xBA decrease together as τ B increases. WithµA
1(ΩB µA − ΩA µB + rµA ) < τ B < ΩB , when τ B rises, xAB falls but xBA is constant.
µA
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 < τ B < µ1 (ΩB µA − ΩA µB − rµA ), type-2
Aequilibrium arises if max{0, µ1 (ΩB µA − ΩA µB − rµA )} ≤ τ B ≤ µ1 (ΩB µA − ΩA µB + rµA ),A
Aand type-3 equilibrium arises if µ1 (ΩB µA − ΩA µB + rµA ) < τ B < ΩB .
A
In Figure 4 (a), an increase in τ A decreases xBA with 0 ≤ τ A < ΩA but does not affectxAB . In Figure 4 (b), with 0 ≤ τ A ≤ µ1 (rµA + ΩA µB − ΩB µA ), both xAB and xBA decreaseB
together as τ A increases. With µ1 (rµA + ΩA µB − ΩB µA ) < τ A < ΩA , when τ A rises, xBA
B
falls but xAB is constant. In Figure 4, the equilibrium remains to be type 1 even if τ A rises orshifts from type 2 to type 1. Type-1 equilibrium arises if max{0, µ1 (rµA + ΩA µB − ΩB µA )}B< τ A < ΩA holds and type-2 equilibrium arises if 0 < τ A ≤ µ1 (rµA + ΩA µB − ΩB µA ) holds.
B
The above results are summarized in the following proposition.
Proposition 2 If country i imposes a tariff, τ i , firm T lowers the freight rate from country
j to country i, Tji (i, j = A, B, i 6= j) and mitigates the effects of the tariff. However, thetrade costs, τ i + Tji , increase and country j’s shipping quantity decreases.
Proposition 3 Suppose xAB > xBA holds under the free-trade equilibrium. Any tariff 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 tariff 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.
Figure 5 shows the effects of country B’s tariff on its welfare. When a specific tariff,τ 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 τ B . Then the freightrate and the capacity are now given by point τ in the lower panel. The freight rate decreases.
10However, the decrease in the freight rate is less than the tariff rate, implying that the total
trade costs from country A to country B increase and the shipping-load decreases. The totaltτ
trade costs from country A to country B are given by TAB(= TAB+τ B ). Therefore, as shownFin the upper panel, the price of good A in country B (importing country) rises from PABtoτ
Fτ
PAB and the price of good A in country A (exporting country) falls from PAA to PAA .
Figure 5 here
Figure 6 here
Next we examine the welfare effects of country B’s tariffs.17 We begin with the case inwhich the profits of firm T are not included in welfare.18 In country B, compared with free
trade, the tariff harms consumers of good A and benefits producers of good A. The tariff
also generates tariff revenue, T RB in Figure 5, and improves the terms of trade of country
B. In the market of good A in country B, the total surplus, which is the sum of consumer
surplus, producer surplus and tariff revenue, increases as long as the tariff rate is small. In
the market of good A in country A, the losses of producers exceed the gains for consumers
and total surplus, which is the sum of consumer surplus and producer surplus, decreases.
These changes in surpluses are basically the conventional optimal-tariff argument and only
these changes arise if type-1 equilibrium is realized with the tariff.
If type-2 or type 3 equilibrium arises with the tariff, we have to take the other market(i.e., the market of good B) into account when analyzing welfare. Because of a decrease in
the shipping capacity, not only exports of good A from country A to country B but also
exports of good B from country B to country A decrease. As a result, 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. Country B’s tariff may not improve country B’s terms of trade. For country A,
the deterioration of its terms of trade is magnified because not only the export price falls
but also the import price rises.
Figure 6 shows the case where type-2 equilibrium arises with and without the tariff.19 As
shown in the lower panel of Figure 6, the total surplus in the market of good B in country B
and that in country A decrease. In country B, therefore, the total surplus in the market ofgood A may increase (see the upper panel of Figure 6), but the total surplus in the market
B decreases. The net change in the total surplus, or, welfare may be negative. In country
A, the total surplus decreases in both markets.
17

The welfare effects of country A’s tariffs are analogous to those of country B’s tariffs.
This is the case if the transport firms are located in a third country.
19
If type-3 equilibrium arises as a result of country B’s tariff, xBA > xAB holds but the qualitative results
would not change.
18

11

We now consider the changes in the profits of firm T . It is obvious that firm T loses fromany tariff, because tariffs reduce the demand for transport services. Thus, the location offirm T is crucial for welfare evaluation. In particular, even if a tariff set by country B underfree trade is small, country B’s welfare necessarily deteriorates when it includes firm T ’s
profits (see Appendix A for the proof). It is obvious that country B’s tariffs worsen country
A’s welfare farther when it includes firm T ’s profits.
Thus, we can establish the following proposition.
Proposition 4 If xAB > xBA holds under the free-trade equilibrium, then a small tariff set
by country B(A) improves its welfare if and only if firm T is not located in country B(A).
However, if xAB = xBA holds under the free-trade equilibrium, then a small tariff by B(A)may not improve its welfare even if firm T is not located in country B(A). In both cases,
country A(B) always loses form country B(A)’s tariff.

3.2

Taxes on Shipping Capacity

In this subsection, we compare a specific tax, t, on shipping capacity with tariffs.20
With the tax, the effective MC for firm T becomes r + t. In type-1 equilibrium, anincrease in the effective MC affects only TAB and xAB (recall Proposition 1). TAB increases
and xAB decreases. We can verify that if country B sets a tax on shipping capacity, the tax
is basically equivalent to country B’s tariff on good A in type-1 equilibrium. With t = τ B ,
τ1
t1
τ1
t1
+ τ B and hence= TAB
but the trade costs are the same, i.e., TAB
6= TAB
we have TAB
τ1t1
xAB = xAB holds. In Figure 5, the freight rate and the capacity are indicated by point t in
the lower panel. Thus, country B’s tax on shipping capacity is equivalent to country B’s
tariff on good A. If country A sets the tax instead, its effects on consumers, producers andfirm T are the same with the effects of country B’s tariff but tax revenue accrues to country
A’s government.
We should note that the effects of country A’s tariff on good B are different from thoseof a shipping-capacity tax in type-1 equilibrium, because in type-1 equilibrium, τ A affects
only TBA and xBA while t affects only TAB and xAB . It is straightforward that in type-3
equilibrium, country A’s shipping-capacity tax and country A’s tariff are equivalent witht = τ A but the equivalence does not hold between country B’s shipping-capacity tax andcountry B’s tariff.21
20

When country i imposes a tax on shipping capacity of firm T , we implicitly assume that firm T is locatedin country i.
21
Since we have assumed xAB ≥ xBA with free trade, type-3 equilibrium does not arise with country A’s
tariff alone (see Figures 4(a) and (b)). We implicitly assume that country B also imposes a tariff in theanalysis of country A’s tariff in type-3 equilibrium.

12

In type-2 equilibrium, a specific tax on shipping capacity increases both TAB and TBA
t2
τ2
t2
τ2
and decreases xAB and xBA . We can easily verify that TAB= TAB+ τ B and TBA= TBA+ τ A.
Also the effects on xji are the same between a shipping-capacity tax and country i’s tariff,
τ i (i, j = 1, 2; i 6= j). Thus, we obtain the following proposition.
Proposition 5 A tax on shipping capacity affects only TAB (TBA ) and xAB (xBA ) in type1(type-3) equilibrium: TAB (TBA ) increases and xAB (xBA ) decreases. In type-2 equilibrium,a tax on shipping capacity increases both TAB and TBA and decreases both xAB and xBA .
Country B’s(A’s) shipping-capacity tax and country B’s(A’s) tariff set at the same levels
are equivalent in type-1(type-3) and type-2 equilibria. In type-1(type-3) and type-2 equilibria,
if country B(A) can impose the tax on firm T , country B(A) can substitute the tax for atariff.

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 B shows that there are five possible equilibria with r1 < r2 , which are statedin the following lemma (see the upper panel of Figure 7).
Lemma 1 Type 1) x1AB > x1BA and x2AB > x2BA hold if Λ (≡ ΩτA µB − ΩτB µA ) < µA (r1 − 2r2 );Type 2) x1AB = x1BA and x2AB = x2BA hold if −µA r1 ≤ Λ ≤ µB r1 ; Type 3) x1AB < x1BA
and x2AB < x2BA hold if µB (2r2 − r1 ) < Λ; Type 4) x1AB > x1BA and x2AB = x2BA
hold if µA (r1 − 2r2 ) ≤ Λ < −µA r1 ; and Type 5) x1AB < x1BA and x2AB = x2BA hold ifµB r1 < Λ ≤ µB (2r2 − r1 ).
Figure 7 here
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 operate13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 6 With r1 < r2 , the range of parameterization for operating without a full load
is larger for firm T1 than for firm T2 .
Figure 7 (the middle panel) also shows the relationship between five types of equilibrium
and country B’s tariff rates (with τ A = 0). Since x1ij > 0 and x2ij > 0 (i, j = A, B), τ B mustsatisfy 0 ≤ τ B < ΩB . The free trade equilibrium is determined by τ B = 0. For example,
if − µ1 (ΩA µB − ΩB µA − µA r1 + 2µA r2 ) < 0 < − µ1 (ΩA µB − ΩB µA + µA r1 ) holds, then theAAfree trade equilibrium (i.e., τ B = τ A = 0) is type 4. We can obtain a similar relationship forcountry A’s tariff rates (see the bottom panel in Figure 7). We should note that neither type3 equilibrium nor type-5 equilibrium arises with country A’s tariff alone, because xAB ≥ xBA
is assumed under free trade. As in the case of country B’s tariff, τ A must satisfy 0 ≤ τ A < ΩAand τ A = 0 determines the free trade equilibrium. If µ1 (ΩA µB − ΩB µA + µA r1 ) > 0, theBfree trade equilibrium is type 2. In this case, as τ 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 by1
1 τ
C1(ΩB + r1 + r2 ) , TBA= ΩτA ,
(5)
3
3
1
1
1 τ
C1
=
(ΩτB − 2r1 + r2 ) , xC1(ΩτB − 2r2 + r1 ) , xC1Ω ,(6)
2AB =
1BA = x2BA =
3µB
3µB
3µA A
1
2 τ
C1
C1
C1
= xC1
(2ΩτB − r1 − r2 ) , xC1Ω .
(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 τ i affects only shipping from country j to i, x1ji andx2ji . 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.
14

A change in τ i affects 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 τ i (i = 1, 2) equallyaffects 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
(3ΩτB µA − ΩτA µB + 2ΩτB µB + 3µA r1 + 2µB r1 + 2µB r2 ) ,(8)
6 (µA + µB )1(2ΩτA µA + 3ΩτA µB − ΩτB µA − µA r1 + 2µA r2 ) ,(9)
6 (µA + µB )1−(Ωτ µ − 3ΩτB µA − 2ΩτB µB + 3µA r1 − 2µB r2 + 4µB r1 ) , (10)6µB (µA + µB ) A B
1(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r2 − µA r1 ) ,(11)
6µA (µA + µB )1(Ωτ + ΩτB − 2r2 + r1 ) ,
(12)
xC4
2BA =
3 (µA + µB ) A
1(ΩτA µB + 3ΩτB µA + 4ΩτB µB − 3µA r1 − 2µB r1 − 2µB r2 ) , (13)6µB (µA + µB )1
(4ΩτA µA + 3ΩτA µB + ΩτB µA + µA r1 − 2µA r2 ) .
(14)
6µA (µA + µB )Although xAB > xBA holds, the characteristics of this equilibrium are different fromthose of type-1 equilibrium with a single carrier. In this equilibrium, a change in τ i (i = 1, 2)affects 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 τ i affects both x1AB and x1BA even thoughx1AB > x1BA holds. This stems from x2AB = x2BA . The direct effect of an increase in τ i isto decrease x1ji and x2ji . The indirect effect 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.

15

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

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

1
(3ΩτB µA − ΩτA µB + 2ΩτB µB − µB r1 + 2µB r2 ) ,(15)
6 (µA + µB )1(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r1 + 2µA r2 + 3µB r1 ) ,(16)
6 (µA + µB )1
(17)(3ΩτB µA − ΩτA µB + 2ΩτB µB − µB r1 + 2µB r2 ) ,6µB (µA + µB )1−(Ωτ µ − 3ΩτA µB − 2ΩτA µA + 4µA r1 − 2µA r2 + 3µB r1 ) , (18)6µA (µA + µB ) B A
1xC5(Ωτ + ΩτB − 2r2 + r1 ) ,
(19)
2BA =
3 (µA + µB ) A
1(ΩτA µB + 3ΩτB µA + 4ΩτB µB + µB r1 − 2µB r2 ) ,(20)
6µB (µA + µB )1
(4ΩτA µA + 3ΩτA µB + ΩτB µA − 2µA r1 − 2µA r2 − 3µB r1 ) . (21)6µA (µA + µB )Although xAB < xBA holds, the characteristics of this equilibrium are different from thoseof type-3 equilibrium with a single carrier. As in type-4 equilibrium above, a change in τ i(i = 1, 2) affects both x1AB and x1BA even though x1AB < x1BA holds.
Figure 8 here
Figure 9 here
Figure 8 illustrates the relationship between shipping volumes and country B’s tariff rates
when type-1 equilibrium arises with free trade (i.e., when ΩA µB − ΩB µA − µA r1 + 2µA r2 < 0holds).22 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 τ B rises. x2BA is constant in type-1 and type-3 equilibria but decreases with τ 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 τ B increases x1BA . Thus,
when country B introduces a tariff 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 are
more likely to occur when r1 is much smaller than r2 , that is, the range of type-2 equilibrium
22

As was mentioned above, the free trade equilibrium is determined by the location of τ B = 0 in Figure 8.
Setting the vertical axis at τ B = 0, we can easily analyze the cases in which the other types of equilibrium
arise under free trade.

16

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 9 illustrates the relationship between shipping volumes and country A’s tariff rates
when type-2 equilibrium arises with free trade (i.e., when µ1 (ΩA µB − ΩB µA + µA r1 ) > 0
Bholds). As in Figure 8, the upper panel and the lower panel show shipping volumes of firm
T1 and those of firm T2 , respectively. Since x1AB increases with τ A in type-4 equilibrium,a tariff 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 ΩB µA − ΩA µB −2µA r1 + µA r2 > 0 holds.
In type-4 and type-5 equilibria, τ 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 effect on firm T1 ’s profits is relatively stronger (weaker)
than the positive effect in type-4 equilibrium (type-5 equilibrium), because x1AB > x1BA
(x1AB < x1BA ) holds. Appendix C proves that an increase in τ 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 τ B only if the gap between x1AB and x1BA is large. When
x1BA is much larger than x1AB , the positive effect of the increase in x1BA on firm T1 ’s profits
could dominate the negative effect of the decrease in x1AB on firm T1 ’s profits.
Similarly, in type-4 equilibrium, τ 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 C also shows that in type-4 equilibrium, an increase inτ A could raise firm T1 ’s total profits. Again, firm T1 gains from an increase in τ A only if thegap between x1AB and x1BA is large.
With respect to the effects of tariffs on each transport firm, the following proposition canbe established.
Proposition 7 Suppose 0 < r1 < r2 . Also suppose τ i increases. Then xhji (h = 1, 2; i, j =A, B, i 6= j) and x2ij necessarily decrease. Shipping x1ij increases in type-4 equilibrium (i.e.,
if µA (r1 − 2r2 ) ≤ Λ < −µA r1 ) and in type-5 equilibrium (i.e., if µB r1 < Λ ≤ µB (2r2 − r1 )),decreases in type-2 equilibrium (i.e., if −µA r1 < Λ < µB r1 ), and is constant in type-1
equilibrium (i.e., if Λ < µA (r1 − 2r2 )) and in type-3 equilibrium (i.e., if Λ > µB (2r2 − r1 )).
Firm T2 always loses but firm T1 may gain from an increase in τ B in type-5 equilibrium andfrom an increase in τ A in type-4 equilibrium.
The changes in firm T1 ’s shipping volume caused by tariffs are not simple, but the effects oftariffs on the “total” shipping quantities from one country to the other are similar to Proposi17

tion 3. That is, any tariff of country B, which satisfies max{0, − µ1 (ΩA µB − ΩB µA − µA r1 + 2µA r2 )} <A
τ B < ΩB , 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 tariff 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 (ΩA µB − ΩB µA − µA r1 + 2µA r2 ) holds.
B
The effects of tariffs on consumers and producers depend not on the shipping volumes ofeach transport firm but on the total volumes of shipping coming in and out from the country.
This implies that as long as the profits of transport firms are not included in welfare, theanalysis of the welfare effects of tariffs with a single carrier remains valid with multiple
carriers. Thus, in view of Proposition 6, Proposition 4 holds for the case of multiple carriers
as well.
Next we examine the effects of taxes on shipping capacity and compare them with thoseof tariffs. 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, we can establish the following proposition.
Proposition 8 Country B’s shipping-capacity tax and country B’s tariff set at the samelevels are equivalent in type-1, type-2, and type-4 equilibria. Similarly, country A’s shippingcapacity tax and country A’s tariff set at the same levels are equivalent in type-2, type-3, andtype-5 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 effects of taxes on shipping capacity withmultiple carriers are basically the 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 effects of tariffs. 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:kτ
k Ak
TAB = ΩA
− µA
k = 1, 2,(22)
B
B xAB ,
18

kwhere xA
AB is the quantity demanded for shipping good Ak from country A to country B. Askτkin the previous section, the intercepts are inclusive of tariffs: ΩA≡ ΩAB
B − τ kB (k = 1, 2)
where τ kB is country B’s specific tariff 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 τΩB − TAB , k = 1, 2.
kµA
BThe total demand for transport services from country A to country B and its inverse demand
are given by
1
A1 τ A2A2 τ A1
A1
A2
Ω
µ
+
Ω
µ
−
µ
T
−
µ
T
,
AB
AB
B
B
B
B
B
B
1 A2
µA
B µB

A2 τ A1
A1 A2
1 τ A2
ΩA
µ
+
Ω
µ
−
µ
µ
x
.
AB
B
B
B
B
B B

A2
1
xAB = xA
AB + xAB =

TAB =

1
A2
1
µA
B + µB

A2
1
Again we have three cases with profit maximization. If xAB (= xA
AB + xAB ) > xBA holds,
we have

M1
TAB

=

1M 1
xA
=
AB

2M 1
xA
=
AB

1
xM
AB =

A2 τ A1
A1
A2
1 τ A2ΩτAΩA
M1
B µB + ΩB µB + r(µB + µB )

,
T
=
,
BA
A2
1
2
2 µA
B + µB
1A1 τ A2A1 τ A1
A1
A2
2 τ A1
 ΩA− A1 A1,
B µB − ΩB µB − 2ΩB µB + rµB + rµB
A22µB µB + µB
1A1 τ A2A2 τ A1A2 τ A2
A1
A2

− A2 A1
Ω
µ
−
Ω
µ
−
2Ω
µ
+
rµ
+
rµ
,
B
B
B
B
B
B
B
B
2
2µB µB + µA
B
 M1
ΩτA
1
A1 τ A2A2 τ A1
A1
A2
.
Ω
µ
+
Ω
µ
−
rµ
−
rµ
,
x
=
BA
B
B
B
B
B
B
1 A2
2µA
2µA
B µB

If xAB < xBA holds instead, we haveA2 τ A1
1 τ A2ΩτA + rΩA
M3
B µB + Ω B µB

,
T
=
,
BA
A2
1
2
2 µA
B + µB
1A2 τ A1
A1 τ A2A1 τ A1
= − A1 A1
Ω
µ
−
Ω
µ
−
2Ω
µ
,
B
B
B
B
B
B
2
2µB µB + µA
B

1A2 τ A1A2 τ A2
1 τ A2 ΩA= − A2 A1,
B µB − ΩB µB − 2ΩB µB
A22µB µB + µB
 M 3 ΩτA − r
1
A1 τ A2A2 τ A1Ωµ+Ωµ, xBA =
=
.
B
B
B
B
1 A2
2µ
µ
2µA
A
B B

M3
TAB
=
1M 3
xA
AB

2M 3
xA
AB

3
xM
AB

In both cases, an increase in τ 1B or τ 2B decreases TAB , while an increase in τ A decreases
TBA . Thus, a tariff on good Ak affects not only the market of good Ak but also the market of19

good Al (k, l = 1, 2; k 6= l) through a change in the freight rate. That is, a tariff on good Akkhas a spillover effect on the the market of good Al . An increase in τ kB directly decreases xA
AB
A1
A2
l
but indirectly increases xA
AB . The total load from country A to country B, xAB = xAB +xAB ,decreases, because the direct effect dominates the indirect effect.
If xAB = xBA holds, then we have another spillover effect. In type-2 equilibrium, we
obtain
M2
=
TAB

Γ
A2
A1
A1 A2
A2
1 A2
1
{µA
µA
ΩτA
B µB r(µB + µB ) − µB µB
B + µB
A1
2µB + µA
B A1 τ
 A2 τ
A2
A2
A1
A1
A1 A2
A1
A2
1 A2
+µB µA
µ
+
2µ
µ
+
2µ
µ
Ω
+
µ
µ
µ
+
2µ
µ
+
2µ
µ
B B
B A
B A
B
B
B B
B A
B A ΩB },


 τ
A1
A2 τ
A2
A1 τ
A2
A1 A2
A1
A2
M2
1
= Γ{rµA (µA
TBA
B + µB ) + 2µB µB + µB µA + µB µA ΩA − µB µA ΩB − µB µA ΩB },A1
A2
A1 τ A2A2 τ A1
A1
A2
τ
M2
2
xM
AB = xBA = Γ{ΩB µB + ΩB µB + (µB + µB )ΩA − r(µB + µB )},



A1
A2
1 A2
where Γ ≡ 1/ 2 µA
. An increase in τ 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 effects is as follows. When τ 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 inτ A , firm T increases TAB to reduce the load from country A to country B.
Alk
In any equilibrium, an increase in τ kB (k, l = 1, 2; k 6= l) decreases xA
AB but increase xAB .
Thus, an increase in τ 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 tariff ongood Ak set by country B under free trade may benefit country A.
The above results are summarized in the following proposition.23
Proposition 9 Suppose xAB ≥ xBA holds under the free-trade equilibrium. Any tariff on
A1 A2
A τ
A
A τ
A
A
A
µB −ΩB1 µA µB2 −ΩB2 µA µB1 +rµA (µB1 +µB2 )AµA µBl
A
A
A τ
A
A τ
A
A
A
ΩA µB1 µB2 −ΩB1 µA µB2 −ΩB2 µA µB1 +rµA (µB1 +µB2 )
kB
Al
µA µB
A
A
A τ
A
A τ
A
A
A
−ΩA µB1 µB2 +ΩB1 µA µB2 +ΩB2 µA µB1 +rµB1 µB2kB
AµA µBl
A1 A2
A1 τ
A2
A2 τ
A1
A1 A2
−ΩA µB µB +ΩB µA µB +ΩB µA µB +rµB µB
B
AµA µBl
A
A
A τ
A
A τ
A
A
A
ΩA µB1 µB2 −ΩB1 µA µB2 −ΩB2 µA µB1 +rµA µB1 +rµA µB2AAAµB1 µB2
A1 A2
A1 τ
A2
A2 τ
A1
A1
A
ΩA µB µB −ΩB µA µB −ΩB µA µB +rµA µB +rµA µB2AAAµB1 µB223Ω µWith τ A = 0, we have type-1 equilibrium if 0 < τ kB < − A B

type

2

equilibrium

if

−

<

and

type-3equilibrium(k, l = 1, 2; k 6= l). With τlibrium if 0
τ

<

τ

<

if

τ

τ

,

<
>

= 0, we have type-2 equiand type-1 equilibrium if}.

> max{0,20good Ak set by country B lowers the freight rate from country A to country B, decreases
country B’s imports of good Ak , and increases country B’s imports of good Al (k, l = 1, 2; k 6=l). Any tariff 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 tariff 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 τ kB is large enough.
Appendix D shows that this case actually occurs under some parameter values.
Thus, we obtain the following proposition.
Proposition 10 An increase in τ 1B (τ 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
ΠT = TABxAB + TABxAB + TBA xBA − rk,
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 1τ
1
A1 m1
,
TAB
= r + ΩA
2
2 B

1
1 2τ
A2 m1
TAB
= r + ΩA
,
2
2 B

1
m1
TBA
= ΩτA .
2

Type-3 equilibrium is
1 1τ
A1 m3
= ΩA
,
TAB
2 B

1 2τ
A2 m3
TAB
= ΩA
,
2 B

1
1
m3
TBA
= r + ΩτA .
2
2

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

21

Type-2 equilibrium isA1 τ A2A2 τ A1
A1 τ
A1
A1 m2
1 τ A1TAB= Γm 2ΩA
B µB + ΩB µB + ΩB µB + ΩB µA − ΩA µ1 + rµB µA ,

A2 τ A1A2 τ A2
A2 τ
A2
A2
A2 m2
1 τ A2
µ
+
Ω
µ
+
2Ω
µ
+
Ω
µ
−
Ω
µ
+
rµ
µ
TAB
= Γ m ΩA
A
A
B
B
B
B
B
B
B
B
B A ,

A1 τ
A2 τ
A2
A1
A2
m2
1
= Γ m Ω A µA
TBA
B − ΩB µA − ΩB µA + ΩA µB + 2ΩA µA + rµB µA + rµB µA ,


A2
A1
1
where Γm ≡ 1/ 2 µA
. An increase in τ 1B or τ 2B decreases both TAB
and
B + µB + µA
A2
A1
A2
TAB
and increases TBA while an increase in τ A increases both TAB
and TABand 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 τ 1B or τ 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 τ 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 different freights rates among different exportable goods, the effects of tariffs
are qualitatively similar to those of tariffs 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 tariffs could decrease not only domestic imports
but also domestic exports given other types of other 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 tariffs decrease both domestic imports and exports, consumers inboth countries lose because of higher consumer prices. There are two conflicting effects oftariffs on the firms, the direct effect and the indirect effect, the sizes of which depend on
parameter values in the model. The direct effect is conventional, that is, domestic import22

tariffs benefit the domestic firm at the cost of the foreign firm. The indirect effect stemmingfrom a decrease in domestic exports benefits the foreign firm at the cost of the domestic firm.
As a result, domestic import tariffs 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 tariff 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,
tariffs are also detrimental to consumers because they face both higher consumer prices andless varieties. Import tariffs do not affect the profits of producers, which always equal zero
because of free entry and exit.

6.2

Suggestive evidence

Our main result implies that domestic tariff reductions may increase domestic exports.
Whether removing import restrictions (such as reducing tariffs) 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 tariff reduction may influence export. Though earlystudies indicate a negative effect 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 effects. For example, a tariff reduction onintermediate goods may expand the sectors that use those goods as inputs, enabling themto increase their exports (Cruz and Bussolo, 2015). This effect via supply chain may bethrough direct effects on production costs (that drop due to lower input costs) or indirect
effects through more intense import competition and resulting productivity increases forthe affected firms (Trefler, 2004; Amiti and Konings, 2007). Our study identifies anotherchannel—endogenous transport costs—through which import liberalization has a positiveeffect on the country’s exports—an empirical question of high policy relevance.
Which channels are present or have larger effects in magnitude than others? Answering
this question would require careful empirical investigations. The case of India’s trade liberalization in the 1990s, which has been studied as an example of externally imposed reductions
in trade barriers (e.g., Topalova and Khandelwal, 2011), suggests that our finding regarding
the link between tariffs and transport costs may be empirically relevant.24
The United States has been a major destination of India’s exports (about 20% as of2000). Figure 10 describes the trend of India’s import tariffs and the real transportation
24

The authors thank one of the referees for her/his suggestion that the unilateral trade liberalization by
India in 1990s should be investigated.

23

costs of the top exports from India to the United States.25 In the figure, the transport costs
for all HS categories considered (except for HS68 stone and cement) demonstrate a clear
downward tread during the period of India’s trade liberalization. While HS68 exhibits a more
erratic trend, overall the transport costs declined by more than 40% over the period. Thisobservation is consistent with our theoretical prediction regarding the response of transport
costs to changes in trade policy due to backhaul problems.26
Figure 10 here

7

Conclusion

This paper explicitly incorporated the transport sector into a standard international trademodel and studied the effects 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 effects of import tariffs ontransported goods and taxes on shipping capacity.
Our analysis reveals that domestic tariffs reduce domestic exports as well as domestic
imports when transport firms try to avoid the backhaul problem. Domestic tariffs, which
benefit the domestic import sector and harm the foreign export sector in a standard modelof international trade, can also harm the domestic export sector and benefit the foreign import sector. Thus the tariffs may not improve the country’s welfare. This unconventional
result occurs because transport firms choose their shipping capacity levels, subject to back25
The figure displays the average unit transport costs on for the two sectors with the highest export sharein volume (HS68 “stone, plaster, cement, asbestos, mica, etc articles” and HS73 “articles of iron or steel”)
and the two sectors with the highest export share in value (HS 71 “pearls, precious stones, metals, coins,etc” and HS62 “articles of apparel, accessories, not knit or crochet”). All values are normalized so that the1991 values equal one. Appendix E details how we compute the average import tariff rates.
26
Our theory also predicts that the transport costs of India’s imports from the United States increase as
India’s import tariffs 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 10 on
India’s imports.

24

haul problems, while the export sector cannot export beyond the transport firm’s shipping
capacity. Clearly, tariffs reduce the transport firms’ profits.
A tax on shipping capacity could be equivalent to an import tariff on shipped goods.
This implies that the subsidies on shipping capacity may work as a substitute for an export
subsidy on shipped goods. If a foreign country hesitates to lower its tariffs, 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 tariff could decrease the shipping volumes in both directions.
We also obtained additional results in the extensions. When multiple exportable goods are
considered, a tariff affects 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 at several
places en route. In our analysis, we can regard one of the two countries as the rest of theworld. However, a promising direction for future research is to explicitly investigate the casewith more than two countries.27

Appendix A
In this appendix, we prove that even if the tariff set by country B is small in the type-1
free-trade equilibrium, country B’s welfare deteriorates when it includes firm T ’s profits.
In the upper panel of Figure 5, free trade increases the total surplus in the market ofF
good B by abPAB
in country B. Free trade also generates firm T ’s profits. The profits fromF
F
shipping good B from country A to country B are given by its revenue bcPAA
PAB
minus its
F
costs to ship xAB units. In the lower panel of Figure 5, point F gives the largest profits on
the derived demand curve DDAB .
τ
When a tariff is imposed, the total surplus in the market of good B is given by ab0 PAB
plus the tariff revenue T RB in the upper panel. Firm T ’s profits from shipping good B fromτ
country A to country B are given by its revenue τ xτAB OTAB
minus its costs to ship xτAB units
in the lower panel. In the lower panel, the sum of the tariff revenue and firm T ’s profits is
27

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

25

t
given by txτAB OTAB
minus firm T ’s costs, which actually equals firm T ’s profits at point t
without the tariff. Since point F gives the largest profits of firm T along DDAB , the sum of
the tariff revenue and firm T ’s profits is smaller than firm T ’s profits under free trade.
Thus, the sum of the total surplus in the market of good B and firm T ’s profits fromτ
shipping good B from country A to country B with the tariff, which equals ab0 c0 PAA
minus
F
firm T ’s costs, is less than that without the tariff, which equals abcPAA
minus firm T ’s costs.

Appendix B
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.
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 byΠ1 = TAB x1AB + TBA x1BA − r1 x1AB , Π2 = TAB x2AB + TBA x2BA − r2 x2AB .
In equilibrium, we have (6) - (7).
Second, suppose that x1AB = x1BA and x2AB = x2BA hold in equilibrium. Then
Π1 = (TAB + TBA )x1AB − r1 x1AB , Π2 = (TAB + TBA )x2AB − r2 x2AB .
In equilibrium, we have
C2
TAB
=
C2
=
TBA

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

1
(3ΩτB µA − 2ΩτA µB + ΩτB µB + µB r1 + µB r2 ) ,3 (µA + µB )1(ΩτA µA + 3ΩτA µB − 2ΩτB µA + µA r1 + µA r2 ) ,3 (µA + µB )1
xC2(ΩτA + ΩτB − 2r1 + r2 ) ,
1BA =
3 (µA + µB )1xC2(Ωτ + ΩτB + r1 − 2r2 )2BA =
3 (µA + µB ) A
1(2ΩτA + 2ΩτB − r1 − r2 ) ,3 (µA + µB )1(2ΩτA + 2ΩτB − r1 − r2 ) .
3 (µA + µB )

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

Third, suppose that x1AB < x1BA and x2AB < x2BA hold in equilibrium. Then the profits26

of firms T1 and T2 are given byΠ1 = TAB x1AB + TBA x1BA − r1 x1BA , Π2 = TAB x2AB + TBA x2BA − r2 x2BA .
In equilibrium, we have1 τ(Ω + r1 + r2 ) ,(A7)
3 A
1 τ C3
1
1= xC3ΩB , x1BA =(ΩτA − 2r1 + r2 ) , xC3(Ωτ + r1 − 2r2 )(A8)
,
2AB =
2BA =
3µB
3µA
3µA A
2 τ C31
C3
C3= x1AB+ xC3ΩB , xBA = xC3(2ΩτA − r1 − r2 ) .
(A9)
2AB =
1BA + x2BA =
3µB
3µA

C3
=
TAB

xC3
1AB
xC3
AB

1 τ
Ω ,
3 B

C3
TBA
=

Fourth, suppose that x1AB > x1BA and x2AB = x2BA hold in equilibrium. Then
Π1 = TAB x1AB + TBA x1BA − r1 x1AB , Π2 = (TAB + TBA )x2AB − r2 x2AB .
In equilibrium, we have (8) - (14).
Fifth, suppose that x1AB < x1BA and x2AB = x2BA hold in equilibrium. Then
Π1 = TAB x1AB + TBA x1BA − r1 x1AB , , Π2 = (TAB + TBA )x2AB − r2 x2AB .
In equilibrium, we have (15) - (21).
Sixth, suppose that x1AB = x1BA and x2AB > x2BA hold in equilibrium. Then
Π1 = (TAB + TBA )x1AB − r1 x1AB , Π2 = TAB x2AB + TBA x2BA − r2 x2AB .
In equilibrium, we have1(Ωτ + ΩτB − 2r1 + r2 ) ,3 (µA + µB ) A1= −(Ωτ µ − 3ΩτB µA − 2ΩτB µB + 3µA r2 − 2µB r1 + 4µB r2 ) ,6µB (µA + µB ) A B
1=(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r1 − µA r2 ) .
6µA (µA + µB )

C6
= xC6
x1AB
1BA =
C6
x2AB

xC6
2BA

Seventh, suppose that x1AB = x1BA and x2AB < x2BA hold in equilibrium. Then
Π1 = (TAB + TBA )x1AB − r1 x1AB , Π2 = TAB x2AB + TBA x2BA − r2 x2AB .

27

In equilibrium, we have
C7xC7
1AB = x1BA =

1

xC7
2AB =
xC7
2BA

1
(Ωτ + ΩτB − 2r1 + r2 ) ,3 (µA + µB ) A(3ΩτB µA − ΩτA µB + 2ΩτB µB + 2µB r1 − µB r2 ) ,6µB (µA + µB )1
= −(ΩτB µA − 3ΩτA µB − 2ΩτA µA − 2µA r1 + 4µA r2 + 3µB r2 ) .
6µA (µA + µB )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 have11(ΩτB − 2r1 ) , x2AB =(Ωτ + r1 ) ,
3µB
3µB B
1
1
=
(ΩτA + r2 ) , x2BA =(Ωτ − 2r2 ) .
3µA
3µA A

x1AB =x1BA

We need x1AB −x1BA = − 3µ 1µ (ΩτA µB − ΩτB µA + 2µA r1 + µB r2 ) > 0, which implies ΩτA µB <A B
ΩτB µA . However, we also need x2BA − x2AB = − 3µ 1µ (ΩτB µA − ΩτA µB + µA r1 + 2µB r2 ) > 0,A Bwhich implies ΩτA µB > ΩτB 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(ΩτB − 2r2 + r1 )) > x2BA (= 3µ1 ΩτA ), which becomes ΩτA µB − ΩτB µA − µA r1 + 2µA r2 < 0,3µB
Ai.e., Λ (≡ ΩτA µB − ΩτB µA ) < µA (r1 −2r2 ). Now the condition under which x1AB > x1BA arises
given x2AB > x2BA is that x1AB (= 3µ1 (ΩτB − 2r1 + r2 )) > x1BA (= 3µ1 ΩτA ), which becomesBAΩτA µB − ΩτB µA + 2µA r1 − µA r2 < 0, i.e., Λ < 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 Λ < 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
τ
τ
τ
x2AB = −(Ω µ − 3ΩB µA − 2ΩB µB + 3µA r2 − 2µB r1 + 4µB r2 )6µB (µA + µB ) A B
> x2BA =1
6µA (µA + µB )

(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r1 − µA r2 )28.

Thus, the condition under which x2AB > x2BA does not hold given x1AB = x1BA is x2AB −x2BA ≤ 0, i.e., Λ ≥ −µA r2 . Suppose 2AB < x2BA given x1AB = x1BA . Thenx2AB =
< x2BA = −

1
6µB (µA + µB )(3ΩτB µA − ΩτA µB + 2ΩτB µB + 2µB r1 − µB r2 )

1
6µA (µA + µB )(ΩτB µA − 3ΩτA µB − 2ΩτA µA − 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., Λ ≤ 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


=

(ΩτA µB − 3ΩτB µA − 2ΩτB µB + 3µA r1 − 2µB r2 + 4µB r1 )
1
6µA (µA + µB )(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r2 − µA r1 ).

Thus, the condition under which x1AB > x1BA does not hold given x2AB = x2BA is x1AB ≤x1BA , i.e., Λ ≥ −µA r1 . Suppose x1AB < x1BA given x2AB = x2BA . Thenx1AB =
≤ x1BA = −

1
6µB (µA + µB )1

6µA (µA + µB )(3ΩτB µA − ΩτA µB + 2ΩτB µB − µB r1 + 2µB r2 )(ΩτB µA − 3ΩτA µB − 2ΩτA 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., Λ ≤ µB r1 . Therefore, the combination of x1AB = x1BA and x2AB = x2BA arises asa Nash equilibrium if −µA r1 < Λ < µB r1 .
The condition under which x2AB < x2BA arises given x1AB < x1BA is that x2AB (=1(ΩτB )) < x2BA (= 3µ1 (ΩτA + r1 − 2r2 )), which becomes ΩτA µB −ΩτB µA +µB r1 −2µB r2 > 0.
3µB
AThis condition is equivalent to Λ > µB (2r2 −r1 ). Now the condition under which x1AB < x1BA
arises given x2AB < x2BA is that x1AB (= 3µ1 ΩτB ) > x1BA (= 3µ1 (ΩτA − 2r1 + r2 )), which beBAcomes (ΩτA µB − ΩτB µA − 2µB r1 + µB r2 ) > 0. This condition is equivalent to Λ > µB (2r1 −r2 ). Since r1 < r2 , the combination of x2AB > x2BA and x1AB > x1BA arises as a Nashequilibrium if Λ > 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 (ΩτB − 2r2 + r1 )) > x2BA (= 3µ1 (ΩτA )). As pointed out
B

A

29

above, the combination of x2AB < x2BA and x1AB > x1BA never occurs. Thus, the condition
under which x2AB = x2BA arises given x1AB > x1BA is that 3µ1 (ΩτB − 2r2 + r1 ) < 3µ1 ΩτA
B
Aholds, that is, (ΩτA µB − ΩτB µA − µA r1 + 2µA r2 ) > 0 holds. Thus, the condition becomesµA (r1 − 2r2 ) < Λ. Now the condition under which x1AB > x1BA arises given x2AB = x2BA is
that


1
τ
τ
τ
(Ω µ − 3ΩB µA − 2ΩB µB + 3µA r1 − 2µB r2 + 4µB r1 )x1AB = −6µB (µA + µB ) A B
> x1BA =

1
6µA (µA + µB )(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r2 − µA r1 ),which becomes (ΩτA µB − ΩτB µA + µA r1 ) < 0. This condition is equivalent to Λ < −µA r1 .Thus,
the combination of x2AB = x2BA and x1AB > x1BA arises as a Nash equilibrium if µA (r1 − 2r2 ) <Λ < −µA r1 .
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 . Then
we have x2AB = 3µ1 ΩτB ) < x2BA (= 3µ1 (ΩτA − 2r2 + r1 ) . Thus, the condition under which
B
A
x2AB = x2BA arises given x1AB < x1BA is that 3µ1 ΩτB > 3µ1 (ΩτA − 2r2 + r1 ) holds, that is,
B
A(ΩτA µB − ΩτB µA + µB r1 − 2µB r2 ) < 0 holds. Thus, the condition becomes Λ < 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 )(3ΩτB µA − ΩτA µB + 2ΩτB µB − µB r1 + 2µB r2 )(ΩτB µA − 3ΩτA µB − 2ΩτA µA + 4µA r1 − 2µA r2 + 3µB r1 ),which becomes (ΩτB µA − ΩτA µB + µB r1 ) < 0. This condition is equivalent to Λ > µB r1 .
Thus, the combination of x2AB = x2BA and x1AB < x1BA arises as a Nash equilibrium ifµB r1 < Λ < 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
1τgiven x1AB > x1BA . Then we have x1AB = 3µ (ΩB − 2r1 + r2 ) > x1BA = 3µ1 ΩτA . 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 (ΩτB − 2r1 + r2 ) < 3µ1 ΩτA
B
Aholds, that is, (ΩτA µB − ΩτB µA − µA r2 + 2µA r1 ) > 0 holds. Thus, the condition becomes
2µA (r2 − 2r1 ) < Λ. Now the condition under which x2AB > x2BA arises given x1AB = x1BA

30

is thatx2AB = −

1
6µB (µA + µB )

> x2BA =(ΩτA µB − 3ΩτB µA − 2ΩτB µB + 3µA r2 − 2µB r1 + 4µB r2 )
1
6µA (µA + µB )(2ΩτA µA + 3ΩτA µB − ΩτB µA + 2µA r1 − µA r2 ),which becomes (ΩτA µB − ΩτB µA + µA r2 ) < 0. This condition is equivalent to Λ < −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 11ττhave x1AB = 3µ ΩB < x1BA = 3µ (ΩA − 2r1 + r2 ) . Thus, the condition under which
B
A
x1AB = x1BA arises given x2AB < x2BA is that 3µ1 ΩτB > 3µ1 (ΩτA − 2r1 + r2 ) holds, that is,
B
A(ΩτA µB − ΩτB µA − 2µB r1 + µB r2 ) < 0 holds. Thus, the condition becomes Λ < µB (2r1 − r2 ).
Now the condition under which x2AB < x2BA arises given x1AB = x1BA is thatx2AB =
< x2BA = −

1
6µB (µA + µB )1

6µA (µA + µB )(3ΩτB µA − ΩτA µB + 2ΩτB µB + 2µB r1 − µB r2 )(ΩτB µA − 3ΩτA µB − 2ΩτA µA − 2µA r1 + 4µA r2 + 3µB r2 ),which becomes (ΩτB µA − ΩτA µB + µB r2 ) < 0. This condition is equivalent to Λ > µB r2 . SinceµB (2r1 − r2 ) < µB r2 with r1 < r2 , the combination of x1AB = x1BA and x2AB > x2BA neverarises as a Nash equilibrium.

Appendix C
In this appendix, we first prove that an increase in τ B decreases firm T1 ’s total profits in
type-4 equilibrium and then show that an increase in τ A may increase firm T1 ’s total profits
in type-4 equilibrium and an increase in τ 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 ΠC4
1 = µB (x1AB ) + µA (x1BA ) .
Differentiating this with respect to τ i (i = A, B), we have
C4
dxC4
dΠC4
1
1AB
C4 dx1BA= 2µB xC4
+
2µ
x
.
A 1BA
1AB
dτ i
dτ i
dτ i
dxC4

dxC4

3µA +2µB
C4
1AB
1BA
In type-4 equilibrium, xC4
1AB > x1BA with τ A = 0. Since µB dτ B = − 6(µ +µ ) and µA dτ B =dΠC4µA, we obtain dτ1B < 0 in type-4 equilibrium.
6(µA +µB )

31

A

B

Next we consider the effect of an increase in τ A on firm T1 ’s total profits in type-4
C4
dx1BA
dxC4
µB
C4
1AB
equilibrium. With τ B = 0, xC4
1AB > x1BA . We have µB dτ A = 6(µ +µ ) and µA dτ A =
A

B

dΠC4

2µA +3µB
C4
1− 6(µ. Thus, as long as the gap between xC4
1AB and x1BA is small, we obtain dτ A < 0.
+µ )
A

B

The gap becomes the largest with τ A =for example,ΩA µB −ΩB µA −µA r1 +2µA r2. Thus, if the following holds,
µB

C1
C4
xC4
1AB τ = ΩA µB −ΩB µA −µA r1 +2µA r2 ( = x1AB ) < 3 x1BA τ = ΩA µB −ΩB µA −µA r1 +2µA r2
A

A

µB

µB

⇔ 2ΩB + 5r1 − 7r2 > 0,

(A10)

dΠC4

then we have dτ1A < 0 in type-4 equilibrium. We can easily find a set of parameter values,
C4
C4
C4ΩA , ΩB , 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
dΠC4
is small, or, the gap between r1 and r2 is small. However, if the gap is large, dτ1A > 0 coulddΠC4hold. To see this, suppose µA = µB . Then we have dτ1A > 0 for τ A the range of which isΩ µ −Ω µ −µ r +2µ r
close enough to A B B Aµ A 1 A 2 if the following holds:
B

C1
C4
xC4
1AB τ = ΩA µB −ΩB µA −µA r1 +2µA r2 ( = x1AB ) > 5 x1BA τ = ΩA µB −ΩB µA −µA r1 +2µA r2
A

A

µB

µB

⇔ 4ΩB + 7r1 − 11r2 < 0.

(A11)

We consider the conditions under which (A11) holds. Setting ΩB = ar1 and r2 = br2 , (A11) isΩB +r1
C4⇔ 2b < a+1.
equivalent to 4a+7−11b < 0. For xC4
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, ΩA , ΩB , µA , µB , r1 and r2 , which satisfies (A11), TAB
> 0,
C4
C4
C4
C4
> 0, xC4
TBA
1AB > x1BA > 0, and x2AB = x2BA > 0. For example, ΩA = 30, ΩB = 20, µA = 1,
µB = 1, r1 = 11 and r2 = 15 are such a set of parameters.
Lastly, we consider the effect of an increase in τ B on firm T1 ’s total profits in type-5
C5 2
C5 2
equilibrium, which is given by given by ΠC5
1 = µB (x1AB ) + µA (x1BA ) . Differentiating thiswith respect to τ B , we have
C4
C5
dΠC5
1
C5 dx1ABC5 dx1BA= 2µB x1AB
+ 2µA x1BA
.
dτ B
dτ B
dτ B
dxC5

dxC5

3µA +2µB
µA
C5
1BA
1AB
With τ A = 0, xC5
1AB < x1BA . We have µB dτ B = − 6(µ +µ ) and µA dτ B = 6(µ +µ ) . Thus,
A

B

dΠC5

A

B

C5
1
as long as the gap between xC5
1AB and x1BA is small, we obtain dτ B < 0. The gap becomes32the largest with τ B =−ΩA µB +ΩB µA −µB r1 +2µB r2. For example, if the following holds:
µA

C5
C3
xC5
1AB τ = −ΩA µB +ΩB µA −µB r1 +2µB r2 ( = x1AB ) < 3 x1BA τ = −ΩA µB +ΩB µA −µB r1 +2µB r2
B

A

µA

µA

⇔ 2ΩA + 5r1 − 7r2 > 0,

(A12)

dΠC5

then we have dτ1B < 0 in type-5 equilibrium. The difference between (A10) and (A12) isthat ΩB in (A10) is replaced by ΩA in (A12). It is easy to find a set of parameter values,
C5C5C5ΩA , ΩB , µA , µB , r1 and r2 , which satisfies (A12), TAB> 0, TBA> 0, xC5
1BA > x1AB > 0,
C5
dΠ1
C5
and xC5
2AB = x2BA > 0. Similarly, we have dτ B > 0 for τ B which is close enough to−ΩA µB +ΩB µA −µB r1 +2µB r2
if
µ
A

xC5
1AB τ = −ΩA µB +ΩB µA −µB r1 +2µB r2
BµA> 5 xC3
1AB τ = −ΩA µB +ΩB µA −µB r1 +2µB r2
BµA⇔ 4ΩA + 7r1 − 11r2 < 0(A13)

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

Appendix D
In this appendix, we show Proposition 10. For this, we find a case in which an increasein τ 1B (τ 2B ) actually leads firm T to stop shipping good A1 (good A2 ). For simplicity, we
A2
1
assume τ 1B > 0, τ 2B = 0 and xA
AB + xAB < xBA . Then we have
M3
TAB
=

A2 τ A1
1 τ A2ΩA
B µB + ΩB µB
 ,
A2
1
2 µA
+
µ
B
B

k
xA
AB =


1  Ak τ
−
T
Ω
AB .
B
k
µA
B
2

(ΩAB1 τ µAB2 +ΩAB2 τ µAB1 ). WhenA
A
A
A
4µB2 µB1 (µB1 +µB2 )2τfirm T ships only good A2 , we have
TAB = 21 ΩA
and the profitsB from shipping only good A2q
A2 τ 2
A1 τ

(Ω
)
Ω
A2
2τ
1
1
1
are BA2 . Thus, if ΩA> 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.

Appendix E
We describe details on computing the tariff rates used in Figure 10.28 The World Integrated Trade Solution (WITS) database does not contain tariff data for 1991, 1993-95, and28

The authors thank Kazunobu Hayakawa for sharing with them the tariff data computed with the following procedure.

33

1998. For these years with missing tariff data, we assume that tariff rates did not change
and apply the rates from the previous year. (Thus the 1991 tariff rates are equal to the 1990
level in the data, the 1995 rates equal to the 1992 level, etc.) In the figure the tariff rate
appears to change every year because import values, and hence the weights on the sectoral
tariff rates, differ across years.
Tariff rates are typically defined at a level finer than the HS six-digit level. We took asimple average of tariff rates within each HS six-digit level to compute the sectoral tariff
rates. The six-digit level import value weights are then applied on the sectoral tariff rates
to derive the weighted-average tariff rates. The import values are taken from the United
Nations Commodity Trade Statistics Database (UN Comtrade).
For the purpose of this analysis, the weighted average was taken over those commodities
that are subject to containerized trade (instead of all traded commodities).
We use the weighted average tariff rates in the figure (instead of the tariff rates for eachsector) because a container may carry a mixture of products from various sectors: freightrates on a particular manufacturing good may depend on not only the trade volume of
the good itself but the total trade volume between countries. We also note that, in thecomputation of the average tariff rates, we use the weighted average in terms of imports at acommodity-level because the effect of tariff rates on freight rates will be larger for productswith larger trade volume/values.

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37

FigurePi

Figure 1: Trade in goods and freight rate
a
b

PFij

EXi

TFij
PFii
d

IMi

c

Tij

xFij

TFij

Fi

xij

Ωj
DDij
μj
xFij

xij

PA

Figure 2: Type-2 equilibrium

PFAB
EXA

TFAB

IMA

PF AA
PB
PF

xFAB

xAB
EXB

BA

TFBA
PF BB

IMB
xFBA

xBA

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

ΩA/2μA

xBA

FB

B’

(ΩA-r)/2μA

xAB
A’
Type 1B
O

Type 2B

Type 3B

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

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

xBA
B’

(ΩA-r)/2μA

xAB
Type 2BO

A’Type 3B(ΩBμA- ΩAμB+rμB)/ μA

τBFigure 4 (a): Tariffs set by country A(xAB > xBA with free trade)xAB, xBA(ΩB-r)/2μB

A’

FA

xAB

ΩA/2μA FBxBAType 1AO

B’τAFigure 4 (b): Tariffs set by country A(xAB = xBA with free trade)xAB, xBA(ΩA+ΩB-r)/2(μA +μB) F

xAB(ΩB-r)/2μB

A’xBA
Type 2AO

B’Type 1A(ΩAμB- ΩBμA+rμA)/ μB

τA

Pτ AB
PFAB

PA

Figure 5: Tariffs and surpluses
TRB

a
b’

b

Pτ AB -τB
TτAB

TFAB

PFAA
Pτ AA

c’

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 6: Tariffs and surpluses with balanced shipping
PA
Pτ AB

PF AB
Pτ AB -τB

ESA
IMA
τB

PB

xτAB xFAB

xAB
ESB

PF BB
Pτ BB

IMB
xτBA xFBA

xBA

Figure 7: Multiple transport firms(with r1 <r2)Type 1x1AB>x1BA
x2AB>x2BA

Type 2x1AB=x1BA
x2AB=x2BA

Type 4x1AB>x1BA
x2AB=x2BA

μA(r1-2r2)-μAr1

Type 5x1AB<x1BAτB
x2AB=x2BA
μ B r1

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 8: 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 9: 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 10: India’s import tariffs and transport costs
on exports to the United States, 1991-2003

Note: Average unit transport costs (in 1990 US dollars) for goods categorized in HS 62,
68, 71, and 73 are from OECD Maritime Transport Costs database (adjusted with US
GDP deflator). Tariff rates refer to the weighted average of India’s HS six-digit level
MFN rates using total imports as a weight. The data on MFN rates and total imports are
obtained from WITS database and UN Comtrade, respectively.