Transport liberalization and regional imbalances with endogenous freight rates.
Date: 2018-07-11
Institutions: Joint Research Centre
Subjects: cost analysis, economic activity, freight rate, liberalisation of the market, regional transport, research report, tariff reduction, transport economics, transport market, transport policy, transport price

Transport liberalization and 
regional imbalances with 
endogenous freight rates 

Francesco Di Comite 

2018 

EUR 28989 EN 

This publication is a Technical report by the Joint Research Centre (JRC), the European Commission's science
and knowledge service. It aims to provide evidence-based scientific support to the European policymaking
process. The scientific output expressed does not imply a policy position of the European Commission. Neither
the European Commission nor any person acting on behalf of the Commission is responsible for the use that
might be made of this publication.

Contact Information
Name: Francesco Di Comite
Address: Edificio Expo, Calle Inca Garcilaso, 3, 41092 Sevilla
E-mail: francesco.di-comite@ec.europa.eu
Tel.: +34954488237

JRC Science Hub
https://ec.europa.eu/jrc

JRC92386

EUR 28989 EN

PDF

ISBN 978-92-79-77224-5

ISSN 1831-9424

doi:10.2760/022302

Luxembourg: Publications Office of the European Union, 2018

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How to cite this report: Di Comite, F., Transport liberalization and regional imbalances with endogenous freight 
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Contents

Abstract ............................................................................................................................ 1

1 Introduction ................................................................................................................. 2

2 The model .................................................................................................................... 3

2.1 Consumers.............................................................................................................. 3

2.2 Firms....................................................................................................................... 4

2.3 Market outcomes in the short run .......................................................................... 5

2.4 Factors' remuneration............................................................................................. 6

3 The long run: industrial agglomeration and regional imbalances................................ 7

3.1 Industrial concentration and market outcomes...................................................... 8

4 Introducing the transport sector in the economy ........................................................ 9

4.1 Market structure in the transport sector ................................................................ 9

4.2 Endogenization of the transport costs under a unique tariff .................................. 10

4.3 Endogenization of the transport costs under segmentation ................................... 11

4.3.1 Redefining economic variables under a segmented transport sector ............... 12

5 Comparing regulatory regimes .................................................................................... 13

5.1 Transport liberalization under symmetric tariffs ..................................................... 13

5.2 Complete deregulation ........................................................................................... 16

5.2.1 Global welfare comparisons .............................................................................. 17

6 Concluding remarks ..................................................................................................... 18

References ........................................................................................................................ 24

List of figures .................................................................................................................... 26

List of tables ..................................................................................................................... 27

i

Abstract

This paper develops a tractable two-region New Economic Geography model with footloose
capital and endogenous freight rates to investigate the welfare implications and long-run
industry reallocation patterns triggered by different types of transport liberalization. Two
policy scenarios are considered: one where a unique tariff per route is imposed, indepen-
dently of the direction of shipment, and one of complete deregulation. Carriers in fully
deregulated transport markets are shown to charge higher markups in shipments towards
the periphery. This pricing behavior counterbalances the welfare-decreasing agglomeration
forces associated with lowering trade costs and ensures welfare gains in both regions in the
short and long run.*

JEL codes: R12 - R32 - L51 - L91

Keywords: Transport liberalization; endogenous transport costs; regional imbalances; Home
Market Effect

*European Commission, Joint Research Centre, Institute for Prospective Technological Studies (IPTS), Sevilla,
Spain. I am grateful to Kristian Behrens, Florian Mayneris, Gianmarco Ottaviano, Pierre Picard, Jacques Thisse,
Kenmei Tsubota and Hylke Vandenbussche for useful comments and suggestions. The opinions expressed are
those of the author only and should not be seen as representative of the European Commission ofﬁcial position.
Neither the European Union institutions and bodies nor any person acting on their behalf may be held responsible
for the use which may be made of the information contained therein.

1

1 Introduction

In the absence of product differentiation, economies of scale and ﬁrm location considerations,
trade costs can be seen as just a source of price distortion, decreasing the welfare for all
market participants by driving prices up and proﬁts down, besides leading to a misallocation
of resources. This consideration has led policy makers to develop an attitude towards
transport costs that can be epitomized as: the cheaper, the better. Lower transport costs
are expected to lead to better integrated markets which in turn trigger improvements in
citizens’ welfare through price reductions due to stronger competition in the ﬁnal products’
market.

But are early welfare improvements meant to last in the long run? Do they depend on
the market structure in the transport sector? And are the resulting gains evenly distributed
across regions? This paper tries to answer these questions in the context of a New Economic
Geography (NEG) framework in which products are differentiated and ﬁrms’ interactions
are described following the monopolistic-competition tradition (Dixit and Stiglitz, 1977;
Krugman, 1991) with the additional feature of an endogenous transport sector where ﬁrms
are also allowed to price discriminate by direction of shipment. NEG models with footloose
capital are typically adopted to draw predictions on the spatial distribution of economic
activities, which then map into location-speciﬁc market outcomes (Martin and Rogers, 1995).
The key underlying idea is that, once ﬁrms are allowed to relocate from one region to the
other to equalize returns on capital investments, market outcomes are affected in both
origin and destination markets because of an alteration in the competitive interactions
between ﬁrms (Fujita, 1988; Gaigné and Behrens, 2006; Ottaviano and Thisse, 2004).

This paper investigates the spatial agglomeration patterns and welfare implications of
a cost-reducing liberalization of the transport sector, with and without the possibility for
carriers to price discriminate by the direction of shipment. Following the intuition of Behrens
et al. (2009), transport costs are not treated as parameters after liberalization, but they
are determined endogenously by proﬁt maximizing carriers providing an undifferentiated
transport service subject to capacity constraints. Two scenarios are analyzed: the ﬁrst one
is a regulated liberalization regime in which prices are ﬁxed per route (or, say, distance),
independently of the direction of the shipment, which follows the modeling strategy of
Behrens et al. (2009). The second is a complete deregulation regime, allowing for price
discrimination based on the direction of the shipment, similarly to Behrens and Picard (2011),
who analyze the case of a transport industry characterized by carriers committing the same
given level of capacity in the two direction of a route and deﬁning a pricing strategy that
allows them to avoid "empties" (the so-called back-haul problem). Differently from Behrens
and Picard (2011), in this paper the carriers are allowed to set up a different level of capacity
in the two directions so as to relax the constraint of an equal amount of quantities shipped
in the two directions, as for example in Takahashi (2011).

The empirical relevance of developing a model where prices and quantities shipped may
vary by direction of shipment in the absence of ad hoc regulation or constraints is warranted
by recent empirical studies. For example, Jonkeren et al. (2011) observe trade imbalances
in quantities shipped in the inland waterway transport market in north-west Europe and
similar ﬁndings are reported by Tanaka and Tsubota (2014) based on micro-level data on
carriers connecting different Japanese prefectures. They also ﬁnd variation in prices based
on the direction of shipment within the same route.

Final goods in the model are supplied in horizontally differentiated varieties produced
by ﬁrms operating in a monopolistic competition framework with variable elasticity of
substitution (Di Comite et al., 2014; Melitz and Ottaviano, 2008) characterized by increasing
returns to scale and a limited amount of market power granted from the assumption that
consumers value variety. Transport costs are assumed linear so as to be able to explicitly
model them as resulting from competitive interactions in the transport sector.

Differently from most NEG literature, in the framework explored in this paper there is
no reversal of the short-run (static) welfare gains in the long run. Similarly to Behrens and
Picard (2011), transport liberalization is shown to increase agglomeration, which affects
welfare negatively, but the gains in terms of lower prices and higher proﬁts more than
compensate the negative impact of agglomeration. The more so in the case of complete
liberalization, which is shown to yield less industrial agglomeration than a symmetric

2

transport cost reduction. The results is driven by the fact that tougher (softer) competition
in the core (peripheral) region’s goods market forces carriers to charge a lower (higher)
price to ﬁrms supplying those markets from the periphery (core), luring some ﬁrms towards
the periphery to enjoy softer competition. One way to interpret this result is to look at the
combined problem of the carriers and variable-elasticity-of-substitution ﬁnal good producers
in terms of double marginalization (Tirole, 1988), where the proﬁts that the two types of
agents can extract from the ﬁnal consumers depend on the toughness of competition in the
downstream market.

The model presented here has relevant policy implications in terms of the impact of
transport liberalization on total welfare and geographical fairness. In terms of total welfare, a
reduction in transport costs is always beneﬁcial, but it comes at the cost of higher disparities
in industrialization between regions. The latter effect can be mitigated by allowing carriers
to price discriminate by direction of shipment, increasing the welfare improvements of
liberalization further. Therefore, a clear policy message stems from the model: a full
liberalization regime not imposing any restrictions on the market segmentation of carriers
seems to be superior to a regulated market with symmetric low tariffs or a liberalization
where carriers are required to charge the same price in the two directions of shipment
of the same route (or to follow any other direction-invariant pricing strategy, such as a
distance-based one).

The paper is organized as follows. In Section 2, the model is developed in the short run.
In Section 3 the relocation of ﬁrms in the long run is described. In Section 4 the transport
sector yielding endogenous freight rates is introduced in the model, under two different
regulatory settings: complete deregulation and unique-bilateral-tariff liberalization. The two
different regulatory regimes are compared in terms of welfare and geographic distribution
of industrial activity in Section 5. Finally, Section 6 concludes.

2 The model

Consider an economy composed of two regions: a more populated core, H, and a less
populated periphery, F (for notational purposes, the two regions are called  and j when
considered in general terms). Consumers exhibit quadratic preferences and the economy
is characterized by two sectors, one displaying constant returns to scale and using one
unit of labor to produce the numeraire, the other exhibiting increasing returns to scale and
using inter-regionally mobile capital and local labor to produce varieties of a differentiated
good. When the differentiated good is produced in  and sold in j, it incurs a linear transport
cost tj, whereas t = 0. The value of tj is initially taken as a parameter (under a regulated
transport sector) and independent of the direction of the shipment (tj = tj = t); then, it is
determined endogenously in the transport sector following two types of liberalization, one
imposing tj = tj, which is called unique-bilateral tariff (or symmetric tariff), and the other
allowing carriers to price discriminate by the direction of shipment, t,j (cid:54)= tj, which is called
complete deregulation (or full liberalization).

Here follows a description of the economy, ﬁrst in the short run and then taking ﬁrm

relocation into account (the long run).

2.1 Consumers

The economy is inhabited by M identical consumers which are exogenously distributed in
the two regions and are endowed with one unit of labor, L, which is geographically immobile,
and one unit of capital, K, which can be invested in either region (so that M = L = K). The
share of people living in region  is expressed by θ, i.e. θH ∈ [ 1
; 1] and θF = 1 − θH, so that
2
the absolute number of consumers living in that region is M = θM. To simplify the notation,
in the rest of the paper whenever a parameter (say, θ, λ) is left without subscript, it refers
by convention to the largest region (say, θH, λH), which can be interpreted as a measure of
demand concentration in the economy. The preferences of each consumer are captured by

3

a standard quadratic utility function (Belleﬂamme et al., 2000; Ottaviano et al., 2002):

(cid:90)

U = α

qs,ds −

s∈N

β

(cid:90)

2

s∈N

q2


(s)ds −

γ

(cid:150)(cid:90)

2

s∈N

(cid:153)2

qs,ds

+ q0,

(1)

Where N ≡ N + Nj is the mass of varieties present in region , each variety being
of negligible size for the market, qs, is the amount of variety s ∈ (0; N] consumed by
each consumer , the parameter α deﬁnes the intensity of preference accorded to the
consumption of the differentiated good, as compared to the homogeneous one, q0, whose
marginal utility is normalized to unity and used as the numeraire of the economy. The
parameters β ∈ (0; ∞) and γ ∈ [0; ∞] determine consumer’s love for variety by capturing
perceived horizontal differentiation of varieties (β) and the degree of substitutability (γ)
between varieties (Di Comite et al., 2014). Consumers are subject to the following budget
constraint:

(cid:90)

(cid:90)

ps,qs,ds +

ps,jqs,jds + q0 = y + ¯q0,

(2)

s∈N

s∈Nj

where ps, and qs, are the price (in terms of the numeraire) and quantities sold of a
variety s of differentiated good bought by a consumer living in the same region as the
producing ﬁrm; ps,j and qs,j are the price and quantities sold of a variety of differentiated
good bought by a consumer living in a region different from the one where the producing ﬁrm
operates; the parameter ¯q0 represents the consumer’s  initial endowment of homogeneous
good (assumed to be large enough to allow the consumer to enjoy any level of consumption
of the differentiated good); ﬁnally, y is consumers’ nominal income earned through the
provision of factors L in region  and K in either one of the two regions, in addition to the
proﬁts redistributed from the transport sector.2

Optimizing Eq. (1) subject to Eq. (2) with respect to qs, leads to the following linear

demand function:

qs,j =

α − ps,j − γQ
β

,

where Q = (cid:82)

s∈N

qs,ds. This can be rewritten as

qs,j =

αβ + γN ¯p
β(β + γN)

−

ps,j
β

,

(3)

where

(cid:82)

s∈N

ps,ds

¯p =

N
is a price index capturing the average price of all the varieties of the differentiated good

sold in region .

2.2 Firms

Turning to the production side of the economy, two factors are used in the production
processes: regionally mobile capital (K) and immobile labor (L). The perfectly competitive
constant-returns-to-scale sector produces the homogeneous numeraire employing only
labor. The monopolistically competitive differentiated manufacturing sector, with single-
product ﬁrms operating under increasing returns to scale, employs both factors, capital in
ﬁxed amounts and labor proportionally to production. Manufacturing ﬁrms’ proﬁt can be
expressed as follows:

s, = (ps, − c)qs,M + (ps,j − c − t)qs,jMj − rƒ ,

(4)

2Notice that since wages are determined in the numeraire producing sector and proﬁts are redistributed to
consumers in the two regions, no differences arise between the two regions in terms of nominal income. The
numeraire is assumed here to be freely traded, as common in NEG models, even if this assumption has been
shown from Picard and Zeng (2005) to have stronger implications than generally thought. Indeed, the presence of
transport costs in the homogeneous goods’ market (which is assumed to be an agricultural good in their case)
turns out to be a rather important dispersion force.

4

where c is the amount of labor needed to produce one unit of the differentiated good, t
is the linear transport cost, taken as exogenous, r is the return on capital invested, and ƒ is
the amount of capital needed to set up a ﬁrm, which can be interpreted as a ﬁxed entry
cost. Plugging Eq. (3) into Eq. (4) the proﬁt function can be rewritten as:

s, = (ps, − c)

(cid:20) αβ − (β + γN)ps, + γN ¯p
β(β + γN)

(cid:21)

M +

+(ps,j − c − t)

(cid:20) αβ − (β + γNj)ps,j + γNj ¯pj
β(β + γNj)

(cid:21)

Mj − rƒ .

(5)

Notice that the total number of ﬁrms in the economy, N = N + Nj, is a function of the
amount of capital in the economy and the ﬁxed entry cost, N = K/ ƒ , but it is split between
the two regions according to the fraction of capital, λ, allocated to each region, so that:

N =

λK
ƒ

; Nj = N − N.

(6)

2.3 Market outcomes in the short run

Manufacturing ﬁrms maximize their proﬁts determining prices independently in the domestic
and the foreign markets. Since regions are not fully integrated (tj > 0) and the extent of
competition varies (captured by price indices), two different prices are likely to emerge for
the same good sold in the two markets. Firms are assumed to be of negligible size and
thus treat price indices as exogenous. Assuming no other source of heterogeneity except
location, four segments can be identiﬁed in the markets: HH and HF for the ﬁrms located in
the core; FF and FH for the ﬁrms located in the periphery.

The proﬁt-maximizing prices chosen by the ﬁrms in region  are:

ps, =

αβ + γN ¯p
2(β + γN)

+

c

2

; ps,j = ps, +

t

2

=

αβ + γN ¯p
2(β + γN)

+

c

2

+

t

2

,

(7)

Goods’ prices rise as consumers’ bias toward the consumption of differentiated goods (α),
marginal costs (c) or price indices ( ¯p) increase. Product differentiation as well, as captured
by the parameter β (the higher, the more variety in consumption is appreciated) plays an
important role, as can be better understood by developing equation Eq. (7). Indeed, taking
into account that

¯p = P/ N =

(cid:90)

s∈N

ps,
N

ds =

N
N

ps, +

Nj
N

ps,j = ps, +

Nj
N

t

2

= ps, + λj

t

2

(8)

and expressing p∗ only in terms of structural parameters (taking λ as a parameter too,

at least in the short run), it can be seen that:

p∗
s,

(t) =

β(α + c) + γN(c + λj

t
2

)

2β + γN

; p∗
s,j

(t) = p∗
s,

+

t

2

.

(9)

From Eq. (9) it can be noticed that as β → 0 (or similarly as γ → ∞) consumers’ love
for variety disappears and p∗
. This is exactly equal to the
s,
marginal cost of production plus a markup component deriving from the acknowledgment
that a share λj of ﬁrms in the market is characterized by higher marginal costs of production
and delivery, c + t, thus affecting the price index and relaxing price competition. In fact,
imported varieties pass-through to their consumers half of the transport costs incurred, t
.
2
Similarly, average prices in market  can be expressed in terms of the structural parame-

→ c + λj
2

→ c + λj
2

t and p∗
j

t + t
2

ters and transport costs:

¯p =

P
N

=

αβ + (c + λjt)(β + γN)
2β + γN

,

(10)

5

which conﬁrms that, as β → 0 (or γ → ∞), then ¯p → c + λjt. This result is explained by
the fact that a share λ of the varieties found in the region has marginal costs equal to c
and a share λj of varieties has marginal costs equal to c + t. The higher marginal costs due
to transport thus hurt consumers through the reduction in manufacturing ﬁrms’ proﬁts and
higher prices, which is a common result in the NEG literature. In particular,

p∗
s,

(t) = ¯p −

t

2

λj

; p∗
j

(t) = ¯p + (1 − λj)

t

2

= ¯p +

t

2

λ,

from which two considerations derive. The ﬁrst is that price differentials between
domestically produced and imported varieties are directly related to the magnitude of
transport costs. The second is that transport costs affect asymmetrically the optimal pricing
of the two varieties. Since λ > λj, importers’ deviation from the average price in region 
(charging a higher price than the average) is higher than domestic ﬁrms’ (charging a lower
price than the average).

Equilibrium prices, as expressed in Eq. (9), could also be plugged into the demand
function Eq. (3), so as to obtain the equilibrium quantities only as a function of structural
parameters:

q∗
s,

(t) =

β(α − c) + γNλj
β(2β + γN)

t
2

; q∗
s,j

(t) = q∗
s,

(t) −

t

2β

.

(11)

As expected, the transport cost, t, enters positively in q∗


and negatively in q∗
j

, but

asymmetrically. Indeed,

∂q∗

∂t

=

λj
2

γN
β(2β + γN)

;

∂q∗
j
∂t

= −

λ
2

β + γN
β(2β + γN)

.

(12)

This means that even if transport costs shift demand towards domestically produced
goods at the expense of imported ones, they create less demand on the domestic segment
than they destroy on the imported one. This implies that the total amount of consumption
in the differentiated sector is reduced and this implies that prices in each region rise for
both segments, as shown in equations Eq. (9) and Eq. (10).

As for the effects of industrial agglomeration, it can be noted that as long as λ > 1
2

, both
prices and quantities are always lower in the bigger region than in the smaller one, when t
is equal in the two directions, because of the larger presence of ﬁrms not incurring transport
costs in the local market. Therefore, tougher competition in the bigger region induced
by lower transport costs beneﬁts consumers in H by raising their real wage (because the
nominal wage is normalized to unity, but goods’ prices are declining). However, the same is
not true for the ﬁrms located in H. Indeed, in the short run the proﬁts of the ﬁrms located in
the periphery increase in their export segment while the proﬁts and market share of the
domestic ﬁrms decrease in the local market.

2.4 Factors' remuneration

As for labor remuneration, since it can be used to produce the two types of good, the
homogeneous under constant returns to scale and the differentiated under increasing
returns to scale, its supply results perfectly elastic at the wage level corresponding to the
value of the homogeneous good. Thus, the resulting wage in nominal terms will be equal in
the two sectors of the two regions.

As for capital, it is taken as ﬁxed in the short run but it becomes mobile in the long
run. This means that, after a shock in transport costs, remuneration can temporarily differ,
but will eventually equalize across the two regions. Its remuneration is directly related to
the operating proﬁts generated by ﬁrms in the two regions. Because capital is the scarce
resource in this economy, ﬁrms’ operating proﬁts are absorbed by its remuneration. This
can be interpreted as the result of a bidding process in which any new entrant ﬁrm, if
incumbents are making proﬁts, has room to offer a slightly higher remuneration to attract
capital, thus leading to ﬁerce competition between ﬁrms to the advantage of capital holders.
As a consequence, as far as there is free entry of enterprises in the differentiated goods’

6

manufacturing market and no heterogeneity across ﬁrms, consolidated proﬁts are equal to
zero and the remuneration of capital in the two regions equate the operating proﬁts:

rs, =

(ps, − c)qs,M + (ps,j − c − t)qs,jMj
ƒ

,

which can be rewritten as

rs, =

M

ƒ β

(cid:2)(ps, − c)2θ + (ps,j − c − t)2θj

(cid:3) .

From this expression, it can be understood where the trade-offs concerning capital
remuneration stem from. Each variety is in fact extracting proﬁts from two segments, the
domestic and the foreign, each having a different number of consumers (θM and θjM),
different marginal costs of production and delivery (c and c + t) and different local price
indices yielding different prices (ps, and ps,j). This explains how, even in the absence of
any technological difference, subsidy or barrier to trade, the two regions can reach very
different levels of industrialization, just on the basis of differences in market size.

3 The long run: industrial agglomeration and regional imbal-

ances

In the long run, capital is free to move between the two regions. Thus, it will ﬂow from one
region to the other until capital holders are indifferent between investing in one region or in
the other, i.e. when r = rj, which can be rewritten as

(cid:148)(p∗
s,

− c)2θ + (p∗
s,j

− c − t)2(1 − θ)(cid:151) = (cid:148)(p∗

s,jj

− c)2(1 − θ) + (p∗
s,j

− c − t)2θ

(cid:151) .

As long as transport costs t are taken as exogenous, it must be noted that this relation
holds only if transport costs are not excessive, i.e. if there is trade between the regions. The
maximum value consistent with the existence of international trade in the two directions,
which can be called ttrde, can be computed as the value which ensures qj in Eq. (11) or,
equivalently, pj in Eq. (9) to be positive. In terms of the structural parameters, it is

ttrde =

β(α − c)
β + γN
2

.

(13)

Focusing on cases in which t (cid:182) ttrde and solving the capital rent equalization equation,
it can be seen that the following relation holds between the agglomeration of consumption
and production:

1

λ −

2β(α − c − t
2
γN t
2
which implies that λ > θ as long as there is trade between the two regions (t < ttrde)
and θ > 1/ 2. This means that the region displaying a higher share of consumption,
θ > 1/ 2, will attract more than proportional quantity of capital and thus ﬁrms, λ > θ. This
phenomenon is called the Home Market Effect (HME).

θ −

(14)

=

2

1

2

(cid:18)

(cid:19)

)

,

Furthermore, it can be noted that ∂λ
∂t

< 0 when θ > 1/ 2, this meaning that lower
transport costs, when t is equal in the two directions, always lead to a higher degree of
industrial concentration in the regions with the highest level of consumption.

The magnitude of the effect is inversely related to the level of transport costs in the
two directions, so that a decrease in transport costs is bound to result into more industrial
concentration in the core (θ > 1/ 2) and intensify the HME.

The interaction between θ and t in determining the equilibrium agglomeration of eco-
nomic activities is illustrated in the simulation in Figure 1, where the lowest possible level of
trade costs (interpretable as the marginal cost of providing the transport service), τ has
been normalized to unity (which is the prevailing remuneration for labor in the economy) and
the other structural parameters have been chosen respecting the restrictions on variable

7

domains.3 Each line represents a different level of concentration of consumption in the
core (H) region, θH. It can be observed, for instance, that even low levels of consumption
concentration, θH = 0, 53, associated with very low transport costs, can lead to a complete
agglomeration of economic activities in the core.

INSERT FIGURE 1 HERE.

3.1 Industrial concentration and market outcomes

Looking at price, quantity and proﬁt equations Eq. (9), Eq. (11) and Eq. (5) it can be noted
that all the relevant market outcomes are affected by the level of industrial concentration, λ.
Before turning to the impact of changes in freight rates on the consumers, it can be useful
to sum up how industrial concentration, λ affects equilibrium prices and quantities, holding
transport costs ﬁxed (as could result for example from an exogenous shock in the relative
concentration of consumption, θ), in Table 1.

Table 1: Core and periphery effects of marginal changes in industrial agglomeration (λ) on market
outcomes.

Market
outcomes

HH variety

FH variety

HF variety

FF variety

impact of (cid:37) λ impact of (cid:37) λ impact of (cid:37) λ impact of (cid:37) λ

n

q

p

(cid:37)

(cid:38)

(cid:38)

(cid:38)

(cid:38)

(cid:38)

(cid:37)

(cid:37)

(cid:37)

(cid:38)

(cid:37)

(cid:37)

Summing up, while the number of varieties and the quantity per variety produced in F
and sold in H decrease, the number of varieties and the quantity per variety produced in
H and sold in F rise. But what will then be the overall effect on international trade? The
answer is not a priori clear, as it depends on transport costs and structural parameters in a
complex way. The two directional ﬂows of total trade ﬂows move asymmetrically in opposite
directions, i.e. QFH monotonically decreases in λ whereas QHF increases. The total volume
of inter-regional trade in the two directions is determined by three elements: the number of
people living in the importing region, M,the individual consumption of each imported variety
qs,j and the number of ﬁrms in the exporting region, Nj. Formally, it is Qj = λNjθjMjqj
which, plugging Eq. (11), can be written in terms of speciﬁc regional ﬂows as

QHF(t) = λN(1 − θ)MqHF =

λN(1 − θ)M

(cid:20)

β(2β + γN)

(α − c)β −

(2β + γ(1 − λ)N)

(cid:21)

t

2

and

QFH(t) = (1 − λ)NθMqFH =

(1 − λ)NθM

(cid:20)

β(2β + γN)

(α − c)β −

(2β + γλN)

(cid:21)

.

t

2

Therefore,

∂QHF
∂λ

(cid:190) 0 and ∂QFH
∂λ

< 0 ∀ feasible t (i.e. t < ttrde as deﬁned in equation Eq. (13)).

3For example, β should be bigger than γ for the own substitution effect to be larger than the cross substitution

effect.

8

This means that an increase in industrial agglomeration increases the shipments from
the core to the peripheral region and decreases them from the periphery towards the
core. The overall effect can be seen by combining the trade ﬂows in the two directions,
Q(t) = QHF(t) + QFH(t), which can be written explicitly as

Q(t) = NM

(α − c)β(θHλF + θFλH) − t (cid:148)λHλFγ N
2

(θH + θF) + β(θHλF + θFλH)(cid:151)

β(2β + γN)

.

(15)

Notice that the effect is always positive, for every feasible level of inter-regional transport

costs. Formally

∂Q(t)

∂λ

> 0 ∀t < ttrde.

4 Introducing the transport sector in the economy

Up to this point, the transport cost t in the model has been treated as an exogenous
parameter, shaping market outcomes in the differentiated good sector and the location
choice of ﬁrms. From now on, a transport sector is introduced in the economy, turning the
exogenously given transport costs into endogenously determined freight rates, similarly
to Behrens et al. (2009) and Behrens and Picard (2011). This analysis then feeds into the
next Section, whose focus is on how freight rates affect market outcomes and shape the
economic geography of the regions. Two different regulatory regimes for the transport
sector are considered, each one corresponding to a different type of liberalization:

(cid:136) First, the case is considered of a transport sector in which carriers are allowed only
to charge the same price per route or, equivalently, to set the tariff based only on
distance and not on the direction of the shipment. This is referred to as the unique-
bilateral-tariff liberalization, or just symmetric freight rates;

(cid:136) Second, the case is considered of a transport in which carriers are left free to set their
prices freely and possibly segment their market based on the direction of the shipment
(which is the only source of heterogeneity among their clients). This is referred to as
complete deregulation, or full liberalization.

The central difference between the two regimes is, thus, the possibility of segmenting
the transport market into HF and FH sub-markets, shipping different amounts of goods for
different rates.

Regulators are also allowed to determine the intensity of competition in the transport
sector by choosing the number of carriers in the market.
It is important to notice that
differences between the two regulatory regimes hold as long as the number of carriers is
small. When the number of competitors increases in the transport sector and competition
intensiﬁes, prices converge to the marginal costs of production in the two regimes.

4.1 Market structure in the transport sector

There are several dimensions over which carriers can differentiate their service, both
vertically (speed, punctuality, traceability and so on) or horizontally (specializing in particular
sector of the economy or geographical areas). Yet, none of this would be conceivable in an
economy characterized by identical consumers and identical ﬁrms producing a continuum
of horizontally differentiated varieties of the same good in four segments, whose only
distinctive features are the regions of production and sale. Following this consideration,
the transport sector is modeled in a more classical way, treating the transport service
as homogeneous in a standard oligopoly framework, in which a ﬁxed number of ﬁrms, k,
compete in quantities or, equivalently, compete in prices after having committed to a certain
capacity (Vives, 1999) per destination of shipment. This market structure is convenient in
terms of analytical tractability, as the only decision available to regulators to shape the
market outcomes is to decide the numbers of competitors to allow in the transport sector.4

4For simplicity, without loss of generality, the number of ﬁrms in the transport sector is chosen by the regulator.
In alternative, the amount of ﬁxed entry costs could be decided by the regulator and indirectly determines the
number of carriers associated with a sufﬁcient level of proﬁts to cover the ﬁxed costs.

9

Behrens and Picard (2011) as well model the transport service as homogeneous and
produced under constant returns to scale, but they model the market interactions as
perfectly competitive with freight rates equal to the costs of a round-trip. In contrast, the
oligopolistic structure suggested here allows ﬁrms to retain some market power and charge
a markup which can be used to repay the ﬁxed costs of entry into the transport sector if
the regulator sets the number of competitors by issuing licenses (or simply redistributed to
consumers if no ﬁxed cost is involved and the number of carriers is chosen exogenously).
The advantage of the approach followed here is that, while it can also generate a perfectly
competitive framework by setting the number of competitors arbitrarily high, it still leaves
one degree of freedom to regulators (the number of competitors to allow in the market or
equivalently the ﬁxed entry costs) to compare different policy options.

The other difference with respect to Behrens and Picard (2011) concerns the constraint
on carriers’ capacity, which is not assumed here to be the same in the two directions of
shipment, thus relaxing the back-haul problem. Even though the cargo space may be the
same in the two directions, indeed, additional ﬁxed costs have to be incurred to ship the
goods from and to a speciﬁc destination (as for example the personnel devoted to deal with
import procedures, or the stocking facilities, or any kind of regulatory asymmetries in the
exporting and importing region).5 As for the marginal costs associated with the shipment, it
may be argued that the route-speciﬁc part (such as fuel consumption), when considered
per unit of good transported, may be much less relevant than direction-speciﬁc marginal
costs such as insurance, so that the cost of returning half-empty or not completely full in
the return trip can be assumed negligible. This assumption can be found also in the spatial
competition model of Anderson and Wilson (2008).

It has been remarked that the relevance of route-speciﬁc costs depends on the goods
shipped. As noted by Hummels (2007), shipping the same volumes of coal or computer
microchips would result in a different relative importance of insurance over other types of
costs. Hence, depending on the types of goods that are shipped over a given route, different
sets of assumptions may be more appropriate. The set of assumptions used in this paper are
notably consistent with the shipment of goods with high value added per unit of weight. In
addition the assumptions on direction-speciﬁc capacity and a ﬁnite number of carriers allow
the model to be consistent with the observed shipment patterns of asymemtric volumes
and prices. In fact, as noted by Behrens and Picard (2011) "about 60% of the containers
shipped from Asia to North America in 2005 came back empty, and those that did come
back full were often transported at a steep discount for lack of demand".

4.2 Endogenization of the transport costs under a unique tariff

Assuming that all the carriers have the same marginal costs of shipment, after having
committed to a given direction-speciﬁc capacity, the operating proﬁt function determining
the kth carrier’s behavior resulting from the market structure adopted for the transport
sector can be written as

k,j = (tj − τ)qk,j,

(16)

where t is the freight rate, τ is the marginal cost of transport and qk,j represents the
quantity of goods delivered by each carrier, qk,j = Qj/ k . Notice that the expression
capturing the total amount of international trade, as computed in equation Eq. (15), can
now be seen as the demand function associated with the transport sector. It is well behaved
in the sense that it linearly decreases in the parameter of interest, the freight rate t, so
that the carriers’ problem is well deﬁned and yields an interior solution: as the price of the
transport service rises, the imported goods become more expensive and the inter-regional
trade ﬂows decline. The elasticity of international trade to transport costs is positive and

5Notice that a preliminary commitment plays also in their own interest, as it allows carriers to compete in
quantities, ï¿‰ la Cournot, rather than in prices, ï¿‰ la Bertrand, as discussed by Vives (1999). For an analysis of
how carriers can investments in different technologies to adapt their cost structure to demand see Kleinert and
Spies (2011).

10

increasing in t:6

εQt = −

∂Q

Q

·

t

∂t

≡ −

∂Q

∂t

·

t

Q

⇒ εQt =

t[θλj(2β + γNλ) + θjλ(2β + γNλj)]
2(α − c)β(θλj + θjλ) − t[θλj(2β + γNλ) + θjλ(2β + γNλj)]

,

where εQt ∈ [0; +∞] ∀ t ∈ [0; ttrde]. A visual representation of the carrier’s problem
is provided in Figure 2, where it can be observed that the problem of the carriers closely
resembles the problem of suppliers of an intermediate input in the context of a double
marginalization setting (Tirole, 1988).

INSERT FIGURE 2 HERE.

In order to solve analytically the carrier’s problem, it is convenient to express the freight
rate, t , in terms of the inter-regional ﬂow of goods, given by Eq. (15), and then maximize
proﬁt function Eq. (16) with respect to total quantities shipped. The inverse demand for
inter-regional transport is then

t(Q) =

(α − c)β(θλj + θjλ) − Q β(2β+γN)
λλjγ N
(θ + θj) + β(θλj + θjλ)
2

NM

and the resulting optimization problem of each carrier results in the pricing function

t∗ =

k

k + 1

τ +

2(α − c)β

(cid:20)

(k + 1)

θλj
(θλj + θjλ)

(2β + γNλ) +

θjλ
(θλj + θjλ)

(2β + γNλj)

(cid:21)−1

.

(17)

This expression has the advantage of being fairly ﬂexible in terms of market outcomes. In
fact, t∗ declines as the number of competitors, k, increases. Ranging from k = 1 to k → ∞,
freight rates can be as high as standard monopoly pricing or as low as perfect competition
pricing (t∗ → τ). Regulators can thus indirectly determine the resulting price in the transport
sector by just setting the number of competitors. The impact of consumption concentration
and competition on equilibrium freight rates is illustrated with a simulation Figure 3.7

INSERT FIGURE 3 HERE.

4.3 Endogenization of the transport costs under segmentation

In a completely deregulated regime, proﬁt-maximizing carriers are expected to segment
their markets because all the conditions for segmenting are satisﬁed: their revenues will be
higher, consumer screening is costless and arbitrage between consumers (ﬁrms involved in
inter-regional trade, in this case) is not proﬁtable.

The ﬁrst condition can be inferred by the analysis of the elasticities of trade ﬂow to the
freight rate in the two segments. Since the elasticity in the segment from F to H can be
shown to be higher than the one from H to F, applying the same price to both segments
would imply too high prices in the former segment and too low price in the latter, which
would not be proﬁt-maximizing in the short run.8

6The analysis of the elasticity is rather convenient too in the study of monopolies and oligopolies. Indeed, the
multiplicative inverse of the price elasticity equals exactly the relative mark-up that a pure monopolist will charge
in the market. This result is easily generalizable to oligopolists by simply dividing this value by the number of
competitors. For example, in the case here analyzed, it would hold the following relationship:

t∗ − τ

t∗

=

1

k

·

1

εQt

7The equilibrium outcomes are shown in terms of simulation because the explicit analytical solution for the

freight rates would be analytically intractable.

8An interesting result is that in the long run, after ﬁrms relocate due to the carriers pricing strategy, the proﬁts of
the carriers turn out to be lower when they segment the transport markets as compared to imposing a symmetric
tariff, but it would probably not be reasonable to expect that each carrier takes into account the aggregate
relocation patterns of manufacturing ﬁrms when setting its freight rate on an individual shipment.

11

The second condition holds because the key characteristic for segmentation is impossible
to hide, since the very purchase of the transport service in one region rather than the other
gives information about the segment which is being served.9

Finally arbitrage can be excluded, as the third condition states, because it is never
proﬁtable to carry it out as can be argued from the following relationship, based on equations
Eq. (9) deﬁning equilibrium prices:

p∗
FF

− p∗
HH

=

t

2

·

γN(λH − λF)
(2β + γN)

< t.

This means that no third agent could make proﬁts out of buying a good in one region and

reselling it in the other one, as long as some transport service has to be purchased.

4.3.1 Redefining economic variables under a segmented transport sector

Under transport market segmentation, equilibrium price and quantity equation have to be
rewritten to take into account the direction of shipment:

ps,(tj) =

αβ + c(β + γN) + γNλj
2β + γN

tj
2

; ps,j(tj) = ps, +

tj
2

,

qs,(tj) =

(α − c)β + γNλj
β(2β + γN)

tj
2

; qs,j(tj) = qs,(tj) −

tj
2β

(18)

(19)

Carriers’ maximize their proﬁts in each segment of shipment, i.e. each Qj(tj) is consid-
ered individually. The sum of these two regional components determines the aggregate
inter-regional trade ﬂow:

where, for each region, exports to the other can be expressed as

Q = QHF(tHF) + QFH(tFH),

Qj(tj) = λNθjMqj =

λNθjM
β(2β + γN)

(cid:20)

(α − c)β −

(2β + γλjN)

(cid:21)

tj
2

(20)

This means that the transport services offered in the two segments are now traded in
different markets, each one characterized by a speciﬁc elasticity of inter-regional trade
ﬂows to transport cost:

εQjtj = tj

(2β + γλjN)
2(α − c)β − tj(2β + γλjN)

(21)

which are both increasing in the freight rate and in λ, but since λ = 1 − λj the trade
elasticity in the two regions move in opposite directions as industrial concentration increases.
Indeed it can be veriﬁed that

∂εQjtj
∂λ

> 0 ;

∂εQjtj
∂λj

< 0.

From Eq. (20) it is then possible to derive the inverse demand function in each region:

tj =

1

(cid:20)

2β + γλjN

2(α − c)β −

β(2β + γN)

λNθjM

(cid:21)

Qj

Then, plugging them into equation Eq. (16) and optimizing with respect to quantities,

the prevailing freight rates on the two segments become

tj =

k

k + 1

τ +

2(α − c)β

(k + 1)(2β + γλjN)

(22)

9It can also be noted that the assumption of identical ﬁrms (or, at least, technologies of production) rules out
the possibility of alternative, cheaper ways of getting from one region to the other: if even one ﬁrm were able to
deliver its products to the other region in a cheaper way, indeed, all the other ﬁrms would be also able to, leaving
no room for the existence of a speciﬁc transport sector.

12

This direction-speciﬁc differentiated freight rate can be compared with the equation in
Eq. (17), which describes the freight rate carriers would choose for the transport service
if not allowed to price discriminate. It can be noticed that their second term displays the
same numerator, but the denominator, which is the part in square brackets in Eq. (17), is
the weighted average sum of the value of the denominator in Eq. (22) in the two directions
of shipment. Given the higher elasticity of demand in the core region because of the price
pressure imposed by the presence of a higher number of varieties in the market not being
subject to transport costs, transport from the smaller to the bigger region will be cheaper
than under the unique tariff, but transport from the bigger to the smaller would be more
expensive in the short run:

tFH < t∗ < tHF.

(23)

A long-run simulation of equilibrium freight rates in the two directions of shipment is pre-
sented in Figure 4, showing that this short-run relation need not hold after capital relocation
in taken into account. Even if tFH < tHF is always true, the different levels of λ associated
with different liberalization regimes, for a given level of competition in the transport sector
(as approximated by the number of carriers), imply that it is possible that tFH < tHF < t if
the agglomeration patterns induced by the symmetric tariffs are much stronger than those
induced by asymmetric tariffs. This is shown in Figure 5, where equilibrium freight rates
in the long run are simulated for a monopolist carrier (k = 1) and for an oligopoly of ten
carriers (k = 10).

INSERT FIGURES 4 AND 5 HERE.

Further simulations are shown in the next Section to study the impact on welfare and

spatial agglomeration patterns of transport regime’s changes.

5 Comparing regulatory regimes

In this section, the two types of liberalization are considered. The starting point is an
economy with high, symmetric transport costs before regulatory intervention. The two
policy options are compared in a sequential way. First, the transition from an expensive
and heavily regulated framework to a unique-bilateral-tariff liberalization is considered, as
captured by an increase in the number of carriers. Then, the additional effect of allowing
carriers to price discriminate by the direction of shipment is explored. The two regimes
yield different results as long as the number of carriers is ﬁnite, but converge to the same
outcomes (pricing to marginal costs) as the number of carriers increase.

5.1 Transport liberalization under symmetric tariffs

The focus of the welfare analysis is on the effects of transport liberalization on prices,
quantities and industrial agglomeration in the differentiated good sector.

Prices and quantities

As for prices, equation Eq. (9) implies that prices of the differentiated goods decrease
together with transport costs in the short run, but with different intensities in the different
segments. Looking at the ﬁrst derivatives of Eq. (9) (or, equivalently, Eq. (18)) with respect
to t, it sufﬁces to remind that λH > λF to see that

∂pHF
∂t

>

∂pFH
∂t

>

∂pFF
∂t

>

∂pHH
∂t

> 0.

(24)

A reduction in transport costs thus affects all manufacturing ﬁrms in the economy, but
while in the domestic segment ﬁrms located in the peripheral region (F) are more affected
than those in the core region (H), the opposite is true in the export segments. From a

13

consumers’ standpoint this means also that prices in F will decrease more than prices in H:
this is a consequence of the higher share of imported varieties in the smaller market:

∂ ¯pF
∂t

>

∂ ¯pH
∂t

,

which implies higher consumer surplus gains in the periphery than in the core in the
short run, with the overall impact in the long run depending on the extent of agglomeration
after the liberalization.

As for the quantities, Eq. (12) ensures that in the short run

and

∂qHH
∂t

∂qFF
∂t

> 0 ;

∂qFH
∂t

< 0

> 0 ;

∂qHF
∂t

< 0.

Note that, interestingly, movements in opposite directions have been found also as a
consequence of changes λ. However there is an important difference between the effects
of variations in the parameters t and λ: the latter, in fact, implies a zero-sum transfer of
quantities sold, i.e. a perfectly balanced and symmetric variation. However, this is not the
case for transport costs, whose variation yields

(cid:12)
(cid:12)
(cid:12)
(cid:12)

∂q
∂t

(cid:12)
(cid:12)
(cid:12)
(cid:12)

<

(cid:12)
(cid:12)
(cid:12)
(cid:12)

∂qj
∂t

(cid:12)
(cid:12)
(cid:12)
(cid:12)

.

(25)

Since there are no attribute or technological differences between varieties produced in
region  and j and the marginal rate of substitution between all the varieties is the same, the
price and quantity wedges between otherwise equivalent varieties for the consumer can be
interpreted as a distortion if they result from transport market regulation or the exertion
of market power from carriers. Therefore, equations Eq. (25) and Eq. (24) show how a
reduction of transport costs is expected to unambiguously improve welfare in the short run.

Agglomeration and Manufacturing firms' Operating Profits

As for the agglomeration of economic activities, it can be seen from equation Eq. (14) that
a reduction in transport costs implies a magniﬁcation of the disparities in the long run,

∂λH
∂t

< 0,

This reallocation of resources is triggered by a disproportionate impact of changes in t
on the ﬁrms based in the smaller region. It may appear counterintuitive, as ﬁrms in the
peripheral region have to incur lower transport costs to serve customers in the other region.
However, this effect has to be traded off against tougher competition coming from the
ﬁrms located in the core region, which now have easier access to the peripheral markets.
Equation Eq. (14) is derived from the equalization of capital remuneration across the two
regions and it signals that proﬁts of ﬁrms located in the smaller region are affected more
severely than those in the bigger region from the intensiﬁcation of competition due to lower
transport costs, so as to lead a higher share of region F’s capital to ﬂow toward H and a
higher relative number of varieties produced there.

For ease of comparison with the effect changes in agglomeration, shown in Table 1, a
summary of the short-run impacts of an increase in transport costs on the number of ﬁrms
producing each variety and their equilibrium prices and quantities are displayed in Table 2
for the four segments.

14

Table 2: Core and periphery effects of marginal changes in transport costs.

Market
outcomes

HH variety
impact of (cid:37) t

FH variety
impact of (cid:37) t

HF variety
impact of (cid:37) t

FF variety
impact of (cid:37) t

n

q

p

(cid:38)

(cid:37)

(cid:37)

(cid:37)

(cid:38)

(cid:37)

(cid:38)

(cid:38)

(cid:37)

(cid:37)

(cid:37)

(cid:37)

Global welfare

The analysis above shows how, at least in the short run, transport liberalization (as any
other shock or policy whose result is to reduce the transport costs) is welfare improving for
the entire economy. The result is mainly driven by the evolution of prices, which fall in all
the four segments of the differentiated goods’ sector, as the transport costs fall.

The indirect utility function stemming from Eq. (1) can be expressed as a function of

prices and income,

W =

α2N
2(β + γN)

−

α

(cid:90)

β + γN

s∈N

ps,ds +

(cid:82)

s∈N

p2
s,

ds

2β

−

γ

(cid:150)(cid:90)

2β(β + γN)

s∈N

(cid:153)2

ps,ds

+ y + q0,

(26)

which shows that, ceteris paribus, the more a variety is consumed, the higher the welfare

gained from a reduction in its price:

∂W
∂ps,

= −

αβ − (β + γN)ps, + γN ¯p
β(β + γN)

= −qs,j < 0.

An important remark is that the distribution of economic activities gets more unbalanced
while global welfare rises, which creates a clear trade-off for policy makers. Nonetheless,
welfare improvements in the de-industrializing region, F, are stronger than in the bigger
region, because price reductions are more intense. However, from Eq. (8) it can be seen that,
when t is identical in the two directions of trade, F dwellers could never catch up entirely
with the welfare level of consumers living in H, in the absence of proper redistribution
mechanisms.

Simulations show that in the long run the welfare gains realized in the short run are not
reversed under a wide range of parameter combinations.10 The increase in agglomeration
does affect welfare negatively in itself and lower the level of redistributed proﬁts form
carriers, but these are second-order effect as compared to the ﬁrst-order effect of lower
prices (price indices decrease in both regions) and higher proﬁts in the manufacturing sector
(because of higher markups in the inter-regional shipments) caused by the decrease in
transport costs.

10Welfare losses can be observed in the long run only when the number of ﬁrms approaches the number of
consumers, i.e. when the ﬁxed costs of setting up a ﬁrm are very low. However, the effect is entirely driven by the
redistribution of proﬁts to consumers and not by the consumer surplus as captured by prices, but the quadratic
utility framework is not the best suited to capture income effects because of the assumption of a large enough
endowment of numeraire to satisfy any level of consumption, so it would be fair to say that the most robust results
in this framework are the ones related to consumer surplus.

15

5.2 Complete deregulation

The analysis of full deregulation leads to qualitatively similar but quantitatively different
conclusions. The departure from the symmetric transport cost towards a direction-speciﬁc
pricing implies that unique-bilateral-tariff liberalization and full deregulation have different
impacts on regional prices. In particular, the symmetric outcome shown in equation Eq.
(17) is the weighted average for the two regions of equation Eq. (22), where weights are
represented by the relative number of ﬁrms and consumers. Therefore, moving from a
unique-bilateral-tariff liberalization to full deregulation, transport prices in the two directions
move in opposite directions, counteracting the agglomeration effect due to lower freight
rates.

Prices and quantities

The regional differentials on prices in the short run can be easily deducted by using equation
Eq. (18), keeping in mind the impact on prices in the two directions shown in Eq. (23):

and

pS

HH

< pHH ; pS
FH

< pFH

pS
FF

> pFF

; pS
HF

> pHF,

where S stands for market outcomes after carriers are allowed to segment the transport
market. What is worth noting is that prices increase for consumers in the smaller region for
both domestic and imported goods. The opposite holds for consumers in the bigger region.
This results in price indices diverging further:

¯pS
H

(tFH) < ¯pH(t)

;

¯pS
F

(tHF) > ¯pF(t).

This effect reinforces the relation noted in Eq. (8) and yields

¯pS
H

(tFH) < ¯pH(t) < ¯pF(t) < ¯pS
F

(tHF) .

Therefore, in the short run, segmentation is expected to increase the gap in prices
between the two regions as compared to a unique tariff in the two directions. Interestingly,
this result is reverted in the long run, due to the restraint in agglomeration due to asymmetric
tariff, which keeps more ﬁrms in the peripheral region (for the same level of competition in
the transport sector) and thus reduces the share of varieties in the periphery that have to
incur transport costs to be consumed.

As for quantities, the impact of segmentation in the short run can be seen from equation

Eq. (19), taking into account the effect on prices shown in Eq. (23):

and

qS

HH

< qHH ; qS
FH

> qFH

qS
FF

> qFF

; qS
HF

< qHF.

Hence, once carriers are allowed to segment the transport market, each variety produced
by the ﬁrms located in region F would sell more than under symmetric tariffs in the short run,
both in the local (because freight rates from the core are higher) and the export segments
(because shipping goods from the periphery to the core is cheaper). The opposite is true
of the ﬁrms located in H. Hence, compared to a unique-bilateral tariff, in the short run
complete deregulation implies higher levels of production in F and higher employment in
the manufacturing sector. In addition, given the higher level of domestic prices, complete
deregulation engender higher proﬁts in the short run to the ﬁrms located in F, as compared
to a unique-bilateral tariff. This latter effect plays against agglomeration and yields the
following result. This result holds only partly in the long run. After also relocation of ﬁrms is
taken into account, indeed, simulations show that quantities on the inter-regional export
segment are higher under asymmetric tariffs than under symmetric tariffs, but the opposite
is true for the domestic segment in the periphery, whose sales are lower.

16

Agglomeration and Manufacturing Firms' Operating Profits

In terms of agglomeration, due to the analytical intractability resulting from the feedback
loop of transport costs and agglomeration, the most suitable way to compare a unique-
bilateral-tariff liberalization regime with complete deregulation is through simulations. Once
carriers are allowed to price discriminate by the direction of shipment, equation Eq. (14)
must be generalized to allow for the possibility of segmentation. The agglomeration patterns
as a function of transport costs and structural parameters can thus be computed as

,

j

β

2

1

(cid:33)

(cid:33)

+

=

γN

γN

λ −

θt2

2β(α − c)

(cid:32) θjt2
j
θt2

− θt2
j
j + θjt2

(cid:32) θtj − θjtj
j + θjt2
where capital remuneration in the two regions is now expressed in terms of two different
freight rates and the changes in proﬁtability of ﬁrms in the two regions depend on structural
parameters and levels of concentration of consumption, θ, in a highly non-linear way. It
should be noted that replacing tj and tj with t, equation Eq. (27) turns into Eq. (14).
Thus, intuitively, it can be argued that, since the only difference between Eq. (27) and
Eq. (14) is transport segmentation and transport costs in the two directions follow the
ranking shown in equation Eq. (23) for a given level of λ, then agglomeration should be
restrained by the possibility of transport market segmentation. Simulations show that this
intuition is correct, as shown in Figure 7, which should be compared to 6, where exactly the
same structural parameters, levels of consumption concentration and number of carriers are
used as inputs of the simulation, the only difference being the transport liberalization regime.

(27)

j

INSERT FIGURES 6 AND 7 HERE.

The simulation conﬁrms the intuition that transport market segmentation, as opposed to
a symmetric tariff, makes the core region less attractive for ﬁrms because it increases the
costs of shipping their products to the periphery and, at the same time, makes it cheaper to
produce goods in the periphery and ship them to the core. This result is robust to different
structural parameters and number of competitors in the transport sector.

5.2.1 Global welfare comparisons

As in the case of symmetric tariffs, transport liberalization increases welfare under a com-
plete deregulation regime because of the impact on prices in the two regions. In order
to compare the two liberalization regimes in terms of welfare, a simulation has been per-
formed, whose results are shown in Figure 8 for a given level of consumption concentration,
θ. The simulation is based on equation Eq. (26), where y includes the proﬁts redistributed
from manufaturing ﬁrms and carriers (assuming they are evenly distributed across all the
consumers in the economy). Welfare levels under a complete deregulation are plotted in
black for the two regions and for the overall economy (weighing the welfare level of each re-
gion by its share of consumers); they are plotted in gray for the unique-bilateral-tariff regime.

INSERT FIGURE 8.

Complete liberalization is shown to yield higher levels of welfare in the two regions as
compared to a liberalization regime imposing a unique tariff per route. A welfare analysis
based on consumer surplus alone shows that the ranking of liberalization regimes is robust
to changes in the structural parameters.11

11A caveat is due on the welfare impact of the extent of competition in the transport sector when also proﬁt
redistribution is taken into account. In fact, when the number of manufacturing ﬁrms increase as compared to the
number of consumers (for example, by altering the ﬁxed amount of capital needed to set up a ﬁrm, ƒ ) unreported
simulations show that intermediate levels of competition in the transport sector may be welfare superior to high
levels of competition. This result is driven by the income effect of higher levels of competition in the ﬁnal goods
sector (causing reduction in returns on capital in the economy) that generate welfare losses in the peripheral
region only partly compensated by the gains from lower prices. At the limit, when there are as many ﬁrms as
consumers (ƒ = 1), any reduction in transport costs decreases welfare instead of increasing it. However, when the
analysis of welfare is restricted to consumer surplus because income effects are not easily captured in a standard
quadratic utility setting and cannot properly take into account of general equilibrium feedback effects.

17

There is an important implication stemming from the welfare comparison of transport lib-
eralization regimes. Since asymmetric tariffs are shown to be welfare superior to symmetric
tariffs, any policy aimed at reducing transport costs should keep in mind that a decentralized
market-driven reduction in transport costs (which can be obtained by regulating only the
number of entrants in the market) is to be preferred to an exogenous reduction in transport
costs, as can be obtained for example by keeping the transport sector highly regulated
and decreasing the tariffs. In order to be optimal, a reduction in transport costs that does
not result from a complete liberalization should indeed apply different prices in the two
directions of the same route depending on the elasticities of inter-regional export demand
to transport costs, but that means that the regulated sector should mimic the decentralized
market behavior. So it may be arguably more efﬁcient to allow carriers to set the prices
maximizing their proﬁts per segment of shipment, subject to an entry fee. This solution
ensures that, while in equilibrium the carriers’ proﬁts are redistributed to the public, their
pricing strategies result in direction-speciﬁc freight rates that increase welfare and restrain
agglomeration in the core region.

One ﬁnal remark on the impact of agglomeration on total welfare of the economy is due.
As often discussed in NEG models, agglomeration may be inefﬁcient in terms of welfare
In the particular framework
and turn static welfare gains into dynamic welfare losses.
studied in this paper, this has been shown not to be the case, even if the negative impact of
agglomeration on welfare is conﬁrmed. In Figure 9 is shown how the exogenous distribution
of consumption affects the level of welfare that can be attained in the two regions. On the
left pane is shown the case of a monopolist carrier and on the right pane a more competitive
transport sector. On the one hand, it can be noticed that when carriers can segment the
transport sector (black lines) the overall negative impact of consumption concentration on
welfare is the result of an improvement in the core region more than compensated by a loss
in the periphery, even if the weight of the welfare level in the core increases with θ. On the
other hand, when a symmetric tariff is imposed (gray lines), high levels of concentration in
consumption cause losses in both the core and the periphery, which signals a very inefﬁcient
level of agglomeration.

INSERT FIGURE 9.

6 Concluding remarks

In this paper, a New Economic Geography model has been presented where the only
source of heterogeneity across varieties is the location of producers and consumers. Goods
produced in one region and shipped to another have to incur transport costs, which are ﬁrst
assumed exogenous and treated as a parameter and then endogenized and obtained as the
market outcome of a decentralized transport sector. Through the endogenization of freight
rates in the model, it has been possible to study the welfare impacts of different transport
liberalization regimes and the corresponding location patterns of the economic activity. Two
liberalization policies have been analyzed, the ﬁrst one imposing symmetric tariffs the two
directions of a route, the second one leaving carriers free to price discriminate. Notably,
the former type of liberalization is equivalent to an exogenous reduction in transport costs,
whereas the latter describes a competitive behavior, under given market conditions.

The model shows that transport liberalization is indeed expected to yield static and
dynamic welfare gains for consumers of the entire economy under rather general conditions,
with complete deregulation being superior to a symmetric reduction in transport costs in
terms of both welfare and geographical dispersion of economic activities. The result is
not trivial because, whereas gains are clear in the short run due to cheaper inter-regional
connections inducing tougher competition in the manufacturing sector, in the long run the
relocation of economic activities due to the liberalization may be inefﬁcient in terms of
welfare, making the overall impact in the two regions’ welfare not a priori clear. In fact, in
the long run the concentration of economic activities in the larger region compounds welfare
gains in the core and partially offsets them in the periphery. However, also the peripheral
region has been shown to experience net welfare gains in the long run.

Finally, two remarks in terms of policy relevance are in order. First of all, in the present

18

model only interactions between manufacturing and transport sectors have been analyzed,
thus nothing can be easily inferred about transport liberalization processes affecting com-
muters or travelers. Second, the implicit simplifying assumption on which this work has
relied is that the most direct effect of liberalizations is to reduce prices. This is not always
true, but this does not invalidate the underlying analysis, which can be extended to different
types of shocks affecting trade costs. The framework presented here can indeed be applied
to other sources of change in trade costs, such as the efﬁciency gains in transport derived
from technological improvement or, conversely, the inefﬁciencies generated by higher
marginal costs of delivery (for example, trade tariffs, port fees, fuel price and so on). Of
course, when extending this framework to other contexts it should be veriﬁed that the
main modeling assumptions be relevant, such as the oligopolistic market structure or the
possibility of committing capacity (or setting prices) in speciﬁc directions of shipment. When
these assumptions do not hold, the results presented here on welfare in the long run may
not hold anymore, as shown for example by Behrens and Picard (2011), who stress the
back-haul problem faced by carriers by modeling an equal level of capacity in the two
directions of a given trade route and analyze the market and agglomeration outcomes in
such a perfectly competitive setting.

In this paper, a purely theoretical model has been presented. A natural next step is to
test empirically some of the implications of the model, especially the ones concerning the
determination of the freight rate in the transport sector. In addition, the model has been
developed in a two-country setting, excluding labor mobility and vertical linkages. In can be
possible to extend the model to introduce these features but the resulting complexity would
harm the analytical tractability of the model.

19

Figure 1: Simulation of changes in the agglomeration of industrial activities, λH, as a function of
transport costs (ranging from ttrde to τ) and agglomeration of consumption, θH. The values of the
structural parameters used in this simulation are the following: α = 10; β = 6.2; γ = 1.2; c = 1;
τ = 1; M = 100; K = 100; ƒ = 10.

Figure 2: Visual illustration of how final good's demand structure affects the carriers' problem.

20

Figure 3: Simulation of equilibrium freight rates in the long run as a function of agglomeration of
consumption, θH and competition in the transport sector (ranging from k = 1 to k = 10) when tariffs
are symmetric. The values of the structural parameters used in this simulation are the following:
α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

Figure 4: Simulation of equilibrium freight rates in the long run as a function of agglomeration of
consumption, θH and competition in the transport sector (ranging from k = 1 to k = 10) when tariffs
are asymmetric. The values of the structural parameters used in this simulation are the following:
α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

21

Figure 5: Equilibrium freight rates in the long run, as a function of agglomeration of consumption,
θ and the number of carriers (k = 1 and k = 10). The values of the structural parameters used in
this simulation are the following: α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100;
ƒ = 10.

Figure 6: Simulation of agglomeration of industrial activities, λH, as a function of agglomeration of
consumption, θH and competition in the transport sector (ranging from k = 1 to k = 10) when tariffs
are symmetric. The values of the structural parameters used in this simulation are the following:
α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

22

Figure 7: Simulation of agglomeration of industrial activities, λH, as a function of agglomeration of
consumption, θH and competition in the transport sector (ranging from k = 1 to k = 10) when tariffs
are asymmetric. The values of the structural parameters used in this simulation are the following:
α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

Figure 8: Simulation level of welfare in the two regions, and in the entire economy, as a function
of the level of competition in the transport sector (ranging from k = 1 to k = 10) and liberalization
regime. The values of the structural parameters used in this simulation are the following: α = 10;
β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10; θ = 0.55.

Figure 9: Simulation level of welfare in the two regions, and in the entire economy, as a function of
concentration of consumption and liberalization regime. On the left pane with a monopolist carrier,
k = 1, and on the right pane with k = 10. The values of the structural parameters used in this
simulation are the following: α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100;
ƒ = 10.

23

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25

List of Figures

Figure 1. Simulation of changes in the agglomeration of industrial activities, λH, as
a function of transport costs (ranging from ttrde to τ) and agglomeration
of consumption, θH. The values of the structural parameters used in this
simulation are the following: α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100;
K = 100; ƒ = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 2. Visual illustration of how ﬁnal good’s demand structure affects the carriers’

problem.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Figure 3. Simulation of equilibrium freight rates in the long run as a function of
agglomeration of consumption, θH and competition in the transport sector
(ranging from k = 1 to k = 10) when tariffs are symmetric. The values of
the structural parameters used in this simulation are the following: α = 10;
β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

. . . . . . . . . . . . 21

Figure 4. Simulation of equilibrium freight rates in the long run as a function of
agglomeration of consumption, θH and competition in the transport sector
(ranging from k = 1 to k = 10) when tariffs are asymmetric. The values of
the structural parameters used in this simulation are the following: α = 10;
β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

. . . . . . . . . . . . 21

Figure 5. Equilibrium freight rates in the long run, as a function of agglomeration of
consumption, θ and the number of carriers (k = 1 and k = 10). The values of
the structural parameters used in this simulation are the following: α = 10;
β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

. . . . . . . . . . . . 22

Figure 6. Simulation of agglomeration of industrial activities, λH, as a function of
agglomeration of consumption, θH and competition in the transport sector
(ranging from k = 1 to k = 10) when tariffs are symmetric. The values of
the structural parameters used in this simulation are the following: α = 10;
β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

. . . . . . . . . . . . 22

Figure 7. Simulation of agglomeration of industrial activities, λH, as a function of
agglomeration of consumption, θH and competition in the transport sector
(ranging from k = 1 to k = 10) when tariffs are asymmetric. The values of
the structural parameters used in this simulation are the following: α = 10;
β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10.

. . . . . . . . . . . . 23

Figure 8. Simulation level of welfare in the two regions, and in the entire economy,
as a function of the level of competition in the transport sector (ranging
from k = 1 to k = 10) and liberalization regime. The values of the structural
parameters used in this simulation are the following: α = 10; β = 6.2;
γ = 1.2; c = 1; τ = 1; M = 100; K = 100; ƒ = 10; θ = 0.55.

. . . . . . . . . . . 23

Figure 9. Simulation level of welfare in the two regions, and in the entire economy,
as a function of concentration of consumption and liberalization regime. On
the left pane with a monopolist carrier, k = 1, and on the right pane with
k = 10. The values of the structural parameters used in this simulation are
the following: α = 10; β = 6.2; γ = 1.2; c = 1; τ = 1; M = 100; K = 100;
ƒ = 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

26

List of Tables

Table 1. Core and periphery effects of marginal changes in industrial agglomeration
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

8
Table 2. Core and periphery effects of marginal changes in transport costs. . . . . . . 15

(λ) on market outcomes.

27

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