Production Costs, Not Transport Cost Savings, Drive
Trade Patterns: Revisiting Theories of Market Size
Takashi Onoda*
Japan Bank for International Cooperation and
TDB-CAREE, Graduate School of Economics, Hitotsubashi University

July 25, 2024

Abstract
I reconsider the notion that industries with high transport costs concentrate in large markets to save on transport costs. A restudy of the standard model reveals that the literaturemisinterprets the model result, overlooking the incentive to locate in smaller markets, in which
trade barriers lessen competition. Higher transport costs reinforce this incentive, offsetting
transport cost savings. Instead, firms with lower transport costs focus on reducing production
costs to compete in international markets. Thus, they are concentrated in lower-wage countries, creating a base for exports. In simple models, the lower-wage country coincides with thesmaller-market country, causing conflation.
Keywords: Home-market effect, Market size, Trade cost
JEL classification: F12, F16, R12* Email: onoda.takashi@gmail.com

1

1

Introduction

Firms want to locate near large markets to reduce transport costs. This incentive is central to studies inwhich market size affects trade patterns, industrial concentration, and factor prices in international tradeand economic geography (Krugman (1980, 1991)). Among them, Helpman and Krugman (1985), in theirseminal work, show a differentiated-goods industry with increasing returns to scale concentrates in a large
market to save transport costs, using a model of a single such industry. Subsequently, Hanson and Xiang(2004) build a model with many differentiated-goods industries that differ in transport costs, demonstratingthat industries incurring higher transport costs are concentrated in larger countries. Hanson and Xiang (2004)
attribute this result to the industry-specific transport cost savings, establishing the notion that industries withhigher transport costs concentrate in large markets because they have stronger incentives to save on transport
costs. Likewise, Amiti (1998), Laussel and Paul (2007), and Erhardt (2017) explain the same result in theirmodels by using the same economic reasoning.
In this study, I reexamine the model of Hanson and Xiang (2004), revealing that the real driver of the industrial concentration pattern they found is the incentive to lower production costs rather than transport costsavings. Additionally, I interpret the model of Helpman and Krugman (1985) in a unified way, demonstrating
the interpretation of the Helpman-Krugman model result—the transport-cost-saving incentive drives industrial concentration—is not “robust” to infinitesimal changes in the model assumptions; instead, production
costs are predominantly the driver.
Previous studies have overlooked competition intensity as a factor in firms’ locational choice. Indeed,
the incentive for transport cost savings is greater in industries with higher transport costs. However, higher
transport costs strengthen another, infrequently mentioned incentive: the incentive to locate in a smallermarket to avoid intensive competition. Higher transport costs protect a small market more significantly
from competition with an outsized number of firms in a large market, thus reinforcing the incentive to locate
in a small market. Consequently, these two effects offset each other, nullifying the power of market size in
directly driving industrial concentration.
The third effect—the only remaining effect—arises from wages. A lower wage reduces production
costs, attracting firms and, subsequently, the resulting intensive local competition counters this attraction.

2

The strength of this countering force depends on the transport costs. Firms with lower transport costs makerelatively more operating profits from sales in international markets, which implies insensitivity of theiraggregate operating profits to the local competitive environment. Thus, the countering force is relatively
weak; firms in industries with lower transport costs have a relatively stronger incentive to reduce production
costs. Consequently, these industries gravitate toward a country that offers a lower wage, creating a base forexports. Conversely, industries with higher transport costs tend to locate in the country with a higher wage.
Market size influences the industrial concentration pattern of Hanson and Xiang (2004) only throughwages. Transport cost savings in a large country dominate the relaxed competition in a small country forluring firms, generating the market-size effect on factor prices—a higher wage in a larger market. Consequently, the larger-market country coincides with the higher-wage country, which hosts industries with hightransport costs relatively more.
Critically, this production-cost-driven explanation is the uniquely accurate interpretation of the model
result, not another explanation from a different angle. In the Hanson-Xiang model (Hanson and Xiang, 2004),
the higher-wage country coincides with the larger country owing to strong assumptions, causing conflation.
To avoid any doubt regarding my argument, I break this link by introducing country-specific expenditurecompositions into the Hanson-Xiang model. As Onoda (2024) shows, a country with greater expenditures
on industries with lower transport costs, conditional on the country size, commands a higher wage; thus, thisassumption allows the larger country to command a lower wage depending on expenditure compositions. In
this modified model, the result of the wage-driven industrial concentration holds, regardless of the size ofthe higher-wage country, verifying the production-cost-driven explanation.
Furthermore, I show that the transport-cost-saving-driven explanation of Helpman and Krugman (1985)
is not applicable once the model assumptions marginally change. In their model, a freely traded, homogeneous good exists as well as the single differentiated-goods industry, guaranteeing factor price equalization;
thus, the transport-cost saving motive is the only possible explanation for the differentiated-goods industry’s
concentration. Nevertheless, this model can be considered as a limiting case of the Hanson-Xiang modelwith two industries, in which one industry’s transport costs, degree of increasing returns, and elasticity of
substitution are zero, zero, and infinity, respectively. Marginally changing these three parameters alters it
to the Hanson-Xiang model. Subsequently, on the one hand, the (more) differentiated-goods industry with3

(higher) transport costs remains concentrated in the larger country, showing the robustness of the model result. On the other hand, transport cost savings are no longer the driver of industrial concentration, supersededby production costs. Thus, the transport-cost-driven explanation is not “robust.” Instead, the productioncost–driven explanation captures the predominant force behind industrial concentration.
The findings of this study extend beyond those of Hanson and Xiang (2004) and Helpman and Krugman (1985). By using models similar to the one in Hanson and Xiang (2004), Amiti (1998), Laussel andPaul (2007), and Erhardt (2017) explain the distribution of industries and trade patterns by industry-specificstrengths of two forces: transport cost savings and production costs. However, they overlook the industryspecific strength of competition intensity, leading Amiti (1998) and Erhardt (2017) to attribute the concentration of high-transport-cost industries to the transport-cost-saving motive, similar to the conclusion drawn
by Hanson and Xiang (2004).1 This paper revises the explanations for these studies.
This study contributes to the literature on the patterns of trade with increasing returns and trade costsby elucidating the mechanism commonly found in the literature. Interaction between the three factors exists
behind the pattern of trade from relative demand, called the “home-market effect”—a location becomes a
net exporter in a sector for which it has relatively large demand.2 Recent works in this line of research
include Fajgelbaum et al. (2011), Costinot et al. (2019), and Matsuyama (2019). In these models, sectorspecific trade cost savings in a given location generate sector-specific competition intensities. Further, theaforementioned results of Onoda (2024) show the link between sector-specific trade cost savings and wages.
The restudy of Helpman and Krugman (1985) in this paper differs from previous studies in its focus.
Strong assumptions—particularly, the zero transport cost—in Helpman and Krugman (1985) lead to manyextensions and robustness checks on the pattern of trade (e.g., Davis (1998); Head et al. (2002); Crozet andTrionfetti (2008); Behrens et al. (2009); Barbero et al. (2018)). These studies investigate the relationships
between variables in different settings. In contrast, my study focuses on the economic reasoning behind
them, thereby providing new insights.
1

Laussel and Paul (2007) discuss this pattern only in the introduction because it is a replication of Amiti (1998)’s

result.
2
Helpman and Krugman (1985) and Hanson and Xiang (2004) also call their effects the “home-market effect.”
This paper does not use this term hereafter to avoid confusion.

4

Finally, this accurate understanding better informs empirical studies. The relationship between market
size and the pattern of trade within industries with different transport costs—the theoretical predictions by
previous works—encompasses two channels: one from market sizes to factor prices and another from factor
prices to industrial concentration. This suggests a weak relationship in the data. Although Hanson and
Xiang (2004) and Erhardt (2017) find an empirical pattern consistent with the relationship in international
trade flow data, Pham et al. (2014) report that the one found by Hanson and Xiang (2004) is not robust todifferent data handling, sampling, and estimation procedures, potentially revealing a limitation.
The rest of this paper is organized as follows. Section 2 reexamines the economic forces in the modelof Hanson and Xiang (2004), uncovering the real driver of the pattern of industrial concentration. Section 3
revisits the model of Helpman and Krugman (1985) as a limiting case of the Hanson-Xiang model. Finally,
Section 4 concludes the paper.

2

Revisiting Hanson and Xiang (2004)

This section examines the Hanson-Xiang-based model that has country-specific inter-industry expenditure
distributions and is, otherwise, identical to that of Hanson and Xiang (2004). The insight derived can also
be applied to Amiti (1998), Laussel and Paul (2007), and Erhardt (2017).3

Set UpTwo countries, indexed by n ∈ {1, 2}, are identical except for their population size and expenditure distributions. There is a continuum of industries, indexed by z ∈ [0, 1]. Industries differ in iceberg transport costs
τk , elasticity of substitutions σ(z), and linear production parameters. Labor is the only factor of production,and country n is endowed with a mass of Ln workers who are freely mobile between industries but immo3

Amiti (1998) assumes two industries and two factors of production. One factor is considered to be mobile between

countries. However, relative factor endowments are identical, and industries’ factor intensities are also identical when
the author discusses the pattern of trade with different transport costs, thereby nullifying the difference with Hanson
and Xiang (2004). Laussel and Paul (2007) use a model of Amiti (1998) with one factor. Erhardt (2017) employs amodel with firm heterogeneity à la Melitz (2003) that nests the Hanson-Xiang model.

5bile between countries. Workers have Cobb-Douglas preferences and inelastically provide one unit of labor
supply. The representative household’s problem in country n is given by
(∫ 1
max

{Qnz }z∈[0,1] ,{qnz (ν)}ν∈Ωnz ,z∈[0,1][∫s.t. ∀z,Qnz =qnz (ν)σ(z)−1σ(z))αn (z) ln(Qnz )dz ,

exp

(1)

0

] σ(z)

σ(z)−1

dν

,

Ωnz

∫ 1∫
En =

pnz (ν)qnz (ν)dνdz,
0Ωnz

where pnz (ν) and qnz (ν) denote price and consumption, respectively, for variety ν of industry z in country n,Ωnz is the set of available varieties of industry z in country n, and En = wn is the income level in country n.
The expenditure density function αn (z) captures country-specific expenditure distribution. I set the wage incountry 1 as the numeraire (w1 = 1). Consumption optimization yields the demand function for varieties in[∫]1/(1−σ(z))σ(z)
industry z: qnz (ν) = pnz (ν)−σ(z) Pnz Qnz , where Pnz = ν∈Ωnz pnz (ν)1−σ(z) dν
is the priceindex for industry z in country n. In the following part, I omit ν unless necessary.
Production is based on Krugman (1980). For all industries z ∈ [0, 1], there are free entry, endogenous
sets of varieties, homogeneous firms, and monopolistic competition. Each firm in industry z must employ
fz and mz units of labor as the fixed and marginal costs, respectively, to produce a unit of one variety. A
shipment of a variety between two countries requires an industry-specific iceberg transport cost 1 < τz < ∞.
Given the symmetry of varieties in each industry, pniz and qniz denote the price and quantity, respectively,of a variety produced in country n and sold in country i in industry z. The problem for a firm in country n
in industry z is given by

πnz =

max

∑

{pniz ,qniz }i∈{1,2}[pniz qniz − {τz + 1{i = n}(1 − τz )} mz qniz wn ] − fz wn ,(2)i∈{1,2}−σ(z)s.t.∀i ∈ {1, 2}, qniz = pniz

σ(z)

Piz

Qiz ,

where πnz is the profit from optimized production, and 1{i = n} is an indicator function that takes the valueof one when i = n. If industry z in country n has non-zero production in equilibrium, πnz must be zerosuch that there are no new entrants, which is the zero-profit condition. I focus on equilibria in which both6

countries have non-zero production in all industries, following Hanson and Xiang (2004). The definition ofsuch an equilibrium is as follows.

Definition of Equilibrium
An equilibrium is w2 , {pniz , qniz }(n,i,z)∈{1,2}2 ×[0,1] , and {Ωnz }(n,z)∈{1,2}×[0,1] such that
1. workers optimize consumption as eq. (1) for n ∈ {1, 2},
2. workers’ income is given by En = wn for n ∈ {1, 2},
3. producers optimize production as eq. (2) for all z ∈ [0, 1] and n ∈ {1, 2},
4. the zero-profit condition holds such that πnz = 0 for all z ∈ [0, 1] and n ∈ {1, 2}, and[∑]∫5. the labor market clearing condition z∈[0,1] Mnz
{τ
−
1
{i
=
n}(τ
−
1)}
m
q
+
f
z
z
z niz
z =
i∈{1,2}Ln ,where Mnz is the mass of firms in country n in industry z, which holds for all n ∈ {1, 2}.

Zero-Profit Condition
To identify economic forces in the model, I start by manipulating the zero-profit conditions. Given the wellknown optimized prices pnnz = σ(z)mz wn /(σ(z) − 1) and pniz = τz mz wn /(σ(z) − 1) for i ̸= n, theprofit for a firm in industry z in country n becomes
(
πnz =

)
1
1
mz qnnz + τzmz qniz − fz wn ,σ(z) − 1
σ(z) − 1(3)

where i ̸= n. I set mz = (σ(z) − 1)/σ(z) and fz = 1/σ(z) without loss of generality by appropriately
choosing the unit of measurement.4 This normalization implies pnnz = wn and pniz = τz wn . Then, the4This normalization is common in the “new trade theory” and “new economic geography.” See box 2.2. of Baldwin

et al. (2003) for an additional explanation of why this is without loss of generality.

7

zero-profit condition (πnz = 0) becomes
σ(z)−1αn (z)En + τz Li (τz wn )−σ(z) Piz
1 = Ln wn−σ(z) Pnz

σ(z)−1αn (z)Ei .

I rewrite this equation asσ(z)−1 −σ(z)1 = (1 − ϕz )Yn αn (z)Pnz
wn
+

∑


σ(z)−1 ϕz Yi αi (z)Piz

wn−σ(z) ,(4)i∈{1,2}1−σ(z)

where Yi = Li Ei and ϕz = τz

. Appendix A provides the derivations of equations including eq. (4) andproofs of the following lemmas and corollaries. The variable ϕz , often called “freeness of trade” (Baldwin
et al. 2003), measures the effective tradability of an industry considering the transport cost and its impact onsales.5 Eq. (4) equates fixed cost, normalized to one, on the left-hand side to operating profit—profit before
deducting fixed cost—on the right-hand side.
Eq. (4) decomposes a firm’s operating profit into two sources. The first source is the market accessexclusive to local firms, reflected in the first term on the right-hand side of eq. (4).6 This term reflects
transport cost savings that firms can achieve by locating in country n. The second source is the “global
market,” corresponding to the second term—the summation of a fraction ϕz of both markets, which firms
can “access” from either country.

Three Factors in Locational Choice
The operating profit in eq. (4) can differ between the two countries through three country-specific variables—
1−σ(z)

Yn αn (z), Pnzσ(z), and wn

—implying three factors in their locational choice. The first is market size. The

size of the operating profit from exclusive market access increases with the industry’s market size Yn αn (z);
thus, firms prefer to locate in a large market to save on transport costs. The second factor is wages. A higher
wage wn translates into a higher production cost, and, subsequently, a higher price, eventually resulting in
5σ(z)−1

Hanson and Xiang (2004) define a variable x(z) = τz
, called the “effective trade cost.”
6
Foreign firms need to pay transport costs to sell their varieties in country n; they raise the price by a factor of τz
and receive profits that decrease by a factor of 1 − ϕz . One can interpret this as firms selling varieties at the factorygate price (σ(z)mi wi /(σ(z) − 1)) have access to the fraction ϕz of the country n market.

8lower revenues. Thus, it reduces profits from both profit sources in eq. (4). Conversely, a lower wage attracts
firms.
1−σ(z)

Competition intensity is the last factor in locational considerations. The expression Pnz

measuresthis factor and can be rewritten as:

1−σ(z)Pnz= (1 − ϕz )Mnz wn1−σ(z) +∑1−σ(z)i∈{1,2}ϕz Miz wi.

(5)

On the right-hand side of eq. (5), only the first term differs between countries; thus, more competitors (larger
1−σ(z)Mnz ) in the home market increase Pnz

relative to the other country and, consequently, reduce the firstterm of the operating profit in eq. (4). Conversely, firms prefer to locate in a market with fewer firms. Thus, asmaller country—a country generally with a smaller mass of firms—is preferable from this perspective. Eq.
(4) holds for both countries, implying that their advantages and disadvantages in these three factors—market
size, wages, and competition intensity—must offset each other in equilibrium.

Industry Size
1−σ(z)

I translate competition intensity reflected in Pnz

into industry size. We have the zero-profit condition(4) for both countries. Combining them yields
σ(z)−1 −σ(z)(1 − ϕz )Yn αn (z)Pnz
wn
=

where

1
,
1 + µnz−1−1 + 1)w σ(z)(ϕnµnz =  ∑z
− 1 > 0.
σ(z)i∈{1,2} wi

(6)



(7)

The right-hand side (1 + µnz )−1 is the share of the market access exclusive to local firms as operating profit
in equilibrium; thus, µnz measures the importance of the global market. After substituting eq. (5) into eq.
(6), manipulations of the equation for both countries yieldσ(z)Mnz wn = (1 + µnz )αn (z)Yn − ∑

9

wn

∑

σ(z)
i∈{1,2} wii∈{1,2}αi (z)Yi µiz .

(8)Normalization fz = 1/σ(z) makes labor demand by a firm equal one; subsequently, Mnz and Mnz wn equal
the mass of workers and industry size in value, respectively. Given wages and market sizes, firms continue
to enter an industry until the profit becomes zero and the industry size reaches Mnz wn in eq. (8).
Crucially, eq. (8) shows the direct economic forces distinctly from market size and wages; it does so
by not reflecting the labor market clearing condition, which would otherwise relate the two variables andpotentially introduce terms that capture indirect effects from market size through wages.7 The two direct
forces are as follows. First, industry size increases with the market size αn (z)Yn more than one-for-one
because µnz > 0, which is a common result for this type of model. A larger market attracts firms until the
resulting intensive competition offsets it, requiring a disproportionate number of entrants. Second, indusσ(z) ∑σ(z)try size decreases with wages because wages decrease with µnz and increase with wn / i∈{1,2} wi ,reflecting diminishing operating profits from the global market and exclusive market access, respectively.

Industries with Different Transport Costs
Remarkably, higher transport costs do not reinforce the large industry size from a large market; the factor
1 − ϕz in eq. (4) is absent from eq. (8). To understand this absence, we consider how varying transport
−σ(z)

σ−1 w
costs affect the share of exclusive market access in operating profit (1 − ϕz )Yn αn (z)Pnz
n. Higher7

The algebra of Hanson and Xiang (2004) imposes the condition for household income to equal the sum of sales∫1
from all industries—Y = 0 n(z)p(z)q(z)dz in their notation, corresponding to the labor market clearing condition
in my algebra—at an early stage. This manipulation makes the observation of direct economic forces difficult. Nevertheless, transforming the algebra (6) in their paper can lead to the conclusion that the higher-wage country becomesa net exporter in these industries, independent of the order of market sizes, as follows.

g(z) > 0 ⇐⇒
wσ(z)
⇐⇒
σ(z)
x(z) − wσ(z)w1 x(z) − 1)(
w2σ(z) − 1σ(z)wσ(z) ,
Y > w+
x(z) − wσ(z)Y>where I use their notation. The country with Y and w becomes a net exporter in industry z if and only if this inequality
holds. The right-hand side decreases with x(z) (ϕ−1z in my notation) if and only if the wage is higher than that of theother country (w > 1).

10

transport costs generate two opposing effects on this term. On the one hand, they raise (1 − ϕz )Yn αn (z),making locating in a large market a more significant advantage. This effect corresponds to the notion thathigher transport costs reinforce the incentive to locate in a large market to save on transport costs (Hanson and
1−σ(z)

Xiang (2004)). On the other hand, they also increase (1 − ϕz )Mnz wn

1−σ relativein eq. (5), raising Pnz

to the other market; higher transport costs protect a small market—a market with fewer competitors—more
substantially. This second effect nullifies the first effect, removing 1 − ϕz from eq. (8). In other words,
higher transport costs strengthen both the advantage and disadvantage of being located in a larger market tothe same extent, generating no net effect.
Previous studies have overlooked this equally important and strengthening disadvantage of a larger market. Amiti (1998), Erhardt (2017), Hanson and Xiang (2004), and Laussel and Paul (2007) discuss the“trade-off” between transport cost savings and production costs, examining how this differs depending on
industry transport costs and other characteristics. However, they do not consider the disadvantage of a large
market, which is critical when comparing industries because it varies across industries.
Consequently, a difference in market sizes does not directly generate a trade pattern. Eq. (9), following
from eq. (8), expresses the trade balance of industry z in country n.
(
Mnz wn − αn (z)Yn =1
1 + αi (z)Yi µiz /αn (z)Yn µnz

−

)

1
σ(z)

1 + wi

∑

σ(z)

/wn

αi (z)Yi µiz

(9)

σ(z)

/wi

i∈{1,2}Thus, country n is a net exporter in industry z if and only if αn (z)Yn µnz /αi (z)Yi µiz is greater than wnσ(z)We can derive three patterns of trade from this equation. First, greater expenditure density αn (z) makes theσ(z)country more likely to be a net exporter in that industry because αn (z)Yn µnz /αi (z)Yi µiz − wn

σ(z)

/wi

increases with αn (z)/αi (z) conditional on (wn /wi )σ(z) and ϕz . This is the home-market effect from relative demand on trade (Krugman (1980)). Second, we compare industries with common relative expenditure αn (z)/αi (z) and common elasticity of substitution σ(z) but with different transport costs. The term
αn (z)Yn µnz /αi (z)Yi µiz increases with τz for the higher-wage country. In contrast, (wn /wi )σ(z) is invariant
across these industries. These properties imply Lemma 1.
Lemma 1. Suppose that the higher-wage country is a net exporter in industry y. Then, it is a net exporterin any industry z with τz ≥ τy , σ(z) = σ(y), and αn (z)/αi (z) = αn (y)/αi (y).

11.

The patterns of net exports and industry sizes are equivalent as long as countries have identical CobbDouglas preferences. In this generalized model, a greater αn (z) increases Mnz conditional on net exports(Mnz wn − αn (z)Yn ). Thus, I condition the value of αn (z)/αi (z) to state the pattern of industrial concentration in Corollary 1.
Corollary 1. Suppose industry y with α1 (y) = α2 (y) is concentrated in the higher-wage country n in thesense that Mny /Miy > Ln /Li . Then, any industry z with τz ≥ τy , σ(z) = σ(y), and αn (z) ≥ αi (z) isconcentrated in the higher-wage country n in the same sense.
The real driver of these trade and concentration patterns is wages. For economic reasoning, we consider
industries in the lower-wage country. A lower wage is an advantage, which requires intensive competition
or a smaller market size as a counter in equilibrium. This trade-off exists in all industries, but the relative
power of a lower wage against intensive competition differs across industries. As discussed, a lower wage
boosts operating profits from both exclusive market access and the global market. In contrast, intensivecompetition tempers only the operating profit from exclusive market access, which accounts for (1 + µnz )−1of aggregate profit (eq. (6)). Low transport costs increase the significance of the global market, shrinking
the share of exclusive market access (∂(1 + µnz )−1 /∂ϕz < 0). Consequently, a given intensity of competition becomes a weaker disadvantage, requiring more intensive competition to offset the advantage. In
other words, wages weigh relatively more, strongly incentivizing firms to locate in the lower-wage country.
Conversely, the higher-wage country tends to become net exporters in industries with high transport costs,
which have relatively weak incentives to pursue lower wages.

Industries with Different Elasticities of Substitution
Similarly, I compare industries with different elasticities of substitution, replicating the result of Hanson and
Xiang (2004). In general, the trade pattern is not straightforward, unlike that of transport costs, because σ(z)σ(z) 8changes the values of ϕz as well as wn. Following Hanson and Xiang (2004), I condition the value ofσ(z)ϕz .9 Then, for the higher-wage country, αn (z)Yn µnz /αi (z)Yi µiz and wn
8

σ(z)

/wi

decrease and increase,

Laussel and Paul (2007) show a non-monotonic response of net exports to σ(z) in one of two differentiated-goods

industries.
9
When I compare different values of σ(z), τz changes in the background so that ϕz remains the same.

12

respectively, with σ(z) conditional on ϕ(z). Thus, we obtain Lemma 2 and Corollary 2.
Lemma 2. Suppose that the higher-wage country is a net exporter in industry y. Then, it is a net exporterin any industry z with ϕz = ϕy , σ(z) ≤ σ(y), and αn (z)/αi (z) = αn (y)/αi (y).
Corollary 2. Suppose industry y with α1 (y) = α2 (y) is concentrated in the higher-wage country n in thesense that Mny /Miy > Ln /Li . Then, any industry z with τz ≥ τy , σ(z) ≤ σ(y), and αn (z)/αi (z) ≥αn (y)/αi (y) is concentrated in the larger country n in the same sense.
This result on industries with different σ(z) is the same as that of Hanson and Xiang (2004) and the driveris wages. Demand is sensitive to price differences when varieties are less differentiated, making lower wages
a more significant advantage. Thus, firms in less-differentiated industries have a stronger incentive to locate
in the lower-wage country.

Wages
Market size indirectly influences industrial concentration through wages. Aggregating eq. (8) with the labor∫market clearing condition ( Mnz dz = Ln ) yields


∫ 1
Yn

−1

σ(z)
(ϕ−1 + 1)wn
αn (z)  ∑z
− 1
σ(z)
0
w
i∈{1,2} iwhere I used

∫10 αn (z)dz



∫ 1
σ(z)
wn
dz =
α (z)µiz dz  ,Yi ∑σ(z) i0w
i∈{1,2} ii∈{1,2}∑(10)= 1. As a common result in the literature, wages increase with market sizes.

Suppose that two countries have identical expenditure distributions (∀z, αn (z) = αi (z)) to isolate thisforce. Then, wn increases with Yn —the market-size effect on factor prices. This market-size-driven wage,in turn, generates the wage-driven industrial concentration in Corollary 2.
However, market size cannot perfectly predict the pattern of industrial concentration when αn (z) ̸=αi (z) for some z. Onoda (2024) shows that locations with higher expenditure shares in industries withlower transport costs command higher wages conditional on population size. This force is operative here;
a greater Yn does not necessarily imply a higher wn . In contrast, the wage-driven industrial concentration
pattern of Corollary 2 always holds, verifying the production-cost-driven explanation.

13

Implications for Empirical Tests
The indirect and imperfect link between market size and industrial concentration makes empirical tests of themarket-size effect challenging. A test of the relationship between the two variables à la Hanson and Xiang(2004) or Feenstra et al. (2001) effectively tests the two channels jointly: one from market size to wages andanother from wages to industrial concentration. Thus, there are two windows through which other factors
disturb this relationship. One example of a disturbance is country-specific expenditure distributions, as thisstudy demonstrates, and another example is influence from third countries (e.g., a large neighboring country).
Any factor influencing the terms of trade between countries becomes noise by changing the relative wage.10
Pham et al. (2014) reexamine the empirical evidence of the market-size effect on industrial concentration
found by Hanson and Xiang (2004). They change the data handling, sampling, and estimation procedures,
suggesting that the evidence is not robust. This weak evidence may be attributed to the fact that it tests thetwo effects jointly.
Furthermore, the proper interpretation implies an issue in the empirical evidence of the market-size effectthat Hanson and Xiang (2004) obtain. The main difference-in-difference specification involves two groups
of industries: those with high transport costs and low elasticities of substitution—those predicted to be concentrated in large markets—and those with low transport costs and high elasticities of substitution—thosepredicted to be concentrated in small markets. This analysis examines differences in export values between
these two groups and between two exporting countries. The primary regressor is relative GDP, which serves
as a proxy for the relative market size of the exporting-country pairs. Additionally, the specification includes
covariates, controlling for “industry production costs.” Among these, relative wage levels in low-skill industries (namely, apparel and textiles) are included, and this inclusion can be problematic. These relative
wages reflect cross-country differences in overall wage levels as well as wages in these industries relative
to other industries. The former reflects the market-size effect on factor prices—the direct or actual driver of
the trade pattern they found. Thus, controlling for these relative wages complicates the interpretation of thecoefficient for relative GDP.
10

The relative wage in the model of this paper corresponds to the productivity-adjusted relative wage in a model inwhich the countries differ in productivity. Thus, relative productivity does not directly affect the (productivity-adjusted)
relative wage, although it does so indirectly by changing relative market size (Onoda (2024)).

14

3

Revisiting Helpman and Krugman (1985)

This section reinterprets the model of Helpman and Krugman (1985) as a limiting case of the Hanson-Xiang
model, discussing the robustness of the economic mechanism. The Helpman-Krugman model features one
differentiated-goods industry under monopolistic competition with increasing returns to scale, labeled as“manufacturing” following Davis (1998), and one freely traded homogeneous-goods industry under perfectcompetition with constant returns to scale, labeled as “agriculture” again following Davis (1998). Two asymmetrically sized countries have identical Cobb-Douglas preferences. Similar to the Hanson-Xiang model,labor is the only factor of production and is freely mobile between industries but immobile between countries. The existence of freely traded homogeneous goods ensures factor price equalization—wages in the twocountries are equal at equilibrium. Thus, there is no room for wage differences in driving industrial concentration. In equilibrium, firms in manufacturing are concentrated in the larger country because the incentive
to save on transport costs by locating in the larger country dominates the incentive to reduce competition
intensity by locating in the smaller country; firms in the agricultural industry have neither incentive.
However, this economic reasoning is not “robust” to infinitesimal changes in the model parameters. Toalign the Hanson-Xiang model with the Helpman-Krugman model, I replace the continuum of industries inthe Hanson-Xiang model with two industries, m and a. All the theoretical results obtained above hold true. I
make industry a resemble the agricultural industry in Helpman and Krugman (1985) by setting transport costlower (τa < τm ) and elasticity of substitution higher (σ(a) > σ(m)). Then, Corollary 2 implies that firms inindustry m are concentrated larger country, similar to the manufacturing industry in the Helpman-Krugman
model, although the economic reasoning is different. Subsequently, I make industry a almost identical tothe agricultural industry by taking the limit of ϕa → 1 and σ(a) → ∞, which implies τa → 1. The infinite
σ(a) converts monopolistic competition to perfect competition and the normalized fixed cost fz = 1/σ(z)to zero. Thus, industry a transforms into the agricultural industry at the limit, and the model itself becomesthe Helpman-Krugman model. Throughout the convergence path, industry m is concentrated in the larger
country and it remains so at the limit, as it becomes the manufacturing industry. In contrast, the economic
reasoning behind the concentration does not stay the same. Until τa and σ(a) converge to 1 and ∞, respectively, the reasoning is the pursuit of lower production costs. Once convergence is complete, firms in the15

agricultural industry never cease relocating to the smaller country until the factor price equalizes, eventuallynullifying the reasoning of production costs. Conversely, the economic reasoning of transport-cost savingsat the limit does not apply outside the limit—the case with marginally imperfect competition and marginally
positive transport costs in the agricultural industry. In reality, assuming non-zero product differentiation andnon-zero transport costs, even for agricultural goods, is plausible (Davis (1998)). Therefore, we can conclude that, unlike the suggestions drawn from the Helpman-Krugman model, the incentive to lower productcosts contributes to the pattern of industrial concentration in the real world.1112

4

Conclusion

This study demonstrates that the literature neglects to consider that higher transport costs protect a small
market more significantly from competition. Thus, higher transport costs do not reinforce the advantages of alarge market. Instead, the predominant force behind trade patterns between industries with different transport
costs is the effect of production costs. When firms compete internationally with each other intensively at
low trade costs, they choose a country with low wages as a base for exports.
This rediscovery poses a challenge for empirical works that study the relationship between market size
and trade patterns because it effectively tests two effects: one from market size to wages and another fromwages to trade. The former channel has seen “an apparent empirical success,” as surveyed by Head andMayer (2004), by considering the proximity to and size of other markets (Harris (1954); Hanson (2005);
Redding and Venables (2004)). I would like to see studies that apply this perspective to the channel fromwages to trade patterns in the future.
11

Helpman and Krugman (1985) acknowledge the limitation of their model, stating “[w]e have been able to work

only with a highly specialized example.”
12
Similarly, we can interpret the model of Davis (1998) as another limiting case of the Hanson-Xiang model. Davis(1998) demonstrates that the industrial concentration in the model of Helpman and Krugman (1985) disappears when
the agricultural industry incurs the same transport costs as the manufacturing industry. The model corresponds to thelimiting case of τa = τm and σ(a) → ∞, which implies ϕa → 0. Lemmas 1 and 2 imply two opposing trade patterns:
σ(m) < σ(a) and ϕm > ϕa make the larger country a net exporter and importer, respectively, in the manufacturingindustry. These two forces offset one another, generating no net exports.

16

Appendix
A

Derivation of Theoretical Results

A.1

Eq. (4) and (8)I use a matrix Rz that is defined by








 1 0 
 1 1 Rz = (1 − ϕz )  + ϕz .
1 1
0 1
The inverse matrix isRz−1 =

1  1 0 1
 1 1 .

−1 − ϕz(1 − ϕz )(ϕ−1
z + 1)
1 1
0 1

Using Rz , eq. (4) for two countries can be summarized asσ(z)−1α1 (z)  Y1 P1z

Rz σ(z)−1Y2 P2z=α2 (z)



σ(z)
 w1

σ(z)

.

w2

Premultiplying Rz−1 yields∑ σ(z)
1wn−wi−1
1 − ϕz(1 − ϕz )(ϕz + 1)σ(z)σ(z)−1Yn Pnzαn (z) =i∈Nσ(z)−1⇐⇒ (1 − ϕz )Yn Pnz
αn (z)wn−σ(z) =

17

∑

1
(w /λ )σii∑
1 + (1/ϕk +N −1)(wi∈Nσn /λn ) −σi∈N (wi /λi ),1−σ(z)from which eq. (4) follows. Substituting eq. (5) for Pnz


makes the matrix form be









σ(z)
w1

 Y1 α1 (z) −1   · Rz 
 = diag Rz 
1−σ(z)σ(z)M2z w2w2
Y2 α2 (z)1−σ(z)
 M1z w1



⇐⇒

⇐⇒













σ(z)
1−σ(z)
 Y1 α1 (z)  −1  w1
 M1z w1
=
diag
R
R


 z 
 z σ(z)1−σ(z)
Y2 α2 (z)w2M2z w2−1 

σ(z) −1  w1
−1
=
R
diag
R


 z 

z
σ(z)
1−σ(z)w2M2z w21−σ(z)
 M1z w1 (
1 − ϕz 
Rz−1

=





 Y1 α1 (z) 
Y2 α2 (z)∑ σ(z) )−1wiσ(z)w1 − ϕi−1 +1
z


0
(
σ(z)

0

w2

∑
1
∑
σ(z) − ϕ−1 +1
i
w
z
i i

−

∑
σ(z)
 σ(z)j wj
σ(z) w1 − −1
w
−
−1
i

ϕz +1
ϕz +1
=
∑

Y2 α2 (z)Yi αi (z)1∑∑σ(z) − ϕ−1 +1
σ(z)
i
w
w
σ(z)

w2

−

i i
ϕ−1
z +1

z

σ(z)

wi

−

j

σ(z)
i wi
−1
ϕz +1

  Y1 α1 (z) 
)−1 


Y2 α2 (z)Yi αi (z)Y1 α1 (z)

∑



j




.



ϕ−1
z +1

Eq. (8) follows from this matrix form.

A.2

Proofs of Lemmas and Corollaries

Proof of Lemma 1. Plugging eq. (7) into αn (z)Yn µnz /αi (z)Yi µiz yields
∑
σ(z)
σ(z)
−1
αi (z)Yi (ϕz + 1)wn − i∈{1,2} wi
·
∑
σ(z)
σ(z)
αn (z)Yn (ϕ−1− i∈{1,2} wi
z + 1)wi
−σ(z)−σ(z) ∑
σ(z)
(wi
− wn
) i∈{1,2} wi 
αi (z)Yi 
.
1+
·
=
∑
σ(z)


αn (z)Ynw
i∈{1,2}i(ϕ−1
z + 1) −σ(z)wiIn equilibrium, (ϕ−1z + 1) −∑σ(z)i∈{1,2} wiσ(z)wi> 0; otherwise, the zero-profit conditions for an equilibriumwith non-zero production in all industries in both countries cannot occur simultaneously, as presented inAppendix A.1 (Lemma 1 of Hanson and Xiang (2004)). Thus, this term increases with ϕz if and only if

18

wn > wi , implying Lemma 1.
∑∑
Proof of Corollary 1. Aggregate revenue equals aggregate expenditure for an industry ( j Mjy wj = j αj (y)Yj ),implying country n is a net exporter as
Mny wnLn w nαn (y)Yn>==⇒ Mny wn > αn (y)Yn .
Miy wiLi w nαi (y)Yi
Subsequently, the same algebra as in the proof of Lemma 1 with αn (z) ≥ αi (z) implies that country n is a
net exporter in industry z. Thus, I obtain the following inequality, which completes the proof.
Mnz wnαn (z)Yn
Yn>>.
Miz wiαi (z)Yi
Yi

Proof of Lemma 2. The term αn (z)Yn µnz /αi (z)Yi µiz decreases with σ(z) for the higher-wage country nas the main text states. It follows from(
) ( )σ(z)−σ(z)αi (z)Yi µiz
αi (z)Yi (ϕ−1wn
z + 1) − 1 + (wn /wi )
(
) ·
=
·
.
σ(z)
αn (z)Yn µnz
αn (z)Yn (ϕ−1wiz + 1) − 1 + (wn /wi )σ(z)The other term wn

σ(z)

/wi

increases with σ(z), implying Lemma 2.

Proof of Corollary 2. The same steps as in the proof of Corollary 1 imply that country n is a net exporterin any industry z with τz ≥ τy , σ(z) = σ(y), and αn (z)/αi (z) ≥ αn (y)/αi (y). Subsequently, Lemma 2
implies that country n is a net exporter in any industry z with τz ≥ τy , σ(z) ≤ σ(y), and αn (z)/αi (z) ≥αn (y)/αi (y). The same last step as that in the proof of Corollary 1 completes the proof.

19

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