Home Market Effect and the Agricultural Sector∗
Dao-Zhi Zeng†and Toru Kikuchi‡
December 27, 2004

Abstract
The “home market effect” (HME) is an essential topic of the new trade theory.
Assuming the transport costs only for the manufacturing goods, Krugman (1980)shows that the country with bigger market size is a net exporter. The assumptionof free transport of the agricultural good was shown mattering a great deal rather
than being innocuous by Davis (1998). Particularly, when manufacturing and agricultural goods have identical transport costs, the HME disappears. However, wefind that the homogeneous-agricultural-good assumption in Davis’ model derives
the discontinuity of inverse demand functions, which causes the disappearance ofthe HME. After establishing an analytical solvable model and assuming two differentiated agricultural goods in two countries, we find that the HME does exist even
if the transport cost of the agricultural goods is positive.

∗

The first author acknowledges financial support from Japan Society for the Promotion of Science,

Grant-in-Aid for Science Research 14730017 and 13851002. The second author is grateful to the Ministryof Education, Culture, Sports, Science and Technology of Japan for support to the 21st Century Centerof Excellence Project.
†
Dao-Zhi Zeng, Graduate School of Management, Kagawa University, Saiwai-Cho 2-1, Kagawa 7608523, Japan; e-mail: zeng@ec.kagawa-u.ac.jp‡
Toru Kikuchi, Graduate School of Economics, Kobe University, 2-1 Rokkodai-Cho, Nada-Ku, Kobe
657-8501, Japan; e-mail: kikuchi@econ.kobe-u.ac.jp1

1

Introduction

Based on a model of increasing returns to scale, Krugman (1980) first finds that thecountry with larger local demand succeeds in attracting a more-than-proportionate shareof firms in monopolistically competitive industry. This “home market effect” (HME)
implies a link between a country’s market size and its exports that does not exist in
trade models that are based solely on comparative advantage. This topic is extremely
important and now has become standard knowledge and an important element in a filed
named “new trade theory.”
Helpman and Krugman (1985) reformulated the model of Krugman (1980) and confirmed the existence of HME. In their model, there are two countries and each country has
two sectors: one produces a differentiated product (called the manufacturing sector), andthe other produces a homogeneous product (called the agricultural sector). To make themodel tractable, they assume that the homogeneous product is costlessly tradable andboth countries produce it after trade. However, Davis (1998) finds that the assumptionof zero transport costs of the homogeneous good is not innocuous. Specifically, if thetransport costs of the homogeneous good is the same as the transport costs of the manufacturing goods, then the HME disappears. In Davis’s framework, the transport costs of
the homogeneous good is large enough to blockade the trade of the homogeneous good.
Recently, Davis’ model is further extended by Yu (2005), assuming there is no trade of
the homogeneous good. Yu uses a CES function to replace the Cobb-Douglas function in
Krugman’s model, and find that the HME for production structure can arise, disappear,
or even reverse in sign, depending on the relative expenditure share on differentiatedgoods in the larger country.
Despite Davis’ negative result, several recent papers find that the HME has greater
generality. For example, Head, Mayer and Ries (2002) find that HME is pervasive in twoother models. By use of a framework of multiple manufacturing industries, Hanson and
Xiang (2004) show that HME takes the form of industries with higher transport costs andmore differentiated products being more concentrated in large countries than industries
with lower transport costs and less differentiated products. They also find strong empirical2

evidence of HME. Meanwhile, Holmes and Stevens (2005) establish another model witha continuum of industries including both models of krugman (1980) and Davis (1998)
as special cases. They conjecture that a high-fixed-cost industry would be produced in
the larger country, and the structure of production and trade would generally dependin systematic ways upon the size of the home market. Unfortunately, two models ofmultiple industries are not completely analytically solvable, and the role of the industry
under constant returns to scale remains unclear.
Both Davis (1998) and Yu (2005) show that the agricultural sector is worthy of more
attention, but their artificial assumption of no trade of agricultural good is essential intheir model. The purpose of this paper is to clarify the relation between the agricultural
sector and the existence of HME when the agricultural goods are traded between countries.
This relation is partially hidden by the tradition of treating the agricultural goods as thenuméraire in the literature. To avoid such kind of confusion, we separate the agricultural
goods from the numéraire. More precisely, the transport cost is zero for the numéraire but
positive in the agricultural sector. In the real world, transporting gold is much cheaper
than transporting rice. On the other hand, the agricultural good of two countries in
the model of Davis (1998) and Yu (2005) is homogeneous. This makes the price of the
agricultural good in a country jumps when it imports (even a little of) the agricultural
good from the other country if the transport cost is positive. Such thing is evidently
not consistent with the economic situation of real life. To avoid this discontinuity ofprices, we treat the agricultural goods of two countries differentiated. In other words, twoagricultural goods are two varieties produced in the agricultural sector. In the real world,
the wool in New Zealand is different from the rice in Japan, and furthermore, Japaneserice is different from Thai rice. In empirical study, the “homogeneous good” of Rauch(1999) (also named organized exchange category) also consists of more than one variety.
A sister version of the new trade theory is the new economic geography (see Fujita, Krugman and Venables 1999), in which some workers are mobile. Similar to new
trade theory, the framework of Cobb-Douglas preference and iceberg transport costs istraditional in the literature, but this generally causes analytical intractability. To overcome this difficulty, Ottaviano, Tabuchi and Thisse (2002) reconstruct the core-periphery3

model by a framework of quadratic utility and linear transport costs, which turns out tobe completely solvable. Their framework is applied to analyze the HME in Section 3.2.2
of Ottaviano and Thisse (2004). Meanwhile, their framework is also extended to include
the agricultural sector by Picard and Zeng (2005), and it is found that the transport costof the agricultural good is very important. Fortunately, the framework of Picard andZeng (2005) can be extended to examine the HME in an analytically solvable way andcan tell us how the trade pattern changes when both the manufacturing and agricultural
goods are subjected to transport costs. This framework be considered as complementary
to Davis (1998) but we will see that the results are completely different.
The paper is organized as follows. Section 2 develops the basic model modified from
Ottaviano et al (2002) and Picard and Zeng (2005). Section 3 examines the HME when
the transport costs of agricultural goods are positive. Surprisingly, the results of thispaper show that HME does exist even when the transport costs of agricultural goods are
positive but small enough to allow trade. Finally, section 4 summarizes the results andsuggests some conclusions.

2

The Model

Our model simply extends that of Ottaviano and Thisse (2004, Section 3.2.2) by reconstructing its agricultural sector. Specifically, assume that the world consists of two
countries: North (n) and South (s). There are H capitalists and L workers in the world,which are endowed to countries n and s with the same fractions θ and 1 − θ, respectively.1
Each capitalist holds a unit of capital and each worker has a unit of labor. Capital
services, but not capital-owners, are perfectly mobile between country whereas labor isimmobile. Without loss of generality, we let θ ∈ (1/2, 1).
There are 3 kinds of goods in the economy: manufacturing goods, agricultural goods
and the numéraire. The manufacturing sector produces a continuum of varieties indexed
by interval [0, N ], whose production requires both capital and labor under increasing
returns to scale. In contrast, there are only two agricultural goods, each of which is pro1

In this way, we rule out comparative advantage à la Heckscher-Ohlin.

4duced in a country by labor only under constant returns to scale and perfect competition.
The reader can think of the agricultural goods as the rice in Japan and the wool in New
Zealand. Finally, the numéraire good is homogeneous, which is produced by nature. The
reader can think of it as gold. The numéraire is initially allocated to L workers and H
capitalists averagely, and let the quantity of endowment to each individual be q̄0 . The
numéraire can be used to buy manufacturing goods and agricultural goods, or consumed
directly.2
In the same way as in Picard and Zeng (2005), the preferences of a representative
worker in both countries are given by utility function
2
Z N
Z N
Z
βm − γ m N r
γm
r
r
2
r
qm (x)dx −U (q0 , qm , qa ) =αm[qm (x)] dx −qm (x)dx22000βa − γa nr 2γa
+ αa (qanr + qasr ) −[(qa ) + (qasr )2 ] − [qanr + qasr ]2 + q0 .
(1)
2
2
r
where qm(x) is the quantity of industrial variety x ∈ [0, N ] in country r, qanr (resp. qasr ) is

the quantity of agricultural product of country n (resp. country s) in country r, and q0 is
the quantity of the numéraire. In this expression, αm (resp. αa ) expresses the intensity ofpreferences for the industrial (resp. agricultural) differentiated product, whereas βm > γm
(resp. βa > γa ) means that consumers are biased toward a dispersed consumption ofvarieties. Particularly, βa = γ represents the situation that consumers do not distinguish
two agricultural goods, which is the model base of Davis (1998).
Transporting one unit of any variety good in the manufacturing sector costs τm , andone unit of any variety good in the agricultural sector costs τa . Both τm and τa arepositive but they are supposed to be small enough so that foreign goods in both sectors
are consumed. Specifically, the following inequalities are assumed:
2am
2bm + cm N
(1 − θ)L − N φ,τa <(ba + 2ca )(H + L)(1 − θ)
τm <

(2)
(3)

where parameters am , bm , cm , ba and ca are defined in (4), (5) and (6) later. The numéraireis assumed to be transported free.
2

We do not include the saving function of gold in our model, and individuals consume gold for deco-

ration only.

5

3Home Market Effect

3.1

Consumer

Each consumer maximizes his/her utility given budget constraint
Z N
pm (j)qm (j)dj + pa (n)qa (n) + pa (s)qa (s) + q0 = y + q̄0 ,0where y is the wage income, pa (·) and pm (·) are the consumer prices and where y is
the consumer’s income. The initial endowment q̄0 is supposed to be sufficiently large
for the equilibrium consumption q0 of the numéraire to be positive for each individual.
This implies that each individual consumes all varieties (provided that prices are smallenough, which is assumed below). Because marginal utility for the numéraire is equal ineach country, its price can be normalized to one without losing generality.
kl
We denote by pkl· (·) and q· (·) the price and the quantity of a variety produced incountry k ∈ {n, s} and sold in country l ∈ {n, s}. Obviously, since country n (resp. s)does not produce the agricultural variety s (resp. n), we have that qann (s) = qans (s) =qasn (n) = qass (n) = 0. We can therefore drop the reference to the varieties of agricultural
goods and denote the quantities of variety r by qann and qans , and the quantities of variety
s by qass and qasn . First order conditions of the consumer program yield the demands for
agricultural goods in country n. These are given bynn
sn
qann = aa − (ba + 2ca ) pnn
a + ca (pa + pa ) for variety nnnsn
qasn = aa − (ba + 2ca ) psn
a + ca (pa + pa ) for variety s

where the parameters
aa =

1
γa
αa
, ba =, ca =
βa + γ aβa + γ a(βa − γa )(βa + γa )(4)measure the size of the demand for agricultural goods, its price sensitivity and the degreeof product substitutability between agricultural varieties. For ca = 0, varieties n and s
are independent, while they are perfect substitutes for ca → ∞. Demands for agricultural
products in country s are given by symmetric formulae.
klklSymmetry between varieties imposes that qm(i) ≡ qm
for all variety i produced incountry k and sold in country l. Similarly to the derivation of expression (3) of Ottaviano
6

et al (2002), we take the first order condition of the consumer’s program with respectkn
to the consumption of each manufactured variety, qm
with k ∈ {n, l} and we get thefollowing demands for manufactured varieties in country n:nnnqm= am − (bm + N cm )pnn
m + c m Pm
snnqm
= am − (bm + N cm )psn
m + c m Pm

where the size of the demand for manufactured goods, the price sensitivity and the degreeof product substitutability between manufactured varieties are measured byαm1, bm =,
βm + (N − 1)γm
βm + (N − 1)γm
γm
cm =
.
(βm − γm )[βm + (N − 1)γm ]

am =

(5)
(6)

These demand functions include the price index of manufactured products in country nsn
Pmn = λN pnn
m + (1 − λ)N pm ,where λ is the share of firms that locate in country n. Demands in countries s are given
by symmetric formulae.

3.2

Equilibrium

Recall that the economy is endowed with H capitalists and L workers each supplying one
unit of their corresponding factor. Capital services, but not capital-owners, are perfectly
mobile between country whereas labor is immobile.
The manufacturing sector produces a continuum of horizontally differentiated varieties
under increasing returns to scale. For convenience, the production of a firm in the manufacturing sector needs only fixed costs of 1 unit of capital and φ unit of labor3 Therefore,
the total number of firms is N = H.
3

The assumption of increasing returns to scale does not necessarily imply the zero marginal cost.

However, the assumption of no marginal cost catches the essence of increasing return and makes theanalysis much more convenient. Furthermore, although Ottaviano and Thisse (2004) include the marginal
cost m into their model, their results do not substantially depend on m. Therefore, as in Ottaviano etal. (2002), Picard and Zeng (2005), we keep this assumption to gain more tractability here.

7

The agricultural sector of each country produces one original product under constantreturns to scale and perfect competition. For convenience, take units so that a unit oflabor produces a unit of agricultural good in each country.
Let λ be the ratio of manufacturing sector located in country n. Then the manufacturing labor is λN φ in country n, and (1 − λ)N φ in country s. The agricultural populationis θL − λN φ in country n and (1 − θ)L − (1 − λ)N φ in country s.
Taking units so that a unit of labor produces a unit of agricultural good in eachcountry. Therefore, the prices of agricultural goods become the wages wn and ws in theircountries, respectively. ThenθL − λN φ = θ(L + H)[aa − (ba + 2ca )wn + ca (wn + ws + τa )]+ (1 − θ)(L + H)[aa − (ba + 2ca )(wn + τa ) + ca (wn + ws + τa )](1 − θ)L − (1 − λ)N φ = θ(L + H)[aa − (ba + 2ca )(ws + τa ) + ca (wn + ws + τa )],+ (1 − θ)(L + H)[aa − (ba + 2ca )ws + ca (wn + ws + τa )].
Solving them obtains
aa ba (θL − λN φ) + ca (L − N φ)−
− (1 − θ)τa ,baba (ba + 2ca )(H + L)aa ba [(1 − θ)L − (1 − λ)N φ] + ca (L − N φ)
ws = −− θτa .
baba (ba + 2ca )(H + L)

wn =Let r be the profit of one unit of capital. Then the profit of a firm in country n is
n
nn
ns
ns
πm
= pnn
m qm θ(L + H) + (pm − τm )qm (1 − θ)(L + H) − r − wn φ.

By the FOC of maximizing this profit, the prices should satisfynnsn
am − 2(bm + N cm )pnn
m + cm [λN pm + (1 − λ)N pm ] = 0,τmssam − 2(bm + N cm )(pns) + cm [λN pnsm −m + (1 − λ)N pm ] = 0.
2

Similarly, for a firm in country s, it holds thatssns
am − 2(bm + N cm )pss
m + cm [λN pm + (1 − λ)N pm ] = 0,τmsn
) + cm [λN pnn
am − 2(bm + N cm )(psnm + (1 − λ)N pm ] = 0.
m −
2

8

Solving the above four equations, we have
2am + cm N (1 − λ)τm
τm
nn
, psn
,
m = pm +2(2bm + cm N )2τm2am + cm N λτm
ss
, pns
.
pss
m = pm +m =2(2bm + cm N )
2

pnn
m =

Then
bm + c m N[2am − (1 − λ)cm N τm ],4bm + 2cm N
bm + c m N
nsqm={2am − [2bm + cm N (1 − λ)]τm },4bm + 2cm N
bm + c m N
ssqm=[2am + cm N λτm ],4bm + 2cm N
bm + c m N
sn[2am − (2bm + cm N λ)τm ].
qm=
4bm + 2cm N
nn
qm
=

ns
sn
For costs τm and τa satisfying (2) and (3), qans , qasn , qm
and qmare all positive. In otherwords, the goods in both sectors are traded.
ns
Due to the free-entry of firms, it should hold that πm= πm= 0, which are simplifiedas(bm + cm N )(L + H)22
θ[2am + (1 − λ)cm N τm ] + (1 − θ){2am − [2bm + cm N (1 − λ)]τm }4(2bm + cm N )2
aa ba (θL − λN φ) + ca (L − N φ)=r+φ−
− (1 − θ)τa ,baba (ba + 2ca )(H + L)
(bm + cm N )(L + H)22
θ[2am − (2bm + cm N λ)τm ] + (1 − θ)(2am + cm N λτm )4(2bm + cm N )2
aa ba [(1 − θ)L − (1 − λ)N φ] + ca (L − N φ)=r+φ−− θτa .
baba (ba + 2ca )(H + L)
Subtracting the second from the first, we obtain(bm + cm N )(L + H)τm
[2(2θ − 1)(2am − bm τm ) + (1 − 2λ)cm N τm ]4(2bm + cm N )(1 − 2θ)L − (1 − 2λ)N φ.
= φ (2θ − 1)τa +(ba + 2ca )(H + L)
The above expression can be rewritten as2
cm N (bm + cm N )(L + H)τm
N φ2
(2λ−1)+
4(2bm + cm N )(ba + 2ca )(H + L)
(bm + cm N )(L + H)(2am − bm τm )τmL= (2θ − 1)+φ− τa2(2bm + cm N )(ba + 2ca )(H + L)
9and hence1,
λ − θ = ∆× θ −
2


(7)

where


L − Nφ(bm + cm N )(L + H)τm [2am − (bm + cm N )τm ]+φ− τa4(2bm + cm N )(ba + 2ca )(H + L)
∆=
. (8)
2
cm N (bm + cm N )(L + H)τm
N φ2+4(2bm + cm N )(ba + 2ca )(H + L)
Because of (2) and (3), the numerator of (8) is positive. Therefore, ∆ > 0 and λ > θ holds
at equilibrium from (7), which shows the existence of home market effect. The above issummarized as follows.
Theorem 1 The HME exists if τm and τa are small so that goods in both sectors aretraded.
In the framework of Davis (1998) and Yu (2005), there is only one agricultural good.
This corresponds to the case of βa = γa in our framework, which implies ca → ∞ and (3)is violated for any positive τa . This explains that why they fail to observe the existenceof HME, which is observed in our model.
On the other hand, if we exclude the parameters in the agricultural sector, (7) degenerates to
2[2am − (bm + cm N )τm ]1
λ −θ =
θ−> 0,
cm N τ m
2
m(9)

which is consistent with (25) of Ottaviano and Thisse (2004).4 Comparing (7) with (9),we find that including the agricultural sector does not decrease the HME at all.

4

Summary and conclusions

The results of Davis (1989) show that the over simplification on the agricultural sector
in traditional new-economic-geography models is not innocuous. Recently, Yu (2005)
extended the result of Davis (1989) and find that, the home market effect may either
disappear, be reversed, or be kept when the transport costs of the agricultural good is
positive. However, their models treat the agricultural good as the numéraire, and over4

Note that our model further assumes f = 1 and m = 0 for simplicity.

10simplifies the agricultural sector again. This paper reconstructs the agricultural sectorin two respects. First, we separate the agricultural goods from the numéraire, whichallows us to distinguish their impact on the home market effect. Second, we differentiate
two agricultural goods produced in two countries so that importing a bit of agricultural
good from the foreign country does not change the price of its own agricultural goodcatastrophically. In this way, we surprisingly find that the home market effect does notdisappear because of positive transport costs of agricultural goods. Therefore, we canconclude that, the results of Davis (1998) and Yu (2005) essentially depend on the factof no trade in the agricultural sector between countries.

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Review 88(5), 1264-1276.
[2] Fujita, M., Krugman, P.R. and Venables, A.J., 1999. The Spatial Economy: Cities,
Regions and International Trade. Cambridge (Mass.), MIT Press.
[3] Hanson, G.H. and Xiang, C., 2004. “The home-market effect and bilateral tradepatterns.” American Economic Review 94(4), 1108-1129.
[4] Head, K., Mayer T. and Ries, J., 2002. “On the pervasiveness of home market effects.”
Economica 69, 371-390.
[5] Helpman, E. and Krugman P., 1985. Market Structure and Foreign Trade. Cambridge,
MA: MIT Press.
[6] Holmes, T.J. and Stevens, J.J., 2005. “Does home market size matter for the patternof trade.” Journal of International Economics, forthcoming.
[7] Krugman, P., 1980. “Scale economies, product differentiation, and the pattern oftrade.” American Economic Review 70(5), 950-959.
[8] Ottaviano, G.T., Tabuchi, T. and Thisse J.-F., 2002. Agglomeration and trade revisited. International Economic Review 43, 409–436.
11[9] Ottaviano, G.T. and Thisse, J.-F., 2004. “Agglomeration and economic geography.”
Chapter 58 of Handbook of Regional and Urban Economics (Vol. 4) (V. Henderson
and J.-F. Thisse, eds.), Elsevier, Amsterdam, pp. 2563-2608.
[10] Picard, P. M. and Zeng, D.-Z., 2005. Agricultural sector and industrial agglomeration.
Journal of Development Economics, forthcoming.
[11] Rauch, J.E., 1999. Networks versus markets in international trade.” Journal of International Economics 48(1), 7-35.
[12] Yu, Z., 2005. “Trade, market size, and industrial structure: revisiting the homemarket effects.” Canadian Journal of Economics 38(1), forthcoming.

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