This paper examines the impacts of country-specific network costs that are provided by a capital-intensive communications sector in a two-country two-factor model, where there are two trading sectors, agriculture and manufacturing. It is shown that when firms in the manufacturing sector incur a fixed cost associated with connection to the communications network upon entry, comparative advantage will be determined by the relative endowments of capital in each country and the size of fixed costs associated with the communications sector. The capital abundant (scarce) country will have a comparative advantage (disadvantage) when the cost-sharing effect (the congestion effect) dominates.

Colin Davis

English

Research Papers in Economics

Capital−Intensive Country−Specific Network Costs and
Intra−Industry Trade 
Colin Davis
Graduate School of Economics and Business Administration, Hokkaido University
Abstract
This paper examines the impacts of country−specific network costs that are provided by a
capital−intensive communications sector in a two−country two−factor model, where there are
two trading sectors, agriculture and manufacturing. It is shown that when firms in the
manufacturing sector incur a fixed cost associated with connection to the communications
network upon entry, comparative advantage will be determined by the relative endowments
of capital in each country and the size of fixed costs associated with the communications
sector. The capital abundant (scarce) country will have a comparative advantage
(disadvantage) when the cost−sharing effect (the congestion effect) dominates.
I would like to thank Hiroshi Ono, Hiroshi Kurata, and Yasunobu Tomoda for their helpful and insightful comments. Any
remaining errors are my own.
Citation: Davis, Colin, (2005) "Capital−Intensive Country−Specific Network Costs and Intra−Industry Trade." Economics
Bulletin, Vol. 6, No. 3 pp. 1−9
Submitted: March 16, 2005.  Accepted: April 13, 2005.
URL: http://www.economicsbulletin.com/2005/volume6/EB−05F10002A.pdf1 Introduction
Recently the e®ect of communication costs on trade has increasingly become
a topic of discussion in the international trade literature. This increased at-
tention is partially due to advances that have been made in the communica-
tions industry with the application of new technologies such as the Internet,
¯ber optics, and satellite based systems. The costs of building, maintain-
ing and connecting to communications networks are usually associated with
their size and complexity and the number and sophistication of users.
Communication costs have, in general, been modelled as ¯xed costs in
the literature and this is the approach that is adopted in this paper. Harris
(1995) presents a strong argument for modelling network connection as a
¯xed cost suggesting that once a communications network is in place the
marginal cost of communication is negligible. Furthermore, the nature of a
communications network as a public good necessitates consideration of con-
sumption externalities that occur with varying volumes of use. Two types
of externalities that may occur are a cost-sharing e®ect and a congestion
e®ect. In the ¯rst case, the ¯xed cost incurred with connection decreases
in the number of users as the large ¯xed costs of establishing the network
are shared over a larger user base. In the second case, the cost of provid-
ing communication services increases with the number of users because of
congestion of the network. Harris (1995) examines how trade patterns are
a®ected by the existence of an international communications network that
is characterized by the externalities described above.
Kikuchi (2002) takes a di®erent approach by analyzing the impact of
local or country-speci¯c communications networks with cost-sharing exter-
nalities. Applying a two-country model with one factor of production, labor,
he demonstrates that the larger country will derive a comparative advan-
tage in the trade of \network goods", for which production requires the use
of communications services, as a result of aggregate increasing returns to
scale. Kikuchi and Ichikawa (2002) extend this analysis to allow for a neg-
ative congestion externality and show that the larger country will have a
comparative advantage when the cost-sharing e®ect dominates and a com-
parative disadvantage when the congestion e®ect dominates. Their results
have implications for the patterns of intra-industry trade in that while a
dominant cost-sharing externality leads to specialization of production, a
dominant congestion externality leads to intra-industry trade. Moreover,
when intra-industry trade does occur the larger country may become a net
importer of the \network good".
This paper extends the analysis of Kikuchi and Ichikawa (2002) to in-
clude two factors of production, labor and capital. The establishment of
a communications network requires a large infrastructure which implies a
high capital intensity for the communications industry. In fact, Wolf (1999)
reports that between 1958 and 1987,in the United States, average annual
1investment in machinery, equipment, and instruments per full time equiv-
alent employee in the communications sector, at a value of $17,872 (1987
U.S. dollars), was second only to that in the electric, gas and sanitary ser-
vices sector. This is well above the value of $2613 for the entire economy.
This high capital-labor ratio for the communications industry suggests a
strong role for capital endowments in the determination of comparative ad-
vantage and trade patterns in a model with country-speci¯c communications
networks. This paper attempts to clarify this role by using a two-country
two-factor model. To simplify the analysis an extreme case, where communi-
cations networks are produced using capital alone, is examined. Under this
model comparative advantage is determined by the relative capital endow-
ments of each country and whether the cost-sharing or the congestion e®ect
dominates, as determined by the size of ¯xed costs in the communications
sector. When the congestion e®ect dominates the country with the smaller
endowment of capital may become a net exporter of manufactured goods
that require the use of capital intensive communications services.
The remainder of the paper proceeds as follows. Section 2 describes the
basic model for a closed economy. Section 3 examines trade patterns for two
cases: a dominating cost-sharing externality and a dominating congestion
externality. Section 4 provides some concluding remarks.
2 Basic Model
There are three sectors: agriculture, manufacturing, and communications
across which the two factors of production, labor and capital, are perfectly
mobile. Firms in the agricultural sector produce a homogeneous good, Y ,
under constant returns to scale. On the other hand, the manufacturing
sector produces a large number of varieties of a manufactured product. Firm
level increasing returns to scale, resulting from a ¯xed cost of entry and a
large set of producible varieties, assure that each variety is produced by only
one ¯rm.1 The communications sector provides communications services in
the form of a network that is used by ¯rms in the manufacturing sector.
Consumer preferences are described by a Cobb-Douglas utility function
U = X¹Y 1¡¹, 0 ¸ ¹ · 1, where
X =
Ã
n X
i=1
c®
i
! 1
®
; ® = 1 ¡
1
¾
; ¾ > 1: (1)
X is the consumption index for the n varieties produced in the manufac-
turing sector, ci is the consumption of variety i, and ¾ is the elasticity of
substitution between varieties. Expenditures on X and Y are ¯xed shares
1See Dixit and Stiglitz (1977).
2of national income, I.
PXX = ¹I PY Y = (1 ¡ ¹)I; (2)
where PX =
¡Pn
i=1 p1¡¾
i
¢ 1
1¡¾ is the aggregate price index for varieties of the
manufactured product and PY is the price of the agricultural good. The
demand function for any given variety is
ci = ¹IP¾¡1
X p¡¾
i =
¹I
np
; (3)
where, assuming symmetry among varieties, the consumption and price in-
dexes respectively reduce to X = n1=®c and PX = n1=(1¡¾)p.2
The agricultural good, Y , is produced for a perfectly competitive mar-
ket. Assuming the unit cost of production is given by w¸r1¡¸ and setting
Y as the model numeraire, all ¯rms in the agricultural sector will equate
marginal revenue with marginal costs so that w¸r1¡¸ = 1. The Y -sector
factor demands for labor and capital are obtained using Sheppard's Lemma.
LY =
¸(1 ¡ ¹)I
w
KY =
(1 ¡ ¸)(1 ¡ ¹)I
r
; (4)
where w is the wage and r is the rental.
The communications sector takes the form of a natural monopoly that
provides network services to ¯rms in the manufacturing sector. Production
of the communications network requires a large capital investment equal to
(F + n2), where F is the initial investment needed to build the network
infrastructure and n2 is the investment required for the network connec-
tion of each ¯rm. Following Kikuchi and Ichikawa (2002) the communica-
tions monopoly charges all ¯rms connecting to the network by applying an
average-cost pricing rule.
°(n) =
µ
F
n
+ n
¶
; (5)
where (F=n+n) is measured in units of capital. A plot of average costs, °(n),
therefore has a U-shaped form because the cost of connecting to the network
is initially falling, the cost-sharing e®ect, but subsequently increasing, the
congestion e®ect, with the number of ¯rms.
Firms in the manufacturing sector, X, produce their varieties for a mo-
nopolistically competitive market. The costs of production include a ¯xed
cost of entry equal to the cost of connecting to the network, °(n), and a
unit cost given by wµr1¡µ . Free entry reduces the pro¯ts of each ¯rm to
zero where operating pro¯ts are just su±cient to cover ¯xed costs.
(pi ¡ wµr1¡µ)xi = r°(n): (6)
2See Helpman and Krugman (1985).
3The ¯rst order condition for pro¯t-maximization determines price, which
will be a constant mark-up over unit cost for each ¯rm, as p = wµr1¡µ=®.
This pricing policy along with the zero-pro¯t condition, equation (6), infers
that the zero-pro¯t level of output is
x =
µ
F
n
+ n
¶³ r
w
´µ
(¾ ¡ 1): (7)
When the market for di®erentiated goods clears, given the constant
mark-up over unit costs, the demand for each variety, equation (3), can
be written as c = ®¹I=nwµr1¡µ and the number of ¯rms operating in the
manufacturing sector and connecting to the communications network can
be obtained as
n =
µ
¹I
¾r
¡ F
¶1
2
: (8)
From Sheppard's Lemma, the demands for labor and capital in the man-
ufacturing sector are respectively,
LX = µ
³w
r
´µ¡1
nx KX = (1 ¡ µ)
³w
r
´µ
nx + (F + n2): (9)
To close the model, assume that labor and capital markets clear so that
L = LX + LY and K = KX + KY . w and r are then determined by sub-
stituting equations (4) and (9) into these factor market clearing conditions
and using nx = (®¹I)=wµr1¡µ and (F + n2) = ¹I=¾r.
w = A
I
L
r = (1 ¡ A)
I
K
; (10)
where A = ®µ¹ + ¸(1 ¡ ¹).
Using the equilibrium rental in equation (10) the equilibrium number of
manufacturing varieties can now be written as
n =
µ
¹K
¾(1 ¡ A)
¡ F
¶1
2
: (11)
The number of varieties is a function of the capital endowment alone.
This is a consequence of the assumption that capital is the sole factor used in
the communications sector. Allowing for the use of labor in the production
of the communications network would alter this result. However, this sim-
pli¯cation can be rationalized with the observation that the communications
industry has a high capital intensity.
In the next section, the free trade equilibrium is examined and it is
shown that comparative advantage and the existence of intra-industry trade
are determined by relative capital endowments and network sizes.
43 Trading Equilibrium
In this section, the e®ects of capital intensive communications networks on
the patterns of trade are examined. Let the world endowments of capital
and labor respectively be KW and LW. There are two countries, home
and foreign, with identical technologies and preferences. The endowments
of capital and labor for home and foreign respectively depend on a share
parameter s, 0 ¸ s ¸ 1, such that
Kh = sKW Kf = (1 ¡ s)KW;
Lh = (1 ¡ s)LW Lf = sLW; (12)
where h and f respectively indicate whether a variable is associated with
home or foreign. Given these capital and labor endowments, the autarky
equilibrium number of ¯rms in each country will be determined by
(nh
a)2 + (nf
a)2 =
¹KW
¾(1 ¡ A)
¡ 2F; (13)
where a indicates autarky.3
The price and consumption indexes for the varieties produced in the
manufacturing sector are
Pi
X =
h
nh(ph)1¡¾ + nf(pf)1¡¾
i 1
1¡¾ ; i = h;f (14)
Xi =
h
nh(ch)® + nf(cf)®
i 1
® : i = h;f (15)
Now with the assumption of free trade in the agricultural good and va-
rieties of the manufactured product, i.e. no tari®s and negligible transport
costs, factor price equalization will occur as long as neither country com-
pletely specializes in the production of manufactured goods.4 With the wage
and rental equalized, the price of manufactures, p = wµr1¡µ
® , will be the same
for manufacturing ¯rms in both home and foreign. The free trade demand
for a given variety in country i is
ci =
®¹[Ih + If]
wµr1¡µ(nh + nf)
: i = h;f (16)
3Equation (13) is obtained by adding
n
h
a =
µ
¹sK
W
¾(1 ¡ A)
¡ F
¶ 1
2
and n
f
a =
µ
¹(1 ¡ s)K
W
¾(1 ¡ A)
¡ F
¶ 1
2
:
4This requires that the Y sector continue to operate in both countries in the free trade
equilibrium. Kikuchi (2002) examines the case where one country completely specializes
in the production of \network goods".
5Equating the free trade demand for each variety given in equation (16)
with the zero-pro¯t output given in equation (7) the number of varieties
produced by country i will determined implicitly by
F + (ni)2 =
¹[Ih + If]
r¾
ni
nh + nf : i = h;f (17)
Given the world endowments of labor and capital and using the fac-
tor market clearing conditions the free trade wage rate and rental can be
obtained as
wW =
A[Ih + If]
LW ; rW =
(1 ¡ A)[Ih + If]
KW ; (18)
where (nhxh + nfxf) = (®¹(If + Ih))=wµr1¡µ has been used. With the
rental equalized across countries, the implicit functions for the numbers of
¯rms in each country can now be written as
°(ni) =
¹KW
¾(nh + nf)(1 ¡ A)
: i = h;f (19)
Equations (19) implicitly determine the allocation curves of home and
foreign,5 respectively shown in Figure 1 as ABO and OBC. These allocation
curves show the number of zero-pro¯t ¯rms for each country given the num-
ber of ¯rms operating in the other country. For numbers of ¯rms outside
these allocation curves, negative pro¯ts are earned and some ¯rms will exit
the market raising the pro¯ts of the remaining ¯rms to zero. On the other
hand, for numbers of ¯rms inside these allocation curves positive pro¯ts
are earned and market entry by new ¯rms will reduce pro¯ts to zero. This
process of entry and exit is described by the arrows in Figure 1. The locus
of autarky ¯rm numbers for home and foreign, equation (13), is shown as
DBE.
Figure 1(a) describes the case where the ¯xed costs of the communica-
tions industry, F, are relatively large and the cost-sharing e®ect dominates
the congestion e®ect in the communications industry. There are two stable
equilibria, A and C, and one unstable equilibrium, B. If the capital endow-
ments, home and foreign, di®er the capital abundant country will have a
comparative advantage in the production of manufacturers as a result of
the aggregate returns to scale derived from the cost-sharing e®ect. This will
lead to a shift in the location of production so that the entire manufacturing
industry locates in the capital-abundant country, e.g. point A or C.
Figure 1b demonstrates the case where F is relatively small, and the
congestion e®ect dominates. Now there are three stable equilibria: A, B,
and C. If the free trade equilibrium is described by point B, then the number
of varieties produced in
5These allocation curves have the same shape as those introduced by Kikuchi (2002)
and Kikuchi and Ichikawa (2002).
6Figure 1
(a) Dominant Cost-Sharing E®ect
n
f
n
h 0
A
B
C
D
E
6 ¾
?
-
6 -
?
¾
(b) Dominant Congestion E®ect
n
f
n
h 0
A
B
C
D
E
?
-
6 ¾
6 -
?
¾
The parameter values ¹ = 0:5, µ = 0:8, ¸ = 0:4, ¾ = 2, K
W = 200 are the same in both
¯gures with the exception of F which equals 35 in (a) and 7 in (b).
each country will be the same. When the capital endowments of home
and foreign di®er the country with the smaller endowment of capital will be
a net exporter of capital-intensive manufactured goods.
4 Conclusion
This paper extends the results of Kikuchi and Ichikawa (2002) to examine
the role of capital in the determination of comparative advantage in a model
with country-speci¯c communications networks. The analysis focuses on the
case where capital is the only factor used in the communications sector.
The model suggests that, when manufacturing ¯rms require the use of
a communications network, trade patterns will be determined by relative
capital endowments and network externalities. A dominant cost-sharing ef-
fect leads to industry level returns to scale in the manufacturing industry
creating a comparative advantage in the production of manufactured goods
for the relatively capital abundant country. Then, specialization of pro-
duction occurs with the relatively capital abundant country producing all
manufactured goods and the relatively capital scarce country only producing
the agricultural product. On the other hand, a dominant congestion e®ect
leads to a comparative advantage for the relatively capital scare country as
a result of lower network connection costs. Then, the number of varieties
of the manufactured good produced in each country will be the same, net-
work connection costs will be equalized, and intra-industry trade will occur
with both countries exporting manufactured goods. In this case the country
with the smaller endowment of capital may become a net exporter of the
7capital-intensive manufactured good.
These results suggest that relative capital endowments are an important
determinant of the patterns of trade for manufactured goods that require
the use of a communications network in production.
References
Dixit, Avinash and Joseph E. Stiglitz (1977) \Monopolistic Competi-
tion and Optimum Product Diversity," American Economic Review 67,
297-308.
Helpman, Elhanan and Paul R. Krugman (1985) Market Structure and
Foreign Trade. Cabridge: MIT Press.
Harris, Richard G. (1995) \Trade and Communication Costs," Cana-
dian Journal of Economics 28, S46-S75.
Kikuchi, Toru and Tetsuro Ichikawa (2002) \Congestible communi-
cations networks and international trade," Canadian Journal of Eco-
nomics 35, 331-340.
Kikuchi, Toru (2002) \Country-Speci¯c Communications Networks
And International Trade In A Model Of Monopolistic Competition,"
The Japanese Economic Review 53, 167-176.
Wolf, Edward N. (1999) \The productivity paradox: evidence from indi-
rect indicators of service sector productivity growth," Canadian Journal
of Economics 32, 281-308.
8

Country-Speci¯c Communications Networks And International Trade In A Model Of Monopolistic Competition,&quot;

Market Structure and Foreign Trade. Cabridge:

Monopolistic Competition and Optimum Product Diversity,&quot;

The productivity paradox: evidence from indirect indicators of service sector productivity growth,&quot;

Toru and Tetsuro Ichikawa

Trade and Communication Costs,&quot;

Capital-Intensive Country-Specific Network Costs and Intra-Industry Trade

http://www.accessecon.com/pubs/EB/2005/Volume6/EB-05F10002A.pdf

Capital-Intensive Country-Specific Network Costs and Intra-Industry Trade

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