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ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
A
Simple Theory of
Multinational Corporations and Trade
with a Trade-off between
Proximity and Concentration
S. Lael
Brainard
Massachusetts Institute of Technology
WP#3492-92-EFA
December 1992 Revised
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
A
Simple Theory of
Multinational Corporations and Trade
with a Trade-off between
Proximity and Concentration
S. Lael
Brainard
Massachusetts Institute of Technology
WP#3492-92-EFA
December 1992 Revised
JAU
1
3
1993
A
Simple Theory of
Multinational Corporations and Trade
with a Trade-off between
Proximity and Concentration
Abstract
This pap>er develops a two-sector, two-country model, where firms
in a differentiated products sector
choose
between exporting and multinational expansion as alternative modes of foreign market penetration, based on a tradeoff between proximity and concentration advantages.
production, with increasing returns
at
The
differentiated sector is characterised
the corporate level associated with
some
by multi-stage
activity such as
R&D,
scale
economies at the plant level, and a variable transport cost that rises with distance. A pure multinational equilibrium,
where two-way horizontal expansion across borders completely supplants two-way trade in differentiated products,
is possible even in the absence of factor proportion differences.
It is more likely the greater are transport costs
relative to fixed plant costs,
The model
and the greater are increasing returns
also establishes conditions for a
*
First draft
**
I
am
mixed equilibrium,
in
at the
corporate level relative to the plant level.
which national and multinational firms
coexist.
August 1992.
grateful to
Gene Grossman, Paul Krugman and
Julio
National Science Foundation for support under grant SES-9111649.
Rotemberg
for helpful discussions,
and
to the
Introduction
I.
(MNEs)
Multinational enterprises
Alan
international trade.
Rugman
(1988) estimates that the largest 500 multinationals control over one-half of
global trade flows, and one-fifth of global
network of overseas
in
are a substantial and imperfectly understood part of the landscape of
GDP. For
affiliates, affiliate sales
tend to
countries such as the
swamp
exjxjrt flows.
markets such as Brazil and the EC, local sales by U.S. -owned
US, which have a well-developed
DeAnne
affiliates are five
Julius (1990) estimates that
times the level of imports
from the U.S.
It is
also striking that a large and
growing share of foreign
direct investment involves industrialized
Between 1961 and
nations as both the source and destination markets, rather than flowing from North to South.
1988, over half of
all
direct investment outflows generated
countries; this share had risen to nearly
70 percent by 1988
by G-5 countries were absorbed by other G-5
absorbed by developed market nations more broadly was 81 percent by the
(1992)).
These trends suggest a large and growing
considerations of market access.
phenomenon. Indeed,
that
The share of
(Julius (1990)).
1980s (Krugman and Graham
late
of two-way activity across borders motivated by
level
But multinational expansion motivated by market access
in her study
direct investment
is
not just a recent
of American multinationals from the 1700s to 1914, Mira Wilkins concludes
market access was the primary motivation for multinational expansion:
TTiese early international businesses established their foreign stakes
foremost in the areas around the world where there were customers
as
-
we have
in Eurojje
seen
-
first
and
and Canada primarily.
where there was demand for their offerings - in the wealthiest
The businesses described ... went abroad to sell and to make profits through
sales in the countries in which they made investments; if they went into manufacturing, refining, or real
estate, it was with marketing considerations paramount. They did not go abroad for supplies or to
They made
their principal investments
nations in the world.
produce abroad for sale
The implications of
in the
United States. (Wilkins, 1970,
p.
these trends for trade and for policy have not been fully explored, partly because
research on trade and on multinationals proceeds along separate tracks.
recent years in explaining the
Meanwhile, the managerial
1966)
phenomenon of
literature
Trade theory has made great
intraindustry trade, and in modelling imperfect competition'.
on multinationals has evolved
to incorporate recent
of the boundaries of the firm.^ However, there have been only a few attempts
characteristics that
have been adduced
strides in
to explain intraindustry trade
1
-
advances in the theory
at synthesis,
even though the
imperfect competition, scale economies.
and differentiated products
-
are precisely the characteristics that are associated with the internalization and
ownership advantages believed to motivate the formation of multinationals.
This f>aper develops a two-sector, two-country model, where firms in a differentiated products sector
choose between exporting and cross-border expansion as alternative modes of foreign market penetration.
differentiated sector is characterized
that
can be spread
by increasing returns
among any number of production
at the
facilities
firm level due to
some
input, such as
The
R&D,
with undiminished value, scale economies
at the
plant level, such that concentrating production lowers imit costs, and a variable transport cost that rises with
distance.
The
transport cost stands in for a variety of advantages
from locating close
according to Wilkins, have been a chief motivation for expansion of
'investments abroad were
made
to save
customer service and to avoid damage
US
to the customer,
multinationals historically:
on transportation costs and warehousing expenses,
in shipping a perishable
product
which,
(p.
67)."
The
to obtain superior
decision whether to
expand abroad via trade or via investment hinges on a trade-off between these proximity advantages and scale
advantages from concentrating production in a single location.
In this model, a pure multinational equilibrium,
supplants merchandise trade in the differentiated sector,
differences,
when proximity advantages
where two-way intraindustry investment completely
is
possible even in the absence of factor proportion
provides a rationale for two-way horizontal expansion across borders, which
rationale for vertical expansion based
of two-way investment
in
on factor endowment
automobile assembly
for
example
US
investments in semiconductor assembly and
-
facilities
in contrast to factor-based theories
This equilibrium
is
more
crowds out trade
differentials.
between the
of multinational
test facilities in
With a simple two-stage production process,
trade in invisibles completely
Thus,
are strong relative to concentration advantages.
in
there
is
US
is
distinct
this
from the
model
traditional
This model formalizes an explanation
and the
activities,
EC
(eg,
which are
Volkswagen and GM),
better suited to explaining
Southeast Asia.
a pure multinational equilibrium in which
two-way
goods, even in the presence of symmetric factor proportions.
likely the greater are transport costs relative to plant-level scale
greater are increasing returns at the corporate level relative to those at the plant level.
economies, and the
Under
circumstances, a symmetric equilibrium with purely national firms obtains, in which there
is
the opposite
balanced two-way
trade in differentiated products.
economies and of returns
at the
For intermediate ranges of transport costs
corporate level relative to the plant level, there
multinational and national firms coexist in the differentiated sector.
two-way
is
a
mixed equilibrium
in
which
In a symmetric mixed equilibrium, there
is
trade in both differentiated products and invisibles.
The incorporation of
a third stage of production, such as sales,
two-way, intrafirm, intraindustry trade
when
relative to plant-level scale
makes possible an equilibrium
in intermediates replaces trade in final goods.
in
which
This equilibrium holds
concentration advantages dominate in upstream activities, and proximity advantages dominate downstream.
The presence of
multinationals has an ambiguous effect
reduction in transport costs, but there
the absence of multinationals, they
imports, so that there
equal quantities of
When
is
a
is
home and
a concomitant reduction in the
consume
home-market
on consumer welfare; consumers benefit from a
bias,
number of
a larger quantity of differentiated
varieties, all else equal.
In
goods produced locally than of
whereas with two-way multinational production, they consume
foreign varieties.
there are both factor proportions and proximity advantages to overseas expansion, the location of
each stage of the production process dej>ends on both considerations.
single-plant multinationals
may emerge, while
When
factor considerations dominate,
dual-plant multinationals prevail in the presence of sufficiently
strong proximity advantages.
I.
Related Research
i.
The model combines elements from both
literature
on multinationals. In recent
the imperfect competition trade literature and the strategy
years, the strategy literature
on multinationals has converged on a
conceptual framework based on transactions cost analysis of the boundaries of the firm.
expansion
is
Roughly, multinational
explained as a firm's optimal response to the conjuncture of three advantages.
ownership advantage in some unique asset
that gives the firm
market power and
is
The
first is
an
associated with increasing
returns across the firm (network capital, proprietary process technology or product designs, or an established
reputational capital); the motivation for expansion
mtemalization advantage, such that the firm
is
is
to
maximize the returns
unable to realize the
full
to this asset.
Second, there
is
an
value of the asset through the market.
due
to transactions costs or other
Third, there
licensing.
makes
is
first
failures.
This determines the choice of direct investment over
an advantage to locating production near consumers or factors across borders, which
international expansion
While the
market
more
profitable than exporting.
two types of advantages are closely linked
transactions costs, the concept of location advantages
is
to literature
loosely defined, and
This disjuncture between location advantages and trade theory
theory.'
is
on the theory of the firm and on
makes no reference
to trade
surprising in light of the important
advances made by trade theorists in recent years in incorporating maricet power and increasing returns to scale
into trade models.
The economics
literature
on multinationals has gone part way
in recent years to incorporate these
Broadly, two strands of research have considered multinational activity.
insights.
choice between licensing and investing across borders.
market failure that prevents firms from
It
The
first
focuses on the
models internalization as an endogenous response
fully exploiting their
market power through the market.
to a
Ethier (1986)
incorporates the internalization decision into a general equilibrium trade model based on specific factor
endowments with a
differentiated manufacturing sector.
imperfections in contracting under uncertainty.
downstream
distribution
must be located
The
reputation for quality.
equilibrium framework.
in the destination
internalization decision of the firm is a response to
location choice is captured by an ad hoc assumption that
in the destination
Horstmaim and Markusen (1987) focus on
framework, where production
The
consumption market.
the internalization decision in a partial equilibrium
market may be chosen over licensing in order to maintain a
Ethier and Markusen (1991) similarly focus on the internalization decision in a partial
The decision between exporting and overseas production
via licensing or investment
dep>ends in part on a trade-off between variable transport costs and a fixed production cost, but the general
equilibrium implications are not explored.
A
second strand of research focuses on the choice between exporting and investing across borders,
which hinges on location advantages.
Krugman
Krugman
(1982),
Helpman (1984), Markusen (1984), Helpman and
(1985), and Horstmann and Markusen (1992) incorporate
models, which
start
from the premise
that firms benefit
MNEs
into general equilibrium trade
from internalization due to increasing returns
at the
level
The model
of the firm, and focus attention on the location decision.
research in focusing on the location decision.
vertical
I
develop below follows
this line
of
But while the Helpman and Helpman, Knigman models explain
expmnsion across borders in terms of factor proportions differences, the model presented in Section
II
formulates the motivation for overseas expansion in terms of a trade-off between proximity and concentration
The model
advantages.^
models
in a
in Section II integrates the central features
more general model;
the
Krugman model' develops
of the Horstmann, Markusen and
a differentiated products
model
Knigman
that focuses
on
proximity advantages alone, while the Horstmann, Markusen model' incorporates a tradeoff between proximity
and concentration advantages
I
briefly
in the context of
Coumot
summarize the main findings of the
duopoly.
factor proportion
comparison.
The Helpman and Helpman/Krugman model
trade model,
where one sector
is
incorpwrates multinationals into a factor proportions
characterized by product differentiation and multiple-stage production.
are multiplant economies of scale associated with a firm-specific input
production of the input
this
is
assumed
to be relatively
model, multinationals arise only
factor
endowments are
no incentive
this
more
There
which has a public goods character, and
capital-intensive than production of the final good.
presence of sufficiently great factor endowment differences.
In
When
sufficiently similar that factor price equalization obtains in the trade equilibrium, there is
in the differentiated sector locate
Thus,
in the
for cross-border investment.
good production
models here, for purposes of
When
factor prices are not equalized under trade,
some of
production of the input in the relatively capital-abundant economy and final
in the relatively labor-abundant
economy, and export back
model explains cross-border investment
to the capital-abundant
as a response to factor price differentials,
and
it
multinational activities will only arise in a single direction within an industry, in single-plant firms.
effectively explains
one-way
differences, but has
little to
the firms
direct investment flows
economy.
predicts that
It
between economies with strong factor proportions
say about two-way intraindustry investment flows between economies with similar
factor proportions.
This contrasts sharply with the model
I
develop below, in which multinational activity can take place in
the absence of factor prop>ortion differences and in
multiplant firms.
To make
two directions
the findings directly comparable,
I
in the
same
industry, and
is
undertaken by
develop a general equilibrium model that closely
parallels the
Helpman and Helpman, Knigman framework, which
also has the virtue of
making the findings
comparable with a monopolistic competition trade model.
Section
II
describes the structure of preferences and production in a framework with symmetric factor
endowments and a two-stage production process, and derives
Section
III
the equilibrium pattern of trade
and investment.
elaborates the production structure in the differentiated sector to incorporate an additional stage.
Section IV elaborates the model to incorporate factor proportions differences as a motivation for overseas
expansion, in addition to the proximity/concentration trade-off.
Section
V
concludes.
Two-Stage Production with Symmetric Factor Endowments
n.
There are two neighboring countries,
A
and B,
between which factors and consumers are immobile.
endowments and
in the distribution
at a distance
The
D
apart.
analysis will initially
Countries are defined by areas
assume symmetry
in factor
of consumers across countries, in order to isolate the role of proximity
advantages in stimulating multinational activity.
n.
Consumption
i.
There are two classes of goods: agricultural goods, which are homogeneous, and manufactured goods,
which are
differentiated.
Consumers have
identical,
homothetic preferences over classes of goods.
assumption permits separation of the consumption decision into two stages:
the allocation of expenditure
between the two aggregate goods, and the suballocation of manufacturing exptenditure among
It is
further
assumed
that
consumers have
identical preferences
This
among
varieties.
varieties of the differentiated
good, which take the form of a constant-elasticity-of-substitutionsubutility function of the Dixit-Stiglitz-Spence
type.
Denoting the differentiated product
Q
and the share of expenditure allocated to differentiated goods Eg,
the consumer's second tier utility maximization problem can be represented as:
^^^
where
market
Max
q^, is
a,
the quantity of variety
and
n, is the
number of
UQ{q^^^,...A^gA^...)
i
originating in market a
varieties
from market
a.
6
s.t.
(
EE
= A,B),
The
''i.'^fa
Pj, is
^
^o
the price of variety
i
produced
in
subutility function is defined over all varieties
of good q available
at
the consumer's location:
B
where
<t
is
the elasticity of substitution
consumption plan
variety
is
among
I
'.
varieties.
Solving for the
first
order conditions yields an optimal
where the share of manufacturing expenditure allocated
that includes all varieties,
to
each
inversely related to the relative price of that variety:
p-"
9b, =
(3)
"^^-^
^^-T~^Q
k
a
Differentiating with respect to the price yields an expression for the elasticity of
.^1^1^
(4)
I
a.
a-A^
(1-q)
drop the second term
k
in the elasticity expression.
analysis without substantially changing the results, for a sufficiently large
Returning to the
first-tier utility
for each variety:
^^^
=
a
Following Helpman, Krugman,
demand
maximization problem,
This vastly simplifies the
number of
varieties.'
total utility for a representative
consumer
is
defined:
U
(5)
where
utility
from consumption of the
agricultural good, Y.
=
UIu/IuqO]
agricultural good, u^(.),
Assuming a Cobb-Douglas
simply assumed to equal consumption of the
is
utility function, the
consumer's
first-tier utility
maximization
decision can be represented as:
Max
(6)
where Py
is
Q'Y'-'
s.t.
the price of the agricultural good, and
I is
Pyy*JiY.P^q^
= I
Solving for the
first
income.
ex{)enditure shares for each of the aggregate goods that are independent of income:
B
(7)
".
EE
f'kJlka
a=A k=\
&
^E^^Ib
I
(8)
—
^
=
1-5
-'fy
= '(!-*)
order conditions yields
II.
Production
ii.
There are two factors of production:
which
used in both sectors.
is
The supply of both
preferences specified above, the
The
price of the agricultural
good
good
is
constant, and
its
The manufacturing
is
sector
is
L,=L and
=
facilities
C\w)
is
i=Afi
characterized by product-specific increasing returns.
treasury,
in the
manufacturing sector
production
all
R&D
in
These
Adopting a
familiar
from increasing
costlessly separable into
two
activities that
have a
and can be spread among any number of
activities are
Such
unique to each variety.
activities
product design or process technology, advertising, or services such as persoimel,
and planning; for simplicity,
total costs
is
is
The corporation performs some
facilities equally,
without diminishing their value to any one.
could include
Thus, the marginal cost of the
transportable at negligible cost between countries.
The business system
public good character; they benefit
in the
just equal to the marginal cost:
is
i
corporate activities and production activities.
activities:
Given the
The production technology
Chamberlinian approach with free entry will yield monoptolistic competition, as
returns trade models.
Gi = G.
and labor, L,
used in the agricultural sector.
and perfect competition prevails.
price in country
1
good
specific to the agricultural sector,
will be taken as the numeraire.
(9)
In addition, the agricultural
is
factors is symmetric:
supply of land
full
agricultural sector has constant returns to scale,
agricultural
G, which
land,
per firm located in market
(10)
I
i
will refer to
them
as
R&D.
Denoting the level of
R&D
activity as
r,
are:
-^^^
C'iw,r)
^
i=/t^
dr
which are simply assumed
to
be nondecreasing.
Production operations are characterized by increasing returns
a variable cost associated with each manufacturing plant.
""
CV„r^,)
=
at the plant level; there is a
Production costs for a plant located in market
F(^)*V{w^^)
^
<
or
To nuke
(12)
the analysis
more
tractable,
it is
useful to
assume
V{w^^)
fixed cost and
=
8
that marginal costs are constant:
V{w^)q^
i
are:
This assumption
is
not critical; the results require only that the cost function exhibit bounded returns to scale.
Notice that variable costs
indef>endent of the
number of
fall
as the level of corporate activity increases, and that this relationship is
Tlie firm chooses r to minimize costs over both markets such
plants in operation.
that:
dC'(w^)
^3^
V'-'''
dV^^^)
dViw^r)
=
dr
dr
Finally, there
is
It is
from destination markets, such as shipping
The
fraction of output that
is lost
in the distance travelled.
and the transport
„
^
j=B
when
.
a,
J
,
.
t=A,
^
and
^
the reverse
intended to stand in for a variety of disadvantages of distance
costs, trade barriers, linguistic or cultural differences,
transport cost
assumed
is
in transit (similar to
Thus, for some amount
shipment to a foreign market
—
dr
'
a transport cost.
responsiveness to consumers.
'-
q,+
Krugman
q,
to increase with distance:
(1979)), which
produced
in
I
it is
and slow
modelled as a
specify as exponentially increasing
market a = A,B, the amount
that survives
smaller by an amount that increases in the distance between the two markets, D,
is
cost, T:
''""
(14)
daa=^' <^ak=D
^a
b=B when a-A, and
a=Afi,
The competition among firms
equilibrium in each stage.
in the differentiated sector takes place in
First, firms in
full
stages,
and there
is
a
= A,B)
Solving the
yields a price to location] as a
first
order conditions for profit
markup over
the marginal cost of
production and transport:
P«
(15)
.
The markup hinges on
II.
iii.
=
a, the elasticity
l-I
F(.)('
"
for
a=A^
and
j=A^
o
of substitution between varieties.
Market Equilibrium
With constant
Nash
knowledge of competitors' configuration decisions, firms
simultaneously choose prices, yielding a Bertrand equilibrium.
at a(
two
both markets simultaneously decide whether to enter the industry and
choose their plant configurations. Then, with
maximization for a firm located
the reverse
returns in the agricultural sector, the equilibrium
product of labor:
9
wage
is
the value of the marginal
w, = -^^^^^^
(16)
With symmetric
factor supplies,
and
i=A^
identical preferences, the
wage
is
equal across countries.
Together, the markup pricing policy in equation (IS) and the elasticity expression in equation (4) imply
that all varieties
of the differentiated product produced
similarly for
varieties
all
of varieties produced
B
at location B.
market B by an amount that
in
by a consumer
in
market
a(
= A,B)
qJP^)
-
(17)
=
will
be priced equally
is
varieties
— -^
o
produced
from both markets.
a
at
P^P.„...P,
*
In^^n^e^^-')
The quantity demanded of imported
•
IJP'")
(18)
r
varieties
A;.-^. '
.
"^''^.^a
number of
varieties available
is:
^-^AJ'
Tt)~r(n^.„^,'«i-<'))
P'.J'bj'
Pn.'
"-''a^b
the Te\>erse
The optimal
allocation
produced
a single location, and smaller amounts of imported varieties, yielding a
varieties implies that each
consumer consumes equal amounts of
1
facilities, all
firms operate a single production facility, or there
will characterize the conditions for each type of equilibrium in turn.
plant configurations, variable profits
where
B
t
on
sales of each variety
denotes the single-plant equilibrium.
produced
is
all
varieties
all
home market
Depending on the parameter values, there are three possible types of equilibrium:
production
demanded
is:
a=B when b=A, and
at
exceeds that
^-TDo
— _]
-
among
A
at
in each market, the quantity
increasing in the distance between the markets, and decreasing in the
is
produced
proportional to the transport cost differential, and
of a representative variety produced
K(.)
a given location, and
at
In maiicet B, the price of varieties
Given equilibrium prices and numbers of
the reverse.
which
at
produced
A
at
bias.
firms operate two
a mixture of both configurations.
Starting with the equilibrium with single-
at
A
and sold
in
A
can be expressed
Variable profits on sales of each variety produced
at
A
in
market
are:
(20)
Profits are higher the closer
n'^iPrn)
is
=
-^
the production location to the destination market,
10
as:
and the fewer competing
varieties there are.
Thus,
an equilibrium where
in
markets for a firm located
Assuming
ft^e entry, the
Further, given the
at
A
all
firms have a single production facility, total profits over both
are:
number of firms producing
symmetry assumptions made above,
symmetric across firms and markets, and the wage
number of firms
that the
at
located at
number of firms
A
and B are equal
in
the optimal choice of the firm-specific input,
both markets
in equilibrium,
located in each market
is
equal,
which
r,
is
in turn implies that the
nA=nB=n,. Together, these two conditions imply
is:
*^
n, -
(22)
each location adjusts endogenously to yield zero profits.
<3[F{w)*C\w/)-\
The number of
the elasticity of substitution between varieties,
To check whether
configuration.
A
this is
and
in the level
of per-firm and per-plant fixed costs.
an equilibrium, consider the incentive for a firm to change
firm will open a second production facility only
if the
increase in
its
a plant located at
(23)
its
A
opens an additional production
facility at B.
Prices and profits in
its
production
fixed costs
compyensated by the increase in variable profits from locating closer to foreign consumers.
firm lowers
and decreasing in
varieties is increasing in the expenditure allocated to differentiated products,
A
is
more than
Suppose a firm with
are unchanged.
price in market B, to reflect the reduction in the variable costs of serving that market:
p'^
=
The
equilibrium:
F(w)
(26)
Comparative
plant
is
more
statics
^
(i-^nxi-.))
on the equilibrium conditions
establish that the equilibrium in
likely to prevail the higher is the fixed production cost, the
distance between the markets, and the lower
to 0, a single-plant equilibrium
is
The
always prevails.
effect
defection on the market price index,
the elasticity of substitution.
is
it
number of
of substitution
do not take
is
is
ambiguous.
into account the effect of their
more
likely to hold the smaller is
firms, a single-plant equilibrium is
more
likely
the foreign market.
In this case, a firm serves
market
that firms
lower are the transport cost and the
elasticity
can be shown that the equilibrium
In addition, for a fixed
Next consider an equilibrium
production
of the
which each firm has a single
In the limit, as the corporate cost goes
the corporate fixed cost.
However, by simplifying the no-defection condition, so
the smaller
n,(Ug"^'-''>)-g"^'-')
facility at B.
consumers
in
in
which
all
market
A
firms have production facilities in both markets, denoted m.
from
its
production
facility at
A, and consumers
in
B from
Solving for equilibrium prices and quantities yields sales for each variety in each
of:
qZiP^^J
(27)
-
—^-^
«=
^3
associated with variable per-firm profits in each market of:
5/
(28)
«"(^.^J
Total per-firm profits over both markets
(29)
is:
n"(/',,yij = 27i-(/'_,nJ-2/^H')-C'(>v^)
Again, given symmetry in factor proportions and demand, the number of firms in each market
Da— ig=n„. Then assuming
equilibnum
free entry,
and solving for the number of firms under zero-profits
is
equal,
in a dual-plant
yields:
8/
n_ =
(30)
o[2Fiw)*C'iw^y\
Again the number of firms
is
decreasing in the level of
total fixed costs,
12
but here the per-plant fixed costs are
its
weighted more heavily.
Notice that under plausible conditions, there are fewer varieties in
total in the dual-
plant equilibrium, regardless of the level of transport costs.'
A
down
firm
is
tempted to defect from the dual-plant equilibrium
a production facility
foreign market.
more than
Consider a firm
however, the firm's price
if the
offset the loss in variable profits
that shuts
down
its
savings in fixed costs from shutting
due to higher transport costs to the
Pricing and profits in
plant at B.
A
are unchanged.
In B,
rises to reflect the increase in transptort costs:
P' = -2-V{.)e^
(31)
o-l
yielding lower variable profits of:
«T
^AB^P'J'.^J
(32)
Thus, firms have no incentive
to defect
—
=
-7D(I-o)
from a dual-plant configuration only
if:
gTD(l-o)
(33)
Fiw) i
-^
a
Combining
the zero-profit
'^"m
(n.-l)+<
^
2n,(l-."X'-°))-(l-."^'-'>)
In^-a-e^^-'^
2F(>v)+C'(H'^)
A
fully multinational equilibrium,
smaller
is
never sustainable.
ambiguous.
elasticity
where
all
firms have production facilities in both markets,
is
more
likely the
the fixed production cost, the higher are transport costs and the distance between markets, and the
higher are economies
is
7I)(l-o)
and no-defection conditions yields equilibrium conditions:
2F(w)
(34)
J
By
at the corjKDrate.
Here, as the corporate fixed cost goes to 0, a dual-location equilibrium
Again, the effect of an increase in the elasticity of substitution between varieties
simplifying the no-defection condition as above,
it
can be shown that an increase in the
of substitution makes the multinational equilibrium more likely to hold.
the dual-plant equilibrium
is
more
likely to hold the larger is the foreign market.
single-plant equilibria are characterized
is
For a fixed number of firms,
Thus, the dual-plant and
by precisely reversed conditions.
In the intermediate range of parameter values, there
multinational firms coexist with national firms.
In the
is
a third possible equilibrium, in
mixed equilibrium, some
which
fraction, a, of firms
have a
single production facility and export, and the remaining fraction have production facilities in both markets.
13
The condition
for the
mixed equilibrium can be derived from combining no-defection conditions
for both single
plant and dual-plant firms:
(35)
n^(2-a(l-e"^'-°')) > l+«"^'->
where
n^ is the
number of firms
mixed equilibrium.
in the
When
equalized, the expression for the proportion of single plant firms
where
r;
proportion with production
additional
With
R&D
two configurations are
is:
2
W
(l-^rocJ-))
a„^ (F(k')+C'(h'^j)-C'(h-^,))
the profit-maximizing level of
is
returns to the
facilities in
R&D
input for a firm with
i
plants.
For a given number of
firms, the
both markets declines with the size of the fixed production cost and the
investment, and rises with the size of the transport cost and the distance between markets.
free entry, this equilibrium holds only
when
the following conditions
on
the fixed costs
and the transport
costs are satisfied:
The
fixed production costs must be greater the greater
relative to a dual-plant firm,
If this
condition
II.
iv.
It is
is satisfied,
is
the size of the
and the smaller are the transport
R&D
cost, distance,
investment for a single-plant firm
and the
elasticity
of substitution.
any mixture of firm types can be supported.
Factor Market Clearing
now
possible to go back and solve for equilibrium conditions in the labor market.
returns in the agricultural sector imply that the per unit labor input
function with respect to local wages.
Thus,
(36)
in
is
Constant
simply the derivative of the unit cost
= A,B:
market
i
,,(,^
__
^^^(^
dw
In the differentiated sector, the
demand
demand
for labor can be separated into corporate
and production
activities.
for labor for corporate activities is the derivative of the cost function with respect to the local
the equilibrium level of corporate services:
14
wage
The
at
(37)
,.(.^,
.
i£^
dw
Production activities generate a demand for labor associated with the fixed production cost, which
is
simply the
derivative with respect to the local wage:
LVJ
(38)
And
they generate a
demand
output produced at location
i
for labor for production
and sold in j
I'^iwj-) = e^'^
(39)
^
and transport of the differentiated goods; for a unit of
demand
this
-—-^
=
is:
d.=0, d^=D;
iMA
*=« ^hen iM, and
the reverse
^w^
Labor demand varies according
wages across countries,
in the single-plant equilibrium, factor clearing conditions in each
L
('^0)
where
q' is
to the type of equilibrium in the differentiated sector.
=
With symmetric
market
are:
P{w)Y'*n\L\w/)*L''(.w)*l^(w/)q'\
per firm output in the single-plant equilibrium.
In the pure dual-plant equilibrium, factor clearing
implies:
1
(41)
where q™
is
= /''(>v)y"+njL''(>v^)+LV)+2/<?(H',r)4"]
per firm output in the dual-plant equilibrium.
In the
mixed equilibrium,
factor
demands are
straightforward to calculate, and depend on the mix of firms.
II.
V.
Commodity Market Clearing
The income-expenditure
equality can then be expressed in market
('*2)
/-
while in the single-plant equilibrium
Then commodity market
A
= y+2«.[/»7<7;(/>-)]
it is:
clearing requires a single market clearing condition.
this is:
(44)
in the dual-plant equilibrium as:
(l-») =
L
n=m^c
I"
15
For agriculture
in
equilibrium n
n.
Trade Balance
vi.
Given synimetry
agricultural
good and
in population size
for differentiated products.
with purely national firms.
and the
Given symmetric
intraindustry trade
elasticity
The
single-plant equilibrium
is
in
both markets for the
essentially a trade equilibrium
own demand
factor proportions, each country satisfies its
for the
and there are balanced flows of two-way trade in the differentiated manufacturing sector:
agricultural good,
The volume of
and income, there are symmetric demands
is
a decreasing function of the transport cost, the distance between markets,
of substitution, and an increasing function of income and the expenditure share allocated to
differentiated goods.
In sharp contrast, there is
trade in
goods
each direction
It
rises
no trade
in
goods
in the
pure multinational equilibrium.
in the differentiated sector, there is balanced
two-way trade
Instead of
in corporate services.
two-way
The flow
in
is:
with the amount of labor employed in corporate activities and with the number of firms, which in turn
is
an increasing function of the expenditure allocated to differentiated products, and a decreasing function of the
of substitution and fixed costs.
elasticity
Thus,
this
model yields an equilibrium
in
which multinational production
arises in the absence
of factor
proportion differences, and two-way intraindustry trade in invisibles completely crowds out intraindustry trade
in
These
goods.
differences,
factor
results contrast sharply with the predictions
where
the only motivation for cross-border expansion is factor price differentials caused
endowments.
In a factor proportions
in the capital-intensive
by
different
framework, the presence of multinationals reduces the share of
trade accounted for by intraindustry trade, but need have
headquartered
from a model based on factor proportions
no
effect
on the
total
volume of
total
trade, since varieties
country and produced in the labor-intensive country are exported back to
the capital-intensive country.
Lastly, in the
differentiated sector.
mixed equilibrium, there
is
balanced two-way trade in both goods and invisibles in the
Multinational sales are a relatively larger share of total foreign sales for each country, the
16
higher the proximity advantage relative to the concentration advantage.
Three-Stage Production with Symmetric Factor Endowments
ni.
So
far, the
model suggests the
stark result that, given large benefits to proximity relative to benefits
from concentration, multinational enterprises
sits
uneasily alongside two stylized facts.
First, there is a large share
of intraindustry trade in
total trade
(Loertaches, Walter (1981)), and second, multinationals account for a significant share of trade
Indeed, there
(1988)).
is
evidence that suggests that multinational activity on balance
rather than a substitute for trade
The
first fact
(Swedenborg (1979), Blomstrom
et. al.
is
(Rugman
complementary
to
(1984)).
could be explained in the model developed above by a combination of low benefits to
proximity and large scale economies.
The second
fact is
not explained by the model developed above with a
simple two-stage production function in the differentiated sector.
would explain
This
will either in part or totally substitute for intraindustry trade.
the second fact in
two ways.
First,
multinationals, finished goods are exported back
A
factor proportions account of multinationals
given a two-stage production process and single-plant
from the country of production
to the headquarter country.
Second, with a three-stage production process, multinationals produce intermediate inputs in the economy that
relatively
abundant
in the factor
downstream production
is
used relatively intensively in intermediate production, and exf)ort them to
facilities in the
intensively in final goods processing.
economy
A
that is relatively
factor proportions
well-endowed with the factor used relatively
model thus predicts
that either final
goods or
intermediates will flow across borders in a single direction, contributing to interindustry rather than intraindustry
trade.
Alternatively, the
with both stylized
facts.
model developed above can be elaborated
By
in a
way
that is sensible
and accords well
elaborating the production structure in the differentiated products industry to
incorporate additional stages characterized by different proximity/concentration trade-offs, the model predicts
that multinationals will generate intraindustry, intrafirm trade
under plausible conditions. This prediction differs
from a factor proportions account, which would predict one-way flows of intrafirm
Again, the contrast between commodity semiconductors and cars serves to
17
trade."*
illustrate the differences in
the
two models.
facilities in
In the 1970s,
US commodity
made
chip firms
substantial investments in
Southeast Asia, which were motivated entirely by factor price differentials."
assembly and
Tlie test
test
and
assembly stages were intensive in low-skilled labor, in contrast to the design and manufacturing stages, which
were intensive
in engineering skills
and
capital.
manufacturing complexes to assembly and
destinations in the
US
Semiconductors were shipped from the
and elsewhere. '*
expansion into destination markets.
been substantial two-way investment and multinational
A
typical pattern of expansion
distribution and sales facilities in the destination market, followed
was
would
in
two-way multinational
economies and proximity advantages provides more
with the establishment of
facilities
when
the share in the
Factor price differentials provide
sufficient to warrant the fixed investment."
relative factor prices in periods of substantial
start
by assembly
EC
into these investment patterns, since the markets in question, such as the
scale
design and
Southeast Asia, and then shipped back to sales
test facilities in
In contrast, in the automobile industry, there has
foreign market
US
and the US, have had similar
activity.
scale
insight:
insight
little
Instead, the relationship
between
economies are substantial but bounded
auto assembly, and smaller in sales and distribution, trade barriers into several countries in the
EC
are high,
and the advantages of a local presence and customization to the local market are high.
To
formalize an explanation for the latter pattern,
additional stage,
which has
I
modify the production structure
a distinct proximity /concentration trade-off.
manufacturing (q) stages detailed above, there are sales activities
(s),
'*
to incorporate an
Thus, in addition to the
whose production
R&D
(r)
and
requires a fixed cost and
a constant marginal cost:
(45)
C'iw^^^)
=
F'iwJ^V'iw^^ys
a=Afi
Similar to the upstream relationship between corporate activities and manufacturing, the variable cost in sales
a decreasing function of the input from the manufacturing stage,
R&D
input,
which
is
proprietary to the firm.
however, the manufactured input lowers the cost only of the sales
In addition, there is a transport cost,
simplify notation,
I
facility that
both for the manufactured input, and for the
replace the exponential transport cost with a
both the distance between markets and the shipping cost.
18
The
more general parameter,
uses
Unlike the
it.
final output.
t,
To
which subsumes
cost of transporting the output of each stage,
is
ti>
1
(i
= q,s),
is
the reciprocal of the fraction lost in shipment; only the portion of output that
borders incurs the transport cost.
The
is
shipped across
transport cost between manufacturing and sales can be interpreted in
terms of a co-location advantage.
Each firm chooses
its
production configuration to trade off additional fixed costs against additional
variable costs of transtmrt at each stage of production.
commonly
activities
dispersed near consumers, while manufacturing
R&D
such as
are the most concentrated.
equilibrium,
in prices.
w^ = Wg, and
Given symmetry
the
(or
confine attention to firms headquartered in market
it
can invest in sales
facilities in
R&D
A
and costless
is
equal in markets
output can
A
and B, so
by
in
we
sales in a single
both markets, and concentrate manufacturing in a single market;
The
it
can
There are four possible
without loss of generality.
can invest in manufacturing
it
facilities in
can
both
fourth configuration can be ruled out, since the firm
by shutting down a manufacturing
activities are concentrated in a single location,
facility.
In any
due to the combination of scale economies
by deriving conditions
for each pure type
of equilibrium
-
where
market have identical configurations.'* The equilibrium conditions are derived
market.
R&D
transport.'^
I start
in Section
that
and demand, factor prices are equal
investments)
fixed production costs and transport costs
R&D
assume
II, I
Each firm can concentrate both manufacturing and
markets, and concentrate sales in a single market.
configuration,
be concentrated, and corporate
in production configurations is followed
spread both sales and manufacturing activities across borders; or
would save both
likely to
1).
in factor proportions
number of firms
configurations in the differentiated sector.
more
Nash equilibrium
Again, firms compete in two stages:
Nash equilibrium
is
Accordingly, as in Section
be transported costlessly to manufacturing plants (t,=
market;
Casual empiricism suggests that sales activities are most
II,
all
firms headquartered in each
in precisely the
by combining zero-profit conditions with no-defection conditions for
all
same manner
firms located in each
However, with three possible configurations, there are two no-defection conditions
for each
equilibrium.
Firms choose configurations and prices taking as given the prices and configurations of
Variable profits for each firm across both markets in equilibrium
19
j
are:
their rivals.
as
*'
-^
./p/-^ _
i^iPiJ^i^n) =
(46)
where
Dj is
the
number of firms
The number of firms
free entry.
in
located in each market under market structure
each equilibrium
is
n, =
(47)
II,
j.
determined endogenously by the zero-profit condition under
Thus, in an equilibrium where firms concentrate
Just as in Section
H,m^
all activities in
a single location (denoted
t), it is:
—[CXw^)*F*(w)^F'iw)]
in each equilibrium the no-defection conditions are obtained
by comparing the change
in
variable profits associated with each alternative production configuration with the corresponding change in fixed
costs.
The equilibrium
is
then obtained by solving the no-defection and zero-profit equations simultaneously,
yielding conditions on the relative size of the transport costs to the fixed costs, and on the activity-specific scale
economies
Combining the condition ruling out defection
relative to the firm-wide scale economies.'^
to a fully
diversified configuration with the zero-profit condition yields an equilibrium condition:
C'(w^)
where the cost of
(U2l,'"')
trans[)orting intermediate inputs raises variable costs
7-,=
by a proportion,
T
,
defined:
(^;CV^^
(K,(.)+K,(.))
And
the equilibrium condition ruling out defection to a
In the equilibrium
where only downstream
equilibrium number of firms
(50)
is:
(Tl-''-tl")[n,(l*tyW,-']
F'(w)
(49)
downstream diversified configuration
activities are dispersed across
borders (denoted d), the
is:
«
'd
=
^[C'(,w^)*F^(w)*2F'(w)]-^
There are two no-defection conditions, corresponding
to the
two alternative configurations. Combining the
zero-profit condition with the condition ruling out defection to a single-location configuration yields:
20
(r;"'-rj-')[>./u7:;-')-r;-']
^
(51)
n/UTl-')iU2tl"'-Tl-'')-iTi-'-tl-'')(l-Tl-')
And combining
f.(^)
C'iw,r)*F*(w)
the zero-profit condition with the condition that firms have
no incentive
to extend their
multinational activities by opening an additional manufacturing facility yields:
F^(w)
(52)
(i-r;->^u7:;-)-r;-°]
^
C\w^)*2F'(w)
Lastly, the
number of firms
across borders (denoted
m)
nJ,l*Tl")2f^"Hl-'li'')il*2Tl")
in the equilibrium
where firms diversify both manufacturing and
sales
is:
(53)
=
n
*^[C'(H'^)+2F«(>v)+2F'(H')]-'
a
The combination of
production
the zero-profit condition with the condition that firms have
facility yields the
down one
to close
equilibrium condition:
(2n„-l)(l-7^-'')
f,(H,)
4«_r'-°
m'l
C'(w^)*2F'{w)
(54)
And
no incentive
the equilibrium condition ruling out defection to a concentrated, single-location configuration
(2n,-l)(l-r,'"°)
(55)
is:
^ F'iw)+F''(w)
Notice that together, equations (47), (50), and (53) imply that under plausible conditions, the number of
varieties
is
greatest in the single-location equilibrium,
and smallest
in the fully diversified dual-location
equilibrium.'*
Comparative
statics
on the equilibrium conditions establish
firms establish sales and manufacturing facilities in both markets,
manufacturing, the greater are fixed costs in
intermediate input
(T^" and
the final
good
concentrated, single-location equilibrium
fixed cost of
the smaller
R&D,
is
the lower
is
is
R&D,
(t,),
A
likely the smaller are fixed costs in
is
the elasticity of substitution.^
A
fully
likely the greater is the fixed cost in sales, the smaller is the
the transport cost of the final
the elasticity of substitution.
more
where
the greater are the costs of transporting both the
and the greater
more
is
that a fully diversified equilibrium,
good
relative to that
downstream-diversified equilibrium
21
of the intermediate input, and
is
more
likely to obtain the
smaller
is
the fixed cost in sales, the greater
is
the fixed cost in manufacturing,
transporting the intermediate input relative to that of the final good.
equilibrium
when
only possible
is
is
is
the cost of
In addition, the downstream-diversified
the transport cost of the intermediate
Similar to the two-stage case, a diversified equilibrium
and the smaller
is
smaller than that of the final good.
increasingly likely the larger are the returns to scale at
the corporate level relative to those in manufacturing and sales.
The
pattern of trade and production associated with each equilibrium can be derived following the
analysis in Section
commodity
II,
so that
I
clearing conditions.
will simply discuss the
The
main conclusions here, without detailing the factor and
addition of a stage of production generates
demand
for labor, analogous to
Conditions for factor market clearing and commodity market clearing can then be
equations (38) and (39).
derived analogously to equations (40) through (44), with a similar set of conditions for the downstream
diversified equilibrium.
patterns will
emerge
Just as in Section
in the
II,
with equal relative factor endowments, identical production
two markets; given symmetric demand, trade
in the differentiated sector will
be
balanced, and the agricultural sector will be autarkic.
The equilibrium
which
in
all
firms concentrate
trade patterns identical to those in a pure trade
proportions:
there are balanced flows of
intrafirm trade.
all
model with
two-way trade
three production stages in a single market results in
differentiated products and
in differentiated products,
symmetric factor
and no interindustry or
Just as in a trade model, the flows will be greater, the larger is the share of expenditure
allocated to differentiated products, the higher
The equilibrium
results in balanced
which
in
all
is
income, and the lower are transport costs.
firms invest in both manufacturing and sales facilities in both markets
two-way flows of intrafirm
trade in
R&D
completely crowding out trade in goods.
Here
multinational production completely substitutes for trade.
The addition of
a production stage introduces the possibility of a third equilibrium, in
which firms
diversify their sales activities across borders but concentrate their production activity in a single market.
In this
equilibrium, there are balanced two-way flows of intraindustry, intrafirm trade in intermediates, which substitute
completely for trade
in final
stylized facts cited above:
goods and
in invisibles.
This equilibrium
is
thus consistent with both of the
the existence of multinationals generates intraindustry trade.
22
Asymmetric Factor Proportions
IV.
In reality, firm configuratioos are likely to reflect considerations of both factor and proximity
advantages; in this section
I
a pure factor proportions account of
relatively
abundant in the factor
in
MNEs predicts
which
R&D
which
in
factors are completely mobile
-
is relatively
intensive,
the integrated equilibrium
hybrid model of multinationals, since there
in analyzing a
equilibrium
when
transport costs are introduced.
Instead,
benchmark and analyze how firm configurations and
I
-
It is
is
in the country
and a single manufacturing plant
Such accounts use as
intensive.
is
configurations and trade patterns of dividing up the supply of factors.
approach
R&D
configurations in which a firm locates
country abundant in the factor in which manufacturing
world
As described above,
develop a hybrid model to accommodate both considerations.
their
in the
benchmark a
and analyze the implications for firm
somewhat complicated
no obvious counterpart
to use this
to the integrated
adopt the symmetric equilibrium as an alternative
become
trade patterns change as factor proportions
increasingly unbalanced.
This section returns to the simplified two-stage production structure of the
are
assumed
to
be used
are divided between the
wages of
skilled
in the
production of both goods:
two countries and immobile. Type
workers
to that
for skilled labor in activity
that the factor intensity
relative
wage
l.V^/KXW) >
with
of unskilled workers as
its first
W=
R&D
paid
wage
Wj'/Wj'.
W,
the
most
skill-intensive activity
section.
and unskilled labor
Wj' in
country
i.
Two
(L^).
factors
The
Define the
factors
ratio
of
Next, define the equilibrium unit input
and similarly for unskilled labor.
of production in the three productive activities
is
and agriculture the
Further,
ranked consistently
least:
VO^/^z'O^
at
any
-*
1/(W)/1,^(W).
In addition, assume that there
locate
j is
k as 1,'tW), given relative wages
assume
rate,
skilled labor (L,)
first
is
manufacturing plant with
some small advantage
its
R&D
to co-location,
facilities, all else equal. ^'
factor proportions, the existence of a co-location advantage,
such that a firm chooses to co-
In the equilibrium with equal
however small, eliminates single-plant
multmationals.
Starting in the
benchmark case with equal
fully multinational equilibrium
where
all
factor
endowments, there are three possible
equilibria:
a
firms in the differentiated sector have manufacturing facilities in both
23
markeUi, a pure trade equilibrium where
firms have a single manufacturing plant, and a mixed equilibrium.
all
two markets, and there
In all three cases, given equal factor proportions, factor prices are equalized across the
IS
symmetry
in the
number of
will analyze the effect
B
in the
Suppose
firms.
of moving skilled labor from market
same proportions
B
of skilled to unskilled labor
A
to market
B
is
the
monopoly supplier of unskilled
the center along the diagonal toward the northwest
comer
labor.
pressure on the relative
imbalance by moving
equalization.
R&D
wage of
activities to
skilled labor in
to
B, there
is
is
the
Helpman diagram.
in the
A, and upward pressure
A, while agriculture expands
A
corresponds to
Tliis
A
In the pure trade equilibrium, as the ratio of skilled to unskilled labor rises in
downward
A
economy
We
is Lj/Lj.
and unskilled labor from market
as the aggregate skilled to unskilled ratio, so that in the limit
monof)oly supplier of skilled labor, and
movement from
that the aggregate ratio
and
in B.
falls in
Firms respond
to the
B, thereby maintaining factor price
in
In this case, firms adopt multinational configurations in response to factor availabilities; these
configurations are distinct from those found in the symmetric multinational equilibrium in that each firm has a
Here there are two-way flows of
single plant.
differentiated products of the
same
symmetric equilibrium, but these flows may be unbalanced, reflecting income
additional trade flows of agriculture
As
from B
to
A
R&D
in return for
diverge, and different production techniques are adopted in the
concentrated before agriculture.
Take
the point at
additional increment of skilled labor from
plant will
move
to
A
B
to
A
which the
last
two-way
in
from B, and agriculture will continue
to
move
B
to
one-way flows of
facility
has
A
that
moved
to B.
R&D
from
A
A
in
to
With unequal
becomes
A, and transfer an
a manufacturing
sufficiently strong
A, and manufacturing
B and
Here, there
is
B
to A.
means of
factor prices, the payoff to concentrating manufacturing activities
24
is split
unbalanced,
agriculture from
interesting feature of this equilibrium is that firms continue to use trade as the sole
foreign penetration.
intensifies,
R&D
to
Now
B from A. With
and/or
R&D
skills in
Assume
countries.
R&D
to B.
that juncture, factor prices
unequal proportions and utilizing different production techniques.
trade in differentiated products and
The
At
and of unskilled labor from
factor imbalances, either agriculture concentrates completely in
between the two
two
A
abundance of
R&D.
and there are
differentials,
from
services
reallocation of factor supplies continues, so that the relative
eventually one country becomes the sole producer of agriculture or
overall magnitude as in the
must be
at
least as great as
it is
with equal factor prices.
Thus, the introduction of factor imbalances gives
rise
only to
single-plant multinationals, if any.
Performing the same experiment starting from a pure multinational equilibrium, the
progressive unbalancing of factor proportions
B, and factor price equalization
that there are flows
is
is
similar.
R&D
moves
to
B
to
response to a
market A, agriculture moves to market
maintained, along with plant configurations.
of agriculture from
initial
A, balanced by reverse flows of
The
R&D
pattern of trade adjusts, so
services.
Eventually, the imbalance in factor endowments becomes sufficiently extreme that one industry
concentrates in a single market.
Now
a factor price differential between the two markets
economies motivation for concentrating manufacturing
activities in a single location.
is
added
TTius, a
to the scale
few firms will
concentrate production in the market with favorable factor conditions, and exptort, while others will maintain
production
facilities in
although the
both markets.
total extent
In equilibrium, the returns to both configurations will
be equal.
So here,
of multinational activity may remain unchanged, the number of firms with multiplant
configurations will diminish, and there will be unbalanced two-way trade in differentiated products along with
flows of
R&D
services and agriculture.
Thus, the introduction of different factor proportions across the two markets permits a broader range of
possible trade and production patterns.
With unequal
production process depends on two considerations:
factor intensities.
factor proportions, the location
of each stage of the
the relative concentration/proximity trade-off and relative
Unequal factor proportions introduce the
possibility
of single-plant multinationals, and make
the likelihood of single-plant firms higher outside the range of factor price equalization.
V.
Conclusion
The
introduction of an explicit trade-off between scale economies and proximity advantages in a
differentiated products
investment.
model of trade permits
a
much
richer set of predictions about the pattern of trade
and
In particular, consideration of this trade-off introduces the possibility of two-way, horizontal
multinational activity, even in the absence of factor price differentials, and of intrafirm trade in intangibles
completely supplanting trade in goods.
It
also introduces the possibility of multi-plant configurations across
25
These
borders.
results,
which
apf)ear to be of increasing importance empirically, are inexplicable in an account
of multinational expansion driven purely by factor proportions differentials.
An
equilibrium characterized by multinational production and multiplant configurations
is
more
likely
the higher are returns to scale at the corporate level relative to the plant level, the higher are transport costs
across markets, the greater
is
expenditure on differentiated products in the foreign market, and the higher
of substitution between
elasticity
is
the
varieties.
This framework also can explain equilibria in which national firms coexist with multinational firms in
the
same
industry.
returns to the
A
mixed equilibrium
two configurations
differ
is
by
Consumption patterns vary with
sustainable for intermediate ranges of the parameter values,
less than the differential
the type of equilibrium in the differentiated sector.
multinational equilibrium, equal quantities of
pure trade equilibrium, there
Consumers
there
is
benefit
is
a
between the associated fixed
all
home market
varieties are
consumed, regardless of
costs.
In a pure
their origin,
while in a
bias in the consumption of the differentiated product.
from the presence of multinationals, due
to the reduction
a concomitant loss in consumer surplus from a reduced overall
The
when
of the price of imported goods, but
number of
varieties.
prediction that intraindustry flows of intangibles substitute for trade depends on the structure of
production in the differentiated sector and the relative proximity/concentration tradeoff of each stage of
production.
activities,
With multiple production
stages, if concentration advantages
dominate in upstream production
while proximity advantages dominate downstream, then intraindustry, intrafirm flows of intermediates
supplant intraindustry flows of final goods.
In this case, multinational activity
is
complementary
to trade in
goods, and multinationals generate intraindustry trade.
When
both factor proportions differences and proximity advantages are incorporated within the same
framework, the pattern of trade and investment depends on their relative strength.
When
concentration
advantages are high relative to proximity advantages, the introduction of moderate factor proportions differences
results in the formation
agriculture and in
R&D
of single-plant multinationals, and there are unbalanced one-way flows of trade
services in the reverse direction.
factor price differentials arise,
and flows of trade
With more extreme
in differentiated
26
in
factor proportion differences,
products become increasingly unbalanced, as
manufacturing
facilities are distributed increasingly
unevenly across the two markets.
When
proximity
advantages dominate, moderate factor proportions differences result in unbalanced one-way flows of trade in
agriculture in return for
R&D
services, but firms maintain multiplant, multiiuitional configurations.
As
factor
proportions become increasingly unbalanced, the resulting factor price differmtials create an incentive to
concentrate production in a single plant.
This model has strong implications for policy.
transport costs, and
Most obviously,
makes penetration by multinational production more
of intangibles (or profits) has the reverse
the imposition of a tariff raises
attractive,
while a tax on the earnings
Further, the relative structure of tariffs on final goods and
effect.
intermediate inputs influences firms' decisions about which activities to concentrate and which to disperse across
borders.
The model
further implies that restrictions
on foreign
direct investment
may be more damaging
to
welfare than restrictions on trade in industries where natural proximity advantages are high and scale economies
at the corptorate level are
high relative to those
at the plant level,
trade blocs are not deleterious to global welfare.
natural barriers are
If
and suggests conditions under which regional
regions are geographically coherent areas within which
low and between which they are high, and
if different
regions have similar region-wide
factor proportions (while the factor proportions of countries within regions could differ significantly), then the
welfare gains from free trade
may be exhausted
within regions, while free interregional investment flows raise
welfare by permitting maximal returns to investment
at the
corporate level, and a greater variety of products.
Future research will analyze these conditions.
Further, this model lends itself to testable hypotheses.
In particular,
it
suggests that firms' observed
choices between exports and multinational expansion as alternative modes of foreign market {jenetration should
reflect trade-offs
between measurable proximity and concentration advantages.
employs a gravity equation approach
to test this hypothesis.
27
Research currently underway
.
Seminal contributions to
1.
and growing
this large
literature include
Knigman
(1979), Lancaster (1980),
Helpman
(1981), and Ethier (1982).
See Caves (1982) and Dunning (1988).
2.
This
3.
may be
attributable in part to the failure of earlier attempts to explain multinational activity in terms
capital flows in a factor proportions trade
In the
4.
Markusen model,
factor
of
framework with perfect conq>etition.
endowments are symmetric, but
sector-specific capital plays a
key role in
explaining multinational production.
The Krugman model
5.
differs in its
In the model presented below,
assumptions about the production function.
firms incur an additional fixed cost to open production facilities abroad, and save on variable transport costs.
the
Krugman model,
multiplicative factor.
there
no
is
fixed production cost, and variable costs differ between markets by
In
some
The predictions differ in two respects. First, in the Krugman model, only uniform equilibria
is a mixed equilibrium. Second, in the model below, the decision whether to produce
are possible, while here there
abroad depends on the potential scale of production, and thus on the market
size,
while in the Krugman model,
firms do not discriminate between markets based on size or share.
The Horstmann, Markusen model assumes that there are 2 potential entrants, one headquartered in each country,
is Coumot-Nash equilibrium if both enter the market.
Below, the number of firms is determined
endogenously in a monopolistic competition framework. This framework lends itself more readily to predictions
about the pattern of trade, and introduces an additional welfare effect from the number of varieties produced.
6.
and there
The
7.
analysis
would be messier
in the absence
of
this simplification,
but the qualitative results would not change
significantly.
The no-defection conditions
8.
fixed the level of
a fixed
R&D
that the
configuration by
10.
input.
reflect the additional costs that are required to
open a production
holding
facility,
This can be interpreted either in terms of a sequential decision-making process, or
requirement.
Assuming
9.
R&D
R&D
more than
investment for a single-plant configuration does not exceed that for a dual -plant
the size of the fixed production cost.
Unfortimately, the empirical
work
in this area
does not distinguish between the two types of trade when
referring to multinationals.
See Yoffie (1992) for a complete account of investment and trade patterns in the global semiconductor industry.
1 1
12.
The current
pattern of trade and investment in the semiconductor industry
is
probably best explained by a
hybrid between the two models (see Section IV).
13.
In the interests of tractability,
I
ignore dynamic considerations in this model.
relationship between exports and multinational expansion in a
14.
in
The model can be generalized
country a
is
assumed
to
dynamic
any number of production stages,
to entail a fixed cost, a variable
used as an mput,
q,.,,
at
and
each stage
all
is
assumed
to
where each stage of production
i
located
production cost, and a variable transjxjrt cost:
I
where the variable cost
Future research will model the
setting.
a'*! '(a. -a')]
be a decreasing function of the output from the previous stage
mtemally produced inputs are assumed proprietary
28
to the firm.
In addition, there is
.
a multiplicative transport cost for each unit of output that
above
is
is
transported to the foreign market.
The model developed
just a sp>ecial case.
I assume it is always optimal for a firm to locate its first manufacturing plant in the same market as R&D, due
some arbitrarily small co-location advantage between R&D and manufacturing. This assumption is useful because
makes the flows of invisibles determinate, and sensible because it accords well with casual empiricism. It could
15.
to
it
be modelled formally as
16.
t,
>
1
confine attention to uniform equilibria for simplicity; mixed equilibria can be derived similarly to Section
I
Similar to Section
17.
II,
the no-defection condition excludes changes in the
R&D
investment.
interpreted either in terms of a sequential decision-making process, or in terms of a fixed
18.
if
it
Assuming
that the
R&D
Tq
is
This can be
input requirement.
investment does not decrease with the number of production and sales locations, or,
does, that the increase in the fixed costs of production or sales
19.
R&D
II.
more accurately described
is at least
as great as the
R&D
savings.
as the ratio of the variable cost gross of the cost of transporting the
intermediate input to the variable cost net of transport costs.
20.
This result
is
derived by differentiating the no-defection conditions, simplified so that firms do not take into
account the effect of their configuration decisions on the market price index. This
of a large number of firms, used in simplifying the
21.
elasticity
is
consistent with the assumption
expression
This assumption can be formalized in a variety of ways, such as assuming a variable transport cost between
R&D
and manufacturing, or a lower fixed cost for manufacturing when
it
is
co-located with
R&D.
simply follow Helpman in making an ad hoc assumption, since the results are essentially the same.
29
Instead,
I
"
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.J
/
b G
/
U
in
Ken Froot
(ed.),
Date Due
m.
V
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1994
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