\
\ ?".
V
.\
HD28
.M414
no.
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72.
ALFRED
P.
WORKING PAPER
SLOAN SCHOOL OF MANAGEMENT
A Simple Theory of
Multinational Corporations and Trade
with a Trade-ofT between
Proximity and Concentration
S. Lael
Brainard
Massachusetts Institute of Technology
WP#3492-92-EFA
September 1992
MASSACHUSETTS
INSTITUTE OF TECHNOLOGY
50 MEMORIAL DRIVE
CAMBRIDGE, MASSACHUSETTS 02139
A
Simple Theory of
Multinational Corporations and Trade
with a Trade-ofT between
Proximity and Concentration
S. Lael
Brainard
Massachusetts Institute of Technology
WP#3492-92-EFA
September 1992
M.I.T.
NOV
LIBRARfE?
1
8 1992
A
Simple Theory of Multinational Corporations and Trade
with a Trade-off between Proximity and Concentration
Abstract
This paper 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.
The differentiated sector is characterized by multi-stage
production, with increasing returns at the firm level, due to
any number of production
facilities
some
activity
such as
with undiminished value, scale economies
transport cost that rises with distance.
A
R&D
that
can be spread among
at the plant level,
and a variable
pure multinational equilibrium, where two-way intraindustry trade
in
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 the fixed cost of production, and
the greater are increasing returns at the firm level relative to the plant level. The model also examines how the
pattern of trade and production varies with additional stages of production.
intangibles completely supplants
*
I
am
grateful to Paul
Krugman and
Julio
Foundation for support under grant SES-9 111649.
Rotemberg
for helpful discussions,
and to the National Science
Introduction
I.
Multinational enterprises
(MNEs)
Rugtnan (1988) estimates
international trade.
global trade flows, and one-fifth of global
(FDI) and
as the
are a substantial and imperfectly understood part of the landscape of
in overseas
that the largest
GDP
by the early 1980s.
boom
in foreign direct
affiliates, foreign affiliate sales
EC,
Julius (1990) estimates that in markets such as Brazil and the
affiliates are five
It is
After the
expansion during the 1980s, these numbers are probably even higher.
US, which have a well-developed network of overseas
export flows.
500 multinationals controlled over one-half of
local sales
For countries such
tend to
swamp
by U.S. -owned
times the level of imports from the U.S.
also striking that a large and
growing share of foreign
direct investment involves industrialized
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
These trends suggest a large and growing
Between 1961 and
by G-5 countries were absorbed by other G-5
The share of
(Julius (1990)).
absorbed by developed market nations more broadly was 81 percent by the
(1992)).
investment
late
direct investment
1980s (Knigman and Graham
of two-way activity across borders motivated by
level
considerations of market access.
But multinational expansion motivated by market access
is
not just a recent phenomenon.
Indeed, in
her study of American multinationals from the 1700s to 1914, Mira Wilkins concludes that market access was
the primary motivation for multinational expansion:
These early international businesses established
foremost
in the areas
They made
their foreign stakes
around the world where there were customers
as
-
in
we have
seen
-
first
and
Europe and Canada primarily.
where there was demand for their offerings - in the wealthiest
The businesses described in this chapter went abroad to sell and to make profits
the countries in which they made investments; if they went into manufacturing,
estate, it was with marketing considerations paramount. They did not go abroad for
their principal investments
nations in the world.
through sales in
refining, or real
supplies or to produce abroad for sale in the United States. (Wilkens, 1970, p. 1966)
The
implications of 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
phenomenon of
literature
intra-industry trade,
and
on multinationals has evolved
1
Trade theory has made great
in
strides in
modelling imperfect competition'.
to incorporate recent
advances
in the theory
of the boundaries of the firm.^ However, there have been few attempts to synthesize the two, even though the
characteristics that
have been adduced
and differentiated products
-
to explain intraindustry trade
-
imperfect competition, scale economies,
are precisely the characteristics that are associated with the internalization and
ownership advantages believed
to
motivate the formation of multinationals.
This paper 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.
by increasing returns
differentiated sector is characterized
that
can be spread among any number of production
at the
facilities
firm level due to
some
The
R&D,
input, such as
with undiminished value, scale economies
at the
plant level, such that concentrating production lowers unit 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 Wilkens, have been a chief motivation for expansion of
"investments abroad were
customer service and
made
to
multinationals historically:
save on transportation costs and warehousing expenses, to obtain superior
damage
to avoid
US
which,
to the customer,
The decision whether
shipping a perishable product (p. 67)."
in
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, where
supplants merchandise trade in the differentiated sector,
is
two-way intraindustry investment completely
possible even in the absence of factor proportion
differences, given sufficiently strong proximity advantages relative to concentration advantages.
model provides a rationale
distinct
from the
for
EC
(eg,
traditional rationale for vertical expansion associated with factor
Volkswagen and GM),
which are better suited
this
two-way investment based on horizontal expansion across borders, which
model formalizes an explanation of two-way investment
the
Thus,
for
to explaining
example
US
-
in
automobile assembly
endowment
facilities
in contrast to factor-based theories
investments in semiconductor assembly and
is
differentials.
between the
of multinational
test facilities in
US
This
and
activities,
Southeast
Asia.
With a simple two-stage production process,
trade in invisibles completely
crowds out trade
in
there
is
a pure multinational equilibrium in
which two-way
goods, even in the presence of symmetric factor proportions.
This equilibrium
is
more
likely the greater are transport costs relative to plant-level scale economies,
greater are increasing returns at the corporate level relative to those at the plant level.
Under
circumstances, a symmetric equilibrium with purely national firms obtains, in which there
For intermediate ranges of transport costs
trade in differentiated products.
economies and of returns
at the
is
two-way trade
in
a third stage of production, such as sales,
two-way, intra-firm, intra-industry trade
is
a
mixed equilibrium
in
which
symmetric mixed equilibrium, there
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 on consumer welfare; consumers benefit from a
reduction in transport costs, but there
the absence of multinationals, they
there
balanced two-way
both differentiated products and invisibles.
The incorporation of
when
In the
the opposite
relative to plant-level scale
corporate level relative to the plant level, there
multinational and national firms coexist in the differentiated sector.
is
and the
is
is
a concomitant redaction
consume a
a home-market bias, whereas with
home and
I.
larger quantity of
number of
varieties, all else equal.
goods produced locally than of imports, so
two-way multinational production, they consume equal
In
that
quantities of
foreign varieties.
Related Research
i.
The model combines elements from both
literature
in the
the imperfect competition trade literature and the strategy
on multinationals. In recent 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
reputation); the motivation for expansion
is
to
maximize the returns
to this asset.
Second, there
is
an
internalization advantage, such that the firm is unable to realize the full value of the asset through the market,
due
to transactions costs or other
market
failures.
This determines the choice of direct investment over
Third, there
licensing.
makes
is
an advantage to locating production near consumers or factors across borders, which
international expansion
While the
first
more
profitable than exporting.
two types of advantages are closely linked
transactions costs, the concept of location advantages
theory.'
is
loosely defined, and
This delinking of location advantages from trade theory
advances made by trade theorists
in recent years in
to literature
is
on the theory of the firm and on
makes no reference
surprising in light of the
incorporating market
to trade
enormous
power and increasing
returns to scale
into trade models.
The economics
these insights.
literature
on multinationals has gone
way
in recent years to incorporate
Broadly, two strands of research have considered multinational activity.
choice between licensing and investing across borders.
market failure
part
that prevents firms
from
It
The
first
some of
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
The
internalization decision of the firm
locational choice
in the destination
is
is
a resjx)nse to
captured by an ad hoc assumption that
consumption market.
Ethier and Markusen (1991) similarly focus on the internalization decision, but in a partial equilibrium
framework.
part
The decision between exporting and overseas production
on a trade-off between variable transport
equilibrium implications are not explored.
in
via licensing or investment depends in
costs and a fixed production facility cost, but the general
Horstman and Markusen (1987) focus on the
a partial equilibrium framework, where production in the destination market
internalization decision
may be chosen over
licensing
m
order to maintain a reputation for quality.
A
second strand of research focuses on the choice between exporting and investing across borders,
which hinges on
locational advantages.
Krugman (1985)
incorporate
MNEs
Krugman
(1982),
Markusen (1984), Helpman (1984), and Helpman,
into general equilibrium trade models,
which
start
from the premise
that
firms benefit from internalization due to increasing returns at the level of the firm, and focus attention on the
location decision.
The model
I
develop below follows
this line
of research in focusing on the location decision.
^
But while the Helpman and Helpman, Knigman models explain vertical expansion across borders in terms of
factor proportions differences, the
model presented below formulates the motivation for overseas expansion
terms of a trade-off between proximity and concentration advantages/ The
however,
I
it
focuses on proximity advantages alone, and thus can be seen as a
briefly
summarize the main findings of the
factor proportions
comparison.
The Helpman and Helpman/Krugman model
trade model,
where one sector
is
With a two-stage production
endowment
obtains in the trade equilibrium, there
equalized under trade,
some of
models here, for purposes of
is
which has a public goods character.
assumed
to
be relatively more capital-intensive
factor
is
endowments are
sufficiently similar that factor price equalization
no incentive for cross-border investment.
When
to the capital-abundant
economy.
factor price differentials, and
it
factor prices are not
the firms in the differentiated sector locate their headquarters in the relatively
capital-abundant economy, while locating production in the relatively labor-abundant
back
There
In this model, multinationals arise only in the presence of sufficiently great
When
differences.
case of the model below.
characterized by product differentiation and multiple-stage production.
function, production of the input
than production of the final good.
sp>ecial
similar in spirit;
is
incorporates multinationals into a factor proportions
are multiplant economies of scale associated with a firm-specific input
factor
Krugman model
in
Thus,
this
economy and exporting
model explains cross-border investment as a response
to
predicts that multinational activities will only arise in a single direction within
an industry, in single-plant firms.
It
effectively explains
with strong factor proportions differences, but has
little
one-way
direct investment flows
to say about
between economies
two-way intraindustry investment flows
between economies with similar factor proportions.
This contrasts sharply with the model
I
develop below,
the absence of factor proportion differences and in
To make
multiplant firms.
parallels the
in
two directions
the findings directly comparable,
Helpman, Krugman framework, and compare
I
my
which multinational
in the
same
activity
industry, and
is
can take place
in
undertaken by
develop a general equilibrium model that closely
findings directly with theirs, as well as with
predictions from trade theory.
Section
II
describes the structure of preferences and production in a framework with symmetric factor
endowments and a two-stage production
Section
III
process, and derives 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 and a Continuum of Consumers
II.
There are two neighboring countries,
A
and B,
between which factors and consumers are immobile.
endowments and
n.
to a single
a distance
Most of
D
apart.
Countries are defined by areas
the initial analysis will
assume symmetry
in factor
of consumers across countries, in order to isolate the role of proximity
in the distribution
advantages in stimulating multinational activity.
need refer only
at
immobile
With symmetry
factor, labor or L,
endowments across
in factor
countries,
we
and a single factor payment, wages or w.
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 expenditure 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-substitution subutility function of the Dixit-Stiglitz-Spence
type.
Denoting the differentiated product Q, and assuming
differentiated
goods
is
Eg, the consumer's second
^^^
Max
that the share
of expenditure allocated to
maximization problem can be represented
tier utility
UQ{q^^^^,...,q^g,q^...)
s.t.
B
".
Y,
E
as:
^kJlka ^ ^<?
a=A k=l
where q^
is
market
and
a,
the quantity of variety
n, is the
of good q available
number of
at the
i
originating in market a
varieties
from market
consumer's location:
a.
(
= A,B),
The
P;, is
the price of variety
subutility function
is
i
produced
defined over
all
in
varieties
where a
is
the elasticity of substitution
consumption plan
variety
is
among
Solving for the
varieties.
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:
(3)
=
'?*"
^=^.^
^rr^.-. ^c?
a
k
Differentiating with respect to the price yields an expression for the elasticity of
-^i^_^
(4)
I
o.
a=A^
(i-a)
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, Knigman,
demand
maximization problem,
This vastly simplifies the
number of
varieties.'
total utility for a representative
consumer
is
defined:
where
utility
from consumption of the agricultural good,
agricultural good, Y.
Assuming a Cobb-Douglas
assumed simply
\\(.), is
utility function, the
consumer's
to equal
consumption of the
first-tier utility
maximization
decision can be represented as:
(6)
Max
where Py
is
(?»y"-»
SJ.
the price of the agricultural good, and
I
is
PyY^'tj^P^q;^-!
income.
Solving for the
first
expenditure shares for each of the aggregate goods that are independent of income:
EE
(7)
^k^^ka
*^
/
—
W
We
^-
will use the price
=
1-6
-^r
of the agricultural good as the numeraire.
=
A^-*)
order conditions yields
n.
Production
ii.
The production technology
competition prevails.
in the agricultural sector
has constant returns to scale, and perfect
Thus, the marginal cost of the agricultural good
is
constant, and
its
price in country
is
i
just equal to the marginal cost:
(9)
=
1
In addition, the agricultural
The manufacturing
good
is
sector
i=AJ
Cj(w)
transportable at negligible cost between countries.
characterized by product-specific mcreasing returns.
is
Chamberlinian approach with free entry will yield monopolistic competition, as
The business system
returns trade models.
public good character; they benefit
production
all
R&D
These
costlessly separable into
is
and can be spread
activities are
from increasing
two
activities that
have a
among any number of
unique to each variety.
Such
activities
product design or process technology, advertising, or services such as personnel,
in
and planning; for simplicity,
total costs
familiar
The corporation performs some
facilities equally,
without diminishing their value to any one.
could include
treasury,
manufacturing sector
corporate activities and production activities.
activities:
facilities
in the
is
Adopting a
per firm located in market
(10)
C;
which are simply assumed
to
=
I
i
will refer to
them
as
R&D.
Denoting the level of
R&D
activity as
r,
are:
^^^
O,^)
i=A^
i
dr
be nondecreasing.
Production o(>erations are characterized by increasing returns
and a variable cost associated with each manufacturing
plant.
at the
plant level:
there
is
a fixed cost
Production costs for a plant located in market
i
are:
(11)
C,'^(w.^,q) =
^
F(w)*nw,j;q)
<
or
To make
the analysis
more
tractable,
it is
(12)
useful to
assume
that
marginal costs are constant:
V(w,j;q) = V(w.j-)q,
This assumption
is
not
critical; the results
Notice that variable costs
fall
require only that the cost function exhibit
bounded returns
to scale.
as the level of corporate activity increases, and that this relationship
8
is
independent of the number of plants
The firm chooses
in operation.
r to
minimize costs over both markets such
that:
dC'iw./)
(12)
'*''
dViw/)
dV(w.,r)
=
a,*
dr
Finally, there
is
dr
It is
from destination markets, such as shipping
The
and the transport
is
.
.
i=A,
and^
,.
the reverse
'
costs, trade barriers, linguistic or cultural differences,
transport cost
assumed
is
Krugman
Thus, for some amount
shipment to a foreign market
r.
u
when
j=B
<j,
intended to stand in for a variety of disadvantages of distance
fraction of output that is lost in transit (similar to
in the distance travelled.
—
dr
'
a transport cost.
responsiveness to consumers.
'-
q,
to increase
with distance:
(1979)), which
produced
in
it
is
and slow
modelled as a
specify as exp)onentially increasing
I
market a = A,B, the amount that survives
smaller by an amount that increases in the distance between the two markets, D,
cost, T:
«.<"*
(14)
d^=0.d^=D
a=A^, b=B when a-A, and
The competition among firms
equilibrium in each stage.
in the differentiated sector takes place in
First, firms in
full
stages,
and there
is
a 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
= A,B)
Solving the
yields a price to location
j
first
order conditions for profit
markup over
as a
the marginal cost of
production and transport:
P^
(15)
l-I
Vt)e ""
for
a=AM and j=A^
a
The markup hinges on
n.
varieties
amount
clear
produced
location B.
of substitution between
varieties.
Market Equilibrium
iii.
It is
a, the elasticity
The
from the markup pricing policy
at
A
in equation (15)
will be priced equally at a given location,
price of varieties produced at
A
and the
elasticity in equation (4) that all
and similarly for
exceeds that of varieties produced
that is proportional to the transport cost differential,
9
and the reverse.
all
at
varieties
B
in
produced
at
market B by an
Given equilibrium prices and
numbers of
varieties
produced
in
each market, the quantity demanded by a consumer in market a( = A,B) of a
representative variety produced at a
i
qJ.P,n)=—^^
(16)
which
is:
is
PbP
^
.PJ>
P
increasing in the distance between the markets, and decreasing in the
from both markets.
The quantity demanded of goods produced
^^(P'"^ =
(17)
in the foreign
n=n.^.
number of
market
varieties available
is:
^'^^" Vsi'-^n.' n-ri^^B
KO^(n,.«,e'^'-">)
a=B when b=A, and
the reverse
Thus, the optimal allocation among varieties implies that each consumer consumes equal quantities of
varieties
produced
at a single location,
home market
yielding a
and smaller amounts of the varieties produced in the foreign market,
bias.
Depending on the parameter values, there are three possible types of equilibrium:
production
I
facilities, all
firms operate a single production facility, or there
will characterize the conditions for each type
of equilibrium
in turn.
B
t
denotes the single-plant equilibrium.
is
all
firms operate two
a mixture of both configurations.
Starting with the equilibrium with single-
plant configurations, variable profits on sales of each variety produced at
where
all
A
and sold
in
A
can be expressed
Variable profits on sales of each variety produced at
A
in
as:
market
are:
"^
Profits are higher the closer
is
•
-^
oin^e'^-'-Kn,)
the production location to the destination market, and the fewer competing
varieties there are.
Thus, in an equilibrium where
markets for a firm located at
Assuming
free entry, the
A
all
firms have a single production facility, total profits over both
are:
number of firms producing
Further, given the synunetry assumptions
at
made above,
each location adjusts endogenously to yield zero profits.
the optimal choice of the firm-specific input,
10
r, is
symmetric across firms and markets, and the wage
number of firms
that the
located at
number of firms
A
and B are equal
both markets
in
in equilibrium,
located in each market
equal,
nA = nB = n,.
which
in turn implies that the
Together, these two conditions imply
is:
n, =
(21)
is
^-l
a[F(H')+C'(>v^)]
The number of
varieties
is
increasing in the expenditure allocated to differentiated products, and decreasing in
the elasticity of substitution between varieties, and in the level of per-firm and per-plant fixed costs.
To check whether
A
configuration.
firm will open a second production facility only
compensated by the increase
a plant located at
firm lowers
its
an equilibrium, consider the incentive for a firm to change
this is
A
if
from locating closer
in variable profits
opens an additional production
facility at B.
the increase in
to foreign
its
production
fixed costs
consumers.
Prices and profits in
its
A
is
more than
Suppose a firm with
are unchanged.
The
price in market B, to reflect the reduction in the variable costs of serving that market:
(22)
/>i
B
yielding variable profits in market
=
-^K)
a-l
of:
—
T^ABiPr".) =
(23)
Thus, firms are discouraged from defecting only
if
the increase in variable profits
is
insufficient to cover the
increase in fixed costs:
(24)
at:
=
—XT
,TD{l-a)
1
^ Fiw)
o [(„,-i)cW-o)^(„^^l)]
nji^^nxi-o)]
Putting the no-defection condition together with the zero-profit condition yields the condition for
equilibrium:
F(w)
(25)
>
F(>v)+C'(H',r)
Comparative
plant
is
more
statics
(l-e"^'-»))
n,{Ue^'-''^-e^'-'^
d+e"^'-"))
/.,(l+e"X'-<'>) + l-«r"^'-''»
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
always prevails.
the firm-level fixed cost.
The
effect
11
of the
which each firm has a single
lower are the transport cost and the
In the limit, as the corporate cost goes
elasticity
of substitution
is
ambiguous.
However, by simplifying the no-defection condition, so
defection on the market price index,
the elasticity of substitution.
the smaller
is
that firms
do not take into account the
can be shown that the equilibrium
it
In addition, for a fixed
number of
is
more
effect
of their
likely to hold the smaller is
firms, a single-plant equilibrium
is
more
likely
the foreign market.
Next consider an equilibrium
which
all
firms have production facilities in both markets, denoted m.
In this case, a firm serves consumers in market
A
from
production facility
market
at B.
in
production
its
facility at
A, and consumers
in
B from
its
Solving for equilibrium prices and quantities yields sales for each variety in each
of:
=
^^(/>^^j
(26)
_^£zi
a-AJB
associated with variable per-firm profits in each market of:
6/
^-(P^^J
(27)
Total per-firm profits over both markets
(28)
is:
n-(P„,«J
=
2n''iP^jiJ-2F(w)-C'iw^)
Again, given symmetry in factor proportions and demand, the number of firms in each market
°a=1b=°iii-
Then assuming
free entry,
is
and solving for the number of firms under zero-profits
in
equal,
a dual -plant
equilibrium yields:
„
(29)
*Z
=
a[2F(w)*C\w,r)]
Again the number of firms
is
decreasing in the level of total fixed costs, but here the per-plant fixed costs are
weighted more heavily.
A
down
firm
is
tempted
from the dual-plant equilibrium
if
the savings in fixed costs
from shutting
a production facility more than offset the loss in variable profits due to higher transport costs to the
foreign market.
Consider a firm that shuts
however, the firm's price
(30)
to defect
down
its
plant at B.
Pricing and profits in
rises to reflect the increase in transport costs:
/./
=
_£_K(>n>
a-l
12
A
are unchanged.
In B,
yielding lower variable profits of:
^^1>
^amCP'J'.^J
—
=
=rr—
Thus, firms have no incentive to defect from a dual-plant configuration only
F(w) i
(32)
Combining
»/
e
1
^ InJl-.^^-Vd-e"^'-'))
2F(H.)
2n^-{l-e^^">)
2/-(H')+C'"(H',r)
fully multinational equilibrium, where
smaller
is
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
never sustainable.
ambiguous.
elasticity
TD(l-o)
the zero-profit and no-defection conditions yields equilibrium conditions:
(33)
A
if:
By
at the
firm level.
Here, as the firm fixed cost goes to 0, a dual-location equilibrium
Again, the effect of an increase in the
elasticity
simplifying the no-defection condition as above,
it
of substitution between varieties
is
more
likely to hold the larger
single-plant equilibria are characterized
is
multinational firms coexist with national firms.
The condition
for the
For a fixed number of firms,
Thus, the dual-plant and
the foreign market.
by precisely reversed conditions.
In the intermediate range of parameter values, there
single production facility
is
can be shown that an increase in the
of substitution makes the multinational equilibrium more likely to hold.
the dual-plant equilibrium
is
is
a third possible equilibrium, in
In the mixed equilibnum,
some
fraction, a,
and export, and the remaining fraction have production
facilities in
which
of firms have a
both markets.
mixed equilibrium can be derived from combining no-defection conditions
for both single
plant and dual-plant firms:
n^(2-a(l-«"^'-'>)) > l**"^'')
(34)
where
n^ is the
number of firms
in the
mixed equilibrium. When
equalized, the expression for the proportion of single plant firms
^
For a given number of
returns to the
two configurations are
is:
2
8/
(l-^froc"))
an^ F(w)
firms, the proportion with a single production facility rises with the size of the fixed cost
13
and
with the size of the transport cost and the distance between markets.
falls
holds only
The
ratio
when
With
free entry, this equilibrium
the following conditions on the fixed costs and the transport costs are satisfied:
of firm-level to plant-level fixed costs
is
inversely related to the elasticity of substitution.
positively related to the transport cost and distance, and
condition
If this
is satisfied,
any mixture of firm types can be
supported.
iv.
II.
It is
Factor Market Clearing
now
equilibrium wage.
possible to go back and solve for equilibrium conditions in the factor market and derive the
Constant returns
in the agricultural sector
imply
derivative of the unit cost function with respect to local wages.
(35)
=
/>^)
In the differentiated sector, the
demand
demand
that the
Thus,
in
per unit labor input
market
= A,B:
and production
activities.
the derivative of the cost function with respect to the local
is
the equilibrium level of corporate services
simply the
"EM
for labor can be separated into corporate
for labor for corporate activities
i
is
wage
The
at
:
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:
F.
d^(^)
.
L,V^
(37)
dw.
And
they generate a
demand
output produced at location
(38)
i
for labor for production
and sold
l^(w.,r) = e^'^
in j this
^
and transport of the differentiated goods; for a unit of
demand
is:
d^.=0. </^=D;
i^A^; k=B when i=A, and
the reverse
dw^
Labor demand and wages vary according
to the type
of equilibrium
single-plant equilibrium, factor clearing conditions in each market are:
14
in the differentiated sector.
In the
(39)
where
L, =
is
qj
lJi^)Yl*n^L\{w,^yL!'{w)*lf(M,,^)ql\
per firm output in the single-plant equilibrium.
i=AJ
for
In the pure dual-plant equilibrium, factor clearing
implies:
(^)
where
L, = l^(yv)Y,''*n^L;(w,^)*L!'(,w)*2ll^iw,j-)qr]
q*^
is
per firm output in the dual-plant equilibrium.
In the
straightforward to calculate, and depend on the mix of firms.
supplies and consumer distributions,
II.
V.
wages
fori=AJB
mixed equilibrium,
In all three cases,
due
factor
demands are
to synmietry in factor
both markets are equal.
in
Commodity Market Clearing
Denoting wages
in the
dual and single equilibria as
expenditure equality to be expressed in market
(41)
/"•
while in the single-plant equilibrium
Then commodity market
=
A
w" and
w' respectively, permits the income-
in the dual-plant equilibrium as:
^"L
= y+2n^[/'"(j"(P'0]
it is:
clearing requires a single market clearing condition.
For agriculture
in equilibrium
n
this is:
(l-«) =
(43)
—
n=mu
I"
II.
vi.
Trade Balance
Given symmetry
agricultural
good and
in
for differentiated products.
with purely national firms.
agricultural good,
population size and income, there are synunetric demands in both markets for the
Given symmetric
The
single-plant equilibrium
is
essentially a trade equilibrium
factor proportions, each country satisfies
and there are balanced flows of two-way trade
15
in the differentiated
its
own demand
for the
manufacturing sector:
The volume of
and the
intra-industry trade
elasticity
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
goods
in
in the differentiated sector, there is
in the
pure multinational equilibrium.
Instead of
balanced two-way trade 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
goods.
These
differences,
factor
results contrast sharply with the predictions
where the only motivation
endowments.
trade accounted for
headquartered
for cross-border expansion is factor price differentials caused
In a factor proportions
by intra-industry
in the capital-intensive
from a model based on factor proportions
by different
framework, the presence of multinationals reduces the share of
trade, but
need have 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
higher the proximity advantage relative to the concentration advantage.
in,
Three-Stage Production with Symmetric Factor Endowments
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.
will either in part or totally substitute for intraindustry trade.
First, there is a large share
16
of intraindustry trade in
total trade
This
(Loertaches, Walter (1981)), and second, multinationals account for a significant share of trade (Rugnian
(1988)).
Indeed, there
evidence that suggests that multinational activity on balance
is
rather than a substitute for trade
The
first fact
(Swedenborg (1979), Blomstrom
could be explained
proximity and large scale economies.
fact in
The second
two ways.
single plant multinationals, finished
complementary
to
(1984)).
model developed above by a combination of low benefits
in the
fact is not
to
explained by the model developed above with a
simple two-stage production function in the differentiated sector.
would explain the second
et. al.
is
A
factor proportions account of multinationals
above, given a two-stage production process and
First, as described
goods are exported back from the country of production
to the headquarter
country.
Second, with a three-stage production process, multinationals produce intermediate inputs in the
economy
that is relatively
abundant
in the factor
export them to downstream production
used relatively intensively
in final
used relatively intensively in intermediate production, and
facilities in the
goods production.
goods or intermediates will flow across borders
economy
A
that is relatively
factor proportions
well-endowed with the factor
model thus predicts
that either final
in a single direction, contributing to inter- rather than intra-
industry 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 intra-industry, intra-firm trade
differs
under plausible conditions. This prediction
from a factor proportions account, which would predict one-way flows of intra-firm
Again, the contrast between commodity semiconductors and cars serves to
the
two models. In the 1970's,
facilities in
stages
US commodity
chip firms
made
illustrate the differences in
substantial investments in assembly
Southeast Asia, which were motivated entirely by factor price differentials.'
were intensive
in low-skilled labor, in contrast to the
trade.'
The
test
and
test
and assembly
design and manufacturing stages, which were
US
design and manufacturing
intensive in engineering skills and capital.
Semiconductors were shipped from the
complexes
Southeast Asia, and then shipped back to sales destinations in the
to
assembly and
test facilities in
US.'"
17
In contrast, in the automobile industry, there has been substantial
expansion into destination markets.
A
typical pattern of expansion
would
two-way investment and multinational
start
with the establishment of
distribution and sales facilities in the destination market, followed by assembly facilities
foreign market
was
sufficient to warrant the fixed investment."
scale
of substantial two-way multinational
economies and proximity advantages provides more
in auto
the share in the
Factor price differentials provide
EC
into these investment patterns, since the markets in question, such as the
relative factor prices in periods
when
Instead, the relationship between
economies are substantial but bounded
assembly, and smaller in sales and distribution, trade barriers mto several countries in the
and the advantages of a
To
local presence
and customization
to the local
formalize an explanation for the latter pattern,
additional stage,
which has
I
insight
and the US, have had similar
activity.
scale
insight:
little
EC
are high,
market are high.
modify the production structure to incorporate an
a distinct proximity /concentration trade-otf.
manufacturing (q) stages detailed above, there are sales activities
(s).
'•
Thus,
whose cost
in addition to the
R&D
(r)
and
structure entails a fixed cost, a
constant marginal cost, and a variable transport cost:
a=AM
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, which
R&D
input,
simplify notation,
I
is
(i
= q,s),
is
facility that
uses
it.
a transport cost, both for the manufactured input, and for the final output.
replace the exponential transport cost with a
both the distance between markets and the shipping cost.
1
Unlike the
proprietary to the firm.
however, the manufactured input lowers the cost only of the sales
In addition, there
ti>
is
The
more general parameter,
t,
The
To
which subsumes
cost of transporting the output of each stage,
the reciprocal of the quantity lost in shipment; only the portion of output that
borders, q-q, (a = A,B), incurs the transport cost.
is
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 transport at each stage of production.
commonly
Casual empiricism suggests that sales activities are most
dispersed near consumers, while manufacturing
18
is
more
likely to
be concentrated, and corporate
activities
such as
R&D
in Section II,
number of
R&D
its
value to any one.
number of
discriminate
more
Nash equilibrium
in prices.
w^=Wb, and
the
= 0),
and spread among any
in sales
This accords well with the
sales.
and service, and
that trade barriers
against final goods than against in'ermediate goods.
Nash equilibrium
Given symmetry
number of firms
(or
attention to firms headquartered in market
the differentiated sector:
(t,
A
in factor
R&D
in
production configurations
is
and manufacturing
in a single location,
I
start
due
investments)
equal in markets
is
without loss of generality.
A
and B, so
activities across borders.
can confine
There are 3 possible configurations
to the
in
can
it
can spread both
R&D
activities
combination of scale economies and costless transport.'^
by deriving conditions for each pure type of equilibrium
same manner
it
In all 3 configurations, each firm concentrates
I
as in Section
firms located in each market.
-
where
all
firms headquartered in each
confine attention to the uniform equilibria due to the complexity of
analyzing mixed equilibria with three possible firm configurations.
all
we
each firm can concentrate both manufacturing and sales in a single market,
market have identical configurations;
precisely the
followed by
proportions and demand, in equilibrium, factor prices are
invest in sales facilities in both markets, and concentrate manufacturing in a single market, or
sales
As
special assumptions.
Second, the benefits from scale economies relative
an important advantage
is
Again, firms compete in two-stages:
equal,
a
from proximity are assumed greater for manufacturing than for
observation that customer-responsiveness
commonly
make
I
output can be transported costiessly to manufacturing plants
plants without diminishing
to the benefits
Accordingly,
are the most concentrated.
II,
The equilibrium conditions
are derived in
by combining zero-profit conditions with no-defection conditions
for
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
their rivals.
Variable profits for each firm across both markets in equilibrium j( = t,m,d) are:
APiJ'i^j)
(45)
=
—
J=t^M
on.
where
Uj is
the
number of firms
The number of firms
free entry.
Thus,
in
located in each market under market structure].
in each equilibrium is
determined endogenously by the zero-profit condition under
an equilibrium where firms concentrate
19
all activities in
a single location (denoted
t),
it
is:
(46)
n, =
Just as in Section
II, in
—o [C'(w^)+F«(>v)+f'(H')]"'
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
relative to the firm-wide scale economies.
The
condition ruling out defection to a fully diversified
configuration combined with the zero-profit condition yields an equilibrium condition:
F'M^F'>(w) ^ K(l^^'"°)-0"'']
(47)
C'(w,r)
where the cost of transporting intermediate inputs
(l*2r,''°)
raises variable costs
'
And
F'(w)
downstream
c'(w/)*F%w)
In the equilibrium
equilibrium
,
defined:
-t,
diversified configuration
)+r,
)[/i,(l*r,
is:
]
n,(i*t;''')(i*2t;'''-Ty'')HT,-t;'°)(U2t;''')
where only downstream
number of firms
(49)
(T,
^
T
(K,(.)*K(.))
the equilibrium condition ruling out defection to a
(48)
by a profxirtion,
activities are dispersed across
borders (denoted d), the
is:
n. =
•"
—a [C'"(H'/)*F«(H')+2FV)]''
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:
iTl-''-t:-'-)[n/l^Tl-')X'^
(50)
And combining
F'iy.)
^
the zero-profit condition with the condition that firms have
no incentive
multinational activities by opening an additional manufacturing facility yields:
20
to extend their
(l-7;-°)[n^U7',-'')-r;-°]
FHw)
(51)
^
C'(w,r)+2FV)
Lastly, the
number of firms
sales across borders (denoted
m)
/Jj(l+r,'"°)27'^'"''+(l-r,'"°)(l+2r,'"°)
equilibrium where firms have diversified both manufacturing and
in the
is:
„^ = -^[C''(h'^)+2F<(w)+2F"(w)]-'
o
(52)
The combination of
production
the zero-profit condition with the condition that firms have no incentive to close
facility yields the
equilibrium condition:
(2«,-l)(l-r;-')
F^y.)
^
(53)
C\w,r)*2F\w)
4nX-''
And
down one
the equilibrium condition ruling out defection to a fully concentrated configuration
is:
(2n,-l)(l-f;-°) ^ F'(y^).F''M
(54)
Notice that together, equations (46), (49), and (52) imply that in the special case where fixed costs are
equal in the three equilibria, 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
that a fully diversified equilibrium is
likely the smaller are fixed costs in manufacturing, the greater are fixed costs in
of transporting both the intermediate input (T^'^ and the
substitution."
A
of
R&D,
the intermediate input, and the smaller
likely to obtain the smaller
smaller
is
is
of the
is
the lower
is
and the greater
(tj,
more
the fixed cost in sales, the greater
is
final
good.
is
only possible
when
the elasticity of
likely the greater is the fixed cost in
the transport cost of the final
the elasticity of substitution.
the greater are the costs
A
is
good
relative to that of
downstream-diversified equilibrium
In addition, the
the transport cost of the intermediate
is
smaller than
Similar to the two-stage case, a diversified equilibrium becomes increasingly likely the
larger are the returns to scale at the corporate level relative to returns to scale in manufacturing and sales.
21
is
the fixed cost in manufacturing, and the
the cost of transporting the intermediate input relative to that of the final good.
downstream-diversified equilibrium
that
good
fully concentrated, single-location equilibrium is
sales, the smaller is the fixed cost
more
final
R&D,
more
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
demand
addition of a stage of production generates additional
for labor,
Conditions for factor market clearing and commodity market clearing can
analogous to equations (37) and (38).
then be derived analogously to equations (39) through (43), with a similar set of conditions for the downstream
diversified equilibrium.
will be equal,
Just as in Section
II,
with equal relative factor endowments, wages in the two markets
and identical production patterns will emerge.
in
which
firms concentrate
all
trade patterns identical to those in a pure trade
proportions:
there are balanced flows of
intra-firm trade.
all
three production stages in a single market results in
model with differentiated products and symmetric factor
two-way trade
in differentiated products,
Just as in a trade model, the flows will be greater, the larger
allocated to differentiated products, the higher
The equilibrium
results in balanced
in
which
is
is
and no inter-industry or
the share of expenditure
income, and the lower are transport costs.
firms invest in both manufacturing and sales facilities in both markets
all
two-way flows of
in the
and the agricultural sector will be autarkic.
differentiated sector will be balanced,
The equilibrium
Given symmetric demand, trade
intra-firm trade in
R&D
completely crowding out trade
in
Here
goods.
multinational production completely substitutes for trade.
The addition of
a production stage introduces the possibility of a third equilibrium in which iirms
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 intra-industry, intra-firm trade in intermediates, which
substitute completely for trade in final
the stylized facts cited above:
IV.
goods and
in invisibles.
Thus,
this
equilibrium
is
consistent with both of
the existence of multinationals generates intra-industry trade.
Asymmetric Factor Proportions
In reality, firm configurations are likely to reflect considerations of both factor and proximity
advantages; in this section
I
develop a hybrid model to accommodate both considerations.
a pure factor proportions account of
MNEs
predicts configurations in
22
which a firm locates
As described above,
R&D
in the
country
abundant
relatively
in the factor in
which
R&D
is
relatively intensive,
country abundant in the factor in which manufacturing
world
in
which
factors are completely mobile
is
when
the integrated equilibrium
-
hybrid model of multinationals, since there
transport costs are introduced.
analyze
how
Here
I
Such accounts use as
intensive.
configurations and trade of dividing up the supply of factors.
in analyzing a
and a single manufacturing plant
is
-
benchmark a
and analyze the implications for firm
somewhat complicated
It is
their
in the
to
use this approach
no obvious counterpart to the integrated equilibrium
adopt the symmetric equilibrium as an alternative benchmark and
firm configurations and trade patterns change as factor proportions become increasingly
imbalanced.
This section returns to the simplified production structure of the
Assume
production.
there are
two types of
Type
the two countries and immobile.
workers
activity
to that
j
W'=
of unskilled workers as
k = r,q,y as
1|''(W),
wage
w/Zwj'.
given relative wages
W,
w^' in
country
R&D
i.
and adds a factor of
which are divided between
Define the ratio of wages of skilled
Next, define the equilibrium unit input for skilled labor in
and similarly
factor intensity of production in the three productive activities
with
section,
skilled (L,) and unskilled (Lj),
labor:
paid
is
first
is
Further, assume that the
tor unskilled labor.
ranked consistently at any relative wage
the most skill-intensive activity and agriculture the least:
l,'(W)/l2'(W)
>
l|XW)/ljXW)
rate,
>
V(W)/1/(W).
In addition,
locate
its first
assume
that there is
manufacturing plant with
some small advantage
its
R&D
to co-location,
facilities, all else
factor proportions, the existence of a co-location advantage,
equal."
such that a firm chooses to co-
In the equilibrium with equal
however small, eliminates single-plant
multinationals.
Starting in the
benchmark case with equal
multinational equilibrium where
all
factor
endowments, there are 3 possible
all
is
symmetry
in the
number of
will analyze the effect of
firms.
moving
fiilly
firms have a single manufacturing plant, and a mixed equilibrium.
three cases, given equal factor proportions, factor prices are equalized across the
all
a
firms in the differentiated sector have manufacturing facilities in both
markets, a pure trade equilibrium where
In
equilibria:
Suppose
skilled labor
that the
two markets, and there
aggregate ratio of skilled to unskilled labor
from market B
23
to
market
A
is L,/!^.
and unskilled labor from market
We
A
to
B
in the
same proportions
monopoly supplier of
movement from
skilled labor,
and B
is
monopoly supplier of unskilled
the
the center along the diagonal toward the northwest
comer
R&D
imbalance by moving
equalization.
the relative
wage of
activities to
skilled labor in
the
Helpman diagram.
in the
A, and upward pressure
A, while agriculture expands
is
This corresponds to
labor.
A
In the pure trade equilibrium, as the ratio of skilled to unskilled labor rises in
downward pressure on
A
economy
as the aggregate skilled to unskilled ratio, so that in the limit
in B, thereby
and
in B.
falls in
B, there
Firms respond
is
to the
maintaining factor pric
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 in return for
As
R&D
eventually one country becomes the sole producer of agriculture or
abundance of
R&D.
At
additional increment of skilled labor
plant will
move
to
A
from B
to
from B, and agriculture
at
A
which the
last
Assume
unbalanced trade
in
facility
and of unskilled labor from
will continue to
move
factor imbalances, either agriculture concentrates completely in
between the two
R&D
to
has
A
to B.
R&D
R&D
from
A
intensifies,
A
R&D
to
Now
B from A. With
B and/or
products and one-way flows of
that
moved
becomes
A, and transfer an
a manufacturing
sufficiently strong
A, and manufacturing
in
unequal proportions and utilizing different production techniques.
in differentiated
skills in
that juncture, factor prices
diverge, and different production techniques are adopted in the two countries.
Take the point
and there are
differentials,
services.
reallocation of factor supplies continues, so that the relative
concentrated before agriculture.
overall magnitude as in the
to
Here, there
B and
is
agriculture
is split
two-way,
from B
to
A.
The
interesting feature of this equilibrium
foreign penetration.
With unequal
with factor price equalization.
is
that firms continue to use trade as the sole
factor prices, the payoff to concentration
must be
Thus, the introduction of factor imbalances gives
rise
at least as
means of
favorable as
it is
only to single-plant
multinationals, if any.
Performing the same experiment starting from a pure multinational equilibrium, the
24
initial
response to a
progressive unbalancing of factor proportions
B, and factor price equalization
that there are flows
is
similar.
R&D
moves
to
market A, agriculture moves
maintained, along with plant configurations.
of agriculture from B
to
Eventually, the imbalance in factor
concentrates in a single market.
is
Now
A, balanced by reverse flows of
endowments becomes
sufficiently
The
R&D
pattern of trade adjusts, so
services.
extreme that one industry
a factor price differential between the two markets
economies motivation for concentrating manufacturing
market
to
activities in a single location.
is
added
to the scale
Thus, a few firms will
concentrate production in the market with favorable factor conditions, and export, 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
With unequal
possible trade and production patterns.
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
borders.
These
results,
in
goods.
which appear
It
to
also introduces the possibility of multi-plant configurations across
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
25
is
more
likely
the higher are intrafinn returns to scale relative to intraplant returns, the higher are transport costs across
markets, and the greater
is
expenditure on differentiated products in the foreign market.
of firms, a multinational equilibrium
is
more
also
likely the higher is the elasticity
With a large number
of substitution between
varieties.
This framework also can explain equilibria
the
same
industry.
A
mixed equilibrium
in
which national firms coexist with multinational firms
sustainable for intermediate ranges of the parameter values, in
is
the equilibrium ratio of fixed costs at the firm level to fixed costs at the plant level
is
•'
the type of equilibrium in the differentiated sector.
multinational equilibrium, equal quantities of
all
varieties are
pure trade equilibrium with single plant firms, there
is
a
consumed, regardless of
home market
bias in
which
an increasing function of
the transport cost and a decreasing function of the elasticity of substitution.
Consumption patterns vary with
in
In a pure
their origin, while in a
consumption of the differentiated
product.
The
prediction that intra-industry 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.
With
multiple production stages, if concentration advantages dominate in upstream production activities, while
proximity advantages dominate downstream, then intra-industry, intra-firm flows of intermediates supplant intraindustry flows of final goods.
while in the
first
When
In this latter case, multinational activity
mode of
complementary
to trade in
goods,
case they are substitutes.
both factor proportions differences and proximity advantages are incorporated within the same
framework, the pattern of trade and investment depends on both.
the
is
For moderate factor proportions differences,
foreign market penetration and firm configurations are identical to the symmetric case, with the
sole difference that single-plant multinationals
The consumption
may
replace single-plant uninationals in the trade equilibrium.
patterns and factor intensities that characterize the symmetric case can be maintained, and the
Moderate factor differences induce one-way trade
primary difference
is in
and one-way trade
in agriculture in the reverse direction; in the trade equilibrium,
differentiated products
the pattern of trade.
may be unbalanced,
two-way trade
reflecting differences in aggregate income.
26
in intangibles
in
With increasingly
unbalanced factor proportions, eventually one activity becomes completely concentrated
factor price differentials arise.
in a single market,
and
Factor price differentials introduce an added impetus to concentrate production
in a single plant.
Tliis
model has strong implications for policy. Most obviously, the im{K>sition of a
transport costs, and
makes penetration by multinational production more
intangibles (or profits) has the reverse effect.
likely,
tariff raises
while a tax on the earnings of
Further, the relative structure of tariffs
on
final
goods and
intermediate inputs influences which parts of the business system are concentrated and which dispersed.
The model implies
to scale are
on
trade.
Tliis suggests conditions
if different
which natural
barriers are
differ significantly), then the welfare gains
more
maximal
Future research will analyze
rigorously.
Further, this model lends itself to testable hypotheses.
In particular,
choices between exports and multinational expansion as alternative
reflect trade-offs
from free trade
regions, while free interregional investment flows raise welfare by permitting
returns to investment at the corporate level, and thus a greater variety of products.
these conditions
low and between
regions have similar region-wide factor proportions (while the relative
endowments of countries within regions could
may be exhausted within
may be more damaging
under which regional trade blocs are not
If regions are geographically coherent areas within
which they are high, and
factor
where natural proximity advantages are high and intrafirm returns
high relative to intraplant returns, restrictions on foreign direct investment
to welfare than restrictions
deleterious.
that in industries
to test this hypothesis.
27
suggests that firms' observed
modes of foreign market penetration should
between measurable proximity and concentration advantages.
employs a gravity equation approach
it
Research currently underway
1.
Seminal contributions to
and growing
this large
Krugman
literature include
(1979), Lancaster (1980),
Helpman
(1981), and Ethier (1982).
See Caves (1982) and Dunning (1988).
2.
may be
This
3.
attributable in part to the failure of earlier attempts to explain multinational activity in terms of
capital flows in a factor proportions
4.
In the
Markusen model,
framework with perfect competition.
factor
endowments are symmetric, but
sector-specific capital plays a
key role in
explaining multinational production.
5.
The models
differ in their assumptions about the production function. In the
an additional fixed cost to open production
facilities
model presented below, firms incur
abroad, and save on variable transport costs.
In the
Krugman
no fixed production cost, and variable costs differ between markets by some multiplicative factor.
predictions
differ in two respects. First, in the Krugman model, only uniform equilibria are possible, while
The
here there is a mixed equilibrium. Second, in the model below, the decision whether to produce 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.
model, there
6.
The
is
analysis
would become much messier
in the absence of this simplification, but the qualitative results
would
not change significantly.
7.
Unfortimately, the empirical
work
in this area does not distinguish
between the two types of trade when referring
to multinationals.
8.
See Yoffie (1992) for a complete account of investment and trade patterns in the global semiconductor industry.
9. Not surprisingly, the pattern of trade and investment
by a hybrid between the two models (see Section IV).
10.
In the interests of tractability,
I
in the
ignore dynamic considerations
relationship between exports and multinational expansion in a
11.
The model can be generalized
in country a is
assumed
semiconductor industry
to
in this
dynamic
any number of production stages,
<?'
probably best explained
Future research will model the
setting.
to entail a fixed cost, a variable production cost,
I
model.
is
where each stage of production
and a variable transport cost:
i
located
i
where the variable cost at each stage is assumed to be a decreasing function of the output from the previous stage
used as an input, q*^,, and all internally produced inputs are assumed proprietary to the firm. In addition, there is
a multiplicative transport cost for each unit of output that is transported to the foreign market. The model developed
above
is
just a special case.
assume the presence of an arbitrarily small co-location advantage between R&D and manufacturing, so that
This assumption
it is always optimal for a firm to locate its first manufacturing plant m the same market as R&D.
is useful because it makes the flows of invisibles determinate, and sensible because it accords well with casual
12.
I
empiricism.
13.
T,
is
It
could be modelled more formally as t,>0.
more accurately described
as the ratio of the vanable cost gross of the cost of transporting the
intermediate input to the variable cost net of transport costs.
28
14.
These
results are derived
by differentiating the no-defection conditions, simplified so
account the effect of their configuration decisions on the market price index. This
of a large number of firms, used
15.
is
that firms
do not take
into
consistent with the assumption
in simplifying the elasticity expression
This assumption can be formalized in a variety of ways, such as assuming a variable transport cost between
and manufacturing, or a lower fixed cost for manufacturing when it is co-located with R&D. Instead, I
R&D
simply follow Helpman in making an ad hoc assumption, since the results are essentially the same.
29
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Multinational Enterprise and Economic Analysis (Cambridge:
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Erdilek,
Asim
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(1985):
(New York:
"National and International Returns
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in
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Birgitta (1979):
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5939
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