Review of International Economics, 8(1), 149–163, 2000
International Trade, Technological Development,
and Agglomeration
Karen Helene Midelfart Knarvik and Jostein Tvedt*
Abstract
The paper focuses on how localized dynamic external economies of scale may cause uneven technological
development internationally, and encourage regional agglomeration of industries. Location-specific technological progress depends on the absolute number of local innovating firms, and the relative number of innovating firms; i.e., the share of economic activity in a region that takes place within the innovating sector. The
creation of industrial clusters contributes to explaining regional specialization, factor prices and welfare, and
it appears that the critical size of a region regarding its ability to sustain an industrial cluster depends on
whether factors of production are internationally mobile.
1. Introduction
International specialization in the classical Heckscher–Ohlin setting is determined
by relative differences in factor endowments given equal technology. Technology
is, however, a dynamic phenomenon. Innovations are constantly being made, and
old technologies are replaced by new and improved ones. Yet, technological progress
within a certain industry does not necessarily take place simultaneously worldwide.
It is often argued that the diffusion of innovations takes less time in regions with a
relatively high number of innovating production units; i.e., where a major share of
the region’s economic activity takes place within the innovating sector. Improved
access to new knowledge is reckoned as one of the main reasons why manufacturers
tend to agglomerate and create clusters, and is a view that is supported by empirical
findings.1
This article focuses on the hypothesis that the creation of clusters that provide pools
of knowledge and enable rapid transmission of information may cause uneven technological development internationally, and contributes to explaining regional specialization. A dynamic setting is chosen, in which technological advantage depends on
localized innovations and knowledge spillovers. We study how differences in technology, relative factor endowments as well as factor mobility determine national industrial structures, trade patterns, and welfare.
Consistent with standard endogenous growth theory, we assume that the number of
innovations being made in a region is proportional to the number of active firms. But
the number of innovations alone does not govern the technological development.
Probably, the degree of technological progress also depends on how rapidly an innovation is shared by the firms within an industry. Hence, the speed of knowledge diffusion matters for total productivity growth. It is reasonable to assume that diffusion is
faster within regions where a major share of the active firms are engaged in the same
* Midelfart Knarvik and Tvedt: Centre for International Economics and Shipping, Norwegian School of Economics and Business Administration, Helleveien 30, 5045 Bergen, Norway. Tel: (47) 55 959 510; Fax: (47) 55
959 350; E-mail: karenhelene.knarvik@snf.no and jostein.tvedt@dnb.no. This research has been financed by
the Research Council of Norway. We want to thank Tony Venables as well as Jan I. Haaland, Victor D.
Norman, and two anonymous referees for valuable comments and suggestions. Thanks also to participants
at the European Science Foundation workshop on “Employment, Market Integration, and Regional Economic Development”, Barcelona, 1996, for useful discussions.
© Blackwell Publishers Ltd 2000, 108 Cowley Road, Oxford OX4 1JF, UK and 350 Main Street, Malden, MA 02148, USA
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Karen Helene Midelfart Knarvik and Jostein Tvedt
kind of activity; i.e., within industrial clusters. Silicon Valley and the watch industry in
Switzerland are typical examples of how a high concentration of an industry within an
area gives rise to technologically leading industrial clusters.
However, the question of how the transmission of knowledge comes about still
remains to be answered. The literature refers to different mechanisms which impel
firms to agglomerate in space.2 We have chosen to focus on the assumption that transmission of knowledge is due to intraindustry labor mobility: when people change jobs,
they bring industry-specific knowledge and impulses from their previous employer that
can be utilized in the production of their new employer. Because workers regard geographic mobility as expensive or are impeded by immigration policies, they are mobile
among firms only if these are located within the same region.Therefore, there is a transfer of knowledge within a regional cluster, but not within the industry globally.3 Glaeser
et al. (1992) provide good examples of how intraindustry labor mobility has allowed
ideas to flow among neighbouring firms, entailing overall higher productivity.
Our model draws on two strands of the international trade literature, the analysis
of economic agglomeration, usually referred to as the new economic geography, and
the theory of endogenous growth.4 What these models and the one presented here
have in common is the existence of external economies, which causes internationally
unequal development—but they do not share the way the external economies are
modeled. By allowing not only the absolute number of innovating firms to matter, but
also the significance of innovating activity relative to other types of activities in a
region, both traditional growth effects and what one might call “spillover effects” arise.
Growth and spillover effects determine regional technological progress and the sustainability of industrial clusters over time.
The paper is organized as follows. Section 2 sets out the formal model. In section 3
we consider the case of free international trade in goods, but no international factor
mobility; while in section 4 we allow for trade in goods as well as in capital. Section 5
concludes.
2. The Model
Our world consists of two regions (countries), region h and region f. Both regions
produce two goods, 1 and 2. Thus, the total production of the two goods is given by
x1 = x1h + x1f and x2 = x2h + x2f . Each good is produced by a technology exhibiting constant returns to scale in the two production factors: labor, n, and capital, k. Total factor
input in region i for production of good j is given by {nji, kji}, where i = h, f and j = 1, 2.
Total factor endowment in each region is given by {ni, ki} and is fixed in time. We shall
assume that h is the relatively capital-abundant region.
Perfect competition prevails in both goods and factor markets, and there is free trade
in goods. Workers are internationally immobile, but there is costless intraregional
mobility of both labor and capital across industries.
Production of good 1 is intensive in the use of labor relative to the production of
good 2, and the production technology used in industry 1 is constant in time and equal
across locations. However, the technology in industry 2 improves over time. The production in region i at time t of good 2 is given by:
x2i t = Yti H (n2i t , k2i t ),
(1)
where Yti is a location-specific productivity scalar process. The development of the productivity scalar is influenced by two factors. Each production unit has a constant
innovation trend, f. That is, f represents an incumbent unique improvement to the pro© Blackwell Publishers Ltd 2000
TRADE, DEVELOPMENT, AND AGGLOMERATION
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duction technology of each of the production units. However, through intraindustry
labor mobility this unit-specific knowledge will gradually be shared by the other
production units in the region.5 Having worked in a firm, an employee has acquired
industry-specific knowledge which he takes with him when changing jobs. In this way
knowledge from one firm is transferred to another. The stock of not yet shared knowledge in region i at time t is given by Iit, and the diffusion from the stock of knowledge
is denoted by mit. The increment of the productivity scalar in sector 2 at time t is then:
dYti = (f + m ti I ti )dt .
(2)
That is, the productivity of each production unit in sector 2 increases owing to own
innovation, f, but also through learning from new employees about innovations made
by competitors located within the same cluster; i.e., by mitIti.
Total instantaneous innovation in the industry is given by fx2ti . From the stock we
deduct the shared knowledge at time t, mitIti. Accordingly, the increment of the stock of
unshared knowledge is given by:
dI ti = (fx2i t - m ti I ti )dt .
(3)
Innovation in each firm, f, may differ between the two regions, and may depend on
the level of education and the entrepreneurial and innovative spirit of the workers. It
may also vary through the life-cycle of the industry.To simplify, though, we shall assume
f to be a constant.
The diffusion variable mti depicts the diffusion of innovations (i.e., the knowledge
spillovers) that is generated by intraindustry labor mobility. Knowledge is assumed to
be sector-specific, so that interindustry labor mobility does not add to the diffusion of
knowledge.
Each job–worker pair is faced with an exogenous separation probability owing to
random shocks to the production units in both sectors. The assumption of an exogenous separation rate is common in models within the search theory and matching literature (e.g., Pissarides, 1985). This may be justified by imagining firm-specific shocks
that cancel out in aggregate, such as random obsolescence of products. The exogenous
separation process causes continuous labor turnover, ensuring the spread of sectorspecific knowledge.
Agents are assumed so small, and so many, that they perceive the technological
development as exogenous; i.e., to be independent of their own actions.Thus, the agents
do not act strategically to enhance external economies of scale. The model is based on
an assumption of instantaneous adjustment to equilibrium, which implies that workers
losing their jobs immediately get employed again, and that all workers in a region
earn the same wage regardless of their industry of employment. Hence, unemployed
workers are indifferent between working in the two sectors, and accept the first job
offer they get, regardless of which industry it comes from.
If wages are perceived equal across sectors and pay is the only criterion for choosing between job offers, then the probability that an industry 2 worker in search of a
new job will end up in the same industry is given by n2i /ni. Accordingly, we have a simple
expression for the diffusion rate of knowledge:
m ti = li (n2i t ni ),
(4)
where li represents the exogenous separation probability per time unit. It may also be
thought of as a constant representing the degree of labor mobility.
So, according to our model, both the absolute and the relative size of an industry
influence productivity. An absolutely large industry means that a “lot of talent” is occu© Blackwell Publishers Ltd 2000
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Karen Helene Midelfart Knarvik and Jostein Tvedt
pied within this industry, which may lead to a high number of improvements to the
sector-specific technology. In accordance with endogenous growth theory, we shall
refer to this gain from new innovations as the “growth effect.”
A relatively large industry implies that the innovations of one firm are rapidly shared
by others in the same industry, and shall be referred to as the “spillover effect.”6 Owing
to a high degree of diffusion of innovations, the productivity level may be higher in a
region with a relatively high number of firms of a given industry, even though this
region has only a minor part of total world production of this industry and of overall
innovation in the world.
Consistent with the assumption that ki is fixed in time, we let there be no savings.
The preferences of the representative consumer in region i are assumed homothetic,
and are reflected by an additive separable utility function:
U ti = u(c1i t , c 2i t ),
(5)
where cjti is consumption of good j in region i at time t. To maximize utility in a region
i then reduces to the maximization of u(c1ti , c2ti ) given the budget constraint. The budget
restriction
wti ni + rti k i = p1t c1i t + p2t c 2i t
(6)
implies that the total regional labor and capital income must be equal to total regional
consumption expenditure, where wti is the wage rate, rti is the rate of return on capital,
and pjt is the price of good j, all at time t.
3. Free Trade in Goods
Consider first the case where there is free trade in goods, but no factor mobility. In
order to simplify the discussion of the dynamics of the model, we restrict ourselves to
Cobb–Douglas production and utility functions, and suppress the subscript indicating
time. Let the production function in industry 1 be given by:
a
G(n1i , k1i ) = n1i k1i
1-a
(7)
,
where 0 < a < 1; and let the production function in industry 2 be given by:
e
1- e
Y i H (n2i , k2i ) = Y i n2i k2i
(8)
with 0 < e < 1. We have assumed that industry 1 is intensive in the use of labor, from
which it follows that a > e. Adding the assumption that li is equal across locations (i.e.,
li = l i = h,f ), the external economies of scale prevailing in sector 2 take the same
form across regions.
Agents have identical preferences across regions, and the utility of the consumer in
region i at time t is expressed as:
g
1- g
u(c1i , c 2i ) = c1i c 2i , 0 < g < 1.
(9)
bji depicts the unit cost in industry j in region i, and is given by:
a
a
b1i (wi , r i ) = r i (wi r i ) ((1 - a ) a ) (1 (1 - a )),
-1
b2i (wi , r i ) = Y i r i (wi r
i e
e
) ((1 - e ) e ) (1 (1 - e )).
(10)
(11)
Factor market equilibrium requires that the sum of demands for each factor equals the
supply of each factor:
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TRADE, DEVELOPMENT, AND AGGLOMERATION
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ki =
∂ b1i i ∂ b2i i
x1 +
x2 ,
∂ ri
∂ ri
(12)
ni =
∂ b1i i ∂ b2i i
x1 +
x2 .
∂ wi
∂ wi
(13)
Profit-maximizing in the product market implies that b1i (wi, r i) = p1 and b2i (wi, r i ) = p2,
while maximizing utility gives the total world demand for goods 1 and 2:
c1h + c1f = (g p1 )R,
(14)
f
2
c + c = ((1 - g ) p2 )R,
h
2
(15)
where R depicts total income in the world, R = whnh + r hk h + w fn f + r fk f. Product market
equilibrium requires that total world demand equals total world supply; i.e., c 1h + c1f =
x 1h + x1f and c 2h + c 2f = x2h + x2f .
We use good 1 as numéraire, and solve for the equilibrium characterized by
diversified production in both regions initially. The equilibrium price of good 2 is
given by:
e
a
-1
a -e
p2 = ((1 - e ) e ) (a (1 - a )) (1 - a )(1 - e ) ( AN K )
(16)
,
where
A = ((1 - e )(1 - g ) + (1 - a )g ) (e (1 - g ) + ag ),
a
a
K = (Y h ) a -e k h + (Y f ) a -e k f ,
a -1
a -1
N = (Y h ) a -e n h + (Y f ) a -e n f .
Turning to factor prices, equilibrium returns to capital and wage rates are,
respectively:
r i = Yi
a
a -e
wi = Y i
a
a
(a (1 - a )) (1 - a )( AN K ) ,
a -1
a -e
a
1-a
(a (1 - a )) (1 - a )(N AK )
(17)
(18)
.
In equilibrium the production volumes of the two goods are equal to:
x1i = [(-er i k i + (1 - e )w i n i ) (a - e )],
(19)
x2i = [(ar i k i - (1 - a )wi ni ) (a - e ) p2 ].
(20)
In the following we seek to elucidate how the dynamic development of technological advantage determines industrial structure, trade patterns, and regional welfare. It
is possible to distinguish between two different cases regarding how trade patterns
evolve over time. In the first case, the region that initially possesses a comparative
advantage in the production of good 2, owing to relative factor endowments, reinforces
its position in industry 2 over time. In the second case, there is a reversion of trade
patterns over time as the region that initially possessed a relative disadvantage in the
industry 2 production gradually gains a leading position in the industry, because of the
technological development.
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Karen Helene Midelfart Knarvik and Jostein Tvedt
Case A: A Sustainable Cluster
Let us look first at the case where relative factor endowments dictate which region
ends up exporting what product. Assume that all firms, regardless of initial location,
employ the same technology so that Y0h = Y0f = 1. Since region h is relatively capitalabundant, it has initially a comparative advantage in the production of good 2, which
is relatively intensive in the use of capital. At time zero, region h exports good 2, while
region f exports good 1. It follows that region h initially has a higher percentage of the
workforce employed in sector 2 than region f, and that the spillover effect is stronger
in the region h.
Which region has the stronger growth effect will, however, depend on absolute factor
endowments. If region h is larger than, or equal to, region f in terms of capital as well
as labor supply, not only does region h experience a stronger spillover effect, but it
experiences a stronger growth effect than region f as well. Accordingly, the outcome
is unambiguous. The uneven technological development enhances the position of
region h in industry 2 over time. We observe increased specialization and a trend
towards complete specialization with industry 2 concentrated in region h.
Yet, even if region h is slightly smaller than region f in terms of labor as well as
capital endowment, the same outcome as above will appear. In such a case, region f
actually experiences a more significant growth effect than region h, owing to its larger
size. Because of the stronger spillover effect enjoyed by region h, region f is, nevertheless, not able to challenge the position of region h in industry 2. How much smaller
region h may be, without eventually losing its technological lead, depends on the significance of the growth effect relative to the significance of the spillover effect, as well
as on the share of income spent on sector 2 goods. The smaller this share, the smaller
region h may be, without having to fear the vanishing of its industry 2 cluster.
The case of a sustainable cluster is illustrated in Figure 1 (see also the Appendix).
The cluster of industry 2 in region h is steadily growing. Region h exports good 2 and
imports good 1. The technological development magnifies the comparative advantage
that region h initially possessed in the production of good 2. There is increased specialization and a trend towards complete specialization.An increasing part of the work-
Figure 1. Case A: International Trade in Region h
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TRADE, DEVELOPMENT, AND AGGLOMERATION
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force in region h becomes employed in sector 2, which enhances the spillover as well
as the growth effect and strengthens the cluster.
Given free trade and equal technologies across regions, as is assumed to be the case
at time zero, factor prices are initially equalized. As time passes, region h enjoys a
relatively advantageous technological development in the industry that is intensive in
the use of capital. As a result, returns to capital increase and the wage rate decreases
in region h, while in region f the effect is the opposite: returns to capital fall and the
wage rate rises.
Technological progress is reflected not only by changes in factor prices, but also by
a decrease in the price of good 2. Using per-capita utility as a measure for welfare, we
find that there is a welfare increase in both regions. The world as a whole, and each
nation, gain from the technological advancement. The benefit is, however, more substantial in the region where the industry characterized by external economies gradually becomes concentrated; the uneven technological development causes increasing
differences in welfare across regions.
Case B: A Nonsustainable Cluster
Now assume, instead, that region h is significantly smaller than the other region. In
such a case, the growth effect experienced by region f is so strong that, although region
h initially enjoys a stronger spillover effect, its position in the industry 2 will be challenged. Consequently, there is a reversion of trade patterns over time. Region h
gradually becomes an importer of good 2, and there is a trend towards complete specialization, with all industry 2 production concentrated in region f.
Owing to the initial comparative advantage in capital-intensive production, region
h is initially exporting good 2. However, since the region is too small to keep pace with
the technological development of the large region f, sector 2 eventually disappears
from region h (see Figure 2 and the Appendix).
Factor prices evolve similarly to the way they did in case A, but with opposite signs.
The relatively adverse development of the production technology in region h implies
that the wage rate rises and the returns to capital fall, as the labor-intensive industry
Figure 2. Case B: International Trade in Region h
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156 Karen Helene Midelfart Knarvik and Jostein Tvedt
in this region is enlarged. The opposite is the case in region f. As in case A, factor prices
do not become equalized internationally.
The technological progress caused by growth and spillover effects entails a rise in
world as well as in national welfare. During the first period, while region h is still
exporting good 2, the inhabitants of this region experience a more substantial increase
in welfare than do the inhabitants of the other region. This period will be followed by
an interval characterized by convergence in welfare across regions. As long as there is
technological progress, welfare will continue to rise in both regions, but the inhabitants
of the region that ends up hosting the cluster of industry 2 (i.e., region f ) enjoy a more
significant increase in welfare.A divergent economic development, following the establishment of the industry-2 cluster in region f, entails rising national disparities in
welfare.
Hence, with free trade and no factor mobility, growth and spillover effects cause
increased international specialization and eventually geographic consolidation of
industry 2, while impeding international factor price equalization. Industry structure
and trade patterns are determined partly by relative factor endowments, partly by differences in technological development, and partly by consumer preferences. Positive
externalities lead to a technological progress that benefits all individuals, but especially
those living in the region that attains the industrial cluster.
4. Free Trade in Goods and Capital
We now move on to a situation where there is free trade not just in goods, but in capital
as well. If capital is allowed to move freely across borders, and technology is identical
in both regions, noneconomic considerations, such as firms’ expectations about what
location will become the most attractive, determine industrial structures and trade patterns. But if one region initially possesses a small technological advantage, free trade
in goods and capital produces three different outcomes with regard to international
specialization and economic geography.
First, the region h that initially is the relatively capital-abundant, and therefore has
a technological advantage in the production of the capital-intensive good, is large
enough in terms of labor supply to produce profitably total world demand for this
good. While region h has a diversified production, region f specializes in the production of good 1. In the second outcome, region h is too small to cover the world demand
for the capital-intensive good, and the production of this good is dispersed between
the two regions. Region h specializes completely in the production of good 2, while
region f operates in both sectors. In the third outcome, region h is too small to cover
the world demand for the capital-intensive good, and—in contrast to the case above—
it loses its technological lead over time. Thus region f catches up technologically, and
there is a reversion of trade patterns.
Case C: Complete Concentration: “Factor Price Equalization Equilibrium”
Assume that region h is large enough in terms of factor endowments to cover total
world demand for the capital-intensive good at any time. Allowing for trade in goods
and capital, region h specializes in the production of good 2; and from the assumption
of the regions’ production capacity it follows that x2f = 0, always. International capital
mobility ensures equal returns to capital across borders in equilibrium. Production of
good 1 in both regions entails international factor price equalization in wages too. The
price of good 2 is then:
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TRADE, DEVELOPMENT, AND AGGLOMERATION
a
e
-1
-1
a -e
p2 = (a (1 - a )) ((1 - e ) e ) (1 - a )(1 - e ) Y h ( An k)
h
f
h
157
(21)
f
with n = n + n and k = k + k . The international wage rate and rate of returns to
capital are:
a
1-a
w = (a (1 - a )) (1 - a )(k An)
a
,
a
r = (a (1 - a )) (1 - a )( An k) .
(22)
(23)
Since region h is the sole producer of good 2, total production of this good is given by:
x2 = x2h = [(ark - (1 - a )wn) (a - e ) p2 ],
(24)
while production in region h and f of good 1 is:
x1h = [(-erk + (1 - e )wn h ) (a - e )] + [e (1 - a )wn f a (a - e )],
(25)
x1f = wn f a .
(26)
Since total world consumption of the capital-intensive good continues to be produced in region h, it follows that the other region is completely specialized in production of the labor-intensive good. According to the model, the region that is completely
specialized in the labor-intensive good will not be able to improve its technology in
sector 2. Hence, region f will not, at any stage, challenge the position of region h in the
production of good 2 (see Figure 3 and the Appendix).
Production of good 2 grows steadily in region h owing to the technological progress.
As trade becomes liberalized, intersectoral labor movements and the internationally
mobile capital allow for immediate concentration of the industry subject to growth and
spillover effects in region h, at the same time as both regions share in the production
of good 1.
Because of international capital mobility, and because both regions participate in
the production of the tradable CRS good, factor prices stay constant and equal across
regions over time. The technological progress leading to increased production volumes
in sector 2 is, consequently, reflected only by a decreasing price of good 2. World as
well as national welfare rises. The observed disparities in national welfare are due to
Figure 3. Case C: International Trade in Region h
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Karen Helene Midelfart Knarvik and Jostein Tvedt
differences in relative factor endowments, leaving those living in the relatively capitalabundant region better off.
Case D: Dispersed Production of Good 2
We then turn to the case where region h is too small to profitably produce total world
demand for good 2. From the assumption about factor endowments it follows that the
production of good 1 becomes concentrated in region f (i.e., x1h = 0), while region h specializes in production of good 2. Free capital movements ensure international equalization of returns to capital; but because both regions share in the production of good
2, thereby employing different technologies, equilibrium wage rates come to differ
across regions.
The equilibrium price of good 2 may be expressed as:
a
e
-1
a -e
-1
p2 = (a (1 - a )) ((1 - e ) e ) (1 - a )(1 - e ) Y h ( A k)
[n (Y
h
h
1e
Yf )
+ nf
a -e
]
.
(27)
Equilibrium returns to capital are in both regions given by:
a
a
[
1e
r = (a (1 - a )) (1 - a )( A k) n h (Y h Y f )
+ nf
a
],
(28)
while the equilibrium wage rates in regions f and h are, respectively:
a
a -1
w f = (a (1 - a )) (1 - a )( A k)
[n (Y
h
h
1e
Yf )
+ nf
a -1
]
,
1e
w h = (Y h Y f ) w f ,
(29)
(30)
in region h. Total production in region h is simply given by:
x2h = w h n h ep2 .
(31)
Region f produces both goods, and in equilibrium the production volumes are:
x 2f = [(ark - (1 - a )w f n f ) (a - e ) p2 ] - [a (1 - e )w h n h e (a - e ) p2 ],
f
1
x = [((1 - e )(w f n f + w h n h ) - erk) (a - e )].
(32)
(33)
Production in region h increases over time owing to the technological progress, and
experiences the strongest possible spillover effects because 100% of the region’s labor
force is engaged in the production of good 2 (see Figure 4 and the Appendix).
Relative to the labor stock in region f, the size of the labor stock in region h is above
the critical level, such that the spillover as well as the growth effects created in industry 2 are stronger than those prevailing in region f. Hence, the technological lead of
region h is not challenged at any time, and the importance of sector 2 in region f is
gradually reduced as the technology improvements increase the production potential
of region h.
Labor is restricted in region h. As a consequence, the technological improvements
in this region entail an increasing wage rate. Wages in region f are subject to a continuous decrease, caused by the escalating technology gap between the two regions.
The technological development is in case D reflected by increasing returns to capital,
a decreasing price of good 2, and an evolving wage gap. Increased capital income as
well as a decreasing price of good 2 more than compensate for diminishing wages and
leave the individuals in both regions better off than before trade liberalization. The
inhabitants of region h do, however, gain considerably more over time than do their
neighbours in region f.
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Figure 4. Case D: International Trade in Region h
This case, with dispersed production of good 2, has some similarities with the
Graham equilibrium—Graham (1923), or for a more precise treatment see Ethier
(1982). Graham shows that a region may lose from trade liberalization, owing to the
reduction of the scale in the region’s production of an IRS good proceeding an international specialization process. Region h, which specializes in production of good 2,
continuously improves its productivity owing to the large scale of production, while
the diversified region f shifts production from the IRS to the CRS sector. However,
unlike in Graham (1923), the reduced scale of production does not imply that region
f produces IRS goods less efficiently than before. The effect is not on present production, only on future productivity, because contrary to the Graham’s static model, our
model has IRS in time. Since reduced production volumes do not deteriorate future
productivity, but reduce innovation growth and knowledge spillovers, a gradual loss of
the IRS sector will never imply an absolute—only a relative—deterioration of welfare
in this region compared with the region that specializes in the IRS industry.
Case E: From Dispersion Towards Concentration
In case B a large absolute and relative size of region f deprived region h of its technological lead over time, and led to a reversion of trade patterns. If we do the same
numerical experiment in the case with capital mobility, this does not happen. Region
h reinforces its technological leading position as time passes by. Starting with the same
labor to capital ratios and the same parameter values as in case B, the size of region
f needs to be doubled in order to see trade patterns reversed and factor prices
equalized.
Initially, region h specializes in sector-2 production; but as in case D, the region is
not large enough to cover total world demand for good 2. Relative to region f, the
labor supply (i.e., production capacity) in region h is below a critical level; and although
the spillover effect is stronger in region h than in region f, the growth effect is stronger
in region f. Eventually, the greater growth effect experienced by the firms in region f
outweighs the greater spillover effect in region h, and h is deprived its technological
lead by f. As in a Ricardian equilibrium, wages reflect relative technology differences;
and at the time when regions reach the same technological level, wage rates equalize.
As region f then gets a technological lead, industry 2 becomes completely concentrated
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Karen Helene Midelfart Knarvik and Jostein Tvedt
in f, industry-1 firms are attracted to region h, and economic structures and trade patterns are consequently reversed (see Figures 5 and 6 and the Appendix).
Region h specializes in the production of good 1, region f maintains a diversified
production, and factor prices remain equalized. We reach a situation corresponding to
that of case C, so that in the long run the welfare implications are the same here as in
case C; i.e., world and national welfare increases. The location of the industrial cluster
becomes irrelevant to consumers’ welfare, and only differences in relative factor
endowments may cause national disparities.
In both cases C and E, there is factor-price equalization because (a) both regions
participate in the production of the tradable CRS good, and (b) there is international
factor mobility. When factor price equalization is enforced, the gains from external
economies of scale become reflected through the price on goods only.
Figure 5. Case E: International Trade in Region h
Figure 6. Case E: Factor Prices
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5. Concluding Remarks
Two effects drive the technological development of the model: the innovations in each
production unit and the rate of diffusion of these new innovations among firms in each
region. The number of innovations in a region increases with the size of the region’s
industry, while sector-specific knowledge (innovations) is spread as workers change
jobs within a sector. The probability that a new employee comes from a specific sector
is given by the number of workers in this sector relative to the total number of workers.
Innovations are therefore more rapidly spread if the sector employs a large share of
the workforce in the region.
Some notes on the assumptions regarding the knowledge diffusion process are called
for. By atomistic behavior, an unemployed worker is indifferent to where he becomes
employed, since the wage level is identical across sectors. A different labor market
model could alternatively have been chosen. For example, employers and workers may
be assumed to be aware of the fact that workers have heterogeneous background, or
that the employment in one specific sector improves the human capital of a worker
while the work in other sectors does not. Hence, employers may differentiate wages
to attract certain groups of workers, and workers may have preferences for employment in a firm which gives experience that adds to their human capital accumulation.
A more complex labor market structure (e.g., of the type described here) may lead to
different speed of knowledge transfer among production units, which again influences
the strength of the spillover effect.
If the small region for some reason gets a “head start,” the spillover effect experienced in this region may be so strong that it outweighs a relatively stronger growth
effect in the larger region. Hence, despite its size, the small region may specialize
in goods whose production is characterized by economies of scale—a result that differs
from those found in the trade literature; see, for example, Krugman (1980) and
Venables (1994).
It appears that the minimum size of a region necessary to sustain a cluster is substantially reduced as one allows for free trade, not just in goods, but in capital as well.
Obviously, our results point in the same direction as the traditional trade theory and
new economic geography, which argues that a small country is better off with complete
integration (e.g., Venables, 1994).
As regards an efficient use of resources, for the world as a whole to exploit resources
most efficiently an industrial cluster should be located in the smallest possible region
that is still large enough to cover total world demand for the good in question. By
locating the cluster in such a region, the strongest spillover effects are obtained, and
the most rapid technological progress is ensured.
Finally, technological development can be considered in a more historical
context where we move from a Heckscher–Ohlin type equilibrium towards a Ricardian
type. Imagine that at some point of time a small country has a comparative advantage
in the production of a specific good owing to favorable factor endowments. Over time,
the transport of inputs such as natural resources becomes cheaper and requires less time:
the trend towards “global sourcing” means that the location of inputs gradually becomes
less relevant to the localization of manufacturers. Provided that the small country in
the meantime has reached a higher technological level than the rest of the world,
because of its long experience in producing these goods, it will be able to sustain a competitive cluster despite the increased factor mobility. It appears that the more open the
small country is to trade in inputs as well as outputs, the more sustainable its industrial
cluster.
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Karen Helene Midelfart Knarvik and Jostein Tvedt
Appendix
Case A (Figure 1): Base case assumptions of parameter values and endowments are
p1 = 1, a = 0.6, e = 0.4, g = 0.5, f = 0.008, l = 0.008, nh = 1, nf = 1.5, kh = 2, and kf = 2.5.
Case B (Figure 2): Changes from case A are nf = 3.75 and kf = 6.25.
Case C (Figure 3): Changes from case A are g = 0.7 and trade in capital.
Case D (Figure 4): Changes from case A are nf = 3.75 and kf = 6.25, and trade in capital.
Case E (Figures 5 and 6): Changes from case A are nf = 8.4 and kf = 14, and trade in
capital.
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Notes
1. See e.g., Audretsch and Feldman (1996) and Jaffe et al. (1993).
2. For an early treatment of the subject, see Marshall (1920).
3. Rivera-Batiz and Romer (1991) show that the theoretical treatment of knowledge is decisive
for how integration affects growth, and distinguish between two cases; one in which flows of
knowledge can be separated from flows of goods, and one in which such a separation is impossible. Our model builds on the assumption that such a separation is possible.
4. See Krugman and Venables (1995), Grossman and Helpman (1991), and Brezis et al. (1993).
5. In order to be able to speak about interfirm mobility of workers, we need to determine the
number of active production units (firms) in an industry. We let the number of production units
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be linear in the aggregated production volume, an assumption that (e.g.,) may be justified by
letting constant returns to scale apply at the industry level, but not at the firm level. Each single
firm faces U-shaped average costs, and chooses production quantity in order to minimize average
cost. To simplify, we let the minimum average cost be reached when a firm produces one unit.
It follows that in each region the total number of firms in an industry is equal to the total amount
of output.
6. What we refer to as the “spillover effect” here actually combines two of the types of externalities identified by Marshall as reasons for firms to agglomerate; namely (1) a pooled labor
market for workers with specialized skills, and (2) information spillovers.
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