A classification of the locational patterns of firms (with economies of scope present) is outlined, in order to cast light on the location of the multiplant, multinational firm. This is driven by three forces: economies of scope that follow from the co-location of different activities; transportation costs of the final good; and factor mobility costs. It is concluded that the single-plant firm prevails when spatial economies of scope are strong in relation to either transportation or mobility costs. The vertical (horizontal) multiplant firm emerges when mobility costs of factors (transportation costs on the final good) are high. These two kinds of spatial costs, which are mutually exclusive, favor the formation of multinational firms.Economies of scope; Economies of agglomeration; Multiplant firms; Multinational firms.

John B. Parr

José Pedro Pontes

English

Research Papers in Economics

Economies of Scope, Agglomeration and Location of the Multinational 
Firm  
 
José Pedro Pontes* and John B Parr** 
 
Abstract  A classification of the locational patterns of firms (with economies of 
scope present) is outlined, in order to cast light on the location of the multiplant, 
multinational firm. This is driven by three forces: economies of scope that follow from 
the co-location of different activities; transportation costs of the final good; and factor 
mobility costs. It is concluded that the single-plant firm prevails when spatial economies 
of scope are strong in relation to either transportation or mobility costs. The vertical 
(horizontal) multiplant firm emerges when mobility costs of factors (transportation costs 
on the final good) are high. These two kinds of spatial costs, which are mutually 
exclusive, favor the formation of multinational firms. 
 
Keywords: Economies of scope, Economies of agglomeration, Multiplant firms, 
Multinational firms. 
J.E.L. classification: R30, F23. 
 
Corresponding author: José Pedro Pontes, Instituto Superior de Economia e Gestão, Rua 
Miguel Lupi 20, 1249-078 Lisboa, Portugal (telephone: +351 21 3925916; fax: +351 21 
3922808; e-mail: ppontes@iseg.utl.pt 
 
*Instituto Superior de Economia e Gestão, Technical University of Lisbon, and Research 
Unit on Complexity in Economics (UECE) 
**Department of Urban Studies, University of Glasgow   2
1.  Introduction 
The theory of multinational corporations has provided an explanation for the location of 
the firm within a set of nations. Three possibilities are usually recognized. First, the firm 
can be a single-plant firm, located in one nation and exporting to other nations. Second, it 
can be a vertical multiplant firm, with a segmented production process, each segment 
being undertaken by a plant located in a different nation. Finally, it can be a horizontal 
multiplant firm that supplies the market in each nation from a decentralized plant located 
within that nation. Apart from the work of MARKUSEN et al. (1996), the theory of 
multinational corporation tends to lack a unity. Vertical multinationals (HELPMAN, 
1984) are viewed as resulting from the fact that nations have different relative factor 
endowments and that different segments of the firm (for example, headquarters R&D 
activity and manufacturing activity) have different factor requirements. If transportation 
costs are low, the segments will separate spatially, with each segment locating in a nation 
that is abundant in the factor of production used intensively by that segment. Thus, the 
headquarters will be located in the nation abundant in skilled labor and the manufacturing 
plant locates in the region relatively well endowed with unskilled labor. By contrast, 
horizontal multinationals are seen to result from the fact that economies of scale at the 
plant level are low in relation to economies of scale at the firm level and in relation to 
transportation costs of the final good (HORSTMANN and MARKUSEN, 1992). If fixed 
costs at the firm level (as in the case of R&D activity) are high in relation to economies 
of scale at plant level, it pays the multinational to set up several plants that use jointly the 
R&D activity supplied by the headquarters. If transportation costs are high in relation to   3
economies of scale at the plant level, it is more efficient for each nation to be supplied 
from a local plant rather than from a single central plant. 
The lack of unity within the theory stems from the fact that the concept of economies 
of scale, which is used in the case of the horizontal multinational firm, does not assume 
significance in the case of the vertical multiplant firm. However, as GOLDSTEIN and 
GRONBERG (1984) have argued, the concept of economies of scale can be usefully 
supplemented by the concept of economies of scope (PANZAR and WILLIG, 1981). In 
this case, efficiency does not derive from the fact that an activity is undertaken on a large 
scale, but rather from the fact that different, though related, activities are undertaken by 
the same firm, so that the various activities share the services of a common input such as 
physical equipment or some technical expertise. Important for our purposes are spatial 
economies of scope. These emerge when the relevant activities have to be co-located, 
thus forming the basis for agglomeration economies. 
An attempt has recently been made to classify firms (enjoying economies of scope) 
in terms of their locational patterns within a nation (PARR 2004). According to this 
classification, ‘Firm l’ produces each good at the same location within a region, and 
benefits from spatial economies of scope. ‘Firm 2’ produces each good in a different 
region, in order, for example, to save on transportation costs on the weight-losing input 
that is specific of each product. Finally, ‘Firm 3’ produces all goods in each region in 
order, for example, to save on transportation costs to the consumers in each regional 
market. Interestingly, these three firm types match the categories of firms commonly 
found in the literature on foreign direct investment and multinational corporations. Firm l 
corresponds to the single-plant, multiproduct firm, and Firm 2 corresponds to the vertical   4
multinational firm, while Firm 3 is comparable to the horizontal multinational. The 
advantage of this framework lies in the fact that the different firm types have a common 
basis (namely, the interaction between economies of scope and the transportation costs of 
inputs and final goods), and do not therefore depend on diverse foundations. In what 
follows, this framework is applied to a monopolist firm, in order to isolate the factors that 
determine each firm type. In this way we seek to outline the rudiments of a unified theory 
of location for the multinational firm. 
 
2.  The Background 
We assume that within a spatial economy the following assumptions are satisfied. 
1.  There are two nations (or types of nation) U and S. Nation U has only unskilled 
workers, while nation S has only skilled workers. For simplicity, the distance 
between the nations is set at one, and the distance between two points within the 
same nation is zero. 
2.  A firm produces a consumer good by engaging in two related activities: R&D 
activity  R, involving the design of the good; and manufacturing activity M, 
involving the production and sale of the good. Each unit of the consumer good 
requires one unit of R and one unit of M. This simplification amounts to assuming 
that the good associated with each activity is designed separately. More 
realistically, it should be assumed that there is a specific design capacity for a 
subset of products.    5
3.  The firm is a monopolist in the consumer-good market and charges a fob or mill 
price p. The firm is a price taker in the factor market, with wu and ws, as the 
respective unit costs unskilled and skilled labor. 
4.  For the consumer good the transportation cost per unit of distance shipped, is 
given by t. Labour from one nation can be hired in another nation, if the employer 
pays a mobility cost m per unit of labour hired. Together with the assumption that 
each nation is endowed only with one factor of production, this is a simple way of 
introducing different factor prices across nations. It would be more realistic to 
assume that factors are immobile and that nations have different relative 
endowments. 
5.  The demand function of each consumer is linear, so that q = a - bp, where q is the 
quantity demanded. There are n consumers in each nation. 
6.  The cost functions of the complementary activities have a fixed part F, which 
represents a capital good, and variable part. The variable-cost of activity R is the 
cost of using α  units of skilled labor per unit of output of the consumer good. 
The variable cost of M is the cost of using α  units of unskilled labor per unit of 
output of the consumer good. 
7.  Spatial economies of scope (giving rise to agglomeration economies) are present 
if activities R and M are undertaken at the same location, so that the fixed cost F 
is shared. This sharing reflects the improved coordination between neighboring 
activities. 
Following PARR (2004), it is further assumed that the firm is able to select from three 
locational patterns:   6
Single-plant firm (Firm 1): the firm locates activity R and activity M at the same 
location within a nation. As can be seen below, the cost function does not vary with the 
choice of the nation. 
Vertical multiplant firm (Firm 2): the firm locates activity R in nation S and activity 
M in nation U. 
Horizontal multiplant (Firm 3): the firm locates activity R in nation S and activity M 
in both nations S and U. 
It is easily shown that other locational strategies lead to higher costs. Thus strategies 
with activity R in both nations involve a second mobility cost, but do not lead to 
additional economies of scope or savings in transportation costs of the final good. 
 
3.  Alternative Locational Patterns 
The profit functions of the monopolist firm under the three strategies are as follows: 
 
() [] () ( ) [] {}         1 F t p b a bp a m w w p n s u − + − + − + − − = α α π  (1) 
() ( ) [] {} ( ) F w w p t p b a bp a n s u 2       2 − − − + − + − = α α π  (2) 
() ( ) [] () ( ) F w w p bp a n m w ws p bp a n s u u 2           3 − − − − + + − − − = α α α α π  (3) 
In order to focus on the parameters t, m and F, the following specifications are made: 
1 = = = = u w n b a  (4) 
1 . 0 = α   
2 = ws   
With these specifications, the profit functions become 
() ( ) F t p m p − − − − − = 2 2   1 . 0 3 . 0 1 π  (5)   7
() ( ) F p t p 2 3 . 0   2 2 2 − − − − = π  (6) 
() ( ) () ( ) F p p m p p 2 3 . 0   1 1 . 0 3 . 0   1 3 − − − + − − − = π  (7) 
 
The profit-maximizing prices in each locational pattern can be readily calculated: 
 
m t p 05 . 0 25 . 0 65 . 0
*
1 + − =  (8) 
t p 25 . 0 65 . 0
*
2 − =  (9) 
m p 025 . 0 65 . 0
*
3 + =  (10) 
 
A feasibility condition placed on the parameters is that the firm faces a positive 
demand in each market at the prices given by (8), (9) and (10). The following two 
conditions are necessary and sufficient for this to occur. The first is that 
( ) ( ) 0 05 . 0 25 . 0 65 . 0 1 1 > + + − − = + − =
∗ t m t t p b a q  
which is equivalent to 
m t 01 . 0 6667 . 6 46667 . 0 × − <  (11) 
The second condition is that 
() 0 025 . 0 65 . 0 1 3 > + − = ∗ − = m bp a q  
which is equivalent to 
14 < m  (12) 
Substituting the profit-maximizing prices (8), (9) and (10) in the respective profit 
functions (5), (6) and (7), we obtain the profit functions of the firms in terms of the 
parameters t, m and F.   8
F m tm t m t − + + + − − =
2 2
1 005 . 0 05 . 0 125 . 0 07 . 0 35 . 0 245 . 0 π    (13) 
F t t 2 125 . 0 35 . 0 245 . 0
2
2 − + − = π  (14) 
F m m 2 00125 . 0 035 . 0 245 . 0
2
3 − + − = π  (15) 
 
We now plot the locational choice of the monopolist firm in parameter space. Since 
there are three parameters, two specific values will be assigned to the parameter F. These 
are F = 0.1 and F = 0.05. When F = 0.1, it is easily shown that the locational choice is 
described by the following inequalities: 
( )
m
m m
t
2 14 20 1 . 0
2 1
+ −
− > ⇔ > π π
 (16) 
116 28
10
1
5
1
5
7
3 1
2 + − − − < ⇔ > m m m t π π
 (17) 
m t 1 . 0 2 3 > ⇔ > π π  (18) 
 
Inequalities (16), (17) and (18) are used in Figure 1 to define the regions of the 
parameter space (m, t) for F = 0.1, where each type of locational pattern prevails. The 
upper downward-sloping line corresponds to feasibility condition (11). Condition (12) is 
implicitly fulfilled in each point of the figure. 
It is now assumed that F = 0.05, and the defining inequalities become: 
( )
m
m m
t
2 14 10 1 . 0
2 1
+ −
− > ⇔ > π π
 (19) 
156 28
10
1
5
1
5
7
3 1
2 + − − − < ⇔ > m m m t π π
 (20)   9
m t 1 . 0 2 3 > ⇔ > π π  (21) 
These inequalities, together with feasibility condition (11), define the regions of the 
parameter space (m, t) where each locational pattern holds. These regions are depicted in 
Figure 2. 
It is possible to conclude that the Firm l pattern (the single-plant firm) is more likely 
to occur with high values for spatial economies of scope (as given by F) between 
activities R and M. It is also a dominant choice for the firm if the transportation costs on 
the consumer good and the mobility cost of the factors of production are both low. By 
contrast, the multiplant patterns of Firm 2 and Firm 3 occur at low values for spatial 
economies of scope, since for these firms there is a spatial separation of activities R and 
M. The pattern for Firm 2 occurs if the mobility cost is high and the transportation cost is 
low, while the pattern for Firm 3 prevails if the transportation cost is high and the 
mobility cost is moderate to low. These two multiplant patterns are mutually exclusive. 
 
4.  Concluding Remarks 
It has been argued that under certain conditions the alternative locational patterns of a 
multinational firm are comparable to those of a firm operating within a single nation. 
This correspondence provided a framework for modeling the location of a multinational 
firm, where agglomeration of the firm’s activities resulted from spatial economies of 
scope rather than from economies of scale. However, the agglomeration force deriving 
from spatial economies of scope (leading to a single-plant pattern) might be more than 
offset by the opposing forces of dispersion, involving different relative factor 
endowments across nations (leading to a vertical multiplant pattern) or high   10
transportation costs of the final good (leading to a horizontal multiplant pattern). These 
two forces of dispersion would be mutually exclusive. An extension of this framework 
beyond the case of a monopolist firm is both desirable and feasible. Thus it is possible to 
consider two independent firms, and model their interaction by means of a two-stage 
game. In the first stage each firm would choose its locational pattern, e.g., a single-plant 
firm in nation U or nation S; a vertical multiplant firm or a horizontal multiplant firm. In 
the second stage the firms would compete in the consumer-good market, either in terms 
of quantitites (HORSTMANN and MARKUSEN, 1992) or discriminatory prices 
(BELLEFLAMME  et al., 2000). This extension would enable us to treat spatial 
economies of scope as an agglomeration force, encouraging not only the spatial 
concentration of different activities within each independent firm, but also the co-location 
of the two firms. However, an extention to the case of a small group of firms is unlikely 
to affect fundamentally the qualitative conclusions that follow from our locational 
analysis of the monopolist firm. 
   11
References 
BELLEFLAMME, P., P. PICARD and J.F> THISSE (2000) An economic theory of 
regional clusters, Journal of Urban Economics, 48, 158-184 
 
GOLDSTEIN, G.S. and T.J. GRONBERG (1984) Economies of scope and economies of 
agglomeration, Journal of Urban Economics, 16, 91-104. 
 
HELPMAN, E. (1984) A simple theory of international trade with multinational 
corporations, Journal of Political Economy, 451-471. 
 
HORSTMANN, I. and J. MARKUSEN (1992) Endogenous market structures in 
international trade (natura facit saltum), Journal of International Economics, 32, 
109-129. 
 
MARKUSEN, J.A. VENABLES, D. KONAN and K. ZHANG, (1996) A unified 
treatment of horizontal direct investment and the pattern of trade in goods and 
services, NBER Working Paper 5696.  
 
PANZAR, J.C. and R.D. WILLIG, (1981) Economies of scope, American Economic 
Review (Papers and Proceedings), 71, 268-272. 
 
PARR, J.B. (2004) Economies of scope and economies of agglomeration: the Goldstein-
Gronberg contribution revisited, Annals of Regional Science, 38, 1-11. 
   12
 
Figure 1: Firm types in (m,t) space for F=0.1 
 
 
Figure 2: Firm types in (m,t) space for F=0.05   13
 

A simple theory of international trade with multinational corporations,

A unified treatment of horizontal direct investment and the pattern of trade in goods and services, NBER Working Paper 5696.

An economic theory of regional clusters,

Economies of scope and economies of agglomeration: the GoldsteinGronberg contribution revisited,

Economies of scope,

Endogenous market structures in international trade (natura facit saltum),

Economics of Scope, Agglomeration and Location of the Multinational Firm

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Economics of Scope, Agglomeration and Location of the Multinational Firm

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