Geography Reference
In-Depth Information
therefore frequently used as the starting point for discussions about firm
location behaviour. The reason is that the basic Weber argument, which is
a purely theoretical construct, is framed within a triangular geographical
space, and the triangle is the simplest two-dimensional analytical frame-
work. While this may seem unrealistic for our purposes, in that MPDEs
and MNEs often have hundreds of suppliers and hundreds of market
points all situated in many different locations, the analytical solutions to
the two-dimensional triangular case can also be shown to hold for more
complex multidimensional cases (Eswaran et al. 1981), and in particular
for spatial forms typical of MNEs.
In order to motivate the models, we begin by adopting the standard
microeconomic assumption that the firm aims to maximize its profits.
Later on we will partially relax this assumption when distinguishing
between different firm types. However, for the moment, by assuming the
profit maximizing rationale for the firm, the question of where a firm will
locate within the Weber framework becomes the question of at which loca-
tion a firm will maximize its profits. The optimal location decision is thus
related to profitability, and profits maximization means that returns to the
capital investment are also maximized.
Figure 3.2 describes a Weber location-production triangle, in which
the firm consumes two inputs in order to produce a single output. In this
model, we assume that the goods being produced by the firm are physical
and transportable commodities, as would be the case for a manufacturing
firm.
In the simple Weber location-production model we assume that the
firm consumes material inputs 1 and 2, which are then combined by the
firm at a location
K
in order to produce an output commodity 3.
K
repre-
sents the location of the firm's capital investment and, as yet, this is to be
determined. The production locations of the input sources of 1 and 2 are
defined as
S
1
and
S
2
and are assumed to be given, as is the location of the
output market
M
3
, at which output good 3 is sold. The prices per tonne of
the inputs 1 and 2 are given as
p
1
and
p
2
, at the points of production
S
1
and
S
2
, respectively. The price per tonne of the output good 3 at the market
location
M
3
is assumed to be given as
p
3
, such that the firm is a price taker;
and we also assume that the firm is able to sell unlimited quantities of
output 3 at this given output market price of
p
3
. The transport rates are
denoted as
t
1
,
t
2
and
t
3
, and they represent the costs of transporting one
tonne of each commodity 1, 2 and 3, respectively, over one kilometre.
Finally, the distances
d
1
,
d
2
and
d
3
, represent the distances over which each
of the goods 1, 2 and 3 are shipped.
We also assume that the coefficients of production for the firm located
at
K
are fixed, so that there is a fixed relationship between the quantities of
