Geography Reference
In-Depth Information
maximize the returns to its capital investment the firm will therefore locate
at whichever location allows it to earn maximum profits. In the model
structure, so far we have assumed that the prices of all the input and
output goods are exogenously set, and that the prices of all production
factors are invariant with respect to space. Therefore, in this particular
framework, the only issue which will alter the relative profitability of
different locations is the distance of any particular potential production
location from the geographically fixed input sources
S
1
and
S
2
and the
geographically fixed output market point
M
3
. The reason for this is that
different production locations will incur different costs associated with
transporting inputs from their source production points
S
1
and
S
2
to the
location of the firm
K
, and transporting the output from the location of
the firm
K
to the market point
M
3
.
With these simple assumptions it is now possible to write the profit (p)
function of the firm as:
p 5
m
3
(
p
3
2
t
3
d
3
)
2
m
1
(
p
1
1
t
1
d
1
)
2
m
2
(
p
2
1
t
2
d
2
)
(3.2)
in which the firm's profit is defined as the sales revenue, calculated at the
location of the firm at
K
, minus the total value of the input purchases
minus the transportation costs incurred on both inputs and outputs. The
gross sales revenue at the market point
M
3
is denoted as
p
3
m
3
, but the net
sales revenue accruing to the firm at the location of the firm K is defined
as minus the transportation costs of the output shipments. Therefore, the
first term in brackets on the right hand side of equation (3.2) represents
the net sales revenue received at
K
per tonne of output after taking out the
output transportation costs, and the second two terms in brackets on the
right hand side of equation (3.2) represent the delivered prices of the input
goods at the location of the firm
K
.
Rearranging (3.2) now gives:
p 5
[
m
3
p
3
2
m
2
p
2
]
2
{
m
3
t
3
d
3
2
m
1
p
1
2
m
1
t
1
d
1
2
m
2
t
2
d
2
}
(3.3)
Here we can now split the purchase costs out from the transportation
costs. In equation (3.3) we see that the terms in the square brackets are all
assumed to be invariant with respect to location, while the terms in the
second set of brackets are all dependent on the location
K
of the firm. As
such, if the price per unit of output
p
3
is fixed, the location that ensures
that maximum profits are earned by the firm, denoted as
K
*, is the loca-
tion at which,
ceteris paribus
, the total input plus output transport costs
are minimized. This is known as the
Weber optimum
location
(McCann
2001).
