Geography Reference
In-Depth Information
In principle finding the Weber optimum location
K
* involves compar-
ing the relative total input plus output transport costs at each location: the
actual
K
* will be the particular location at which the sum of these total
costs (
TC
) is minimized. The cost condition that determines the Weber
optimum location can be described as:
3
TC
5
Min
m
i
t
i
d
i
(3.4)
a
t
5 1
where the subscript
i
refers to the particular weights, transport rates, and
distances over which goods are shipped to and from each location point
K
. In the simple Weber location-production model, the value of
i
5 3.
However, this general and simple principle can be applied to any situa-
tions where
i
. 3, in which the firm has multiple input source and output
market locations. With information on the actual values corresponding
to each of the spatial and non-spatial parameters, in the simple triangular
case described here it is quite straightforward using basic geometry to cal-
culate the total production plus transportation costs incurred by the firm
associated with being at any arbitrary location
K
. The total costs for all
locations within the triangular space can then be compared, and the loca-
tion with the lowest total costs is denoted as the Weber optimum location
K
*. For more complex geometrical shapes, in which there are multiple
input source output market locations, it is possible to use operations
research techniques or Geographical Information Systems techniques in
order to compute the total costs associated with any given location
K
.
Once again, by comparing all of the possible locations for
K
, we are able
to identify the Weber optimum
K
*. Given our assumptions that the firm
will behave so as to maximize its profits we can therefore assume that, as
long as the firm has all of the available information at its disposal, the
minimum cost location
K
* will be the actual chosen location of the firm.
Given our Weber model assumptions in which the firm is assumed
to be a price taker for both inputs and outputs, it can be easily demon-
strated that the actual chosen Weber optimum
K
* will be independent of
the values of
p
1
,
p
2
and
p
3
. Moreover, once the Weber optimum has been
found, the optimum location of the firm will remain in the same place irre-
spective of the output level
m
3
, and the required inputs quantities
m
1
and
m
2
, as the relationships between these are assumed to all be exogenously
fixed.
Although it is always possible to calculate the optimum location of the
firm in each specific case, of particular interest to us here is to understand
how the location of the Weber optimum will itself be affected by the levels
of, and changes in, any of the parameters
p
1
,
p
2
,
p
3
,
m
1
,
m
2
,
m
3
,
t
1
,
t
2
,
t
3
. For
the moment, we will ignore the effects of the input and output prices
p
1
,
p
2
