Geoscience Reference
In-Depth Information
Law of Market Areas, which is based on the prices of a good (or composite good) at
two centers and the transportation costs of shipping that good from each center
(Hyson and Hyson
1950
; Isard
1956a
,
b
; Norman
1993
).
5
The boundary is also
similar to the one associated with the Law of Retail Gravitation, which depends on
the populations of two centers and the distance between these (Reilly
1953
; Hoover
1971
; Liang
2008
). In both Laws the boundary is displaced from the halfway point
towards the smaller center, and is also convex to the larger center. In the second
Law, however, the boundary is always in the form of a circle or the arc of a circle, a
restriction not present in the density-function approach considered above.
Under usual circumstances it would be customary to test the results of an
approach (such as the one proposed here) against some objective standard. Unfortu-
nately, because of the subjective nature of the concept of the region no benchmark
of this type can exist. All that is available are the results of previous attempts at
delimitation and regionalization. Nevertheless, we have at our disposal an addi-
tional method for determining the overall extent of an economic region. This should
be seen as complementing rather than rivaling existing theoretical approaches to
regionalization, whether for the purpose of analysis or the design of policy.
Acknowlegement The authors wish to express their thanks to N. Dean, A. Grimes and J. K.
Swales for their comments on earlier versions of this chapter.
Appendix 6.1
Let
T
denote the distance from
A
0
to
B
0
in Fig.
6.2
. Note that equality of densities
requires Eq. (
6.5
) with
x
A
+
x
B
¼
T
, giving
ln
T
ð
x
A
Þ λ ρ
ð
ln
x
A
Þ
¼
0,
where
λ
¼
(ln
N
A
ln
N
B
)/
b
and
ρ
¼
a
/
b
. We assume
N
A
>
N
B
and
a
>
b
, implying
λ >
1. We have:
1. There will be a unique
x
A
between 0 and
T
, say
x
*
, as in Fig.
6.2
, such that
x
A
¼
0 and
ρ>
x
*
, implying the equality of densities.
2. The value of
x
*
/
T
is unchanged by alteration of the units of area in
M
(
x
) and of
distance in
x
in Eq. (
6.1
).
3. The value of
x
*
is unchanged by alteration of the units of population embedded
in
M
(
x
) in Eq. (
6.1
).
4. The value of
x
*
exceeds
x
h
¼
x
*
and
x
*
¼
T
T
/2 if and only if
5
For the Economic Law of Market Areas these spatial features are present in the following cases:
(1) where center
A
0
has a price advantage over center
B
0
but no transportation-cost advantage;
(2) where center
A
0
enjoys a transportation-cost advantage but no price advantage; (3) where center
A
0
has both a price advantage and a transportation-cost advantage. In the case where center
A
0
has a
transportation-cost advantage and center
B
0
a price advantage these two features of the boundary
are only present under certain conditions (Parr
1995
).
