Geoscience Reference
In-Depth Information
6.2.3 Bases for the Regional Density Function
In general terms the density function may be viewed as closely related to the overall
rent gradient within a competitive land market. The association between population
density and land value has been noted by Alonso (
1964
) and Evans (
1973
) among
others. The rent gradient is usually considered in an urban or metropolitan context,
but there is no reason why it cannot be employed at the regional scale.
1
Of importance in this latter connection is the interaction between the
non-metropolitan hinterland and the metropolitan area. The metropolitan area
represents a center of demand for the output of the non-metropolitan hinterland
such as agricultural commodities, raw materials, semi-manufactured goods, etc. It
is also a center for the direct and indirect supply of goods and services to
households and firms throughout this hinterland.
As a center of demand the metropolitan area plays the role assigned to it by von
Th¨nen (
1842
/1966), while as a center of supply the metropolitan area acts in the
manner outlined by L¨sch (
1944
/1954). In both cases, however, transportation costs
cause interaction with the metropolitan area to decrease with distance. The regional
density function may thus be seen as a reflection of the varying spatial interaction
within the region (Kanafani
1978
). The phenomenon of decreasing interaction with
distance from a metropolitan area is commonplace, and manifests itself over the
hinterland in terms of diminishing land-use intensity, declining levels of commu-
ting to the metropolitan area, as well as falling consumer and non-household
purchases made there (Bogue, Chart 3-1). The question of interaction can also be
approached in terms of accessibility (Song
1996
).
6.3
The Form of the Regional Density Function
In discussing certain of his findings, Bogue (
1950
, p. 31) noted that “There is a
fairly constant rate of change between the relative decrease in land occupancy
[density] and relative increases in distance.” This observation points to a regional
density function having the form of an inverse power function (Vining
1955
,
pp. 154-157):
Nx
n
Mx
ðÞ
¼
ð
N
>
0
n
>
0
0
x
R
Þ
ð
6
:
1
Þ
;
;
or
ln
Mx
ðÞ
¼ln
N
n
ln
x
ðÞ
6
:
2
Þ
where
M(x)
is the population density within a thin annular ring at distance
x
from
the center of the region, i.e., the center of the metropolitan area. Under actual
1
In textbooks on urban economics the rent gradient is sometimes shown as ending at the boundary
of the city or becoming horizontal thereafter, suggesting some prevailing level of rent beyond
the city.
