There are three chief methods for lowering transportation costs: the develoapment of means of transport, the change in system of management (concerning which vonThünen and Brinkmann give full details), and the rational location. of a city. This paper examines the third point briefly. In the interest of clarity, total costs of transportation are expressed in geometric terms. The basis of this geometric treatment is explained in annotation (p. 119.).
1. If a certain commodity to be sent to a city i s distributed with a constant density all over the region (which is treated as a segment), and if transportation costs are directly proportional to distance of shipment, then a city located in the center of the region will have minimum total costs of transportation, When a city locates away from the center point, costs will increase in proportion to the square of the distance from the center point. In general, when
n cities are located on any points of the odd number order among the points which divide the region into 2
n parts, costs become a minimal value.
2. However, if the region is treated as a circle and cities exist all along a certain circumference (with an arbitrary radius (
b)), a general express-ion of total costs (T) is:
(
a is the radius of the region)
T=_??_π
b3+_??_π(
a-
b)
2(
a+2
b)
By differentiating
b, it is known that the condition of minimum is “
b=_??_
a”, and minimal value is _??_πa
3. (And if
b=0, then T=_??_π
a3; if
b=
a, then T=_??_π
a3).
3. The above reasoning leads to the conclusion that the equal, division of many types of industry among various cities is rational for purposes of lowering total transportation costs.
4. However, the following factors must be considered:
a) if the establishment, diffusion and development of trafie facilities decreases transportation costs to some extent, then the effect of rational location of a city tends to become neglected. Thus, some large cities appear while many local centers decline.
b) The location of a city must be studied not only from the writer's point of view, but also in regard to measures to counter business cycles and to policies required to bridge the gap between urban and rural income levels.
c) The w riter's conclusion camiot be considered adequate under actual conditions because the reasoning was based on, a host of premises.
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