offset this increased cost, ceteris paribus. Therefore, the optimum vehicle-vessel size
also falls.
Hypothetically, there is also a third possibility, and this is the unique case where:
a ISi
b I ci+ si
Under these conditions, we see that the optimised shipment size, and consequently the
optimum vehicle-vessel size is invariant with respect to the haulage distance.
However, this situation is purely a chance occurrence, which will not continue to hold
in the face of interest rate or product price changes.
There is good empirical evidence that vehicle-vessel transportation generally
does indeed experience significant economies of scale in the essentially static
relationship between vessel movement costs relative and vessel carrying capacities
(Jansson 1980). The observed result of the existence of these vehicle-vessel
economies of scale is that observed shipment sizes are empirically observed to
increase with the haulage distance (Kendall 1972; Jansson and Shneerson 1982,
1987). However, as we have seen here, there is no analytical reason why this should
necessarily be the case. This observed empirical result is simply the outcome of the
optimisation process being carried under conditions of significant economies of scale
in vehicle-vessel movement costs and carrying capacities.
QED
PROPOSITION 2: Freight transport rates per ton are always concave with respect to
the haulage distance, except for the unique case in which the optimised shipment size
is invariant with respect to the haulage distance.
The observed freight rates charged by hauliers to customers will comprise a profit
mark-up on top of the total logistics costs involved in any haulage operation, and the
size of this mark-up will depend on the competitiveness and contestability of the
industry over the particular haulage route in question (Davies 1986). However, there is
no reason why the level of this mark-up should be systematically related to the
haulage length or haulage quantity over all shipment routes. The result of this is that
observation of the structure of total logistics costs with respect to haulage distance and
haulage quantity will explain the behaviour of observed transport rates with respect to
haulage distance and haulage quantity.
Proof of Proposition 2
In order to see why observed transportation costs per-ton vary with respect to haulage
distance and haulage quantity in the way that they do, from our preceding discussion it
is necessary to discuss how optimised total logistics-transport costs per ton of cargo
carried vary with respect to the haulage distance and the haulage quantity. To do this it
is first necessary to substitute equation (11) into equation (9), to give a total logistics-
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